IB Maths Studies: Last blog entries
http://www.thinkib.net/mathstudies/blog
InThinking IB Maths Studies: www.thinkib.net/mathstudies2017 InThinking Educational Consultants. All rights reserved.StudyIB.net
http://www.thinkib.net/mathstudies/blog/22937/studyibnet
Sat, 11 Mar 2017 00:00:00 +0000]]>StudyIB.nethttp://www.thinkib.net/cache/blog-thumbs/21/22937-1489226175-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/22937/studyibnet
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/22937-1489226175-thinkib.jpg" alt="StudyIB.net" /><br /><br /></p> <p>The StudyIB Maths Studies site is a web based learning resource for students, packed with resources to help you to improve your understanding and performance.</p> <p>The site is written by Jim Noble, a hugely experienced Maths Studies teacher, and it has been designed to support student learning from the beginning of the course until the final exams. It is clearly organised by s yllabus topic, simple, attractive layout, and is optimised for mobile devices.</p> <ul> <li>The site includes:</li> <li>100+ Teaching videos covering the key concepts on the syllabus.</li> <li>150+ Slides with visual explanations and examples.</li> <li>200+ Onscreen practice questions with feedback.</li> <li>50+ Revision Flashcards.</li> <li>50+ original exam style questions with video solutions.</li> <li>Regular updates with more videos and questions going up every month.</li> </ul> <p><strong>Teaching videos</strong> allow you to review key concepts you have learned in class.These thoughtful, well-paced, demonstrations and explanations, which you can watch again and again, are designed to make you think and improve your understanding.</p> <p><strong>Visual slides</strong> back up the videos with you can see visual notes that describe and summarise the key ideas.</p> <p><strong>On-screen quizzes</strong> enable you to check your understanding of ideas by giving you instant feedback and advice. Return to them as often as you like.</p> <p><strong>Revision Flashcards</strong> boil the syllabus down to key points which help you to review as exams approach.</p> <p><strong>Exam Style questions</strong> which you can try out on paper yourself and then check your answers against the video solutions.</p> </div> <p>....</p> http://www.thinkib.net/mathstudies/blog/22937/studyibnet#1489190400Percentage perception
http://www.thinkib.net/mathstudies/blog/22414/percentage-perception
Wed, 14 Dec 2016 00:00:00 +0000]]>Percentage perceptionhttp://www.thinkib.net/cache/blog-thumbs/21/22414-1481718583-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/22414/percentage-perception
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/22414-1481718583-thinkib.jpg" alt="Percentage perception" /><br /><br /></p> </div> <p>Even better, the new data comes with a new headline for us to explore. There is a new graphic and a scetion on predictions for 2020 as well! So much to talk about! I am looking forwrad to getting in to the data and updating the activity!</p> http://www.thinkib.net/mathstudies/blog/22414/percentage-perception#1481673600Picture this
http://www.thinkib.net/mathstudies/blog/21597/picture-this
Thu, 01 Sep 2016 00:00:00 +0100]]>Picture thishttp://www.thinkib.net/cache/blog-thumbs/21/21597-1472758376-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/21597/picture-this
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/21597-1472758376-thinkib.jpg" alt="Picture this" /><br /><br /> <h2>Why valuable?</h2> <p>Well, I think what happens to us when we look at these pictures is fascinating, particularly when you have an instinctive reaction to what you see. For example, maybe, like me, you first thought the toothpicks were pencils. Once you have an idea in your head it is very difficult to shift that mindset and imagine it being something completely different. Because we are not seeing 'the big picture' we are prone to making snap, unjustified judgements about what it is. Unless we check ourselves and try to look from a different angle, we are at the mercy of these judgements. </p> <p>I think this happens to students when they tackle exam questions and they go on to make related mistakes. Often when you give the paper back and point out the important feature of the diagram/question that they missed, they experience clarity and say 'I can't believe I didn't see/do that the first time' - much like you can't believe you didn't see the toothpicks in the picture above (perhaps you did, but believe me there are others there you wont get first time!). Bridging the gap between the first 'instinctive response' to the information shown and the 'clarity' becomes a significant goal. Paying attention to key details that give the bigger picture away is crucial and often the reason students do well (or not as the case may be).</p> <p>I found myself recounting to a class today, the lovely picture that Andrew Wiles paints of his exepriences with mathematics that goes something like this.....</p> <div class="greenBg"> <p><em>When you first confront a new bit of mathematics, it is like going in to an unknown room of a house that is pitch black. To start with, you have to move carefully around the room and build a map of the furniture in it - as you do so, you effectively turn the light on in the room and can see it clearly and the door that leads out the other side so you can repeat the process in the next room until eventually, you have illuminated the whole house perfectly.</em></p> </div> <p>WIles was more eloquent and emotionally charged given that his house was 'Fermat's last theorem', but the analogy holds with the card game and classroom mathematics. Those moments of illumination and clarity are priceless right!</p> <p>So I think the exercise is very valuable and I will get the odd card out for a while and warm students up with this idea. Lets illuminate the toothpicks as much as we can this year I say!</p> <p>.....</p> http://www.thinkib.net/mathstudies/blog/21597/picture-this#1472684400IB Americas
http://www.thinkib.net/mathstudies/blog/21359/ib-americas
Sun, 31 Jul 2016 00:00:00 +0100]]>IB Americashttp://www.thinkib.net/cache/blog-thumbs/21/21359-1469971965-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/21359/ib-americas
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/21359-1469971965-thinkib.jpg" alt="IB Americas" /><br /><br /></p> <p >Thanks Toronto - it was nice to see you again</p> http://www.thinkib.net/mathstudies/blog/21359/ib-americas#1469919600Results!
http://www.thinkib.net/mathstudies/blog/21262/results
Thu, 07 Jul 2016 00:00:00 +0100]]>Results!http://www.thinkib.net/cache/blog-thumbs/21/21262-1467960868-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/21262/results
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/21262-1467960868-thinkib.jpg" alt="Results!" /><br /><br /> Reading, writing, arithmetic are important only if they serve to make our children more human.</em></p> </div> <p>So - I suppose I have just been reminding myself that YES, we and our students will be judged by numbers, grades and statistics and YES that is important and OK, BUT NO it is not the main thing by which we should judge our success as teachers nor that by which students should judge their own. The IB philosophy, learner profile and ATTL demands a good deal more than that which will ultimately not be tested by exams and there is always more work to be done on that!</p> <p>Have a great summer Northern Hemisphere teachers and a great weekend everybody else!</p> <p>Jim</p> <p>....</p> http://www.thinkib.net/mathstudies/blog/21262/results#1467846000Further Processes
http://www.thinkib.net/mathstudies/blog/20388/further-processes
Thu, 11 Feb 2016 00:00:00 +0000]]>Further Processeshttp://www.thinkib.net/cache/blog-thumbs/21/20388-1455222238-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/20388/further-processes
<h2><span ><img src="http://www.thinkib.net/cache/blog-thumbs/21/20388-1455222238-thinkib.jpg" alt="Further Processes" /><br /><br /></span>What counts and what doesn't?</h2> <p>The following is a reply I have found myself giving often regarding the use of 'Further processes' in Internal assessment. the question is <em>'Is there a comprehensive list of processes that can be considered as 'Further processes' in criterion C of the Internal assessment?' </em>It is a great question and it makes perfect sense to ask it. Unfortunatelty, the short answer is no, but there are some related issues worth considering. Here is my reply.....</p> <p><em>'I understand the frustration, but there is not a comprehensive list. In defence of their (IB) position, there is a desire to leave some options open and if there was a comprehensive list then this would rule out anything that wasn't on it. In criterion 4 of the IA markscheme it says 'Examples of further processes are differential calculus, mathematical modelling, optimisation, analysis of exponential functions, statistical tests and distributions, compound probability' Of course, this doesn't tell us what exactly we would expect to see. eg what would we expect to see for compound probability? This is part of the reason so many opt for the statistical test, because it is easy to know what is is expected. Of course, many studies students find stats the more interesting and relevant part of the course for them too. The next level issue is that given the greyness surrounding what we might expect to see for - say modelling - it is open to interpretation and so whilst you may argue well that it should be considered further, a moderator may disagree... BUT, whilst this may all sound a bit inconclusive, <strong>I honestly believe that the best approach is to help students follow what they are interested in and do some meaningful mathematics, then try your best to justify the marks you give them.</strong> If you think the modelling is good enough (ie not technology only) then go ahead and mark it as further. Happy to hear anyone elses views on this post and my conclusions and hope I have helped a little..... Jim' </em></p> <p>So you can see the problem! What I would like to see in future guidance though is some specific examples of what a moderator will be looking for if students are to get credit for processes other than statistical tests as further processes. I have a few suggestions on that based on the examples on the TSM and years of podering that question! DISCLAIMER - The following are just suggestions based on my opinion. I would give the following credit as further processes if done correctly and relevantly.</p> <div class="blueBg"> <h3>Optimisation</h3> <p>The general model for this is to set up a problem like, how to package a given volume with minimum surface area of material and given constraints. Then students collect data by examining particular cases and build towards deducing a model for the surface area and optimising with calculus.</p> </div> <div class="greenBg"> <h3>Modelling</h3> <p>This is essentially about collecting information/measurements and trying to find a function that fits the data so that it can be used for forecasting. Of course, like with statistical tests, this can be done with a variety of tech so we have think hard about what manual mathematics we might expect to see....</p> <p>Example - Say a students is trying to fit an exponential curve to some growth (population?) data. I would expect students to sketch a curve through the points and from tjat curve and the data make estimates or duduce the value of both the y - intercept and the equation of the assymptote. Since...</p> <p ><span class="math-tex">\(f(x)=k\times { a }^{ x }+c \)</span></p> <p >and the y-intercept is at (0, k+c) and the assyptotoe is at y = c</p> <p>we could reasonably expect that students then deduce the values of k and c. They might then create a dynamic function that allows them to find the best value of a to make that fit. In this sense the student has done better than a tech only solution and better than a random sliding of variables to make it fit. they have understood the key properties of the data and used them to deduce a possible model.</p> </div> <div class="pinkBg"> <h3>Compound Probability</h3> <p>I have always thought that this should be a problem that involves more than 2 events and conditional probability with probabilities of various combinations being calculated by hand. I am just not confident that a problem with 2 idependent events would really qualify.</p> <p>Example - If you play with the ideas on the <a href="mathstudies/page/2563/fairground-games" title="Logic, Sets & Probability » L,S&P Teaching Ideas » Fairground Games">Fairground Games</a> activity, there are a number of possible avenues. For example, if you get three throws to get the paper ball in the bin, are you more likely to get the second or thrid throw in? A student might determione a relative frequency for the success with the experiment and compare it to more data where people get three throws and so on. thin about it for a while. I think there is lots of possibility.</p> </div> <div class="yellowBg"> <h3>3D geometry</h3> <p>I think this one is definitely harder, but it often goes hand in hand with optimisation. It is hard to think of examples where this is would be used to solve a problem.</p> <p>Example - With the <a href="mathstudies/page/19544/cuboid-challenge" title="Geometry & Trig » G & T Teaching Ideas » Cuboid Challenge">Cuboid Challenge</a> it is possible to make the cuboid from three different pyramids which is nice, for lots of reasons, but mostly because it means they must all have an equal volume because they are all a third of the cuboid they fit in. I think this has potential to be explored in different ways and for some proof, but it would get pretty tricky.</p> <p>Example - When doing this <a href="http://www.teachmathematics.net/page/3096/the-rice-show" target="_blank">rice show activity</a>, the rice was falling in some wonderful shapes. I wonder, for example, how many cones of which dimensions could be made with a kilo of rice..... Again, there is thinking to do, but there is potential.</p> </div> <p>As I said, these are just some suggestions to provoke a little thought on this topic. To finish, I'll re iterate something from my response above. </p> <p><em><strong>'I honestly believe that the best approach is to help students follow what they are interested in and do some meaningful mathematics, then try your best to justify the marks you give them.</strong> '</em></p> <p>Happy marking!</p> http://www.thinkib.net/mathstudies/blog/20388/further-processes#1455148800Exponential (and tooth) decay
http://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay
Sun, 17 Jan 2016 00:00:00 +0000]]>Exponential (and tooth) decayhttp://www.thinkib.net/cache/blog-thumbs/21/20298-1453029601-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/20298-1453029601-thinkib.jpg" alt="Exponential (and tooth) decay" /><br /><br /></p> <p>Once the technique has been practiced it can be used on other, more complex exaples such as those here in the <a href="mathstudies/page/15507/modelling-world-population-growth" title="Mathematical Models » Functions Teaching ideas » Modelling World Population Growth">Modelling World Population Growth</a> activity.</p> <p>Short, sweet (literally) and powerful!</p> http://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay#1452988800Approaches to teaching and Learning
http://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning
Wed, 07 Oct 2015 00:00:00 +0100]]>Approaches to teaching and Learninghttp://www.thinkib.net/cache/blog-thumbs/21/19754-1444140860-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning
<p ><img src="http://www.thinkib.net/cache/blog-thumbs/21/19754-1444140860-thinkib.jpg" alt="Approaches to teaching and Learning" /><br /><br /></p> <h2>Collecting the evidence</h2> <p>This post comes from my thoughts and experiements related to the unit planners that are likely to be a part of the DP teacher's life very shortly as a result of the <a href="mathstudies/page/19408/attl-and-planning" title="IB Core » ATTL and planning">ATTL and planning</a> initiative. That link outlines a lot of the key issues facing teachers. This post is about the process of writing about teaching and gathering evidence of all the things that are happening. As I have already said, I think it is an admirable aim to ask schools and teachers to reflect on the aspects of the practice and try to make sure they are delivering the aims, objectives and philosophy of the course. They key question still remains - 'how?'</p> <p>I have recently been expriementing with some new pages on the site to try and tackle this. The 'Focus on' pages are designed to allow teachers and students to work more easily by topic. See this example - <a href="mathstudies/page/19749/focus-chi-squared" title="Statistics » Focus - Chi Squared">Focus - Chi Squared</a> - that I published today and am still working on. The idea is kind of like a mini 'unit planner' for teaching this topic. The teaching activities are listed, there are some teaching slides, practice activites and then references to the opportunities for Tok. After that it gets difficult. With unit planners, we are supposed to be showing when we provide opportunities for students to develop the attributes of the learner profile and the key teaching and learning objectives outlined in the ATTL document. </p> <div class="greenBg"> <p><strong>Teaching</strong> - Inquiry based, conceptual understanding, collaboration in local and global contexts, assessment and differentiation</p> <p><strong>Learning</strong> - Thinking skills, research skills, social skills, communication skills and self-management skills.</p> </div> <p>These, of course, blend nicely with the attributes of the IB learner profile and the ways of knowing. These aims shouldn't really be seen as mutually exclusive and so it gets tricky when you start to try and list evidence that you have provided the opportunities. Many of the goals are generic teaching goals that infuse practice in different ways. For that reason, it can seem a little contrived to start listing specific instances when these opportunities occur. As teachers who talk to each other, we know when they crop up, we know they will and we know it wont always be as we planned. Still, the challenge is out there to find a solution to this need for providing evidence of planning without making tenuous lists.</p> <p>In response I have bundled the teaching and learning points together with the learner profile attributes - see the diagram above. Becoming a good commuincator and developing communication skills clearly go hand in hand. Developing thinking skills whilst aspiring to be a thinker and engaging in inquiry based tasks again go well together.</p> <p>As such, I am going to write a little about the teaching of each subtopic on the 'focus on' pages and highlight the use of any of these key words as I talk about the teaching and learning of the topic. Check out my latest effort here - <a href="http://www.thinkib.net/mathstudies/page/19756/focus-arithmetic-sequences" title="Number & Algebra » Focus - Arithmetic Sequences">Focus - Arithmetic Sequences</a></p> <p>Let me know what you think!</p> <p>....</p> http://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning#1444172400Curriculum Review
http://www.thinkib.net/mathstudies/blog/19691/curriculum-review
Thu, 01 Oct 2015 00:00:00 +0100]]>Curriculum Reviewhttp://www.thinkib.net/cache/blog-thumbs/21/19691-1443684008-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/19691/curriculum-review
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/19691-1443684008-thinkib.jpg" alt="Curriculum Review" /><br /><br /> <h3>Disclaimer!</h3> <p>The only information published about this is in the two review reports on the OCC. I am not the IB and everything I write here is based on having read and thought about those two documents. As such, the facts are the same as the facts given in the reports, the rest is just discussion of the significance and speculation! Its early days, there is much yet to be decided.</p> <h3>Summary</h3> <p>The following is a summary of the key changes being proposed</p> <div class="greenBg"> <ul> <li>Choice of two courses in group 5 for mathematics - as yet without names</li> <li>Both courses can be done at HL and SL.</li> <li>1st course, much like exisiting SL/HL course only with reduced content to allow for more time developing mathematical thinking skills.</li> <li>2nd course based more on wider 'applications' of mathematics. Possibly like the current mathematical studies course but with a new HL element.</li> <li>A common element to all courses (60hrs)</li> <li>Both SL parts will be subsets of the respective HL courses</li> <li>There will be some intersection between the elements.</li> <li>A combined 'Mathematical Skills and Concepts' element that will encompass the IA.</li> </ul> </div> <h3>The Distinction</h3> <p>This is the key point and we await further clarity on the key difference between the courses. That said, there is plenty of evidence within the reports that points to the following. Again, I must stress that following is speculation based on the reports.</p> <div class="blueBg"> <p>One of the courses will be a development of the current HL/SL arrangement. One imagines that this is still the route we would advise for those with ambitions in the field of mathematics, engineering and other areas that require a significant degree of mathematical competency. This will be more like mathematics as we know it.</p> </div> <div class="yellowBg"> <p>The other course will be a development of the principles behind the current mathematical studies course. This is based on the idea that understanding of mathematical concepts and knowledge is still a fundamental part of any knowledge base AND that there are a broad range of 'applications of mathematics' that apply across a wider range of career paths. </p> <p>The <strong>big change here</strong> is the introduction of an HL element. This is accredited to recognition that fluency in the application and the significance of a wide range of mathematical ideas is increasingly relevant and desirable. The focus here will be less on the mathemmatical structure and more on the mathematical significance. </p> </div> <h3>The Rationale</h3> <p>If anyone has been following <a href="http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers?language=en" target="_blank">Conrad Wolfram's computer based mathematics movement</a>, then you will have already have considered his key contention that there is now less need for 'calculation' and more need for 'application' and that this a natural result of significant technological developments (see <a href="http://www.wolframalpha.com">Wolfram Alpha</a> as an example). Watch the talk to get a fuller idea, but the main thrust is that mainstream compulsory mathematics education should move towards teaching the significance and application of techniques and let computers do the calculation. See the example below..</p> <div class="pinkBg"> <p>Consider the Pearson's product moment correlation coefficient. The mathematical structure behind that calculation is a wonderful bit of mathematics, but I would suggest that few truly understand the structure, whilst many understand the principle of the test and significance of the result.</p> <p>The contention is that, for most, only the latter is necessary, BUT that being an expert in the latter is something we should value highly (hence the HL extension)</p> </div> <p>It is important to note that no one in the field is arguing that mathematics as we know it, no longer has a place, but simply that what we consider what is best for compulsory mathematics education to age 18.</p> <p>Of course, the key knowledge question here (sorry, couldn't resist the ToK reference) is the one about the age/stage at which we might start diversifying. If we still need mathematicians then we mustn't close that route to too many too soon. In the case of the IBDP, this is easily handled. At 16 it is fine to ask students to make this choice.</p> <h3>Avoiding Confusion</h3> <p>Some conversations I have had already with teachers suggests that there will be work to do to avoid confusion. It is currently possible to read the documents and conclude that there will be two new equivalent courses called (for now) 'Pure maths' and 'Applied maths'. I think this is potentially confusing since there is no obvious differentiation in the level of mathematics to be seen there. Clearly, closer reading will help, but there will be work to do to help people understand.</p> <p>Let us not beat around the bush, just as everyone knows that the current Studies course is easier (mathematically) than the SL course despite their equal weighting, surely the 'Applications' course will be easier than the 'Pure' course. As with the current structure, the courses serve different purposes. The 'Pure' course will be for mathematicians as we know them whilst the 'applied course' will be for a new kind of mathematician.</p> <p>It is my belief that the net result will be more 'Mathematicians', and more engagement and understanding of mathematical ideas, concepts and applications and that can only be a good thing.</p> <h3>And finally</h3> <p>At presentations and as part of our philosophy for teaching and learning mathematics where I work, we often describe the following three facets of mathematics. (not always using the same words I might add!)</p> <div class="greenBg"> <p >A unique area of knowledge that is built on logical foundations. Its beauty and elegance is to be appreciated and explored both for pleasure and to develop critical thinking skills.</p> <p >A functional tool for survival. These skills are to be thoughtfully explored, acquired and applied.</p> <p >A crucially important way to understand the world that we live in. Mathematical literacy is essential to understanding, inquiring and pursuing the truth about the world around us.</p> </div> <p>As we try our best to make mathematics education about all of those things, it is poossible to conceive that we can have two IBDP maths courses (HL and SL) that are different blends of those ingredients suited to different students for different purposes. I think so!</p> <p>We will watch with interest!</p> <p>.....</p> http://www.thinkib.net/mathstudies/blog/19691/curriculum-review#1443654000To Chi or not to Chi?
