IB Maths Studies: Last blog entries
http://www.thinkib.net/mathstudies/blog
InThinking IB Maths Studies: www.thinkib.net/mathstudies2018 InThinking Educational Consultants. All rights reserved.This Years projects 2018
https://www.thinkib.net/mathstudies/blog/27380/this-years-projects-2018
Sat, 15 Sep 2018 00:00:00 +0100]]>This Years projects 2018https://www.thinkib.net/cache/blog-thumbs/21/27380-1537026297-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/27380/this-years-projects-2018
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/27380-1537026297-thinkib.jpg" alt="This Years projects 2018" /><br /><br /><h3>Some of this year's ideas</h3><p>Here are a few of the projects I am going to be seeing this year</p><p>100 books to read before you die - This was the inspration and the student is going to be analysing data about those books to try and see what it takes to get on the list. Everything from good reads ratings, to publication date and sales figures are up for grans here.</p><p>La Liga - a football fan has a wealth of stats about a single La Liga (Spanish football league) season and will be looking for the patterns within it.</p><p>Teenage Pregnancy - Where is it most and least prevalaent? What are the possible causes/reasons? these kind of social indicators and always worth exploring and students tend to find out a lot by doing it.</p><p>Carbin emmissions - Very topical and I have already enjoyed what I have learned already. Which countries emit the most and what might explain that? What patterns emerge when looking at carbon emissions over time and what might explain that?</p><p>...</p>https://www.thinkib.net/mathstudies/blog/27380/this-years-projects-2018#1536966000Final Report to teachers
https://www.thinkib.net/mathstudies/blog/26628/final-report-to-teachers
Mon, 18 Jun 2018 00:00:00 +0100]]>Final Report to teachershttps://www.thinkib.net/cache/blog-thumbs/21/26628-1529310817-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/26628/final-report-to-teachers
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/26628-1529310817-thinkib.jpg" alt="Final Report to teachers" /><br /><br /><h3>Whats next?</h3><p>So we wont expect any further communication now until January 2019 when we can expect the publishing of the new guides, the support materials and specimen papers. This will be followed by the subject specific seminars for the launch. We'll be sure to share news about this as soon as we have it. Happy reading!</p>https://www.thinkib.net/mathstudies/blog/26628/final-report-to-teachers#1529276400Problems with surveys
https://www.thinkib.net/mathstudies/blog/26567/problems-with-surveys
Fri, 08 Jun 2018 00:00:00 +0100]]>Problems with surveyshttps://www.thinkib.net/cache/blog-thumbs/21/26567-1528627240-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/26567/problems-with-surveys
<img src="https://www.thinkib.net/cache/blog-thumbs/21/26567-1528627240-thinkib.jpg" alt="Problems with surveys" /><br /><br /><h3>In summary</h3><p>Perhaps, unhelpfully, I have thrown out more questions than answers here, but I feel they are important questions. With data being the new 'Oil' and playing such a leading role in the current studies course and the new applications course, they are the questions that have to be asked and dealt with. As surveys are designed, we have to keep referring back to what the point of the survey is and make sure that the way we ask questions allows respondents to help us converge on truth and not diverge from it.</p>https://www.thinkib.net/mathstudies/blog/26567/problems-with-surveys#15284124002019
https://www.thinkib.net/mathstudies/blog/26486/2019
Mon, 21 May 2018 00:00:00 +0100]]>2019https://www.thinkib.net/cache/blog-thumbs/21/26486-1526913290-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/26486/2019
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/26486-1526913290-thinkib.jpg" alt="2019" /><br /><br /><h3>What are we doing?</h3><p>So this blog is really just about what we are planning on the site and what it is that teachers might be looking for. At this stage, this is the plan for development of the site......</p><div class="greenBg" contenteditable="false"><div contenteditable="true"><ul><li>It seems like the majority of resources on this site as it is will be easily transferable to the new course. As such, it will be reviewed and reorganised in to the new units by the spring of 2019 so that we are offering hige cross section of resources that you can use to teach the new course.</li><li>We will offer a section on making the transition, considering the changes and general management of bringing in the new courses.</li><li>We will offer a detailed scheme of work for the new Applications and Interpretations course for the 2 years starting in September 2019.</li><li>We will aim to have the first term fully resourced well in advance.</li><li>Then we will aim to keep at least few months in advance of the scheme </li><li>After that we will of course continue to add depth, questions and quality to the site so that we continue to offer you more.</li></ul></div></div><h3>What is on your mind?</h3><p>In the mean time we would be really keen to hear from you about what your main priorities are. What do you most want to know? What kind of resources would you most like? How would you like the site to develop? Please add suggestions to this <a href="http://docs.google.com/forms/d/e/1FAIpQLSeKmBR7Lw53SYVs4jvM75KfovRhk3-wDsLhFOCBFZYFjk5_jQ/viewform" target="_blank">google form</a> or comment on this blog post.</p>https://www.thinkib.net/mathstudies/blog/26486/2019#1526857200May TZ2 exams
