# Project Problems

### Introduction

The following is a list and description of some of the most common problems there are involved with choosing and completing projects, along with some ideas about how to overcome them. It is intended for primarily for teachers and as a guide that could be close to hand through out the process. No two schools, classes or students are the same and as such this list cant cover all, but could provide some useful warnings and will hopefully continue to evolve into a useful list.

The 'Project Planner' pages consist of tasks to help students overcome some of these particular difficulties.

### The project curve

By way of a little mathematical modelling and conjecturing it is my view that the Maths Studies project follows an exponential growth curve like the one below! Greater time input is required for less progress in the beginning. Once the clarity and planning exists, students should just be executing tasks and as such making more progress. Obviously this argument hinges on the definition of the word progress!

### Choosing a project

Probably the hardest part of the whole process and unfortunately the bit that has to be done first. It can be very hard for students to narrow down a focussed theme for a Mathematical investigation and a good chunk of time should be allowed to get this bit right. Here is a bullet point list of things that can be done to help with this process.

• Spend some time considering the very nature of 'Mathematical investigation', its different forms and purposes. Look at the page on 'Project Inspiration' for some help with this. It is important to consider what is meant by this concept and what possible outcomes can be
• Look at as many previous projects as possible. Previous projects can really help with the definition above and provoke ideas. Spend time discussing the themes or reading them if they are available and ask searching questions of them. There is a page on 'Possible Ideas' that could be useful here.
• Consider using the 'Choosing a theme' task or something similar to help narrow down some ideas based on students' areas of interest. Occasionally a spontaneous idea will occur and develop, but often a structured approach to choosing is more productive.

### Clarity

Clarity can be very difficult to achieve for any of us, but without it, work can be very frustrating and lack direction. As much as possible it is important for students to have a clear vision of what they are attempting to do with their projects and how they are going to do it. That is not to see they need to have a clear vision of what will happen during the process or what they will find out, but more that they know the questions they are trying to answer and the way in which they are going to try and answer them. If students proceed without this clarity then progress is often slow and aimless.

### Planning

Combining a good idea with a clear vision is a great start. What must follow is a cast iron plan. Mismanagement of tasks and time (which often results from lack of the clarity mentioned above) is the single biggest handicap for students with these projects. The tasks are hard to quantify in terms of time, which does not make planning easy but it is more easily underestimated than anything else. As time runs out, bits of the investigation tend to get cast aside and the time for reflection, adjustment and accuracy disappears and the result is often 'nearly' a good project. Consider using the 'Planning and Scheduling' task for students.

### Statistics or not?

It can be quite hard to distinguish between these two types of tasks especially when both of them will involve an 'Information collection' element. The collected information can almost always be analysed with statistics. The essential difference is that 'Statistical' projects generally refer to use of data that is not generated mathematically, although this could arguably be said of data collected for mathematical modelling that would come under the heading of 'Non-Statistical'. In a sense it is not really important to make the distinction, but more important to be aware that information can be gathered mathematically as well. Students should be aware of the different options here and that consequent difference in the type of analysis that can be done.

### Identifying potential

Turning a good idea into reality can be very challenging. Going from statements like 'I will analyse the data to look for a link....' to very specific statements about tasks, processes and data is often something students find very hard. This is often a consequence of the 'Grand Idea' where the overall aim of a project idea is so big that it is hard to breakdown into smaller parts. In the project planner, students are asked to consider identifying specific potential very early on in the piece and definitely before they have started the data collection.

### Information Collection

It needs to be mentioned on this page that information collection is a major stumbling block that should be given very careful consideration before any work is done or decisions made. There is a big section on the site about this that explains some of the pros and cons of different ways of collecting information and again, a specific related task for students in the project planner.

### Word count

This is often one of the first occasions that students realise that it can be at least as difficult if not more so to keep a word count down to a given number than it is to reach it. The guidelines suggest that 2000 words is a suitable length for a project and that requires students to be particularly succinct! This, of course, can be difficult for them when writing about maths. The standard student response to being asked to write about maths is often a lot of general or waffly remarks that are not helpful or necessary and have the overall effect of reducing the quality of communication. It is worth considering that this is not surprising given how rarely students are asked to write about mathematics. One response is to create more chances to do so throughout the course so that it is not so rare. Another is to ask students to read eac hothers work regularly to help them to see this for themselves.