http://www.thinkib.net/mathstudies/blog/19648/to-chi-or-not-to-chi
Mon, 21 Sep 2015 00:00:00 +0100]]>To Chi or not to Chi?http://www.thinkib.net/cache/blog-thumbs/21/19648-1442846130-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/19648/to-chi-or-not-to-chi
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/19648-1442846130-thinkib.jpg" alt="To Chi or not to Chi?" /><br /><br /></p> <h4>Yates's Continuity Correction</h4> <p>If students end up with a 2 x 2 contingency table then they are required to use this correction approach. Again, this is related to disproportionate effe t of small variations on smaler numbers (degree freedom just 1).</p> <p>This is easily done - When we do Observed frequency subtract expected frequency, we then subtract a further 0.5 before squaring. Students are only required to recognise the need and use the correction rather than explain why it is needed.</p> http://www.thinkib.net/mathstudies/blog/19648/to-chi-or-not-to-chi#1442790000Life's Complexities
http://www.thinkib.net/mathstudies/blog/19589/lifes-complexities
Thu, 10 Sep 2015 00:00:00 +0100]]>Life's Complexitieshttp://www.thinkib.net/cache/blog-thumbs/21/19589-1441872658-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/19589/lifes-complexities
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/19589-1441872658-thinkib.jpg" alt="Life's Complexities" /><br /><br />Hope that we can understand</h2> <p>This is a great <a href="http://www.ted.com/talks/hannah_fry_is_life_really_that_complex" target="_self">10 minute video</a> from <a href="http://www.hannahfry.co.uk/" target="_blank">Hannah Fry</a> based on how mathematics might be able to help us answer the question above. She starts by giving us examples of why things might seem so hopelessly complex that we are never likely to get any understanding of them and then cleverly shows us some other examples of how maybe we might. There is a nice useable example in there about the last London riots and the distances the rioters lived from the places they rioted. Equally there is some more complex mathematics about how 'Burglary hotspots' resemble the patterns of leopard spots - and an understandable explanation for why!</p> <p ><iframe allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/LnQYJa9-aR0?rel=0" width="560"></iframe></p> <p>I think this cane be used in two ways.......</p> <p>1. The very real example of the correlation between distance rioters live from the riot sites and the number riots is a good contextual example to use when looking at this bit of statistics. </p> <p>2. That combined with the other example is great for 'Project Inspiration' it is a good length and I think students will find it interesting.</p> http://www.thinkib.net/mathstudies/blog/19589/lifes-complexities#1441839600Sabbatical
http://www.thinkib.net/mathstudies/blog/19267/sabbatical
Mon, 13 Jul 2015 00:00:00 +0100]]>Sabbaticalhttp://www.thinkib.net/cache/blog-thumbs/21/19267-1436359440-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/19267/sabbatical
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/19267-1436359440-thinkib.jpg" alt="Sabbatical" /><br /><br />Something different!</h2> <p>Hi all, this is just a quick post to share my plans for the near future with you. Term has just ended for us here in Toulouse and the long summer holidays are just beginning. This year felt a bit odd for me though since I am not planning to go back to work there until January 2016. I have been negotiating with my school for ways to change things a little so that I can develop some more ideas I have to help teachers and students of mathematics and, in particular, those of the IB Mathematical Studies courses. So, all that means that I have the next 6 months set a side to really take this website to the next level amongst other things.</p> <p>I must confess that I am quite looking forward to a little break from the madness that is school life. I guess most of us feel like that as holidays approach. I like the idea of being able to manage my own time and am about to find out if I have the discipline. I also think that I will be really keen to get back to school in January. That will be swiftly followed by being totally exhausted 2 weeks later no doubt.</p> <h3>Priorities</h3> <p>Anyway, as I have already said, taking this site to the next level is high up my priority list. I will also be spending some time on <a href="http://www.teachmathematics.net/">teachMathematics</a> posting lots of new ideas. Along with that, I am working on some student support resources for Maths studies - more to follow. With reference to this site, here are some of my immediate priorities.....</p> <p><em><strong>More great ideas and resources for teaching </strong></em>- I still think this is the most important part of our jobs and I have lots of ideas in the making that need polishing and posting.</p> <p><em><strong>More IB style questions</strong></em> - A number of you have made this request and so this is a major area that I hope will blossom in this time period.</p> <p><em><strong>More on the IB core</strong></em> - with the new requirements for evidence of unit planning, I will help teachers to document and take advantage of the opportunities there are to help students develop learner profile attributes and make the important links with ToK and so on.</p> <p><em><strong>Correction of errors</strong></em> - I know that these errors are littered around the site and I do try my best to track them down and correct.</p> <h3>Feedback</h3> <p>I'd love to hear from people about what they think of the site and what areas they would like to see developed. Let me steer you to this page again so you can <a href="mathstudies/page/18637/tell-us-what-you-think">'Tell us what you think!'</a></p> <h3>Workshops</h3> <p>I will also be doing some face to face and online workshops in that time. Please think about signing up if you can and recommend to your colleagues and friends in other schools</p> <p><em><strong>Inthinking Workshops</strong></em></p> <p><a href="http://www.inthinking.co.uk/site/workshop/2015-09-25-bcn.htm" target="_blank">Category 1 - New teachers (new and new to IB) Barcelona, 25th to 27th September 2015</a></p> <p><a href="http://www.inthinking.co.uk/site/workshop/2016-02-05-bcn.htm" target="_blank">Category 2 - Experienced teachers Barcelona, 5th to 7th February 2016</a></p> <p><em><strong>Philpot Education</strong></em></p> <p><a href="http://philpot.nl/maths-studies">Category 2 - Experienced teachers, Amsterdam, 17th - 19th September</a></p> <p><em><strong>IB Online workshops</strong></em></p> <p><a href="http://www.ibo.org/en/event/279678" target="_blank">Category</a><a href="http://www.ibo.org/en/event/279678"> </a><a href="http://www.ibo.org/en/event/279678" target="_blank">3 </a><a href="http://www.ibo.org/en/event/279678">- </a><a href="http://www.ibo.org/en/event/279678" target="_blank">IBDP</a><a href="http://www.ibo.org/en/event/279678"> </a><a href="http://www.ibo.org/en/event/279678" target="_blank">Mathematics</a><a href="http://www.ibo.org/en/event/279678"> </a><a href="http://www.ibo.org/en/event/279678" target="_blank">and</a><a href="http://www.ibo.org/en/event/279678"> </a><a href="http://www.ibo.org/en/event/279678" target="_blank">ICT</a><a href="http://www.ibo.org/en/event/279678">, </a><a href="http://www.ibo.org/en/event/279678" target="_blank">19th August</a><a href="http://www.ibo.org/en/event/279678"> - </a><a href="http://www.ibo.org/en/event/279678" target="_blank">16th</a><a href="http://www.ibo.org/en/event/279678"> </a><a href="http://www.ibo.org/en/event/279678" target="_blank">September, </a>2015</p> <p><a href="http://www.ibo.org/en/event/279702">Category 3 - IBDP Mathematics and ICT, 25th November - 23rd December, 2015</a></p> http://www.thinkib.net/mathstudies/blog/19267/sabbatical#1436742000Chi Squared, regression and causation
http://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation
Tue, 14 Apr 2015 00:00:00 +0100]]>Chi Squared, regression and causationhttp://www.thinkib.net/cache/blog-thumbs/21/18868-1429015580-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/18868-1429015580-thinkib.jpg" alt="Chi Squared, regression and causation" /><br /><br /> HOWEVER - this does not mean students cant use both.... eg a project might be investigating literacy rates and involve a scatter graph of literacy against GDP, and then a chi² to see if literacy rate is dependent on continent for example. This is great. In this case the student has used both tests to investigate a theme involving literacy rates but not on exactly the same data.</div> </div> IF students have done both tests on the same data then I think it is difficult to mark because the student would need to justify what one offers that the other doesn't in order for it to be considered relevant.</div> <p><span >I summary, my advice is that students avoid doing both tests on the same data, but there is no official line that it cant be done. If you want to give students full marks then I would advise noting to the moderator where you see the difference. Otherwise I think the relevance can be questioned.'</span></p> <p><span >......... to be continued</span></p> http://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation#1428966000This years projects
http://www.thinkib.net/mathstudies/blog/18737/this-years-projects
Sun, 22 Mar 2015 00:00:00 +0000]]>This years projectshttp://www.thinkib.net/cache/blog-thumbs/21/18737-1427053909-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/18737/this-years-projects
<img src="http://www.thinkib.net/cache/blog-thumbs/21/18737-1427053909-thinkib.jpg" alt="This years projects" /><br /><br /> <h2>Some Good ideas</h2> <p>As many of you probably are, I am currently putting the finishing touches on this years batch of Internal Assessment projects. It always seems like a monster exercise, but one that is worth it in the end. This year, I am particularly pleased and the main reason is that I feel that all the students in my class got lots out of their projects. The understood the goals and the exercise really felt like it is supposed to philosophically. It isn't that it normally doesn't just particularly so this year. Marking the projects was a real pleasure because students had done some really interesting work and because they have paid attention to my advice! I thought I would quickly share some of the topics they chose.</p> <p><em><strong>Youtube</strong></em> - inspired by the picture above, this was a great project about you tube channels. Who runs them? What are they about? How many subscribers - and so on. There is so much data there and youtube really plays a part in peoples lives these days one way or another. </p> <p><em><strong>Flickr</strong></em> - What makes a photograph popular on Flickr - again, these websites collect so much data and we can be sure that they are analysing it so it seems ripe for students to do so.</p> <p><em><strong>Dance</strong></em> - This seemed like a challenge at first, but this student worked really hard to collect some useful primary data on flexibility and then looked to see what types of people (ie dancers) might be more flexible.</p> <p><strong>GDP and CO2 emissions</strong> - is there a link?</p> <p><strong>Book publishing </strong>- These were some interesting stats I had never seen before. Data on how many books are published in a given year and the literacy rates for different countries.</p> <p><strong>Spotify</strong> - More online data collection - what makes a song popular.</p> <p><strong>Broadway</strong> - what makes more money and how, musicals or plays?</p> <p><strong>Films, cars, smoking and divorce rates</strong> made up the rest and all round I really enjoyed the diversity! No non stats projects this year, but students chose their own areas of interest and I, for one, was pleased with the results!</p> <h2></h2> http://www.thinkib.net/mathstudies/blog/18737/this-years-projects#1426982400Project Ideas
http://www.thinkib.net/mathstudies/blog/18680/project-ideas
Sat, 14 Mar 2015 00:00:00 +0000]]>Project Ideashttp://www.thinkib.net/cache/blog-thumbs/21/18680-1426321139-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/18680/project-ideas
<h2>Mind maps</h2> <p><!--cke_bookmark_77S--><!--cke_bookmark_77E-->Projects are on our minds at the moment! I am just final checking my IB2 projects before submitting marks and just starting my projects with IB1s. this year I have been really happy with the build up to that and really feel like students have a good handle on how to choose good themes. I have more to say about this, which I will put on the <a href="http://www.thinkib.net/mathstudies/page/2075/internal-assessment" title="Assessment » Internal Assessment">Internal Assessment</a> section! Essentially though, the build up results in the production of three 'Mind maps' about project ideas that show the theme, the information and the potential for different analysis. It seems simple, but it has been really effective. Students are asked to produce three of them and then I will help them choose the one with the most potential. Like I said, there is much more to say about this, but for now - which of these ideas would you encourage your students to pursue?</p> <p ><br /> <img src="http://www.thinkib.net/cache/blog-thumbs/21/18680-1426321139-thinkib.jpg" alt="Project Ideas" /><br /><br /></p> http://www.thinkib.net/mathstudies/blog/18680/project-ideas#1426291200Perceived Corruption
http://www.thinkib.net/mathstudies/blog/18049/perceived-corruption
Thu, 04 Dec 2014 03:30:00 +0000]]>Perceived Corruptionhttp://www.thinkib.net/cache/blog-thumbs/21/18049-1417688584-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/18049/perceived-corruption
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/18049-1417688584-thinkib.jpg" alt="Perceived Corruption" /><br /><br /> <div><iframe frameborder="0" height="520" src="http://media.transparency.org/maps/cpi2014-640.html" width="640"></iframe></div> <div>There is so much potential here for statistical analysis and discussion and probably a whole project. Here are just a few ideas...</div> <div></div> <ul> <li>Make hypotheses about the table before the results are shown. Maybe even survey students based on these hypotheses.</li> <li>Use measures of central tendency to compare different geographical areas.</li> <li>Plot box and whisker diagrams to show spread in those areas.</li> <li>Plot scattergraphs of the results of two versions of the survey and do some linear regression.</li> <li>Do the same for geographical areas - which areas show the most correlation? - why might some show more than others?</li> <li>Ask questions about the data collection methods and samples. Look through the website for answers.</li> </ul> <p>I am sure there is so much more, but I am just getting the ball rolling. Thank you Internet for continuing to supply such rich and relevant data for us to work with.</p> <div></div> http://www.thinkib.net/mathstudies/blog/18049/perceived-corruption#1417663800Theory of Knowledge
http://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge
Sun, 16 Nov 2014 03:30:00 +0000]]>Theory of Knowledgehttp://www.thinkib.net/cache/blog-thumbs/21/17966-1416145522-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge
<h3><img src="http://www.thinkib.net/cache/blog-thumbs/21/17966-1416145522-thinkib.jpg" alt="Theory of Knowledge" /><br /><br />A personal perspective</h3> <p>I want to use this opportunity to explain how my own personal approach to ToK has developed. Like many teachers who start the IB, the whole idea was very new to me and seemed very much like a distant 'bolt on that other teachers looked after and didn't need to affect the way I taught. After 2 years of teaching IB, I took over the department in my school and the IB coordinator approached me and asked if I would prepare some subject specialist sessions on ToK and Mathematics for the IB1 students as my predecessor had done! The only answer was yes of course, but I found myself quickly in unchartered water! Eight years later I argue that the ToK course has had a bigger impact on my teaching in general, and in particular Mathematics, than anything else. When teachers feel the time is right, I would recommend and encourage as much understanding of the ToK course as possible. Equally, it is very effective to help students make links between mathematics and ToK from an early stage. Understanding the differences in the way bodies of knowledge grow, develop and change in different subject areas is bot fascinating and lends a sharp perspective to what we expect our students to do day on day in our schools.</p> <p>I am now a teacher of the whole ToK course which has brought new riches in terms of the time I get to spend talking to, watching and learning from my colleagues about their subjects and the rich and fascinating links between them and the way we all accumulate knowledge.</p> <p>I am sure many readers are experienced with ToK and equally sure that there are many who haven't traveled there yet. All I can say is that I recommend that you take the chance as and when it comes along.</p> <h3>ToK, Maths Studies and this site</h3> <p>Many of the resources on this site are already charged with ToK issues as I am sure some of you have noticed. I am now developing a section on <a href="http://www.thinkib.net/mathstudies/page/17595/theory-of-knowledge" title="IB Core » Theory of Knowledge">Theory of Knowledge</a> which aims to be more explicit about how and when ypu might bring ToK discussions in to the Maths Studies classroom.</p> http://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge#1416108600Logic Lab
http://www.thinkib.net/mathstudies/blog/17708/logic-lab
Mon, 13 Oct 2014 03:30:00 +0100]]>Logic Labhttp://www.thinkib.net/cache/blog-thumbs/21/17708-1413202944-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/17708/logic-lab
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/17708-1413202944-thinkib.jpg" alt="Logic Lab" /><br /><br /></p> <p>Here is a list of things I have been thinking about and experimenting with!</p> <ul> <li>Human logic gates - drawing some big ones on the ground and getting the students to be the inputs being either on or off. This could produce some nice pictures and video.</li> <li>Modeling compound logic statements with logic circuits.</li> <li>Getting students to come up with the idea of truth tables themselves as a way of recording all the possible outcomes.</li> <li>Using logic circuits and their outcomes to generate and demonstrate the idea of 'Logical Equivalence'</li> <li>Using logic circuits to demonstrate tautolgies and contradictions.</li> <li>Using logic circuits to model, inverse, converse and contrapositive.</li> </ul> <p>All if this is likely to appear as an activity or series of activities on the <a href="http://www.thinkib.net/mathstudies/page/2233/ls-p-teaching-ideas">Logic, Sets and Probability activity page</a> eventually. In the mean time I can highly recommend that you have a play!</p> http://www.thinkib.net/mathstudies/blog/17708/logic-lab#1413167400May 2014 Results!
