What Are the Benefits of Incorporating Redundancy in Math Test Questions?

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Incorporating redundancy in math test questions can enhance students' understanding by challenging them to discern relevant information from extraneous data. This approach mirrors real-world scenarios where not all provided information is useful. The discussion highlights that creating original problems can deepen comprehension, as students must apply their knowledge to formulate effective questions. Additionally, the proposal encourages instructors to engage students with specific topics, such as permutations and random variables, to assess their mastery. Overall, integrating redundancy in math assessments can lead to a more robust evaluation of student knowledge.
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Homework Statement


I have the proposal of making a math test thread in which instructors test student's knowledge in a specific topic. If you agree then post the same thread.

For example: you have the topics that will be covered in your next exam such as permutations, combinations, bayes theorem, random variables etc. Then some instructor will proceed to challenge your knowledge in those topics with questions.

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The Attempt at a Solution

 
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Could you elaborate on this, I don't exactly understand.
Can you make a specific example?
 
There is a wealth of problems already in these Forums. Just search the topic.

That said, I notice that when students do make up problems for themselves and post them, plus attempted solutions, it is frequently the case that the problems just don't 'work'. This suggests that having to devise problems is an even better test of understanding than solving them.

One area that is perhaps under-probed by the usual questions is redundant information. Relatively few throw in red herrings, so forcing the student to figure out which data are relevant. In the real world, that happens all the time.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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