https://www.thinkib.net/mathstudies/blog/26432/may-tz2-exams
Fri, 11 May 2018 00:00:00 +0100]]>May TZ2 examshttps://www.thinkib.net/cache/blog-thumbs/21/26432-1526062720-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/26432/may-tz2-exams
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/26432-1526062720-thinkib.jpg" alt="May TZ2 exams" /><br /><br /><h2>Paper 2</h2><p>Dangerous though it is to say so out loud, paper 2 did seem very approachable and did not contain many (if any) of the twists that we sometimes see...... but we will have to wait and see how students got on with it!</p><p>Question 1 - Sets and Probability</p><p>This looks like a nice question to start woth. There are plenty of approachable marks and probably the most challenging parts were not in a position where they could put you off or hinder progress on the rest of the question.</p><p>Question 2 - Cumulative Frequency</p><p>Again - this seems like an easy question without any twists or challenges really. I would hope students could cash in here. It does seem as hame though that there is a 15 mark paper 2 question on statistics that doesn't involve any interpretation at all. Clearly, those questions are harder to ask and assess (and maybe even harder to answer) but it is really the point of statistics. Thik there is room for more of this and I expect to see more of it in the new course.</p><p>Question 3 - Normal Distribution and Chi Squared test.</p><p>Another fairly straightforward question I think. perhaps in part b) students might be held up dealing with 1.5 standard deviations instead of a given maximum and minimum, but b)ii) asks them to sketch the curve which, in turn, invites them to work out the uppoer and lower limits. Here is another stats question without any significant interpretation though. </p><p>Question 4 - Sequences</p><p>The context can often make it a little harder to get in to, but I would expect students to spot this as a fairly standard sequences question - again without any real twists.</p><p>Question 5 - Trigonometry</p><p>Part a) really need students to have that 'speculative' approach I mentioned earlier. 'Given what I know - what else can I work out?'. otherwise, since it is a show that question, they could move on using 85° for the rest. There is a a bit of problem solving to do here, but nothing particularly tricky.</p><p>Question 6 - Calculus</p><p>And once more - compared to some optimisation questions that come up on paper 2, I think this is very approachable. I raised an eyebrow at the use of the term stationary points and certainly part f) will leave out a lot of people.</p>https://www.thinkib.net/mathstudies/blog/26432/may-tz2-exams#1525993200Subject report and IA
https://www.thinkib.net/mathstudies/blog/25856/subject-report-and-ia
Thu, 01 Mar 2018 00:00:00 +0000]]>Subject report and IAhttps://www.thinkib.net/cache/blog-thumbs/21/25856-1519901175-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/25856/subject-report-and-ia
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/25856-1519901175-thinkib.jpg" alt="Subject report and IA" /><br /><br />https://www.thinkib.net/mathstudies/blog/25856/subject-report-and-ia#1519862400New Curriculum
https://www.thinkib.net/mathstudies/blog/25772/new-curriculum
Sat, 10 Feb 2018 00:00:00 +0000]]>New Curriculumhttps://www.thinkib.net/cache/blog-thumbs/21/25772-1518274221-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/25772/new-curriculum
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/25772-1518274221-thinkib.jpg" alt="New Curriculum" /><br /><br /></p><p>The above is a bit crude and full details are yet to be made public but it is a good guide for now. So in tems of subscribing to ThinkIB.net sites the following is the planned model</p><p><strong>This MATHSTUDIES site will become the site for the Mathematics Applications and Interpretations and cater for both courses during the transition.</strong></p><p><strong>The HL/SL site will become the site for Mathematics Analysis and Approaches and cater for both courses during the transition.</strong></p><p>So, stay tuned for news of how the restructuring will take place!</p>https://www.thinkib.net/mathstudies/blog/25772/new-curriculum#1518220800Re-organisation
https://www.thinkib.net/mathstudies/blog/23476/re-organisation
Mon, 25 Sep 2017 00:00:00 +0100]]>Re-organisationhttps://www.thinkib.net/cache/blog-thumbs/21/23476-1496053270-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/23476/re-organisation
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/23476-1496053270-thinkib.jpg" alt="Re-organisation" /><br /><br />The IA section</h2> <p>This is just a quick blog post to explain some reorganisation that is coming up for this section of the site so as to explain any gaps or unfinished looking parts. Currently under assessment you have a choice between 'Internal assessment' and 'Exams and Revision' - During reorganisation, this will stay exactly as it is so that you can find things in the same place. During re organisation and building, there will be 2 more pages appearing under that list. The first is 'Internal Assessment teacher management' and the second is 'Internal assessment - planning and writing'. Gradually, the two sections will subsume all the old material. In the mean time, I will leave the old structure in place for reference.....</p> https://www.thinkib.net/mathstudies/blog/23476/re-organisation#1506294000First Draft Feedback