http://www.thinkib.net/mathstudies/blog/17283/may-2014-results
Thu, 14 Aug 2014 03:30:00 +0100<h2>Reflections and Resolutions</h2> <p>Each year I am required to write a report on the IB Mathematics results and, although I am still in holiday mode, I am beginning to think about what I will write this year. Obviously I wont publish confidential results here on this blog, but rather some related reflections. The end of one school year and the start of a new year offer great opportunities for reflection, resolution and new starts!the following are just some thoughts related to the teaching of IB Maths Studies that I have had following the results of the last class.</p> <h3>IA marks</h3> <p>I am a great advocate of not worrying too much about what moderations have been made to your IA marks. The system is such that this is beyond our control. If we have done our best to think about and interpret the criteria as fairly as possible and then justify why we did so then that is the best we can do. Sometimes the sample will be simple and representative and sometimes it wont. Sometimes our moderator will agree with us but theirs wont and so on. That said, it is reassuring when your grades are not changed at all which is what happened this year! I have marked up, marked down and both in the same year, but only twice have all of my marks been unchanged. It seems funny to me that the first time was my very first year teaching IB Maths Studies and the second the first run through of a new syllabus! Anyway, I would be citing the system if my marks had been moved and so I will put this down to laws of probability as much as my efforts. I did write these two posts about IA whilst marking this year if that is of interest to anyone....</p> <div><img src="img/user/generic/48-generic-editor.png" style="width: 48px; height: 48px; vertical-align: middle; margin: 4px 12px 4px 0" /> <a href="mathstudies/blog/15939/ia-issues" target="_blank"><span>IA Issues</span></a></div> <div><img src="img/user/generic/48-generic-editor.png" style="width: 48px; height: 48px; vertical-align: middle; margin: 4px 12px 4px 0" /> <a href="http://www.thinkib.net/mathstudies/blog/16828/ia-moderation" target="_blank"><span>IA Moderating</span></a></div> <div><img src="img/user/generic/48-generic-editor.png" style="width: 48px; height: 48px; vertical-align: middle; margin: 4px 12px 4px 0" /><br /><a href="http://www.thinkib.net/mathstudies/blog/16777/moderator-notes" target="_blank">Moderator notes</a></div> <div></div> <div>Whatever the outcome use it to inform what you do in the future and don't worry too much about it. All we can do is our best.</div> <h3>Exam Marks</h3> <p>I think one of the most important indicators for results is how close your results were to the predicted grades we gave to IB earlier in the year. Sure, there are lots of 50/50 students and some of us go for optimism and some are more cautious and you must bear this in mind as we interpret the correlation. This year I over predicted by an average of half a grade. Although I am self confessed optimist this is unusually high for me and so it has been quite a point for reflection for me. Without going in to details about the class in question I have been asking myself the following questions.....</p> <ol> <li>Did my class, in general, react in the same way as other classes to the mounting pressure of impending exam?</li> <li>Did I do anything particularly differently from previous years throughout the course?</li> <li>What impact has the new syllabus possibly had on my ability to predict?</li> </ol> <p>I have answered the first two questions for myself and drawn some useful conclusions. The third is, however, harder to answer and one I will be thinking about a lot this year as I prepare the next class for exams. As author of this site and a workshop leader for Maths Studies I have spent a lot of time reflecting on the subtle changes to the syllabus, trying hard to make sure I covered them all. After the exam and before completing the G2 form in May I did do the papers myself and have published the <a href="http://www.thinkib.net/mathstudies/page/16886/past-paper-review" target="_blank">written solutions here</a>. As I did the paper I did find myself identifying a number of questions I thought my students would find difficult, but did not conclude that they were particularly difficult in comparison to previous years, although I have made a note to check again as term starts. What I did conclude was that still, students are required to take their understanding of mathematical ideas and apply it to less familiar contexts, even on this course. As produce more <a href="http://www.thinkib.net/mathstudies/page/15871/exam-style-questions" target="_blank">'exam style questions'</a> I will bear this in mind.</p> <h3>Implications for teaching</h3> <p>This is the most important part - what might I do differently as a result?</p> <p>I took the decision to get my IB1 class through their IA already while I was thinking about so much during moderation. I think I will repeat this for the new IB1 class. This will have the added benefit of allowing a bit more time to do some more exam preparation with classes in the IB2 year.</p> <p>Pedagogy Vs passing exams - this is the raging debate in education and fascinating one. As day to day teachers we are the ones that have to walk this line. I have always justified an emphasis on 'thinking skills, discovery and exploration' in mathematics teaching by saying that exam results should be a symptom of what we do not the goal. I stand by this and the philosophy that education and in particular maths education, is about so much more than passing exams. It is always worth stopping to check though - if the symptoms stop appearing then there is a problem. I remain certain that the emphasis must remain on sound educational experiences, but having over predicted this year, I am checking myself by thinking about some ways to help students be better prepared for exams.</p> <p>Anyway I really enjoy the time and space to have these reflections and am looking forward to a few more in the weeks before the new term starts for those of us in the Northern Hemisphere.</p> <p>Thanks,</p> <p>Jim</p> http://www.thinkib.net/mathstudies/blog/17283/may-2014-results#1407983400The Intuition Line
http://www.thinkib.net/mathstudies/blog/12473/the-intuition-line
Wed, 02 Jul 2014 03:30:00 +0100]]>The Intuition Linehttp://www.thinkib.net/cache/blog-thumbs/21/12473-1404317744-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/12473/the-intuition-line
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/12473-1404317744-thinkib.jpg" alt="The Intuition Line" /><br /><br /></p> <h3> When do we trust out guts?</h3> <p> This blog post is about a concept I am defining as 'The Intuition Line'. I am sure I am not the first to do so, but it is currently present in my thoughts so I wanted to write it down! In short, I am defining the intuition line as the point at which intuition stops working for students and needs to be replaced with logical analysis. This comes to mind primarily because of recent work my students and I have done on Probability. As well as this I am struck by the number of questions I see that appear to fall one side or the other of this line. It is perhaps best to start by stating an example of what I am talking about.</p> <p> The question, 'what is the probability of throwing a 6 on an ordinary dice?' seems to draw an intuitive correct response - If the question goes on to ask, 'what is the probability of throwing two 6s?', this tends to draw an incorrect intuitive response.</p> <p> All I wish to do really is to ask people to think about when and where this intuition line occurs. How different is it for different people? How is the position of the line affected by teaching? How much of any given exam can a student answer with intuition?</p> <p> I dont think I can answer these questions yet, but I really think they need answering! I'd welcome any thoughts........</p> <p> <iframe id="buffer_tpc_check" src="https://d3ijcis4e2ziok.cloudfront.net/tpc-check.html" style="display: none;"></iframe></p> http://www.thinkib.net/mathstudies/blog/12473/the-intuition-line#1404268200The Problem with Monty Hall
http://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall
Sun, 11 May 2014 03:30:00 +0100]]>The Problem with Monty Hallhttp://www.thinkib.net/cache/blog-thumbs/21/16848-1399827527-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/16848-1399827527-thinkib.jpg" alt="The Problem with Monty Hall" /><br /><br />The 'Google' generation</h2> <p>Those of you familiar with the Monty Hall problem will know what a wonderfully rich bit of mathematics it is. Those of you who are not are faced with a problem the Internet has brought us. I would suggest that you just google it and get stuck in, but the problem is that the Internet ,as it is today, offers many more answers than questions and it is difficult to find things that dont give the answers away before anyone has had time to experience the richness of the problem.</p> <p>This post was prompted by a post I saw on facebook yesterday from the Khan Academy about the Monty Hall problem. Infact, it was a video explanation of the solution to the problem. I am not going to turn this post into a KA bashing session and there are some wonderful explanations of the Monty Hall problem out there. The one I enjoyed most is the simple one printed in the novel 'The curious Incident of the Dog in the Nightime'. In fact the novel offers a lovely summary of the whole story. I particularly enjoyed the quotes from famous mathematicians who were arguing that Marilyn Vos Savant was wrong. This is a lovely story for ToK lessons. Again, though, the problem is that this is only a wonderfully rich problem if people experience engagement with it themselves. Going straight to the solution is like watching the end of the 'Sixth Sense' first. Actually, I like that analogy, because that film is really good the second time too, because you look at everything differently, but the first time is the real experience.</p> <p>The google generation need to be wary that they have so many 'soultions' on offer to them that they are in danger of not experiencing problems. Knowledge will become a collection of solutions, rather than experience of problems. Teachers have the challenge of presenting problems in a way that lets students experience them. This is a must for Monty Hall. I would love to see a web page on the Monty Hall problem, that did not offer a solution anywhere! In fact, In think I'll put it on my to do list!</p> http://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall#1399775400IA Moderation
http://www.thinkib.net/mathstudies/blog/16828/ia-moderation
Sun, 04 May 2014 03:30:00 +0100]]>IA Moderationhttp://www.thinkib.net/cache/blog-thumbs/21/16828-1399234650-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16828/ia-moderation
<h2><img src="http://www.thinkib.net/cache/blog-thumbs/21/16828-1399234650-thinkib.jpg" alt="IA Moderation" /><br /><br />Moderating</h2> <p>I have just completeed another set of moderating for the Internal Assessment element of the course. It is really important to say that I am only a moderator and that I too am subjecto to moderation and my opinion on the interpretation of marking criteria and the natuire of work is just that, only my opinion. I thought it was worth sharing some thoughts though, just the same</p> <p>In my view it would be more helpful if there was an obligation for teachers to make specific references to the work where they have justified marks. For example. For example, where you might write under criterion C '2 simple relevant correct processes and further process were used' where it would be more helpful to write 'The two simple processes were ..... and ..... which can be seen on page .... and so on.' This is not just born of a desire to make the moderators life easy, but the process would help teachers to check thoroughly for themselves if the candidate has actually completed correct relevant processes. This applies to all of the criteria.</p> <p>Out of 88 projects seen, I only had one 'Non stats' project. I think the new criteria lend themselves more to non stats work than the older criteria did, but they still lend themselves much more to statistics. I don't have a problem with this. I think there are many possibilities to do useful project work with statistics and I saw a number of very interesting project topics. Statistics is a very applicable tool, especially for maths studies students whose interest probably lie outside of mathematics. In general, there was much less of a formulaic approach taken to project work than in previous years. I had a strong sense that students were allowed to choose and pursue their own areas of interest. The downside is that many students chose some very poor limited topics/ideas. The overwhelming majority of projects were base don primary data. Whilst this is fine, it seems a shame given the ever increasing wealth of availability of real relevant data on the internet. Data is the new oil and working with these large quantities of it is a real pursuit these days and so I would like to see more students doing this.</p> <p>The new criterion A and B posed a few issues for me as a moderator. The fine details of both are to be applauded. Students need to explain the purpose of their planned approach and be concise and consistent in criterion A and in B they need to describe their data collection process thoroughly to get full marks. I found that very students had done this. As such the vast majority were awarded 2 in both of these criteria. This has an implication for future teaching. Again, I think these are great additions to criteria and will certainly be placing more emphasis on them in my own teaching.</p> <p>The increased emphasis on 'relevance' and 'conciseness' is excellent, but definitely a challenge for teachers and students. I think it is important that students are exposed to numerous examples of simple, relevant and irrelevant applications of simple statistics and that there is a corresponding emphasis placed on this understanding in classrooms. I think this is a positive change.</p> <p>I have enjoyed working with the new criteria, although it has been a challenge to make the subtle shifts from the old ones. I think the changes are positive and that the project work has become more purposeful as a result.</p> <iframe id="buffer_tpc_check" src="https://d3ijcis4e2ziok.cloudfront.net/tpc-check.html" style="display: none;"></iframe>http://www.thinkib.net/mathstudies/blog/16828/ia-moderation#1399170600Moderator Notes
http://www.thinkib.net/mathstudies/blog/16777/moderator-notes
Mon, 21 Apr 2014 03:30:00 +0100]]>Moderator Noteshttp://www.thinkib.net/cache/blog-thumbs/21/16777-1398085118-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16777/moderator-notes
<p><img src="http://www.thinkib.net/cache/blog-thumbs/21/16777-1398085118-thinkib.jpg" alt="Moderator Notes" /><br /><br /></p> <p>There are more examples of this in the <a href="http://www.thinkib.net/mathstudies/page/2095/marking-moderation" target="_blank">IA section</a> of the website. You might also find this blog post on<a href="http://www.thinkib.net/mathstudies/blog/15939/ia-issues" target="_blank"> IA issues </a>helpful.</p> http://www.thinkib.net/mathstudies/blog/16777/moderator-notes#1398047400Revision Resources
http://www.thinkib.net/mathstudies/blog/16218/revision-resources
Mon, 27 Jan 2014 08:45:00 +0000]]>Revision Resourceshttp://www.thinkib.net/cache/blog-thumbs/21/16218-1390229568-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16218/revision-resources
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/16218-1390229568-thinkib.jpg" alt="Revision Resources" /><br /><br />So I am writing this blog post as a statement of intent about revision resources that I need to make for my IB2 class sitting their exam in May. This is the first time through the new syllabus and so I have some replacement of old resources to do. For years I have used some revision packs that I made at the start of the last new syllabus. Most of this is not available through this site because it uses lots of IB copyrighted questions. This year I am going to be revising all of these and making some new original IB style questions to go with them. The following outlines my plans for creating revision packs.</p> <p> I am going to create 6 revision packs, one for each of the main syllabus areas,</p> <div class="greenBg"> <ol> <li> Number and Algebra</li> <li> Statistics (Both sections together)</li> <li> Logic, Sets and Probability</li> <li> Geometry and Trigonometry</li> <li> Mathematical Models (Functions)</li> <li> Calculus</li> </ol> </div> <p> Each pack will consist of the following structure,</p> <div class="pinkBg"> <p> <em><strong>A comprehension task</strong></em> - This is a series of questions designed to prompt students to think about their knowledge. As such they are different from exam style practice questions. Students might typically search their notes or texts in order to answer these questions.</p> <p> <em><strong>Creating quick reference notes</strong></em> - This is an exercise in studnets making the note cards they can use for last minute reviews. making these 'cards' is an excellent exercise and they can be really useful. We need to be realistic about what can be acheived and so I am suggetsing a handful of note cards for each main topic.</p> <p> <em><strong>Practice IB Style Questions</strong></em> - Once students have reviewed ideas they need to try and put them i to practice with some new questions. To do this there should be 10 - 15 paper 1 and 2 style questions that students have never seen before and look like those they might get in the exam.</p> </div> <p> So obviously there is a good deal of work involved in creating these resources, although I will be reworking some old stuff too. the aim is to produce these one at a time based on the following timetable,</p> <div class="blueBg"> <ol> <li> Number and Algebra - Thursday 26th February</li> <li> Statistics (Both sections together) - Thursday 26th February</li> <li> Logic, Sets and Probability - Thursday 5th March</li> <li> Geometry and Trigonometry - Thursday 5th March</li> <li> Mathematical Models (Functions) - Thursday 12th March</li> <li> Calculus - Thursday 12th March</li> </ol> </div>http://www.thinkib.net/mathstudies/blog/16218/revision-resources#1390812300La Face
http://www.thinkib.net/mathstudies/blog/16160/la-face
Mon, 30 Dec 2013 17:04:00 +0000]]>La Facehttp://www.thinkib.net/cache/blog-thumbs/21/16160-1388437483-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16160/la-face
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/16160-1388437483-thinkib.jpg" alt="La Face" /><br /><br /></p> <h3> Challenges for the new year!</h3> <p> So I am lucky enough to be spending the New Year in the French Alps and enjoying some great wintery weather, lovely snow and some great skiing with my family. The photo on the left is a picture of a black run in Val D'Isere called La Face which bears down on the village offering us all the challenge it presents. It got me thinking about what challenges I will set myself for teaching the maths studies course this year (I may yet chicken out of La Face and satisfy myself with some good teaching challenges instead!) I have also chosen 'Fermats Last Theorem' by Simon Singh as my holiday read am I am really enjoying the ease with which Simon Singh tells the story and makes the mathematics accessible. I love how holidays and all that give you a proper chance to reflect and think about things.</p> <p> Anyway, I have two key drivers for the new year...</p> <p> 1. Applications of mathematics. I want to find more, real applications of the mathematics on the studies course to bring in to the classroom.</p> <p> 2. Bring some mathematical stories to life in the classroom. I want more activities that help students understand what mathematics really is and how it has developed.....</p> <p> watch this space.....</p> http://www.thinkib.net/mathstudies/blog/16160/la-face#1388423040Making Calculators
