# Mathematical question spaces

conference contribution

posted on 31.03.2009, 13:29 by Christopher J. SangwinIt is uncontroversial to assert that learning mathematics is only effective when
it is an active process on the part of the learner. Setting questions is a
ubiquitous technique to engage students, and answering such questions
constitutes a large proportion of the activity they undertake. Indeed, asking
students questions is a central part of all theories of learning.
This paper examines in detail the process of randomly generating versions of
mathematical questions for CAA. In doing this we examine not only a single
mathematical question, but how such questions are linked together into
coherent structured schemes. Two important pragmatic reasons are often
cited by colleagues for wishing to generate a random sequence of questions.
• Randomly generated questions may reduce plagiarism
• Distinct but equivalent questions may be used for practice Even if giving each student a distinct problem sequence reduces plagiarism,
professional experience unfortunately demonstrates it is not eliminated.
However, some students are well aware of the potential benefits of
collaborative learning, possibilities for which are traditionally hard to provide in
the mathematics classroom. As one student commented in their feedback
evaluations:
"The questions are of the same style and want the same things but they are
subtly different which means you can talk to a friend about a certain question
but they cannot do it for you. You have to work it all out for yourself which is
good."
Notice here the student voices the opinion that the questions "want the same
things but they are subtly different". In this paper we address exactly this
issue, by examining equivalent mathematical problems in some detail.

## History

## School

- University Academic and Administrative Support

## Department

- Professional Development

## Research Unit

- CAA Conference