https://www.thinkib.net/mathstudies/blog/23656/first-draft-feedback
Sun, 02 Jul 2017 00:00:00 +0100]]>First Draft Feedbackhttps://www.thinkib.net/cache/blog-thumbs/21/23656-1499004376-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/23656/first-draft-feedback
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/23656-1499004376-thinkib.jpg" alt="First Draft Feedback" /><br /><br />A note on annotations</h3> <p>For anyone out there using managebac, I have found this a really useful way of providing feedback via annotations. If students upload their work to an assignement, then you can annotate the file where it is. When students gon to the assignment and choose 'Annotate' themselves, then they can see your annotations and add their own. This is appealing for 2 key reasons...</p> <ol> <li>There is no subsititute for adding annotations directly on the work to which you are referring. There are a few tools to help and students have a better chance of understanding exactly what you are saying.</li> <li>There is only one copy of the cdocument and its annotations, rather than multiple copies flying around via e-mail etc.</li> </ol> <p>Other tools like, turnit in offer this facility. I don't know enough to say which tool does it better, but I know that many of us are already using managebac so, for that reason, it seemed the most sensible choice.</p> </div> <h2>What did I say?</h2> <p>For interest, I have copied the comments directly below, but thought it would be useful to summarise them in to categories. I was really surpirsed to see that most of what remained for students to do centered around communcation. this was reassuring in some ways, because it meant that my resources had helped them really understand the IA process, the mathematics involved and the ideas of simple relevant investigation. Then I had some refelction to do about why these communication issues are what they are. My conclusion is that actually, theyt are rzquired to do this so rarely that it is to be possibly expected. Interesting that skills they learn for other subjects that require more written communication have not necessarily been translated to maths. These are the key points that I will reflect on in future. </p> <div class="blueBg"> <ol> <li>How do build in more opportunity to practice this kind of communication?</li> <li>How do I help students transfer communication skills from other subjets to this one?</li> </ol> </div> <p>Here is a summary of the categories.....</p> <div class="greyBg"> <h3>Introductions and structure</h3> <p>Much of the advice was about having an explicit plan that was then followed. Even if I am only giving 2/3 here, I want see to this done better. Either separate paragrpahs or ullet points that show clearly how the project will be chopped up in to 3, 4 or 5 pieces that follow a logical order. As the reader, this sets the tone and I know what toe xpect. If the sections that follow mirror that then this does a lot for the communication</p> <h3>Sign posting</h3> <p>Lots of the projects had new sections that started without a heading or an opening paragraph (sentence or two) to help the reader know where they are and what was coming. A seemingly random graph would appear... The result was lost of comments about 'Signposting'. Where are we? Where are we going next?. Use of a headings structure, titles and labels. Next year I think I might introduce another stage where students are required to show me a document outline using the heading structure before they start writing. I was surprised to learn how many did not know about the navigation pane in word.</p> </div> <h3>My Comments</h3> <p>The following are a selection of the comments I found my self writing...</p> <p>Make sure you have an explicit list of the things you are going to do that you then follow exactly. Each process must be justified by a purpose. This was the planning phase. At the moment this is a bit grey and not easy to tell.</p> <p>Consider using a headings structure where the headings match up with the sections you set out in your introduction match up.</p> <p>Again, this just appears without a heading or any explanation. Give it a subheading and then a sentence or two to explain what is about to happen....</p> <p>I think it would be useful to show an example of this in action.... Just show the process for calculating one of the means.</p> <p>It would be good to get a PMCC using tech here just to back up what you are saying....</p> <p>I really have no idea what this table is showing.....</p> <p>I am worried about this. It seems like it could be really interesting, but I still don't get it. I am being a bit devils advocate about this just to point out that to a neutral reader this might get the same reaction</p> <p>I don't think we do see that actually..... I also think this should be a scattergraph..... not a bar chart</p> <p>I have you somewhere between 2 and 3 here. I think it would be useful to hear more of an explanation about your numbers. For example – how is it possible get the number of species in a given country. There must be some problems with this?