http://www.thinkib.net/mathstudies/blog/16089/making-calculators
Fri, 22 Nov 2013 07:30:00 +0000]]>Making Calculatorshttp://www.thinkib.net/cache/blog-thumbs/21/16089-1385124034-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/16089/making-calculators
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/16089-1385124034-thinkib.jpg" alt="Making Calculators" /><br /><br /> trig calculator</a> to see how dynamic geometry can be used to create a trig ratio calculator. the main point is that the programming of these calculators is a rich tasks that requires students to really explore with the mathematics and reason with each other to make them behave properly! I am planning to develop these in to classroom activities and will post links here when I have!</p>http://www.thinkib.net/mathstudies/blog/16089/making-calculators#1385105400IA Issues
http://www.thinkib.net/mathstudies/blog/15939/ia-issues
Thu, 10 Oct 2013 07:50:00 +0100]]>IA Issueshttp://www.thinkib.net/cache/blog-thumbs/21/15939-1381424092-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15939/ia-issues
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15939-1381424092-thinkib.jpg" alt="IA Issues" /><br /><br /> experienced workshop leader</a> for IB Maths Studies and a moderator for the Internal Assessment. Perhaps more importantly than that, I am a full time teacher with Maths Studies classes.</p> <p> Anyway, I hope this was useful - writing it certainly was!</p> <p> *Update on chi<sup>2</sup> tests - Following an exchange with one of the users of this site, I can see that I haven't been quite clear about this regarding how it might be tested in exams. It is quite possible that students will be asked to calculate the chi<sup>2 </sup>statistic and compare it to a critical value in and exam BUT if this happens then the critical value will be given. It is also possible and I think, more likely, that students will be asked to conclude on chi<sup>2 </sup>tests using the p-number from their calculator.</p> http://www.thinkib.net/mathstudies/blog/15939/ia-issues#1381387800IA Surveys
http://www.thinkib.net/mathstudies/blog/15911/ia-surveys
Sun, 22 Sep 2013 13:32:00 +0100]]>IA Surveyshttp://www.thinkib.net/cache/blog-thumbs/21/15911-1379875839-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15911/ia-surveys
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15911-1379875839-thinkib.jpg" alt="IA Surveys" /><br /><br /> Comparing data distributions</a> activity that both help students to think about good project ideas.</p> http://www.thinkib.net/mathstudies/blog/15911/ia-surveys#1379853120Communicating Mathematically
http://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically
Sun, 15 Sep 2013 11:19:00 +0100]]>Communicating Mathematicallyhttp://www.thinkib.net/cache/blog-thumbs/21/15889-1379263193-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15889-1379263193-thinkib.jpg" alt="Communicating Mathematically" /><br /><br /> 3D uncovered activity</a> and came up against some similar issues. The whole point of this activity is about students extracting 2D planes from 3D constructions and then applying trigonometry. In most cases, it was near impossible to trace a students conclusion back to the question because thay had written little or nothing along the way to help.</p> <p> I tried to make my point with students with two examples related to writing,</p> <ol> <li> If asked to do a piece of writing, would students write the words in random unsequential places on the page and expect the teacher to just 'know' what order they are supposed to come in?</li> <li> What use would a book be if you were only offered the first and last chapters?</li> </ol> <p> I know analogies can be dangerous and distracting, but instinctively I suppose I was just observing how there is so much to do to teach people to communicate properly and how that is actually an integral part of strengthening understanding.</p> <p> For maths studies students this a really important point related to project work.</p> <p> Next task - how to place more emphasis on this.</p> http://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically#1379240340Rubik's Race
http://www.thinkib.net/mathstudies/blog/15786/rubiks-race
Thu, 29 Aug 2013 07:01:00 +0100]]>Rubik's Racehttp://www.thinkib.net/cache/blog-thumbs/21/15786-1377691368-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15786/rubiks-race
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15786-1377691368-thinkib.jpg" alt="Rubik's Race" /><br /><br />this isn't possible because it shows 5 yellows!" I stop and think for a while and then realise she is right and that since each cube in the shaker has one of each of six colours on it that it is technically possible to get them all the same colour. Rather than concluding that the game designers have missed an obvious trick I guess that they have concluded that the odds of the shaker throwing up an impossible combination are so small that it isn't worth worrying about. At this point you wonder whether someone has actually worked it out? made some assumptions? tested it out? What ever the outcome you realise that probability has played an important part in the design of this game as it has with so many others. Quickly thinking that I might blog about this, I went to take a picture of the impossible combination, only to notice that my daughter has already shaken again! I said, "do it again until you get another 5 yellows" She dilligently sets out on this mission and quickly realises that it doesn't happen very often. She then asks "can it be 5 of any colour?" and you see a lovely example of how intuitive <em>some</em> probability can be! So now we are left with the question 'What is the probability that the shaker will show an impossible combination?'</p> <p> Happy summing!</p> <p> .....</p> <p> *** For teaching, I am thinking that whilst the theortical probability might get out of hand here, it could be a good example for some experimental probability. How about keeping records of how many times 2 of the same colour turn up and so on....</p> <p><strong>Tags:</strong> <em>probability</em></p>http://www.thinkib.net/mathstudies/blog/15786/rubiks-race#1377756060Planning Diary
http://www.thinkib.net/mathstudies/blog/15670/planning-diary
Tue, 13 Aug 2013 13:50:00 +0100]]>Planning Diaryhttp://www.thinkib.net/cache/blog-thumbs/21/15670-1376420879-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15670/planning-diary
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15670-1376420879-thinkib.jpg" alt="Planning Diary" /><br /><br /> 3D uncovered.</a></p> <p> Anyway, I will give some more thought about how best to share my planning through this blog!</p> <p> thanks!</p> http://www.thinkib.net/mathstudies/blog/15670/planning-diary#1376398200How many ways to use a Venn diagram?
http://www.thinkib.net/mathstudies/blog/15498/how-many-ways-to-use-a-venn-diagram
Sat, 29 Jun 2013 11:20:00 +0100]]>How many ways to use a Venn diagram?http://www.thinkib.net/cache/blog-thumbs/21/15498-1372522240-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15498/how-many-ways-to-use-a-venn-diagram
<h3> A functions Venn diagram</h3> <p> Whilst twitter and the like can be a huge distraction, I persist with it because of the frequency with which it offers me a new idea to work with. Yesterday I had a quick look and saw a post from who <a href="http://twitter.com/tesMaths" target="_blank">Craig Barton </a>who was obviously attending a session at the UK based <a href="http://www.conference.mei.org.uk/" target="_blank">MEI Conference</a>. It was simply a photograph, which I have included below....</p> <p > <img src="http://www.thinkib.net/cache/blog-thumbs/21/15498-1372522240-thinkib.jpg" alt="How many ways to use a Venn diagram?" /><br /><br /></p> <p> I retweeted and later in the evening it turned up again as posted by Andy Donahue in our <a href="http://www.facebook.com/groups/149577565103232/" target="_self">IB Maths Studies Teachers facebook group!</a> Anyway, I liked it because it made me think about using venn diagrams as a teaching tool probably for the first time, which of course has double benefits! What else could the three sets be? What else could we isolate with the intersections? I just wanted to share this quickly for now, but will certainly come back to it at a later date.....</p> <p><strong>Tags:</strong> <em>slp,venn,idea,functions</em></p>http://www.thinkib.net/mathstudies/blog/15498/how-many-ways-to-use-a-venn-diagram#1372501200The Bat Cave
http://www.thinkib.net/mathstudies/blog/15440/the-bat-cave
Fri, 21 Jun 2013 05:43:00 +0100]]>The Bat Cavehttp://www.thinkib.net/cache/blog-thumbs/21/15440-1371812488-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/15440/the-bat-cave
<p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/15440-1371812488-thinkib.jpg" alt="The Bat Cave" /><br /><br /> </iframe></p><p><strong>Tags:</strong> <em>modelling,functions</em></p>http://www.thinkib.net/mathstudies/blog/15440/the-bat-cave#1371789780Facebook for Schools
http://www.thinkib.net/mathstudies/blog/11987/facebook-for-schools
Sun, 18 Mar 2012 07:04:10 +0000]]>Facebook for Schoolshttp://www.thinkib.net/cache/blog-thumbs/21/11987-1332065050-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/11987/facebook-for-schools
<p> <img alt="" class="left" height="230" src="/files/mathstudies/images/blog/10fbreasons.jpeg" width="300"></p> <h3> 10 reasons why facebook should be allowed in schools</h3> <p> I am a vociferous opponent of one sided arguments, but recognise their value in helping people to see the issues. I am not unaware of the risks of embracing facebook in schools and certain that one bad experience could change my views. I am even naturally cautious about these things, but do find myself increasingly incredulous that there is such opposition to it. The following is just what the title says it is and not intended as a fullproof argument. The aim is to get people thinking.</p> <h4> More sophisticated communication tool</h4> <p> This is often overlooked. Facebook is - hands down - a considerable evolution of a communication tool. It offers everything that e-mail does on the side, whilst facilitating and encouraging a whole new level of collaboration and community. No doubt that communication in many industries could benefit hugely from such a tool. Why then will it take so many so long to work it out?</p> <h4> Groups not friends</h4> <p> The whole ability to interact with different groups of people without being 'friends' in a facebook sense has really opened up the options for schools to make use of this tool. Whilst it will always be true that all users must think very carefully about what they post, and that privacy and social networking are rarely synonymous, this is an important barrier.</p> <h4> Sharing links</h4> <p> The other day, I wanted to spontaneously share a link with my class. They all have computers with them so I copied the link and pasted it in to a word document which I then saved on a shared network drive with a memorable name. I shouted out the memorable document name to the class who, one by one, navigated to it to click on the link. This was the most efficient method for this spontaneous sharing. I rest my case.</p> <h4> It is real</h4> <p> We can pretend it is not, but it is. It is a phenomenon and it is happening. Making school a place where it does not happen is just helping detach school from reality.</p> <h4> Preferred choice</h4> <p> In my experience, and it wont last forever, facebook is the communication tool of choice amongst students (and an increasing number of adults). When such a high premium is placed on effective communication why would not use the tool of choice, especially when it is more sophisticated than the alternatives? Stood perfectly still in a traffic jam on the way to school I realised I would be late. I posted instructions to the facebook group for the class concerned and when I got to work 20 minutes late students all knew what they were supposed to be doing and were. The e-mail might have been picked later that evening.</p> <h4> Distractions</h4> <p> It is often argued that students having access to facebook in schools would just add another distraction for them and stop them focussing on the task. Well if that is the case then I think we should ban day dreaming as well. We should all ask ourselves what distracts us and why? When are we truly engaged in an activity organised by someone else? What is it about those moments that stops us following the numerous distractions on offer? If a student is not in to the activities in my lesson then there are already a million other things they could be doing as a distraction. There are hundreds of other apps on their computers, not even mentioning the internet, they could be doing homework for another subject, chatting to their neighbours, playing with their webcams or just plain day dreaming. Yes it is another possible distraction but what it adds to the existing choice is minimal. It is not a problem.</p> <h4> When did banning work?</h4> <p> OK, so there must be some answers to this question, but in the case of facebook, well, we can ban it from networks and computers and so they all get out their phones! Not all of course, but I am just trying to point out how difficult it is to stop a phenomenon like this.</p> <h4> Make it work for you not against you!</h4> <p> No explanation necessary</p> <h4> Get staff collaborating</h4> <p> Rightly or wrongly and even though they work ion the same building, staff do not get much time to talk to each other in school. A facebook group for teachers is a fabulous way for staff to share what they are doing, swap opinions and share interesting and relevant links with each other. It is really great.</p> <h4> Get students collaborating</h4> <p> Again, no explanation necessary</p> <h3> How can this work for teachers of Maths Studies?</h3> <p> Here are three ways to get in to this straight away.</p> <h4> Facebook groups for classes</h4> <p> I can recommend highly the use of these groups for effective communication between students and teachers. I have one group that all students doing maths studies in the school belong to All the maths teachers in the school also belong and students stay in the group even after they have left the school which adds a nice dimension as well.</p> <h4> Facebook groups for teachers</h4> <p> Here is a group for IM Maths studies teachers all over the world. <a href="http://www.facebook.com/groups/149577565103232/" target="_blank">IB Maths Studies Teachers</a> - it is a fantastic opportunity to be able to collaborate and share with teachers with the same issues.</p> <h4> Worldwide IB Maths Studies classroom</h4> <p> This <a href="http://www.facebook.com/groups/231815136900310/" target="_blank">group for students of maths studies students all over the world</a> is just that. I am hoping that we could get students and classes all over the world collaborating in this way.</p> http://www.thinkib.net/mathstudies/blog/11987/facebook-for-schools#1332054250Enquiry based activities
http://www.thinkib.net/mathstudies/blog/11818/enquiry-based-activities
Mon, 20 Feb 2012 07:52:51 +0000]]>Enquiry based activitieshttp://www.thinkib.net/cache/blog-thumbs/21/11818-1329735171-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/11818/enquiry-based-activities
<p> <span ><img alt="" class="left" height="150" src="/files/mathstudies/images/GandT/WR.jpg" width="150">The blog post is just to give an idea of some of the ideas on this website. The theme here is 'Enquiry based learning' and by that I am talking about the sorts of activities that provide opportunities for students to make discoveries on their own through engagement induced enquiry! At least that is the aim! Let explain the point with the following examples The title each links to a fuller, resourced, outline of the activity.</span></p> <p> <span ><a href="http://www.thinkib.net/teachmaths/activities/probability-trees.htm" target="_blank">Probability trees</a> - <span >This activity is about bridging the gap between the intuition of sample space diagrams and the efficiency of tree diagrams. Students will look at a problem from the two points of view, play with multiplying and adding fractions and hopefully see how tree diagrams are a more efficient way of doing the same thing! The activity is good for group work and physical manipulation, although it could be </span><span >completed on computers by individuals if required. It may well take 2 to 3 hours to complete all of the tasks, but at the end, the hope is that students have a strong understanding of how tree diagrams work that they can apply to different problems.</span></span></p> <div > <span ><a href="http://www.thinkib.net/teachmaths/activities/scattertastic.htm" target="_blank">Scattertastic</a> - <span >This activity makes use of two excellent virtual manipulative that are freely available on the web. The activity helps students to begin understanding the concepts of correlation, lines of best fit and degrees of correlation through the use of these manipulative.</span></span></div> <div > </div> <p> <span ><a href="http://www.thinkib.net/teachmaths/activities/meeting-functions.htm" target="_blank">Meeting Functions</a> - <span >Challenge students to really understand the concept of a function. Match a set of input values with a function and a corresponding set of output values. There are eight sets of three to make and only one correct solution. This activity is 'old meets new'. Students work with cut out bits of paper but can use calculators/computers to help them solve the puzzle!</span></span><br> <br> <span ><a href="http://www.thinkib.net/teachmaths/activities/quadratic-links.htm" target="_blank">Quadratic Links</a> - <span >This activity is about linking the graphing of quadratics with the equations themselves by looking at their key features. Students match pieces of information with different graphs using logical deduction. This practical group activity leads to being able to sketch graphs from their equations.</span></span><br> <br> <span ><a href="http://www.teachmaths-inthinking.co.uk/activities/making-cones.htm=cl" target="_blank">Making Cones</a> - Ex<span >plore cones by making one! This activity helps students understand where the formula for the surface area of a cone comes from and play with the associated mathematics. A great practical task that seems easy and works out to be more of a challenge. In making the cone students will confront some great mathematical reasoning and maybe even some algebraic proof!</span><span > </span></span></p> <p> <br> <span ><a href="http://www.thinkib.net/teachmaths/activities/which-rule.htm" target="_blank">Which Rule</a> - <span >This activity is designed to help students solve trigonometry problems by encouraging them to 'Speculate' about what might be possible. Students are asked to state different truths or complete different equations for a given diagram without being told what to solve for. Having completed the equations they are asked to think about which of them is most useful for solving for a particular variable. So often </span><span >students feel that they must know 'the right thing to do' before they proceed and are afraid to try things out to see what happens. Yes, it is possible to learn how to recognise certain types of problems but it is equally important to learn that problems can be solved by trying to use the different pieces of knowledge you have to make new ones. The sine rule and cosine rule can both be applied to any given triangle it is just that often only one of them generates an equation that can be solved. We can either learn to spot types of problems or to speculate with both. In practice, one often leads to the other and then we are better equipped to solve more problems. </span></span></p>http://www.thinkib.net/mathstudies/blog/11818/enquiry-based-activities#1329724371Natural Medium
