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Understanding the Math IA

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I've been having a lot of trouble trying to think of a topic for my math IA, and I think the reason why is that I still don't really understand how I am supposed to approach it.

Is the math IA a "research paper," as in you research a math topic you are interested in and its applications (for example, fourier transform and analyzing sound files) and then write a report on your findings? In this case, the objective is not to come up with original content, but just to understand your topic as much as possible, so that you are able to do the calculations and you can explain the topic in your own words. It doesn't seem like this is what IB wants you to do, from what I've read. They want you to "personalize" the IA somehow..?

Or is the math IA about identifying a very practical problem and solving it mathematically to reach a definitive answer? For example, I can grab a bottle from my desk and decide that I want to calculate the volume of it. Or I try to calculate the length of a road. In this case, it would be more about creative problem solving than learning a new topic. (This seems to be more aligned with what the nightingale IA did, which got a high score). 

Also, how practical should the IA be? Could it be on something more theoretical (for example, exploring the properties of prime numbers, or exploring some theorem) or does it have to connect to something in real life? The problem, I think, is that for something truly practical the math and theory is going to be either too complicated or too simple. I interned at an actuarial department in an insurance company for a short time this summer, and I thought I could learn, on a basic level, how to predict the amount of claims someone or a group of people would make based on multiple risk factors, and possibly use this as my IA topic. I learned about the multiple linear regression model at that internship, but was told that in reality, the data on the claims are not linear or normally distributed and regression doesn't make accurate predictions. Instead, they use a method called "data mining." They said they did use some complicated kind of regression (logistic regression, I think, with a distribution that was either poisson or gaussian, it wasn't normal) for modeling mortality rates. We haven't learned stats yet so most of the stuff feels way over my head =_=. 

I just feel like the instructions for the math IA are so vague. For physics it's simple--you conduct an experiment investigating the relationship between two variables. For the math IA I'm not sure..please help!

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1) Both "research paper" and "practical problem solution" are valid, but not the only, routes to the IA. Both practical and theoretical IAs are ok. You say that Physics the instructions are clear: conduct an experiment. In reality you can also find some existing data or simulation instead of an actual experiment.

2) Explaining the problem / field of math in own words is not enough. Other ways to contribute to the "Personal Engagement" criterion is to also outline your own thinking, in addition to the correct, most direct approach to solving the problem; this shows engagement in solving the problem (as in the example of the Florence Nightingale example you brought up). In IAs where you learn a topic of math rather than solving a specific problem, you can reflect upon the learning process.

You can be slightly TOK-like in examining your thought process, without using any TOK language. In other words, you need to demonstrate that you have converted the math solution/ideas from shared knowledge to personal knowledge. This is my own observation and suggestion rather than a literal interpretation of the criteria.

3) The "Use of Math" criterion wants smooth implementation of multiple topics of syllabus, so even if you go really deep into linear regression and never talk about anything other than statistics, you won't score very high in this criterion. When picking a topic, rather than worrying too much about the depth of topics, look at how many different topics of math you can incorporate (such as statistics and calculus, for example). IAs that involve the more complex ideas in the Core HL or Options are often sufficient in depth. 


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