</p> <p>I am not seeing anything explicit enough here and think you have plenty to talk about…… I think the validity of your actual data is questionable. Not your fault, but you could talk about it. Also You might like to discuss how likely the link with GDP is – if there is a link what do we think about causation?</p> <p>I think you have some work to do here. Pay careful attention to the advice given in the writing guide and in my annotations. Much more signposting is needed. The reader needs to know where they are at and what is about to happen at all points. This does not need to be long winded and can be solved with headings and short explicit sentences.</p> <p>½ at the moment, there is not a lot of maths here to use as evidence….. Also I, like I said, one of your graphs should be a scattergraph and not a bar chart and so this might even knock you back to 0 here…..</p> <p>You need to get all ToK here Freddie. The list was made by an Anglophone magazine based in the USA... Is the outcome really shocking?</p> <p>5/5 This is good stuff Freddie, BUT, I am hesitating a bit about the fact that you calculated a PMCC when it was pretty obvious that there was not going to be any correlation…..</p> <p>What there is is evidence that most of the songs are older. There for there is a preference for older songs. I wonder, can you demonstrate this for us somehow</p> <p>What about…. Grouping your songs in to decades</p> <p>Plot a time series of Decade on the x-axis and number of songs included in the top 500. This might show an interesting pattern – You could then do a PMCC on this….</p> <p>Then you could do it for the top 100. This might be even better because it looks a bit different to the rest….</p> <p>I just think you need to bring this pattern out somehow… Then I will be happier to justify the mark.</p> <p>Have you got the whole table Freddie? Might be worth puttin gin an appendix</p> <p>You are making a good point, but you might need to emphasise that there is difference between judging by eye and calculating. It might also be worth searching for a 'perfect' lack of correlation</p> <p>So at the moment, your introduction does not contain a plan. this is key, please read this section and add.</p> <p>This is a good start at explaining your data. Can I recommend that you have 2 separate sections. 1 for an introduction and another for explaining everything we need to know about the info you collected. Perhaps some annotations of your shown sample would be useful</p> <p>I think you need to tell the reader a bit more. even though I know what your project is a bout, I am still asking 'the mean what?'</p> <p>What is 100 more? 100 what?</p> <p>Explicit labelling needed to stop your reader getting lost</p> <p>These labels are so small as to be nearly illegible</p> <p>use an equation and get a fraction 'Insert Equation'</p> <p>What formula did you use for covariance? Where is it? Where can I see you substituting the numbers in?</p> <p>This doesn't mean anything... A regression line should be in the form of a linear equation (y=mx+c for example)</p> <p>This is not a good scale to use - you need to focus on a section of the scale so we can see differences better.</p> <p>Why? Each section should start with a brief outline of what the reader can expect. This can be a copy of what you put in the plan. this helps the flow a lot.</p> <p>You might ned to give the uninitiated some background on 'Dr Who' Something about its cult following will help your project to make sense</p> <p>I am considering three here because I think it is good data and you worked hard to put it together….. I’ll think about it. Perhaps if, in your section on data, you go through each data heading and tell me why you collected it what patterns you think it might show.</p> <p>This could be clearer. if you wrap the text in the heading box and then narrow the columns, you'll get a better image with bigger text and less empty space....</p> <p>These long left tails are interesting too... why might they be there?</p> <p>And what might that tell us about that population?</p> <p>You might like to try and say more about why you think some results turned out the way they did</p> <p>I think it would also be good to explain a bit more about how you decided on your categories for the test….</p> <p>In general, I think it needs a little more sign posting. The reader should know where they are at any time and what is happening. A sentence or two at the start of each section, clear labels and titles and annotations. Don’t forget, the reader has not been involved with your project and needs everything to be made clear.</p> <p>Each section should begin with sentence or 2 about what is about to come. DOn't leave the reader guessing</p> <p>Make a reference to the whole table appearing at the end. Say that you didn't want to interrupt the flow with the whole thing here</p> <p>You have got two sections mixed up here. You should have an intro that has a very clear plan with the purpose of each thing in it.... THEN you should describe your data collection process. The stroy about the politics is a good one and you should tell it...</p> <p>Does this mean average? If so then say so....</p> <p>All these graphs should have their interpretations nearby... too much work for me to figure which bit of text goes with which graph</p> <p>NO - IT DOESN'T SHOW ANY CORRELATION AT ALL</p> <p>What about a sentence or two that outlines why you are interested in cyber attacks and why you think this might be a worthwhile exercise</p> <p>This whole section is incomprehensible because nothing has labels or titles. The reader has no idea what is happening</p> <p>DC? I am probably not alone in not knowing what you mean.....