### Keeping a Theme

It can be difficult for students to ty their work all together under a particular theme. There is no particular requirement for them to do so but a project is almost always of better quality and is generally more coherent and interesting when it does. An initial idea can be narrowed down to some specific investigations and the challenge is for those to be in some way sequential or related. Students need to reflect on this regularly through out the project period. In the project planner there is a task that asks them to imagine writing a newspaper article about their project. What would the headline be? What would the conclusion be? This type of thinking can help students to 'keep a theme'.

### Validity

The concept of Mathematical validity is definitely a very tricky one and as such hard for students to score on! For students benefit I have tried to describe the follow two categories for discussing mathematical validity.

• the nature of the information used questions the validity of the conclusions reached
• the process used or the way it was used or the place in which it was used was not valid

Students tend to find the former easier to do than the latter. It is a good idea to try and show students examples of this as early as possible to help them remember to consider it as they work.

Examples could include;

• Considering validity based on the expected frequencies in an independence test.
• reading from regression line outside the range of the data used
• plotting and/or using a line of best fit when there is no correlation to speak of.

### Choosing Processes

What processes should be used at what times? This is a key difficulty that relates to a couple of key points;

• students attempting to use as many processes as they can will go looking for opportunities to use the process
• do students really have a good grasp of the statistical processes in question?

Whilst there is definitely merit in the former, the risk is a formulaic approach to projects that will result in a less interesting project. The ideal is that a project idea suggests that it would be interesting to test if two given data sets were independent from each other rather than looking for two different data sets that you could use for an independence test. Either way the concept of an independence test needs to be properly understood before it can be successfully applied and this begins address the second point. In the Statistics teaching ideas, there is an activity that asks students to reflect carefully and research the different processes they have learned so that they understand what they are for and when it is appropriate to use them. Work like this done during the course can be really helpful at these times.

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Grant Fossum 17 January 2017 - 18:41

I am having a fundamental issue with part of this project. I get that when the correlation coefficient is low they should not go further to regression, but what I don't get is why and how they should do chi squared. I am teaching AP stats this year and those tests are not nearly related as this project appears to make them out to be. Do you have any advice?

Jim Noble 19 January 2017 - 08:29

Hi Grant!

Good question - One that comes up a lot. I have answered it before here in this blog post - thinkib.net at least I think that answers your question. Let me know - Thanks, Jim

Grant Fossum 19 January 2017 - 12:01

Hey Jim,
So I love the blog, and my thinking is like yours; however I think that contradicts the IBO. In the examples they give if the r is low, they use chi. What do you advise students to do if their correlation coefficient is low? Here is the direct quote from them regarding a correlation study "It may well be that the correlation coefficient has such a low value that the conclusion
is that there is “no correlation” between the variables. In this case the student should
be encouraged to investigate whether the variables are in fact statistically independent
and use a chi-squared test to test this hypothesis."

Jim Noble 23 January 2017 - 07:12

Thanks Grant - Personally I think that is not a great - and like I suggest in the blog, I question the validity of that and would begin to think of it as irrelevant. The key issue is that students want to get credit for a further process and they should be looking to do this in the context of a relevant meaningful project. I encourage students to investigate 'Themes' rather than'one question' so that they might be looking for things that have an impact on eg 'Homicde rates', they can scatter it against a numerical data field and look for independence against a categorical one. Of course, the full PMCC calculation qualifies as a further process so, students can get that credit by doing that, even if the outcome is a low value of r. I remain skeptical about PMCC and Chi² with the same data..... happy for the debate to continue

Grant Fossum 27 January 2017 - 16:33

Jim, I agree with you completely, but I guess I am concerned then about the grading from IB. If I don't encourage this from my students am I holding them back? Where all would they take the points, probably from process (not including all relevant) and from conclusions?

Jim Noble 30 January 2017 - 07:40

Hi Grant - No, not holding them back at all in my opinion, a student is held back if their information does not have potential for different avenues. If a candidate has their hopes pinned on using chi² for a further process then they should have categorical data that lends itself to such a process. There is non requirement for students to do both regression and chi². Ultimately of course, it is your call, and you must do what you are comfortable with and what you think you can justify in your comments. I think that is always the most important factor......