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Math IA Topic -- Too simple?


MarieClaire

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Hi everyone,

My research question for my IA is:

What is the correlation between the number of hours of sleep and academic performance in mathematics?

I know with this I will be able to get more points in personal engagement but I'm worried it's too simple for mathematical knowledge and I'm afraid my teacher might reject this topic.

Are there any ways to increase the complexity of the topic and what kinds of maths/equations would I be able to do with the statistics/data I collect?

Thank you in advance for your help! :)

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I think this IA is complicated, but not mathematically complex. What I mean is you may spend a lot of effort to analyze the data points properly, but the results might not carry a lot of math content. I think you should not choose a topic simply for personal engagement, and the idea is that personal engagement should be embedded in your IA naturally, but that is only secondary to having quality math. 

Statistics is perfectly fine at SL but you need to make sure you do a bit more than plugging numbers into a formula. A better statistical analysis would be to do something in which you can produce a datapoint very easily, without relying on surveys. I'll give the example. The Geiger-Marsden experiment was shooting alpha particles at gold foil that surprisingly had some alpha particles bounced straight back. Once the experiment is set up, it doesn't take too long for them to collect thousands of data points. Then they concluded that the nuclei must be positively charged. The scientists were able to use statistics to justify a physical fact. I chose that so I you can still independently choose a topic and still get my point. 

Some ways to show personal engagement include: reflect upon the math and see if it makes sense or look for alternative approaches, explain a complex idea in your own words or relating to math in syllabus (eg comparing a statistical tool you learned just for the IA to one that you already know), document your trials and errors and your learning process in the IA, etc. It should be noted that personal engagement only reward you for your time spent if it's clear you demonstrate personal thinking and problem solving. 

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This is a very common topic (hours of sleep vs GPA). Very simple to do. In addition to a linear regression of the 2 variables, I would also include a cumulative frequency graph of the hours of sleep from your data and calculate the probability for getting "good" sleep (e.g. 8 hours or more). If you really want to go further and ensure a high score on the Criterion E (mathematical understanding), I would take this probability of getting good sleep and applying a binomial probability to find the expected number of people in a group of 30 people who get good sleep. Also, if you can apply the binomial probability for finding x out of n people who get good sleep.

The above all sound really confusing for sure. So, if you can do the following problem without difficulty then you can apply the same principles in this problem to your IA: https://drive.google.com/file/d/0B4cD6yF7p2DeRGFIWFZRRDRqT0E/view?usp=sharing Make sure you understand how to do this question. Once you do, taking these concepts and applying them to your IA become really simple.

You've stated that you CAN get more points for Personal Engagement but you haven't explained HOW you will do so. Merely getting some data for students and putting a linear regression will get you at most 2 out of 4 points on Personal Engagement. You really have to think about this one. Let me know if you have any ideas.

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