</p> <p>So we need a clearer outline of your plan. I recommend either separate paragraphs or bullet points for each process....</p> <p>This is a bit blurry and hard to read. Also lots of space - can you format your table so there is less space and the numbers are bigger?</p> <p>Now here I need a sub heading. Clearly something new is about to happen. Sign post it with a heading, then a couple of sentences to explain what you are going to do and why. This might be a repeat of your plan.</p> <p>Again, this is missing sign posts - the reader will be lost. Also the box plots need explicit labelling. I am left asking what variable you have used - guessing... searching... Frustrating..... This is all key to good communication.</p> <p>Is this Marvel and DC combined? (still don't know what DC is)</p> <p>Where are these numbers coming from? How can I check them?</p> <p>Anyway you could format the table so that the numbers are clearer and there is less space?</p> <p>Why might there be?</p> <p>Observations and interpretations should really be put near or on the diagram so we can easily associate the two. here I am having to scroll too far down to see what you are going to say...</p> <p>Wow - I am really impressed with this, although there are lots of problems. In short though, you have too many categories and not enough data, so too many of you expected frequencies are below 5. We need to rethink how you could combine some of your categories.</p> <p>Perhaps you can tell us more about why it is significant that you have used ‘rate’ and ‘per capita’. It is significant!</p> <p>You might need to elaborate here for the neutral reader....</p> <p>It might help to see this as separate paragraphs/bullet points so that the plan leaves a mark on the reader....</p> <p>so what rate - per 1000?</p> <p>Heading needed here.... signpost - what is coming next, then a sentence or two to set the tone....</p> <p>Don't think we need all of these decimal places.... round</p> <p>Distribution? I don't know what is on the Y axis here...</p> <p>OK - we need a more descriptive introduction. What are you going to do and why? What do you think might happen.. Specifically what processes will you go through and why?</p> <p>Would be good to see an example how you calculated one of these....</p> <p>Some work to do here on wording.... correlation goes with scatter graph Not sure what you mean by mean predominant religion.... think is just a case of wording...</p> <p>.....</p> https://www.thinkib.net/mathstudies/blog/23656/first-draft-feedback#1498950000Venns in the news
https://www.thinkib.net/mathstudies/blog/23453/venns-in-the-news
Wed, 24 May 2017 00:00:00 +0100]]>Venns in the newshttps://www.thinkib.net/cache/blog-thumbs/21/23453-1495636139-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/23453/venns-in-the-news
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/23453-1495636139-thinkib.jpg" alt="Venns in the news" /><br /><br /></p> <p>In conclusion, I ask to what exetnet are we allowed to be flexible with the 'protocolas' of mathematical diagrams in order to help communication. In doing so there is an implication that perhaps mathematical diagrams in their purest form don't communicate as well as they might? All just questions and certainly no criticism of the Venn diagrmas used is intended or implied. We teach Venn diagrams, the mdeia uses them. That is a good combination as far as I am concerned.</p> <p>Now I am looking for the ToK angle,</p> <p>cheers!</p> https://www.thinkib.net/mathstudies/blog/23453/venns-in-the-news#1495580400This year's projects
https://www.thinkib.net/mathstudies/blog/23433/this-years-projects
Fri, 19 May 2017 00:00:00 +0100]]>This year's projectshttps://www.thinkib.net/cache/blog-thumbs/21/23433-1495206308-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/23433/this-years-projects
<h2><img src="https://www.thinkib.net/cache/blog-thumbs/21/23433-1495206308-thinkib.jpg" alt="This year's projects" /><br /><br /> <h2>Projects</h2> <p><strong>Cyber attacks</strong> - What is the damaged caused, the danger associated. Who gets targetted and when? This promises to be really interesting and the data has all the potential it needs.</p> <p><strong>How effective is the TB vaccination</strong> - Never seen this one before. Comparing data about prevalanece of the vaccination and the disease along with other factors that might affect both of those.</p> <p><strong>Dr Who Episodes</strong> - Which ones are most popular and why? Some good data here could give the show producers some useful tips on the formula for success!</p> <p><strong>The Happy Planet Index</strong> - This is a really interesting organisation that I have been aware of for a while, but I have never seen the data that this student uncovered before and look forwrad to some of the outcomes.</p> <p><strong>Homework</strong> - although this is a stayed theme, this student looks determined to get some really rigours data on what is going on here. I for one am keen to see the results, because I think perception might be different from reality. This data collection is being well planned so that students in our school will log the time they spend over the period of a week. I have a feeling I might be taking this oroject to a staff meeting!