http://www.thinkib.net/mathstudies/blog/11814/natural-medium
Sun, 19 Feb 2012 18:00:15 +0000 <h3> Are computers a natural medium for mathematics?</h3> <p> One of the reasons I both love and hate twitter! I am casually flicking through some pages over breakfast and I happen on this <a href="http://blog.mrmeyer.com/?p=12782&utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+dydan1+%28dy%2Fdan+posts+%2B+lessons%29" target="_blank">blog post from Dan Meyer</a>. In fairness the blog post seemed mostly to point out how helping mathematics education has not ever risen to the top of silicon valley's priority list. Whilst this is an interesting question, it was the question phrased in the title above that caught my attention. I love this because it is great when some one else's writing makes you stop and think - I hate it when the question pre-occupies your mind when you are trying to do other things. The result is that I am writing this long after I should be asleep, getting ready for tomorrow. Anyway, I think the below can stand alone, but can be put in to context by reading the blog post linked above. This was the response I left on the blog post.</p> <p> As #57 says, who is still reading! I find though that putting these thoughts and reactions in writing is mostly only for my own benefit! In this case, it is beacuse, whilst I understand and sympathise with the general view being expressed, I think I actually disagree with the statement about 'natural medium'! I read most of the responses and scanned the rest but the response from David Wees came closest to my reaction when he said '</p> <p > <em>'There are some tasks for which computers are perfectly suited in terms of mathematics'</em></p> <p > and</p> <p > <em>'What you have suggested is that they are less than ideal for the quick communication of mathematics, and for deeper assessment of what mathematics students understand.'</em></p> <p> Regarding the first point....</p> <p> My relatively short teaching career (13 years) has spanned 'almost no access to computers' to 'working with a one to one program at my current school'. There is no doubt in my mind that computers have had a hugely significant effect on the way mathematics can be taught and, more importantly, discovered,<em>beacuse</em> they provide a considerably <em>more</em> natural, able and versatile medium. A lengthy description of cases could follow, but I will limt myself to just a few...</p> <p> Dynamic geometry, as has been mentioned by some already. This tool has done amazing things for helping teachers to create opportunitites for students to make discoveries on their own and thus enage with mathematics. It can go beyond the teaching of geometry as well.</p> <p> Graphing software - largely by labour saving, but also through dynamic functionality - these tools as well have created new opportunities for exploring relationships.</p> <p> Data Handing - This has come to life through computers with access to real, live data, the functionality to collect it and the ability to process it. All this means that the nature of data handling tasks can now vary in new ways. (I will not say 'more mathematical ways' although that it is what <em>I</em> think.)</p> <p> As suggested, I could go on and will in my head!</p> <p> Regarding the second point....</p> <p> Yes I agree that progress is slow on more able and intuitive user interfaces for communicating mathematics. I think that this has worked in our favour as teachers though. For example, taking the fractions, modern calculators now make it much easier to input and work with fractions than it used to be and this may have resulted in a poorer understanding of what fractions actually mean. The fact that computers dont find it easy to accept fractions means that users have to think about what the fraction actually means in order to input it. A fraction is easily written on a piece of paper with no understanding of its meaning.</p> <p> Likewise, when programming with dynamic geometry (and I do consider constructions a type of programming), there is no 'rectangle tool', in order to construct one you have to know that a rectangle is made by two pairs of parallel sides intersecting at right angles. When you program it correctly it will always be a rectangle regardless of which points are moved. The process of drawing a rectangle on a piece of paper is not at all the same.</p> <p> In summary, dont get me wrong, I estimate that computers are used for about 50% of our lesson time and I am a committed believer in variety of tasks that range from the pencil and paper, to the practical, to the virtual. That said, I am a passionate supporter of what computers have done for mathematics education. I am also a relatively new blogger and always have a sense of fear when 'submitting' such responses. I think most bloggers understand that expressing your views and reactions is the best way to develop them, so thanks Dan for making me think! Apologies if I have missed the point somewhere along the line, I feel better for writing this down either way.</p>http://www.thinkib.net/mathstudies/blog/11814/natural-medium#1329674415Reinventing the textbook!
http://www.thinkib.net/mathstudies/blog/11585/reinventing-the-textbook
Sun, 22 Jan 2012 11:18:39 +0000<p> <img alt="" class="left" height="149" src="http://t3.gstatic.com/images?q=tbn:ANd9GcTFzxLVR1h3euEJXj13FjziYAnKOQC6HbMs0Qk6jlGqCBgEwNJB" width="150"></p> <h3> A reaction to Apple's education event this week!</h3> <p> So the whole apple education announcement on school textbooks has really got me thinking! There are so many related thoughts and I have challenged myself to organise and present them in as few words as possible (didn't do very well on that). As usual this is probably of more benefit to me than anyone else but it helps to publish it.<br> <br> When we think about re-inventing the text book we need to think about 2 key questions...<br> <br> 1. What is wrong with a paper text book?<br> 2. How could/should they be reinvented?<br> <br> I don't intend to list all of the obvious answers to the first question but want to focus on the most important answer. Textbooks, as we know them, are inextricably linked to our educational structure. They ally themselves to particular syllabi, exam boards and courses so that they can focus on particular objectives and appeal to schools and teachers who are judged on results for that course. They are based on the notion that if you are teaching 'Algebra 1' then you need an 'Algebra 1' textbook. They are linked to an educational philosophy. Teachers demonstrate ideas and students practice and review them with a textbook. The textbook becomes a reference for the course, not the subject. As such the textbook has long engendered resignation in students in a 'here we go again' kind of way. I have phased out textbook use where I can in favour of more general references. The best use of a textbook is as a crutch for passing an exam, which is not without value in today's education.<br> <br> And so now in response to the second, I suggest that there is room for evolution and revolution. The ibooks we saw at the apple launch event are an example evolution. The intent is clearly to bring dynamic, interactive content, to add convenience, ease of use and practicality to the supply and use of textbooks. Dynamic also means that the purchased book will evolve, post purchase as well. Errors will be corrected, new content added etc. I am curious about how frequently these books will be updated though and at what point a 'New Edition' might be for sale. I welcome this evolution that has been arriving slowly over the past few years. (It is still along way from actually arriving in a significant number of schools - The announcement of the number of iPads in schools yesterday was a classic case of throwing big numbers at us - the percentage figure is still very small)<br> <br> The revolution of which I speak comes in the possibility for anyone to publish an iBook. Now, educators anywhere can create and publish. Now that is exciting! It will bring with it the inevitable glut of free or dirt cheap, average efforts, but also it means someone, somewhere now has the possibility, and the stage, to reinvent learning resources. (Surely the term textbook will have to go or become ironic!). Education is the most interesting, stimulating, challenging and rewarding field I could ever have hoped to end up working in. I believe firmly that a resource will only ever be as good as the hands it is in. Learning takes place when we are motivated, engaged and interested and that is the ultimate challenge for teachers. Very few textbooks have offered much help with this over the years. Apple's presentation may have owed little to the deep consideration of issues in education, but the tool they have produced, put in the hands of educators has really exciting potential! On balance, these are really exciting developments all round!<br> <br> As I think on I am pondering the following,</p> <ul> <li> What can an iBook do that a website cant and vice-versa?</li> <li> What makes a good reference?</li> <li> When do we imagine students will use these books? </li> <li> Does the new portability change the answer to that question?</li> <li> If yes, should that change the nature and purpose of the book?</li> <li> Are references best when something else we are doing prompts us to look at them?</li> <li> Interactivity is perceived as pinching and dragging. Real interactivity comes when we are prompted to think and progress, examine and conjecture.</li> <li> Who is a textbook for? Students? Teachers? Both? Can it be both?</li> <li> Buying, not subscribing, surely implies that eventually users will have to buy a 'New Edition' - Does this not work against some of the advantages?</li> <li> Can any of this actually bring about changes in an educational philosophy?</li> </ul> <div> Congratulations to anyone that read this far!</div> <br> <br> <br> <br> <br>http://www.thinkib.net/mathstudies/blog/11585/reinventing-the-textbook#1327231119Networking
http://www.thinkib.net/mathstudies/blog/11309/networking
Sun, 18 Dec 2011 17:06:20 +0000]]>Networkinghttp://www.thinkib.net/cache/blog-thumbs/21/11309-1324238780-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/11309/networking
<h2> Professional Networking</h2> <p> <img alt="" class="left" height="150" src="/files/mathstudies/images/blog/Networks.jpg" width="220"></p> <p> I am a self confessed technology and gadget junkie but 3 years ago, if you had talked to me about ‘social networking’ I would have laughed in your face and said all the things that people say to me now when they have no experience of using internet networking tools! </p> <p> Now I can’t imagine being without them. I use lots of tools these days, but Facebook and Twitter are the main ones and the professional development I have gone through as a result is enormous. I most definitely feel like I belong to the biggest staff room in the world and get to exchange ideas, resources, great links and tools with teachers from all over the world. At least once a day I find myself thinking that it is all a bit too much to handle and reminding myself that I don’t have time to read everything and that nobody expects me to! it now seems extraordinary to me that ignored these possibilities for so long. I know it is not everybody’s thing and am not about to suggest that all teachers must do it, but I do think that all teachers should at least consider it and certainly feel that all teachers entering the profession should be strongly encouraged to take part in different professional exchange networks. That is the basic gist of this blog entry so you could easily stop reading here. If you want to know some more of my thoughts and experiences on this then read on. It is worth noting that I am primarily discussing exchanges between teachers but do go on to talk about students later in the piece.</p> <h3> Which tools and why?</h3> <p> There are so many tools to consider using and each group of people will need to find the one that works best for them, all I can do is share my experiences. The main point I would add here is that the most effective tools seem to be the ones that people are already using. Trying to set up exchange groups and forums etc using tools that are new to people involves first showing people how to use the tools and then encouraging them to check regularly. The clearest example of this is the use of facebook. With so many people (1 in 13 on the planet) now using facebook it seems the most obvious tool to get people to use for professional exchange as well.</p> <h4> Twitter - my twitter account - @teachmaths</h4> <p> I have been using Twitter for nearly two years and this is probably the simplest and easiest to work with. 140 characters or less. I try hard to always include a link in my tweets and restrict my comments to describing the link and what I might do with it as a teacher. There are thousands of maths teachers out there doing the same thing. Some send links to their blogs where they discuss their experiences, ideas and views. Many send links to relevant news articles, resource sites and other great stuff that can often be used in the classroom straight away. </p> <p> It can be difficult to get started but a good suggestion is to follow what is called a hashtag. This is a means of filtering tweets. For example, I might include #mathchat in one of my tweets and then if I search twitter for #mathchat I get a list of all the tweets with that hashtag in them which gives me something to follow straight away and some ideas of who is tweeting the sorts of things I might be interested in. A quick google search on ‘getting started with twitter’ will tell you much more.</p> <p> Twitter is fabulous and is my broad daily source inspiration and ideas. It is worth noting what I call ‘the garage sale’ analogy. If you go to a garage sale (car boot sale, flea market etc) looking for something in particular then you are often disappointed. If you go with some money in your pocket then you will usually find something that you are looking for. Twitter is like this - you have to speculate to acumulate!</p> <h4> Facebook</h4> <p> I was a lot slower getting started with facebook because of the huge amount of negative media there is about ‘fb’. The big leap for me was discovering ‘facebook groups’. These user defined communities of people that can share together in that space only without having to be ‘friends’ in the facebook sense. Also groups can be open or closed so members ghet to decided how public their discussions are.This helps people get over the many privacy fears that there are. It has also allowed me to get students involved (see below). What facebook groups do is allow a little more focus than twitter. Group members will only belong if they want to discuss and share the group themes. An example might be the following group ‘IB Maths Studies Teachers’ which is for teachers of a particular course. We have a bout 50 teachers now from all over the world who are all teaching this course and have many common issues. We ask each other questions and share items relevant to the teaching of the course. Posts can be any length and people can ‘like’ or ‘comment’ on the individual posts and thus enter some debate. Clearly this is a little more sophisticated than twitter.</p> <p> After an inset with the prolific professional networker and educator @tombarrett (no one has a real name anymore, just an internet persona!) I was inspired to create a facebook group for the teachers at my school - I cant share this one because we elected to keep it closed and focussed on sharing with each other about our school only. We have other forums for publicising what we do. these days, I find that we spend very little time together in the staffroom and what time we do have we usually spend talking about things other than work. As such, this group has become a great source of exchange for us and I think we have all got a huge amount from it.</p> <p> I have facebook groups with my students as well and this has been a great revelation. I accept all the arguments about the impact social networking has on the changing nature of society, but that does not change the fact that ‘fb’ gives us a fabulous way to communicate with and support each other.</p> <h4> Google + - </h4> <p> This has been googles response to facebook and twitter and it seems that they have tried to take the best bits of both and add some new features as well. I like google + and have been using it, but it is still a distant third for me at the moment.</p> <h4> Blogging</h4> <p> I had no idea how many people were blogging about their teaching - it really is amazing. Having tried a small amount of blogging my self, I am now convinced the the primary beneficiary of the blog is the author. That is fabulous! The author of a blog piece has to think and reflect carefully on their experiences and views before they express them to the world and this is a really valuable process. The fact that you publish them and some somebody might read them is a really important element that changes it a little from private diary writing. The occasional bit of feedback is really motivating too. So many people write that is impossible to read everybody, but I probably read 2 or 3 blog entries a day from other maths teachers and they usually amke me think, even if I disagree with what they wrote, and the often give me ideas. All in all, this is a fabulous way to exchange as well.</p> <p> Of course, reading and writing blogs can be a little time consuming and so it is likely to be less popular than other tools.</p> <h3> Issues to consider</h3> <p> The following is a list of things it is worth considering when trying to take part or encouraging others to take part in social networking</p> <h4> The culture</h4> <p> I have already confessed to being an internet junkie and so it seems normal that I have embraced ‘The Social Network’ - although I am very small scale compared to some prolific networkers. So, given that I may have been somewhat predisposed, but still took some persuasion, it is only natural to imagine that many others will take more persuasion to understand this particular culture. In this case, I think it is very important that people are not overwhelmed from the start with all the tools and all of the options. It may be that something small scale is needed in the first instance. </p> <p> I have thought, for example, about compiling some of the best things to have come out of our staff Facebook group in some other format to share with a wider audience at school as a demonstration of what has come out of our exchanges.</p> <h4> The confidence</h4> <p> There is a big psychological barrier between sharing over coffee in the staffroom and publishing your thoughts for the whole world to see. Again, even predisposed as I am, I still spend too much time worrying about whether or not I have made the best use of my 140 characters on twitter. A scenario where no one gave a stuff what anyone else thought of their posts would not be good either. It takes time for people to reach a compromise here and a little bit of encouragement goes a long way. For example, positive feedback for a new ‘tweeter’ helps people to be less self conscious I think.</p> <h4> The time</h4> <p> There is no doubt that I spend an awful lot of time playing at professional networking, but </p> <h4> The focus</h4> <p> .....to be continued<br> </p>http://www.thinkib.net/mathstudies/blog/11309/networking#1324227980Wanted - The Ultimate Online Teachers Tool!
