I am going to carry out a small scale action research on ratio problems. I would ask the same questions in different ways and see whether wordings would affect students' performance. However, past research showed that numerical values would affect questions' difficulty. Say comparing (1:2 and 1:4) and (3:7 and 5:11), the latter one is obviously more difficult.

How can I control for the numerical factors so that I can make inferences on "problem wordings"?

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    $\begingroup$ Why not just use the same numbers and vary only the wording? If that isn't adequate, you need to look into the theory of experimental design, something like: en.wikipedia.org/wiki/Factorial_experiment $\endgroup$ – John Coleman Sep 30 '17 at 12:02
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    $\begingroup$ What is an action research? $\endgroup$ – Ben Crowell Sep 30 '17 at 13:53
  • $\begingroup$ The first step should probably "Be able to clearly state exactly what you want to do. " I am not sure what you want. For example, what does "Comparing 1:2" mean? How would you like me to compare 3:7? $\endgroup$ – Michael Oct 15 '17 at 15:26
  • $\begingroup$ @Michael Thanks for your reply! By the word “comparing”, I mean comparing the unit rate. The former is obvious that 1:4 is greater while the second one students may have to compare the fractions 7/3 and 11/5, which supposed to be more difficult. $\endgroup$ – IDontKnowMath Oct 15 '17 at 15:45
  • $\begingroup$ I see. Well if you want to "control for something" you need to keep those characteristics the same and change only the thing you want to judge the effect of. Give multiple people the questions, in the same order, with the same numbers. Give everyone the same amount of time, etc...(You probably want to randomly switch up the order of questions to try to eliminate the effect of people getting tired of answering multiple questions) Try hard to make the only thing different be the wording. And then hopefully any differences you see among the answers will be due to the wording. $\endgroup$ – Michael Oct 15 '17 at 16:19

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