</p> <p><strong>Flexibility</strong> - Nice! This will be a primary data collection exercise exploring how flexible we are and what the factors that cause that might be. </p> <p><strong>US Election results</strong> - Wow - some fascinating figures coming out of this one so far on the 2016 Presidential election. This is the kind of work journalists are doing everywhere (and often badly). it couldn't be more relevant.</p> <p><strong>University enrollment</strong> - What factors affect this in different parts of the world.</p> <p><strong>Cancer type prevalance</strong> - This promises to be fairly sobering reading so far. Personally I wonder what differences there are between reality and public perception on this topic.</p> <p><strong>Murder rate</strong> - I have seen this as a bsis before, but this one will focus on links with urbanisation which could be intriguing</p> <p><strong>The Rolling Stone top 100 songs</strong> - A music fan will be breaking these down to figure out what they have in common - or not as the case may be. </p> <p>and seven more.....</p> <p>I know it will be hard work and won't all go well, but I like this stage when students seem genuinely interested in the idea of a mathematical investigation.....</p> <p>Work on the re write of the IA section continues.......</p> https://www.thinkib.net/mathstudies/blog/23433/this-years-projects#1495148400Project Planning
https://www.thinkib.net/mathstudies/blog/23405/project-planning
Fri, 05 May 2017 00:00:00 +0100]]>Project Planninghttps://www.thinkib.net/cache/blog-thumbs/21/23405-1493989127-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/23405/project-planning
<h2>Project Maps</h2> <p>Just a quick post! As one class gets through exams, the other is starting to think about projects. Here is a new image I made to help them brainstorm ideas! More to come soon in the IA section. I spent far too long on it, but I was happy with it....</p> <p ><img src="https://www.thinkib.net/cache/blog-thumbs/21/23405-1493989127-thinkib.jpg" alt="Project Planning" /><br /><br /></p> <p ></p> https://www.thinkib.net/mathstudies/blog/23405/project-planning#1493938800StudyIB.net
https://www.thinkib.net/mathstudies/blog/22937/studyibnet
Sat, 11 Mar 2017 00:00:00 +0000]]>StudyIB.nethttps://www.thinkib.net/cache/blog-thumbs/21/22937-1489226175-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/22937/studyibnet
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/22937/studyibnet#1489190400Percentage perception
https://www.thinkib.net/mathstudies/blog/22414/percentage-perception
Wed, 14 Dec 2016 00:00:00 +0000]]>Percentage perceptionhttps://www.thinkib.net/cache/blog-thumbs/21/22414-1481718583-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/22414/percentage-perception
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/22414/percentage-perception#1481673600Picture this
https://www.thinkib.net/mathstudies/blog/21597/picture-this
Thu, 01 Sep 2016 00:00:00 +0100]]>Picture thishttps://www.thinkib.net/cache/blog-thumbs/21/21597-1472758376-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/21597/picture-this
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/21597/picture-this#1472684400IB Americas
https://www.thinkib.net/mathstudies/blog/21359/ib-americas
Sun, 31 Jul 2016 00:00:00 +0100]]>IB Americashttps://www.thinkib.net/cache/blog-thumbs/21/21359-1469971965-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/21359/ib-americas
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/21359/ib-americas#1469919600Results!
https://www.thinkib.net/mathstudies/blog/21262/results
Thu, 07 Jul 2016 00:00:00 +0100]]>Results!https://www.thinkib.net/cache/blog-thumbs/21/21262-1467960868-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/21262/results
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/21262/results#1467846000Further Processes
https://www.thinkib.net/mathstudies/blog/20388/further-processes
Thu, 11 Feb 2016 00:00:00 +0000]]>Further Processeshttps://www.thinkib.net/cache/blog-thumbs/21/20388-1455222238-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/20388/further-processes
<h2><span ><img src="https://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> https://www.thinkib.net/mathstudies/blog/20388/further-processes#1455148800Exponential (and tooth) decay
https://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay
Sun, 17 Jan 2016 00:00:00 +0000]]>Exponential (and tooth) decayhttps://www.thinkib.net/cache/blog-thumbs/21/20298-1453029601-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/20298/exponential-and-tooth-decay#1452988800Approaches to teaching and Learning
https://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning
Wed, 07 Oct 2015 00:00:00 +0100]]>Approaches to teaching and Learninghttps://www.thinkib.net/cache/blog-thumbs/21/19754-1444140860-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning
<p ><img src="https://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> https://www.thinkib.net/mathstudies/blog/19754/approaches-to-teaching-and-learning#1444172400Curriculum Review
https://www.thinkib.net/mathstudies/blog/19691/curriculum-review
Thu, 01 Oct 2015 00:00:00 +0100]]>Curriculum Reviewhttps://www.thinkib.net/cache/blog-thumbs/21/19691-1443684008-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/19691/curriculum-review
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/19691/curriculum-review#1443654000To Chi or not to Chi?