http://www.thinkib.net/mathstudies/blog/11251/wanted-the-ultimate-online-teachers-tool
Sun, 11 Dec 2011 12:26:47 +0000]]>Wanted - The Ultimate Online Teachers Tool!http://www.thinkib.net/cache/blog-thumbs/21/11251-1323617207-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/11251/wanted-the-ultimate-online-teachers-tool
<p > <img alt="" height="120" src="/files/mathstudies/images/blog/Wanted!.jpg" width="600"></p> <p> There is a truly amazing array of tools out there for teachers and schools these days and between them they do everything I want them to do. Unfortunately none of them do it all. This is a wanted add for the the ultimately teachers planning and communication tool! The following is the list of requirements....</p> <ul> <li> It must be cross platform and either web based or very capable in the syncing department. I currently use a combination of moodle, google docs and iCal. </li> <li> For me to use for planning - I must be able to filter out days, weeks and months, but also classes. That way I can do long term planning by class and then see all of the different classes integrated. I currently achieve this with a google or excel spreadsheet because it is the only tool with all the filtering options. It takes a very long time to prepare this spreadsheet and it's not really what spreadsheets are intended for. </li> <li> For parents and students to follow the plans for the class, the tool needs to be able to publish parts but not all of my planning to different places. Some planning apps have this facility in a limited way but not the filtering mentioned above. Again, I can publish different worksheets from a google doc, but not different parts of a worksheet. (Imagine wanting to publish a filtered selection - and I have already said that I don't think this tool is designed for the diary purpose)</li> <li> For communication - it is great to be able to post regular updates, homework news and enter in to discussion with students. I have been using facebook to communicate with students in this way and really like it because of the way it gets in to their daily news feed.</li> <li> Sharing important dates - Date sharing needs to be wrapped up in to any planning tool. If I schedule an event in my planning I want it to appear in the diaries of all concerned. Currently this can be done in Outlook, iCal and other calendar apps. It can be done through moodle and facebook as well.</li> <li> Keeping records - We have a student information management system that records attendance and assessment data, but it is yet another location and only teachers can input. I would like students and parents to be able to input as well.</li> <li> Feeding back on records and assessments - I am currently puzzling how to create a system for communication between teacher, student and parent that allows all of us to input in to the record of an individual student that all parties can view, but which is obviously private to the student, teacher and parent concerned. It must also allow me to see an overview.</li> </ul> <p> I can do all of these things using different tools except possibly the last one. Call me demanding, but I want a single tool that does all of these things. If I was a software developer or programmer I would see this as a huge hole in the market! I often wonder if developers are looking at what all the tools are doing and thinking - 'hold on! If our tool does all of these things then we will be on to winner!' So if you are reading developers, I m just one teacher, but please think about building such a tool or making your do everything.</p><p><strong>Tags:</strong> <em>teachers wishlist,technology</em></p>http://www.thinkib.net/mathstudies/blog/11251/wanted-the-ultimate-online-teachers-tool#1323606407This Week
http://www.thinkib.net/mathstudies/blog/11101/this-week
Sat, 19 Nov 2011 11:51:11 +0000<h2> What's happening in my Maths Studies classes?</h2> <p> This regular blog feature is ust intended to give a real overview of how one teacher is planning their maths studies classes.</p> <h3> DP1 - Year 12 - Grade 11</h3> <p> <strong>Unit</strong> - 5, geometry and Trigonometry</p> <p> <strong>Subtopic</strong> - Right angled trigonometry</p> <p> <strong>Time allowed</strong> - 3 hours + homework</p> <p> We are in the Geometry and Trigonometry unit just now. We have had a busy couple of weeks looking at the coordinate geometry element (sections 5.1 and 5.2) and now we are on to the right-angles trigonometry. (section 5.3) In most cases this is revision for students. That is not to say that they understood it the first time though. I think the tension here is balancing revision with a fresh chance to understand where it all comes from. With that in mind I plan the following.</p> <h4> The Lessons</h4> <p> <strong>Lesson 1 </strong>- I will do the <img class="ico" src="/img/icons/inthinking.png"> Trig Calculator activity where we use dynamic geometry make a construction that will calculate any trig ratio based on the proportions of the sides of a right angled triangle. I think its important to try and link trigonmetry to to its geometrical roots. This is also makes for a good ToK moment.</p> <p> <strong>Lesson 2</strong> - This lesson I will use the 'Making Statements' activity where the aim is to encourage students to recognise relationships in given diagrams. Once thye have recognised a few they can choose the one that is most appropriate for them. Having done this we will use the solving problems powerpoint to move from choosing the right reltionship to actually solving the problem.</p> <p> <strong>Lesson 3</strong> - This will largely be spent problem solving with right angled trigonometry. Some individual work and some as a whole class.</p> <p> Homework - I will set exercise 5.3 from the OUP Course companion as homework for the week.</p> <h3> DP2 - Year 13 - Grade 12</h3> <p> <strong>Unit 3</strong> - Sets, Logic and Probability</p> <p> <strong>Subtopic</strong> - Probability</p> <p> <strong>Time allowed</strong> - 9 hours - (Students will not be set homework as they prepare for their mock examinations)</p> <p> I love this unit and particularly the way the three elements intertwine. The Stes and logic give teaching probability a new edge for me. The issue, as ever, is what do I have time to do?</p> <h4> The lessons</h4> <p> <strong>Lesson 1</strong> - We will use the <img class="ico" src="/img/icons/inthinking.png"> Probability trees activity as a review of thta which is hopefully already understood about probability. This is a nice intuitive activity that is engaging in nature and prods the memory nicely. Its pushing it to do this in 1 hour so I will probably help them along through some sections.</p> <p> <strong>Lessons 2 and 3</strong> - We will start the <img class="ico" src="/img/icons/inthinking.png"> Fairground games activity - I always worry about wether or not their is time for these students to do these things, but there are few opportunities left for students to have a bit of fun while they are learning as the IB pressure machine winds up. I like this activity because of the way it makes students link the probability with the sets as well as making students test experimental and theoretical probabilities.</p> <p> So thats a busy week planned then!</p>http://www.thinkib.net/mathstudies/blog/11101/this-week#1321703471Education Revolution
http://www.thinkib.net/mathstudies/blog/10827/education-revolution
Sun, 25 Sep 2011 08:57:29 +0100<p> <img alt="" class="left" height="145" src="http://t2.gstatic.com/images?q=tbn:ANd9GcR3xzevXChLR8e76G2XPZKL7zI8YieGk2Nh_0qzAV7aztgdo5a_Ag" width="150"></p> <h3> Just a few thoughts</h3> <p> In this entry I am writing down some of the thoughts I have following two things that I have paid attention to this week. The first is the TEDxLondon event on the theme ‘Education Revolution’. The second is Carol Vorderman’s report to the UK government on the state of mathematics education in the UK (BTW this is interesting reading wherever you live and work). </p> <p> As in most cases with blogs, I suspect that the primary beneficiary of this exercise will be me! Articulating thoughts, reactions and emotions in to coherent statements takes me far too long, but can be satisfying. Importantly, I reserve the right to change my mind in the future based on subsequent thoughts and reactions!</p> <h4> The current State of Education</h4> <p> I have a great fear that those who speak so clearly, well and influentially on the current state of education are not familiar enough with it and thus not qualified enough to do so. Whilst this does not invalidate their arguments it does begin to undermine them. Far too many sweeping statements are made about the terrible things that happen in current education. Most are very careful not to blame teachers, but rather government and micro management, but all tend to imply that teachers follow enforced strategies blindly.... most teachers, from my experience, are educators and capable of taking directives, standards and tests etc in their stride, whilst remembering that their primary role is to provide an education for their students. As such, what happens in classrooms is seldom the blind delivery of someone else’s plan. Maybe I am lucky, but that has been my experience of teachers to date.</p> <h4> Sage on the stage</h4> <p> Much is spoken of how the ‘Sage on the Stage’ idea is outmoded and it is time for change. This relates to what I have said above. I ask, who is teaching like that? There is no way I could ‘lecture’ for the 19 hours a week I spend with my classes. Apart from being pretty dull for all of us, I would not have the energy. I just don’t think this is happening. One of my colleagues @russelltarr pointed out the irony of the format of TED events in this context and I was reminded of this from Jeff Jarvis on the same topic. It is not rocket science, but worth remembering that variety is a huge tool in sustaining engagement and interest. This is as true of a group of adults as it is students. Sometimes I enjoy listening to the sage on the stage – sometimes I enjoy trying to be it, but this makes up a small proportion of what happens.</p> <h4> Revolution/Evolution</h4> <p> I am increasingly leaning towards evolution in this debate. Again, we could easily get caught up in semantics here, but I think I have achieved some clarity on this point. Education – that which happens in schools – has a constant need to ‘evolve’. From my experience it does so all the time. If it didn’t, my job would be easy but dull. Constant reflection, openness and willingness to engage with new ideas and the views of others are key ingredients. How individuals are judged by the wider world as a result of their ‘education’ is quite possibly in need of a revolution. This is perhaps best illustrated by the fact that what happens in schools evolves despite the stranglehold exam boards have on the notion of ‘terminal assessment’. Many courses offer a very sound philosophical basis and then use a horribly blunt assessment tool that does match that philosophy. For example, while schools are embracing technology, we still seem light years away from technology being used in assessment. Mathematics education and technology are deeply interwoven, but students still sit terminal exams without a computer. Revolution is required at that end to allow the natural evolution to happen in schools.</p> <h4> Success and Failure</h4> <p> Related to the above is a need to revise perceptions of success and failure. It is true that success in most schools is still measured mostly by academic achievement and this really does need to change. I believe that lots of schools do a fabulous job of providing a broad range of opportunities for students to succeed but still there are lots of students who leave schools as very able, broad, caring and considerate people with little to show in the way of ‘Official success’. Sure exam results open doors, but being a successful person is about so much more and I would like to see teacher references for students carry a lot more weight than they do at present. I could tell you more about my students than any set of exam results.</p> <h4> Play Vs Work</h4> <p> A colleague tweeted during the TedxLondon event that ‘School leaders need to learn not to see playing and learning as mutually exclusive’ and I could not agree more. I do subscribe to the point of view that ‘play’ is a fantastic way to learn but want to be careful not to imagine it as the only or the best way of learning. It is important here not to get caught up in semantics and I think the word play can be defined very broadly, but on its own can easily be mis interpreted. I much prefer engagement as a term and I base this on my own experiences as a learner. On the one hand we can see that students will be more likely to engage when what they are doing is not perceived as work. On the other hand would it not be better to change the perception of ‘work’?</p> <h4> Technology</h4> <p> There is far too much to discuss here to even think about adding a ‘paragraph’ that sums it up, so I will try and do it in a sentence. Technology it seems is generally considered, toy like, frivolous, flashy, dangerous and unnecessary etc until proven otherwise. This needs to be reversed!</p> <p> For example - If you are a player in the ‘twittersphere’ then you will not get this impression because of the obvious bias of those most likely to engage with each other about education through social media, but Facebook and Twitter are still dirty words in most educational establishments. I am not unaware of the risks, but it is unbelievable to me that we take the ‘communication tools of choice’ for most of our students and brand them too dangerous and frivolous to use for education.</p> <p> As suggested already, there is so much to discuss here regarding hardware, software, access and philosophy, but the world around us will change and move on and schools and education simply cannot afford to be left behind.</p> <h4> Cultural Importance….</h4> <p> The vorderman report does talk about the differing cultural importance of mathematics in different countries and concedes that we can’t just take the methods used in other places and expect them to work. It would be a lot to expect that the report offer suggestions for how we can change the cultural perception of mathematics, but I feel the point is rather glossed over. I can’t speak for other subjects but I feel strongly that the general public’s understanding and perception of mathematics as a subject is dangerously poor and its cultural value is very low. These two things are of great significance to the future of mathematics education.</p> <h4> Talking and Doing…</h4> <p> I am in danger of finishing this piece ironically. I have been prompted to write this by both the TEDxLondon event and the the Vorderman report on the state of mathematics education. Whilst this has been very good in helping me reflect on some of these issues, I cant help but feel that so much is spoken and written about what needs to change in education, whilst most teachers in the practice of simply doing it! On that note I am going to stop writing and do some planning.</p>http://www.thinkib.net/mathstudies/blog/10827/education-revolution#1316937449Physical Manipulatives
http://www.thinkib.net/mathstudies/blog/10717/physical-manipulatives
Sun, 11 Sep 2011 10:53:46 +0100]]>Physical Manipulativeshttp://www.thinkib.net/cache/blog-thumbs/21/10717-1315745626-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/10717/physical-manipulatives
<p> <img alt="" class="left" height="150" src="/files/mathstudies/images/blog/Manipulatives.jpg" width="150"></p> <h3> Pick it up and move it around!</h3> <p> This is a brief reflection on my experiences this week in thinking about the merits of physical Vs virtual manipulatives. Working in a school with a one to one laptop programme always invites yuo to think about what a computer can add to an experience. The number of virtual manipulatives available is staggering and some of them have really helped tthe evolution of teaching methods in mathematics. Having that programme really allows us to take advantage of them. With that in mind, please dont consider this blog post an 'anti technology' entry.</p> <p> Task design happens in a number of diferent ways. It is probably fair to say that most of us start by thinking about what it is we want to teach. At that point we either go looking for existing resources or start thinking of new ways to do it. Being that it is the start of a new term, I am prone to the latter given the energy I have after a summer break. I would like to think that I am disciplined enough not overlook some fabulous existing ones either. The trouble with coming up with new ideas is that they usually involve the creation of new materials! As an optimist, I will always go and look on the internet to see if want I am looking for is already out there, but this is really the wrong way round. The internet is like a garage sale - go in search of something in particular and you are likely to be disappointed, go with some money in your pocket and you will probably find something useful!</p> <p> Havign done some work on introducing the concept of tree diagrams, I decided that want I wanted was some online, interactive tree diagrams where the probabilities were listed but not put in the right place so that the task was to move them into the right places! This would just remove one area for possible error and in the early stages of an idea, I find it a very useful checking mechanism to know that if you have one left over that doesn't make sense then you may well have made a mistake. Anyway, I looked and I looked and I couldn't find it anywhere - I wondered about how long it would take me to program something like this using flash, but resolved that this was not the best use of my time at this time of year. I then decided that I really believed that in this case the 'physical manipulative' would better. (I am not sure it saved me any time). A consequence of having technology at our disposal is that the benefits of the physical manipulative can be overlooked.</p> <p> The result was the creation of this resource <a href="http://www.thinkib.net/mathstudies/teaching-ideas---slp/probability-trees.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Probability trees</a> in which students work in groups with cut out bits of paper to solve problems where they have the answers and just need to put them in the right order. The physical mainpulative really helped the group work aspect because more than one person can be involved in the arranging and the absence of the computer screen allowed both more space and encouraged conversation and reasoning between the group members. In my search I had hoped that I would find something that was 'self-checking' so that students would get instant feedback on their efforts. This is a principle that can be very helpful, but is not without its faults. When no answer is instantly available, students need to reason with eachother and reach some kind of consensus before settling on an answer. None of this is to say that the physical manipulative was 'better' in this context, but rather to say that there are lots of befits to experinecs based on physical mainpulatives. Below are some pictures of the bits of paper!</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2F&set_id=72157627519034031&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157627519034031%2F&set_id=72157627519034031&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p> <p> On this note, the following are just a few examples of similar activities where physical manipulatives are used.</p> <p> <a href="http://www.thinkib.net/mathstudies/nanda-teaching-ideas/visual-sequences.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Visual Sequences</a></p> <p> I love this activity for working with arithmetic sequences.</p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2F&set_id=72157623076372881&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157623076372881%2F&set_id=72157623076372881&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p> <p> <a href="http://www.thinkib.net/mathstudies/teaching-ideas---slp/fairground-games.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Fairground Games</a></p> <p> Sure we can play probability games on line, but that is not half as much fun as playing them for real!</p> <p > <iframe allowfullscreen="" frameborder="0" height="345" src="http://www.youtube.com/embed/9HDRchagB78?rel=0" width="420"></iframe></p> <p> <a href="http://www.thinkib.net/mathstudies/teaching-ideas---slp/monty-hall.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Monty Hall </a></p> <p> Likewise for the Monty Hall problem!</p> <p > <iframe allowfullscreen="" frameborder="0" height="345" src="http://www.youtube.com/embed/WlyBuFZ0L_0?rel=0" width="420"></iframe></p> <p> <a href="http://www.thinkib.net/mathstudies/functions-teaching-ideas/quadratic-links.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Quadratic Links</a></p> <p > <object height="300" width="400"> <param name="flashvars" value="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2F&set_id=72157624445351321&jump_to="> <param name="movie" value="http://www.flickr.com/apps/slideshow/show.swf?v=104087"> <param name="allowFullScreen" value="true"><embed allowfullscreen="true" flashvars="offsite=true&lang=en-us&page_show_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2Fshow%2F&page_show_back_url=%2Fphotos%2F45129828%40N03%2Fsets%2F72157624445351321%2F&set_id=72157624445351321&jump_to=" height="300" src="http://www.flickr.com/apps/slideshow/show.swf?v=104087" type="application/x-shockwave-flash" width="400"></object></p><p><strong>Tags:</strong> <em>task design,group work,manipulatives,reflection</em></p>http://www.thinkib.net/mathstudies/blog/10717/physical-manipulatives#1315734826CAS - which way to go?
