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Quick Research Advice


pheonix46

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Hi guys,
 
I am working on my Masters Thesis methods section and need some advice.  I am looking  for a math related concept or task that has the following traits. (math is not my specialty so I figured asking the experts might me more beneficial then going it alone)
 
1.Multiple identifiable difficulty levels
2.The difficulty levels have to be verified in some way
      -Such as subject matter expert ratings
      - Some sort of research study that has identified the difficulty
      - A previously validated pool of items (as in a good number of participants have all taken the items and we can thus find the average difficulty and put them into level)
       - I am sure there are other ideas that might work
3. I have to be able to teach the concept/task (to undergrads)
 
For example, summation notation might be an example (in this case I would not know were to find the questions)
 
Does this make sense?
 
In essence there are two groups. A control that gets a normal type of training and practice time and an experimental group. The experimental group will be taught a concept (e.g., summation notation etc) and then take a test to measure their ability level. They will subsequently be categorized into levels based off their ability (into level that correspond with their ability) and will be moved around the questions like they might be in an adaptive test. Specifically,  if they get a question right they would move up in difficulty and vice versa.
 
 
When you get a chance, any ideas would be very helpful.
 
Thank you for your time!
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