https://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?https://www.thinkib.net/cache/blog-thumbs/21/19648-1442846130-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/19648/to-chi-or-not-to-chi
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/19648/to-chi-or-not-to-chi#1442790000Life's Complexities
https://www.thinkib.net/mathstudies/blog/19589/lifes-complexities
Thu, 10 Sep 2015 00:00:00 +0100]]>Life's Complexitieshttps://www.thinkib.net/cache/blog-thumbs/21/19589-1441872658-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/19589/lifes-complexities
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/19589/lifes-complexities#1441839600Sabbatical
https://www.thinkib.net/mathstudies/blog/19267/sabbatical
Mon, 13 Jul 2015 00:00:00 +0100]]>Sabbaticalhttps://www.thinkib.net/cache/blog-thumbs/21/19267-1436359440-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/19267/sabbatical
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/19267/sabbatical#1436742000Chi Squared, regression and causation
https://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation
Tue, 14 Apr 2015 00:00:00 +0100]]>Chi Squared, regression and causationhttps://www.thinkib.net/cache/blog-thumbs/21/18868-1429015580-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/18868/chi-squared-regression-and-causation#1428966000This years projects
https://www.thinkib.net/mathstudies/blog/18737/this-years-projects
Sun, 22 Mar 2015 00:00:00 +0000]]>This years projectshttps://www.thinkib.net/cache/blog-thumbs/21/18737-1427053909-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/18737/this-years-projects
<img src="https://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> https://www.thinkib.net/mathstudies/blog/18737/this-years-projects#1426982400Project Ideas
https://www.thinkib.net/mathstudies/blog/18680/project-ideas
Sat, 14 Mar 2015 00:00:00 +0000]]>Project Ideashttps://www.thinkib.net/cache/blog-thumbs/21/18680-1426321139-thinkib.jpghttps://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="https://www.thinkib.net/cache/blog-thumbs/21/18680-1426321139-thinkib.jpg" alt="Project Ideas" /><br /><br /></p> https://www.thinkib.net/mathstudies/blog/18680/project-ideas#1426291200Perceived Corruption
https://www.thinkib.net/mathstudies/blog/18049/perceived-corruption
Thu, 04 Dec 2014 03:30:00 +0000]]>Perceived Corruptionhttps://www.thinkib.net/cache/blog-thumbs/21/18049-1417688584-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/18049/perceived-corruption
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/18049/perceived-corruption#1417663800Theory of Knowledge
https://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge
Sun, 16 Nov 2014 03:30:00 +0000]]>Theory of Knowledgehttps://www.thinkib.net/cache/blog-thumbs/21/17966-1416145522-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge
<h3><img src="https://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> https://www.thinkib.net/mathstudies/blog/17966/theory-of-knowledge#1416108600Logic Lab
https://www.thinkib.net/mathstudies/blog/17708/logic-lab
Mon, 13 Oct 2014 03:30:00 +0100]]>Logic Labhttps://www.thinkib.net/cache/blog-thumbs/21/17708-1413202944-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/17708/logic-lab
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/17708/logic-lab#1413167400May 2014 Results!
https://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> https://www.thinkib.net/mathstudies/blog/17283/may-2014-results#1407983400The Intuition Line
https://www.thinkib.net/mathstudies/blog/12473/the-intuition-line
Wed, 02 Jul 2014 03:30:00 +0100]]>The Intuition Linehttps://www.thinkib.net/cache/blog-thumbs/21/12473-1404317744-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/12473/the-intuition-line
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/12473/the-intuition-line#1404268200The Problem with Monty Hall
https://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall
Sun, 11 May 2014 03:30:00 +0100]]>The Problem with Monty Hallhttps://www.thinkib.net/cache/blog-thumbs/21/16848-1399827527-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall
<h2><img src="https://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> https://www.thinkib.net/mathstudies/blog/16848/the-problem-with-monty-hall#1399775400IA Moderation
https://www.thinkib.net/mathstudies/blog/16828/ia-moderation
Sun, 04 May 2014 03:30:00 +0100]]>IA Moderationhttps://www.thinkib.net/cache/blog-thumbs/21/16828-1399234650-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16828/ia-moderation
<h2><img src="https://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>https://www.thinkib.net/mathstudies/blog/16828/ia-moderation#1399170600Moderator Notes
https://www.thinkib.net/mathstudies/blog/16777/moderator-notes
Mon, 21 Apr 2014 03:30:00 +0100]]>Moderator Noteshttps://www.thinkib.net/cache/blog-thumbs/21/16777-1398085118-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16777/moderator-notes
<p><img src="https://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> https://www.thinkib.net/mathstudies/blog/16777/moderator-notes#1398047400Revision Resources
https://www.thinkib.net/mathstudies/blog/16218/revision-resources