http://www.thinkib.net/mathstudies/blog/10570/cas-which-way-to-go
Mon, 22 Aug 2011 09:53:16 +0100]]>CAS - which way to go?http://www.thinkib.net/cache/blog-thumbs/21/10570-1314013996-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/10570/cas-which-way-to-go
<p> <img alt="" class="left" height="157" src="/files/teachmaths/files/Blogs/CAS.jpg" width="150">This blog entry was written as part of a reflection on the ICTMT 10 conference held in July in Portsmouth, UK.</p> <p> CAS for schools is tricky decision at the moment, but I must confess that this conference has helped me to narrow down some of those decisions. <a href="http://www.wolfram.com/mathematica/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Mathematica</a>, <a href="http://www.maplesoft.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Maple</a> and <a href="http://education.ti.com/calculators/products/US/os-update/" target="_blank"><img class="ico" src="/img/icons/connection.png"> TI-Nspire</a> are the names that seem to rise to the top and I am interested in all three. The first two are probably more capable then we actually need for secondary school. At our school, we still use and enjoy an old version of Derive that we have on our system at school and have been looking at ways to get TI Nspire for all our computers. We have been playing with single user licenses and like what it does, but we don’t want to invest in the handheld technology. We have the luxury of 1 to 1 computers and I am still of the view that advances in smartphone technology will take over handheld calculators as soon as exam boards catch up. This is no small point however, and the exam boards are the ‘joker in the pack’ as one teacher put it, for CAS enabled calculators as the leap into allowing smartphones or effectively computers into exams is huge and one that will cost exam boards a large amount of time and money and so they are likely to hold out as long as they can. More frustrating than this is that TI appear, not surprisingly, much more interested in selling the handhelds than they do the emulator software. As a result, I feel priced out of all three of those top runners, TI, Mathematica and Maple.</p> <p> I was then, fascinated to learn more about the development of the freely available <a href="http://maxima.sourceforge.net/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Maxima</a> from Chris Sangwin. Even better than this is the collaboration with <a href="http://www.geogebra.org/cms/" target="_blank"><img class="ico" src="/img/icons/connection.png">Geogebra</a> to integrate maxima thus creating one great tool that will combine so many of our needs in secondary schools. CAS, graphing and dynamic geometry all integrated and linked! A beta version of this software is available <a href="http://www.geogebra.org/trac/wiki/GeoGebraCAS" target="_blank"><img class="ico" src="/img/icons/connection.png"> GeogebraCAS</a> and the official launch is due this month. I for one am looking forward to it. Of course, the next discussion is to think in more detail about how to get the maximum benefit from this software in the classroom. Watch this space....<br> </p><p><strong>Tags:</strong> <em>CAS,ICT,conference,</em></p>http://www.thinkib.net/mathstudies/blog/10570/cas-which-way-to-go#1314003196ICTMT10
http://www.thinkib.net/mathstudies/blog/10303/ictmt10
Sun, 17 Jul 2011 12:49:58 +0100]]>ICTMT10http://www.thinkib.net/cache/blog-thumbs/21/10303-1310914198-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/10303/ictmt10
<p> <a href="http://ictmt10.org/" target="_blank"><img alt="" class="left" height="53" src="/files/teachmaths/files/Blogs/ICTMT 10.jpeg" width="150"></a>This blog is a short reflection on my experience of the ICTMT10 conference in Portsmouth 5 – 8 July 2011. I will not attempt a complete review of the conference for two reasons. Firstly, it would be impossible because of the number of parallel sessions on offer and secondly because I would not do it justice. As a secondary school mathematics teacher, the most useful thing for me to do is record some of the highlights and, perhaps most importantly, the resulting points of action that I have. Rather than publish this all in one go, I will publish a series of blogs over the next few weeks on some of the main themes. The following serves as an overview of what may follow.</p> <p> It is worth noting from the start that the conference is aimed at a mixture of educational researchers and practitioners from secondary and tertiary education and the sessions are a mixture of keynotes, presenting research and workshops. As such it is a rich mixture of possibilities for all kinds of people. I attended the previous conference, ICTMT9 in Metz, 2009 and I would be lying if I said I wasn’t a little disappointed that there were quite a few less secondary school teachers in Portsmouth and a considerably smaller North American presence. That said, there was a truly international feel to the conference and enough of my peers for some really rich exchange, not to mention some good company and good times.</p> <p> There were keynote speeches from Richard Noss, Paul Drijvers, Colin White and Collette Laborde all of which were thought provoking. One theme that seemed to run through all of these was that there seems to be a general disappointment that progress with ICT in Mathematics teaching has not achieved the potential that was thought to exist 20 - 30 years ago. Having only taught for 13 years I am not able to comment on this, but do think I can reflect on some significant changes during those 13 years!</p> <p> There was research presented on the benefits of using technology as a modeling tool and motivator, particularly in tertiary education. One example was given in the study of sports science where students did not necessarily have a strong mathematical background, but could make progress with modeling tools such as 'Matlab'.</p> <p> There was a particularly interesting workshop on students making videos of themselves solving problems and using these videos of getting students to reflect on their 'working out' and the stages they went through.</p> <p> There was much discussion of various electronic assessment tools and, in particular, their ability to give relevant feedback where mistakes were made. This technology is clearly advancing and does have a place in secondary schools.</p> <p> Handheld technology, mobile apps, GDCs and screen sharing software were all on show and this has prompted me to think about how to move forward with this in my school.</p> <p> Which CAS technology should we be embracing? This is a tough call but I became aware of some very interesting developments with Geogebra and Maxima, that may make this choice a little easier.</p> <p> With London 2012 on the horizon, sport and mathematics was a running theme through the conference and without too many concrete ideas, I am determined to think about strengthening this link in my school.</p> <p> We were treated to an excellent talk from Richard Noble about the 'Bloodhound project' that made me think about the whole land speed thing in a new way. As well as this we had dinner on the HMS Warrior - a 150 year old battle ship restored in all of its glory to round off an excellent week.</p> <p> As I said, I could not do the whole conference justice in one blog entry and so only aimed to give a brief summary. Many of the issues deserve to be returned to in future weeks in more depth.</p> <p> We, from the International School of Toulouse, offered 2 sessions during the conference, the details of which can be found here;</p> <p> <a href="http://www.thinkib.net/teachmaths/conferences/future-curriculum.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Future curriculum</a> 'Use of technology to significantly enhance the development, engagement and skillset of students in the third industrial revolution.</p> <p> <a href="http://www.thinkib.net/teachmaths/conferences/animated-questions.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Animated Questions</a> 'New types of question afforded by developments in technology'</p>http://www.thinkib.net/mathstudies/blog/10303/ictmt10#1310903398Data is out there!
http://www.thinkib.net/mathstudies/blog/10107/data-is-out-there
Sun, 12 Jun 2011 18:11:00 +0100]]>Data is out there!http://www.thinkib.net/cache/blog-thumbs/21/10107-1307909460-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/10107/data-is-out-there
<p> <img alt="" class="left" height="150" src="/files/mathstudies/images/blog/Data.png" width="150">The longer I teach mathematics, the more apsects of it I enjoy teaching. My preferences vary from group to group and course to course, but just at the moment , I think it is really exciting to teach statistics to IB Maths studies students. I find that these classes respond particularly well to the rooting of ideas in concrete contexts and statistics are a fantatstic way to do just that. I should add that I dont subscribe to the view that ideas always have to be rooted in concrete contexts, but that is a whole other conversation.</p> <p> So it has probably always been true that use of context has been very possible in the teaching of statistics, although it is remarkable how much fictional, semi real data is still used. This is particularly true of textbooks and exams, and whilst I believe that the nature of both of those things should change on a big scale, I can't be sure how long that will take. In the classroom however, we are free to move with the times and the use of real, current and intriguing data is more possible than ever. Technology allows the data to be easily shared and for large amounts of it to be analysed with relative ease. For example, the whole question of climate change can be be tackled in classrooms now. Just today, I picked up this <a href="http://www.guardian.co.uk/news/datablog/2011/jun/10/data-store-drought" target="_blank"><img class="ico" src="/img/icons/connection.png"> 100 years of UK rainfall data</a> from one of my my favourite data sources, <a href="http://www.guardian.co.uk/news/datablog" target="_blank"><img class="ico" src="/img/icons/connection.png"> The Guardian Datablog</a>. I grabbed the data really quickly and used <a href="http://www.autograph-math.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Autograph</a> to make a scattergraph as shown in the image below. What conclusions can I draw? The point of this blog is the ease with which data can be gathered and processed and beacuse its real data, it makes one keener to play with it some more to see if there is anything in the data that is not shown in the scattergraph.</p> <p > <img alt="" height="232" src="/files/mathstudies/images/blog/UK rain.png" width="450"></p> <p> Above all this though, what I find particularly exciting is the increasingly high profile that popular media is giving to data analysis. The following are just a few examples</p> <p> <a href="http://www.netflixprize.com//index" target="_blank"><img class="ico" src="/img/icons/connection.png"> The Netflix prize</a> - This is a great example of a project that was put out there for anyone that wanted to enter!</p> <p> <a href="http://www.kaggle.com/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Kaggle</a> - This website is based on a similar idea - real statistics projects for anyone that can.</p> <p> <a href="http://www.informationisbeautiful.net/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Information is Beautiful</a> - David McCandless brings information to us in increasingly inventive and interesting ways with his infographics. In doing so he reminds how are our understanding of the world around us depends in no small part on our ability to understand statistics and their representations.</p> <p> <a href="http://www.coolinfographics.com/blog/2011/6/6/datavis-contest-from-postgrad-and-david-mccandless.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+CoolInfographics+%28Cool+Infographics%29&utm_content=FaceBook" target="_blank"><img class="ico" src="/img/icons/connection.png"> Visulaisation prize</a> - This is just another link I picked up through twitter that is a competition to create an infographic with some data they haven't had time to look at at 'information is beautiful'. To help, here is a blog I found on <a href="http://www.makeuseof.com/tag/awesome-free-tools-infographics/?asid=c228f21b" target="_blank"><img class="ico" src="/img/icons/connection.png"> Tools for making infographics</a>. </p> <p> <a href="http://www.gapminder.org/" target="_blank"><img class="ico" src="/img/icons/connection.png"> Gapminder by Hans Rosling</a> - As many readers will know, Hans Rosling has done a huge amount to help get data in to the public domain and give as tool to help understand it.</p> <p> All this really helps to convince students of the relevance of what you are trying to teach them and the place of these skills and techniques in our world. I particularly like the quote from David McCandless in his <a href="http://www.ted.com/talks/david_mccandless_the_beauty_of_data_visualization.html" target="_blank"><img class="ico" src="/img/icons/connection.png"> TED talk</a> that 'Data is the new soil' and the illusion that much of our future development may depend on our ability to use data to accurately understand the present! Its all very exciting, particularly for mathematics teachers.</p><p><strong>Tags:</strong> <em>statistics popular</em></p>http://www.thinkib.net/mathstudies/blog/10107/data-is-out-there#1307898660Poker Machines and Percentages
http://www.thinkib.net/mathstudies/blog/10026/poker-machines-and-percentages
Sun, 29 May 2011 11:07:43 +0100]]>Poker Machines and Percentageshttp://www.thinkib.net/cache/blog-thumbs/21/10026-1306674463-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/10026/poker-machines-and-percentages
<p> <img alt="" class="left" height="113" src="/files/teachmaths/images/Poker Machine.jpeg" width="150"></p> <h3> Are percentages that basic?</h3> <p> This blog entry is really just designed to ask the question above and not to answer it. The hierarchy of mathematical sub-topics has always fascinated me and I have never really been clear on what I would view as 'the basics'. Equally I have never really been clear on why fractions and percentages often fall into that category when defined by people in discussion. In fact, students' failings with percentages appear to upset fellow teachers regularly and we as maths teachers are often asked by colleagues 'When do you do percentages?' and 'Why cant your students do them in my lessons?' and questions like these. At the risk of of being irritating I might often respond by asking, 'What do you mean 'do' percentages?'. Almost like probability, percentages are a topic that can escalate from simple to difficult very quickly indeed. How about the following classic problem,</p> <p > <em>'Start with 2 glasses of wine of equal size, one red, one white. Take a 10% sample from one of the glasses and put it in the other. Now extract the same size sample from the second glass and put it back in the first. What percentage of each glass is white wine?'</em></p> <p> That problem can be developed in many different ways very quickly and all of a sudden, many of the people who refer to percentages as basic are struggling. The aim is of course not to make people struggle, but to stop and think about the whole idea of percentages in a bit more depth. Many times I have started lessons on percentages by talking about the 10 % pay rise followed by the 10% pay cut and the associated counter intuitive response. Repeated percentage change, percentage error, reverse percentages and so on are one of the most difficult things that happens in my classroom. I know of students who can apply differential calculus in context, but come unstuck with reverse percentages or in a discussion about why 'Jedi Knights' are the fastest growing religion in the world according percentage growth between surveys. So I am not sure that percentages should be generalised as mathematical basics.</p> <p> This view was reinforced this week when I read this article, <a href="http://www.abc.net.au/unleashed/2733166.html" target="_blank"><img class="ico" src="http://www.teachmaths-inthinking.co.uk/img/icons/connection.png" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-top-color: rgb(153, 153, 153); border-right-color: rgb(153, 153, 153); border-bottom-color: rgb(153, 153, 153); border-left-color: rgb(153, 153, 153); border-style: initial; border-color: initial; display: inline; vertical-align: bottom; "> Poker Machine Maths,</a> about poker machines in Australia. In short, the law states that poker machines should give a return of between 85 and 90%. A lady gambles $300 in a day at the machine and walks away with nothing, but the machine stayed within the law. Follow your instinctive reaction to that statement then read the article. Then, if you really fancy a challenge, imagine how you explain that to a class of your students and what other mathematics is involved with this problem?</p>http://www.thinkib.net/mathstudies/blog/10026/poker-machines-and-percentages#1306663663Creativity
http://www.thinkib.net/mathstudies/blog/9910/creativity
Fri, 13 May 2011 17:17:05 +0100]]>Creativityhttp://www.thinkib.net/cache/blog-thumbs/21/9910-1305314225-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/9910/creativity