Mon, 27 Jan 2014 08:45:00 +0000]]>Revision Resourceshttps://www.thinkib.net/cache/blog-thumbs/21/16218-1390229568-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16218/revision-resources
<p> <img src="https://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>https://www.thinkib.net/mathstudies/blog/16218/revision-resources#1390812300La Face
https://www.thinkib.net/mathstudies/blog/16160/la-face
Mon, 30 Dec 2013 17:04:00 +0000]]>La Facehttps://www.thinkib.net/cache/blog-thumbs/21/16160-1388437483-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16160/la-face
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/16160/la-face#1388423040Making Calculators
https://www.thinkib.net/mathstudies/blog/16089/making-calculators
Fri, 22 Nov 2013 07:30:00 +0000]]>Making Calculatorshttps://www.thinkib.net/cache/blog-thumbs/21/16089-1385124034-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/16089/making-calculators
<p> <img src="https://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>https://www.thinkib.net/mathstudies/blog/16089/making-calculators#1385105400IA Issues
https://www.thinkib.net/mathstudies/blog/15939/ia-issues
Thu, 10 Oct 2013 07:50:00 +0100]]>IA Issueshttps://www.thinkib.net/cache/blog-thumbs/21/15939-1381424092-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15939/ia-issues
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/15939/ia-issues#1381387800IA Surveys
https://www.thinkib.net/mathstudies/blog/15911/ia-surveys
Sun, 22 Sep 2013 13:32:00 +0100]]>IA Surveyshttps://www.thinkib.net/cache/blog-thumbs/21/15911-1379875839-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15911/ia-surveys
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/15911/ia-surveys#1379853120Communicating Mathematically
https://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically
Sun, 15 Sep 2013 11:19:00 +0100]]>Communicating Mathematicallyhttps://www.thinkib.net/cache/blog-thumbs/21/15889-1379263193-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/15889/communicating-mathematically#1379240340Rubik's Race
https://www.thinkib.net/mathstudies/blog/15786/rubiks-race
Thu, 29 Aug 2013 07:01:00 +0100]]>Rubik's Racehttps://www.thinkib.net/cache/blog-thumbs/21/15786-1377691368-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15786/rubiks-race
<p> <img src="https://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>https://www.thinkib.net/mathstudies/blog/15786/rubiks-race#1377756060Planning Diary
https://www.thinkib.net/mathstudies/blog/15670/planning-diary
Tue, 13 Aug 2013 13:50:00 +0100]]>Planning Diaryhttps://www.thinkib.net/cache/blog-thumbs/21/15670-1376420879-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15670/planning-diary
<p> <img src="https://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> https://www.thinkib.net/mathstudies/blog/15670/planning-diary#1376398200How many ways to use a Venn diagram?
https://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?https://www.thinkib.net/cache/blog-thumbs/21/15498-1372522240-thinkib.jpghttps://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="https://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>https://www.thinkib.net/mathstudies/blog/15498/how-many-ways-to-use-a-venn-diagram#1372501200The Bat Cave
https://www.thinkib.net/mathstudies/blog/15440/the-bat-cave
Fri, 21 Jun 2013 05:43:00 +0100]]>The Bat Cavehttps://www.thinkib.net/cache/blog-thumbs/21/15440-1371812488-thinkib.jpghttps://www.thinkib.net/mathstudies/blog/15440/the-bat-cave
<p> <img src="https://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>https://www.thinkib.net/mathstudies/blog/15440/the-bat-cave#1371789780Facebook for Schools
https://www.thinkib.net/mathstudies/blog/11987/facebook-for-schools
Sun, 18 Mar 2012 07:04:10 +0000]]>Facebook for Schoolshttps://www.thinkib.net/cache/blog-thumbs/21/11987-1332065050-thinkib.jpghttps://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> https://www.thinkib.net/mathstudies/blog/11987/facebook-for-schools#1332054250Enquiry based activities
https://www.thinkib.net/mathstudies/blog/11818/enquiry-based-activities
Mon, 20 Feb 2012 07:52:51 +0000]]>Enquiry based activitieshttps://www.thinkib.net/cache/blog-thumbs/21/11818-1329735171-thinkib.jpghttps://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.https: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.https: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.https: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.https: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.https: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>https://www.thinkib.net/mathstudies/blog/11818/enquiry-based-activities#1329724371Natural Medium
https://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>https://www.thinkib.net/mathstudies/blog/11814/natural-medium#1329674415Reinventing the textbook!
https://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>https://www.thinkib.net/mathstudies/blog/11585/reinventing-the-textbook#1327231119Networking
https://www.thinkib.net/mathstudies/blog/11309/networking
Sun, 18 Dec 2011 17:06:20 +0000]]>Networkinghttps://www.thinkib.net/cache/blog-thumbs/21/11309-1324238780-thinkib.jpghttps://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>https://www.thinkib.net/mathstudies/blog/11309/networking#1324227980