<p> <a href="http://www.ibo.org/ibworld/" target="_blank"><img alt="" class="left" height="200" src="/files/mathstudies/images/blog/ibworld.jpg" width="149"></a></p> <h3> What is this all about?</h3> <p> I am nervous about writing this blog and have often thought that one of the dangers of blogging is that it invites us to share our thoughts before they are fully developed. Whilst this is to be encouraged in discussion and debate in safe circumstances, there is something a little more edgy about committing these thoughts to the world wide web. One of the reasons I am nervous is because I want to question some of the words of some people that are very highly regarded at the moment. Sir Ken Robinson, for example is currently synonymous with this 'creativity' issue and has somehow rubbed me up the wrong way and its time for me to write it down!</p> <p> Before I go further, I would like to issue the following disclaimers! In principle I agree whole heartedly with the need for allowing and encouraging creativity in schools as endorsed by Sir Ken and others and as is the focus of the current IBWorld magazine (image left) that prompted me to write. I am grateful that people talk and write about these things and for the work of all the people involved and am in no way critisising any of this work. Follow the picture link to find out more about IB World. </p> <p> So to the point. My issue with all of this creativity talk is 'why is this being treated like a new idea?'. I admit that I may have had some fortunate working environments in my teaching career, but those environments have been amongst the most creative I have ever experienced. Teaching and teaching mathematics is a richly rewarding profession that completely depends on creativity to encourage creativity. I was indoctrinated to this school of thought from the very beginning by my PGCSE tutors at Nottingham University, Tony Cotton and Peter Gates and this was continued as I did further post gradutae studies at Oxford University with Anne Watson and John Mason, the latter being the author of 'Thinking Mathematically' which I believe is a must for all maths teachers and was first published 30 years ago.</p> <p> In the midst of making some excellent points, Ken Robinson refers to some annecdotes that paint schools and teachers in a terrible light and get a good laugh - he is an excellent speaker. I find myself asking how much time he has spent in schools. If it is a lot, then he should have some different annecdotes that demonstrate just how creative schools can actually be. In the current issue of IBWorld, there is a little window with the heading 'teaching maths can be creative too' that goes on to talk about how maths is one of the most difficult areas in which to achieve this. As I read this I wonder about how out of the ordinary my own experiences might be that I see it almost the other way round, that it is almost easier to be creative in mathematics than it is in other subjects.</p> <p> I am sure that all this is linked to the stigma that our subject has long suffered from, that maths is black and white, an unquestionable truth, and invariant crutch on which we can depend. This along with the perception that it must be difficult, some people are just born with it but it can be learned with drill and practise. As teachers I think its our duty to challenge these notions and paint a truer picture of our subject. As a result I will make a point of trying to refer to this creativity as I blog in future about teaching maths, with specific examples.</p> <p> For now, and in the interests of fairness I will refer you to some of the work of the people mentioned above....</p> <h4> Ken Robinson does TED</h4> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/iG9CE55wbtY?rel=0" width="425"></iframe></p> <h4> Here is one I prefer from Sir Ken</h4> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/zDZFcDGpL4U?rel=0" width="560"></iframe></p> <h4> Daniel Pink </h4> <p> <a href="http://www.danpink.com/whole-new-mind" target="_blank"><img class="ico" src="/img/icons/connection.png">A whole new mind</a> - This is the book at the centre of the IB World issue above</p> <h4> John Mason</h4> <p> <a href="http://www.amazon.co.uk/Thinking-Mathematically-J-Mason/dp/0273728911/ref=sr_1_1?s=books&ie=UTF8&qid=1305315110&sr=1-1" target="_blank"><img class="ico" src="/img/icons/connection.png"> Thinking Mathematically</a> - One of the books that has inspired me as a maths teacher</p> <p><strong>Tags:</strong> <em>creativity,maths teaching,commentary</em></p>http://www.thinkib.net/mathstudies/blog/9910/creativity#1305303425Animated questions
http://www.thinkib.net/mathstudies/blog/9870/animated-questions
Sun, 08 May 2011 10:48:49 +0100]]>Animated questionshttp://www.thinkib.net/cache/blog-thumbs/21/9870-1304858929-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/9870/animated-questions
<p> <img alt="" class="left" height="150" src="/files/mathstudies/images/blog/DrWho.png" width="150">Dynamic geometry and similar dynamic software have been a major influence on my own understanding of mathematics and consequently my own teaching. Start with the notion that all squares actually meet the minimum requirements to qualify as all other quadrilaterals<img class="ico" src="http://www.teachmaths-inthinking.co.uk/r/f1.png" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-top-color: rgb(153, 153, 153); border-right-color: rgb(153, 153, 153); border-bottom-color: rgb(153, 153, 153); border-left-color: rgb(153, 153, 153); border-style: initial; border-color: initial; display: inline; vertical-align: bottom; "></p> <p > National variations in the definition of a trapezium or trapezoid do provide an interesting challenge to this notion<img class="ico" src="http://www.teachmaths-inthinking.co.uk/r/f2.png" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-top-color: rgb(153, 153, 153); border-right-color: rgb(153, 153, 153); border-bottom-color: rgb(153, 153, 153); border-left-color: rgb(153, 153, 153); border-style: initial; border-color: initial; display: inline; vertical-align: bottom; ">. How often does this notion upset students who somehow want rectangles and squares to be discretely different from each other? I suggest that a mathematical object or phenomenon is best described by its properties and that these properties can best be explored in a dynamic environment. The ability to bend, stretch, and explore a dynamic situation demands that we consider generalities and their limits where static representations provide us only a particular case. Why then, are so many questions in mathematics classrooms asked through a static, fixed and often printed medium? Developments in technology have prompted me to explore the setting of ‘Animated questions’ where students are shown short animations of particular mathematical phenomena and asked to explore and define them by attempting to recreate them. In this workshop I propose to engage the audience with a number of examples of these ‘animated questions’ exploring geometry, functions, sequences and more. In exploring the problems I hope the group is prompted to recognise the benefits of asking questions in this way in terms of exploring generality, engagement and problem solving.<br> <br> I work in a school where students carry their own laptops with them at all times, which aids such experimentation, but this is not a prerequisite for being able to ask these questions. What it does do is make me increasingly curious about how long it will be before external assessment tools for mathematics will be set using technology as a medium and thus allowing a broader, more versatile style of questioning of which these ‘animated questions’ are just an example.<br> <br> The above is the abstract for a session I am planning to run at the <a href="http://ictmt10.org/" style="color: rgb(0, 51, 102); text-decoration: none; " target="_blank"><img class="ico" src="http://www.teachmaths-inthinking.co.uk/img/icons/connection.png" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: 0px; border-left-width: 0px; border-top-style: solid; border-right-style: solid; border-bottom-style: solid; border-left-style: solid; border-top-color: rgb(153, 153, 153); border-right-color: rgb(153, 153, 153); border-bottom-color: rgb(153, 153, 153); border-left-color: rgb(153, 153, 153); border-style: initial; border-color: initial; display: inline; vertical-align: bottom; "> ICTMT 10</a> conference in Portsmouth in July.</p> <h4 style="font-family: 'Arial Narrow', Arial, Helvetica, sans-serif; color: rgb(0, 51, 102); margin-top: 0px; margin-right: 0px; margin-bottom: 0.6em; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; text-align: left; font-size: 1.3em; "> Examples</h4> <p > The following are a few examples of such animations as described above. In each case, the question is essentially quite simple. Can you recreate the animation?</p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/TTLoseMKpgY?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/KohHmcjlnV4?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="390" src="http://www.youtube.com/embed/Q1JkBViqVQo?rel=0" width="480"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/twRF3f4HT7g?rel=0" width="560"></iframe></p> <p > <iframe allowfullscreen="" frameborder="0" height="349" src="http://www.youtube.com/embed/S8p5XyNARZ0?rel=0" width="425"></iframe></p> <h4 style="font-family: 'Arial Narrow', Arial, Helvetica, sans-serif; color: rgb(0, 51, 102); margin-top: 0px; margin-right: 0px; margin-bottom: 0.6em; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; text-align: left; font-size: 1.3em; "> Activities</h4> <p > Please follow the links below to see some examples of how this can be done in the classroom.</p> <p > <a href="http://www.thinkib.net/mathstudies/functions-teaching-ideas/dancing-quadratics.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Dancing Quadratics</a> - Investigating the properties of quadratic functions.</p> <p > <a href="http://www.thinkib.net/mathstudies/functions-teaching-ideas/making-waves-1.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Making Waves</a> - Investigating properties of trig functions</p> <p > <a href="http://www.thinkib.net/mathstudies/nanda-teaching-ideas/dr-who.htm" target="_blank"><img class="ico" src="/img/icons/inthinking.png"> Dr Who</a> - A visualisation of geometric sequences</p><p><strong>Tags:</strong> <em>ICT,innovation,conference,dynamic geometry</em></p>http://www.thinkib.net/mathstudies/blog/9870/animated-questions#1304848129Facebook
http://www.thinkib.net/mathstudies/blog/9289/facebook
Sun, 27 Feb 2011 18:48:30 +0000]]>Facebookhttp://www.thinkib.net/cache/blog-thumbs/21/9289-1298843310-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/9289/facebook
<p> <img alt="" class="left noborder" height="150" src="/files/mathstudies/images/blog/fb.png" width="150"></p> <h3> Love it or hate it!</h3> <p> For one reason or another I have been consumed by a desire to find out more about the implications of facebook for education this week. No doubt what I have learned in a week still leaves me way behind the field, but it has been fun and I have a few new ideas to pursue. I have been a facebooker for a few years now, but not a really serious one. I am probably only just in double figures for status updates, preferring to follow the lives of others, and my students' friends tallies make me look like a hermit by comparison. This week however has probably been my busiest week on facebook and I think that it has been prompted by hearing the statistic that 1 in 13 people on the planet have a facebook profile and knowing what I do about averages tells me that amongst the people I live and work with this figure is likely to be much, much higher! So, this started me thinking, which started me talking to my students and which has lead to the following two useful ideas related to Maths Studies teaching.</p> <h4> Facebook groups for classes</h4> <p> I have learned that I can create a 'group' for me and my students and I dont have to be 'friends' with them or even 'like' them, to use the apt fb terminolgy! My students are really keen and see it as my best bet for getting their attention. My words can cut into their daily newsfeed fix and suddenly get on their radar with frightening regularity. I am going to resist writing too much about what this could be and resolve to blog again soon about how the project has gone.</p> <h4> Facebook as a data source</h4> <p> David McCandless from 'Information is Beautiful' makes some lovely data visualisations with data he has 'scraped' (his words) from facebook status updates. Hans Rosling's recent documentary, 'The Joy of Stats' also highlights a project designed to conclude the mood of the worlds population by collecting words from status updates and more. Both of these ideas have made me think about the potential data harvesting opportuntities there are with facebook. In fact it prompted one of my students this year to do an Internal Assessment on facebook use, collecting data on friends, photos, likes, ages, status updates etc. and I think this has potential.</p> <p> I could write more about the reflections I have had on facebook this week, but will quit while I am still talking about Maths Studies and teaching. Truth is though, love it or hate it, its real and its fascinating!</p><p><strong>Tags:</strong> <em>facebook networking technology communication</em></p>http://www.thinkib.net/mathstudies/blog/9289/facebook#1298832510Negative Power
http://www.thinkib.net/mathstudies/blog/8928/negative-power
Sun, 06 Feb 2011 14:09:41 +0000]]>Negative Powerhttp://www.thinkib.net/cache/blog-thumbs/21/8928-1297012181-thinkib.jpghttp://www.thinkib.net/mathstudies/blog/8928/negative-power
<h3> Why Calculus gets such a bad press!</h3> <p> <img src="http://www.thinkib.net/cache/blog-thumbs/21/8928-1297012181-thinkib.jpg" alt="Negative Power" /><br /><br /> Most of my blog entries will come about as part of my preparations to teach in the coming week and this one is no different. Tomorrow I start the calculus unit with my 2nd year IB Maths Studies students and I can't decide if I am looking forward to it or not! The teaching of this unit always presents a challenge to me. Whats the best time during the course to do it? What is the required knowledge? (and do my students have it?). It is such a wonderful branch of mathematics that it would be a terrible shame to treat it as skills only and yet we are only three months away exams and have a lot of revsion to do. How much time shall we spend exploring? More to the point, what will the overall benefit of exploring be to the students in terms of being able answer exam questions? Lastly, what is going to get in the way?</p> <p> Well, as with most things, the more you do it the more experience you have to draw on and the more prepared you are for the answers to these questions (notice how avoided comitting to a how much better I will teach it). So before I even get started with the calculus I am going to spend at least a lesson exploring the principle in the picture above. This is definitley required knowledge, but, in my experience, it is a notorious barrier to progress and if you are not careful students end up thinking calculus is difficult because they dont understand and cant remember this rule about negative powers. This is completely unfair to calculus! I will go right back to basic laws of indices to get students to explore why this rule is so, in an attempt to remove this barrier once and for all. That way, when I get to differentiating functions with negative powers we will glide smoothly past this potential barrier. This is my top tip for the teaching of this maths studies calculus unit. It<em> is</em> assumed knowledge and not covered anywhere in the syllabus. If it is not dealt with then it will put a major spanner in the works just when you think you are getting somewhere. </p> <p> Negative powers are one of the reasons why I find this calculus unit hard to teach. The calculus element is actually very small and most of the unit is taken up with the associated supporting algebra. I think its very important to help students understand which specific parts of any problem require calculs to solve them so as not to give calculus a bad press. Quite often a 'calculus' question will follow the following pattern</p> <ul> <li> A description of a situation with some variables and expressions given. Students are then expected to manipulate this algebra in order to form an expression for a given quantity in terms of just one other variable by using algebraic substitution. This often involves some very sphisticated algebraic skills and reasoning and can scupper a problem before its even begun!</li> <li> A question may then ask students to optimise the function - enter the calculus. Students differentiate the function, often worth a couple of marks, then put it equal to zero. This is the calculus done! Now they are solving equations, more algebraic manipulation.</li> <li> Students may then be asked to substitute the solutions to these equations back into their original expressions - algebraic substitution.</li> </ul> <p> Of course you cant strip all that algebraic manipulation out of optimisation problems, but it is important to note that much of what students are being tested on here is algebraic manipulation and not calculus. Along with that, this is where the graphical calculators should come in really handy. This is really worth bearing in mind when we teach it!</p> <p> To answer my other questions, I will be giving time to exploration and discovery. I have made previous attempts to rush this module through and just teach the skills, not focussing on the 'why?' and had little success. Calculus is a rich topic and should be shown to maths studies students. Please see the general section on <a href="http://www.thinkib.net/mathstudies/teaching-the-syllabus/7-calculus.htm">calculus</a> in the main part of this website and the <a href="http://www.thinkib.net/mathstudies/7-calculus/calculus-teaching-ideas.htm">activities</a> section for examples of what you can do with your classes and how to deal with 'Negative power'!</p>http://www.thinkib.net/mathstudies/blog/8928/negative-power#1297001381