Posts Tagged ‘procedural understanding’

How are we questioning our students?

December 14, 2015 Leave a comment

This month’s maths journal club is based in the article “Contrasts in mathematical challenges in A – level mathematics and further mathematics, and undergraduate mathematics examinations.” By Ellie Darlington

I found the article quite interesting overall. It looks at the differences in examination questions between A level mathematics and undergraduate mathematics. It starts off with the idea that A level mathematics is tested in a manner that involves routine questions and that as such this doesn’t prepare students for undergraduate mathematics, which it presumes is tested in a higher level. I think this is one of the issues with A level mathematics and I hope that when the new curriculum appears this will have been addressed. The problem is even worst at the transition point between GCSE and A level though, but again, I have hope that the new specification will address this.

Interestingly, my own experience of undergraduate mathematics was that there were a lot of courses that were tested in a routine manner, and that learning the lecture notes by rote and practicing the past papers for a course could allow people to score well despite not understanding what was going on and not being able to apply their knowledge in other contexts. There were some of my peers who had no conceptual understanding of some of the modules yet still scored high enough to achieve firsts.

That said, I still feel that the procedural nature of the GCSE and A level papers is a massive problem. In recent years we have seen a change in the A level papers towards questions that are not answerable in a routine manner, but it needs to go even further.

There are many problems with these procedural questions. My main issue is they allow students to score well without understanding the mathematics behind the questions. This in turn can allow teachers to skip teaching for a relational understanding and just teach an instrumental or procedural understanding, which lets down the learners, especially if they are hoping to go into mathematics or another mathematical based subject at higher education.

So what can we do?

Well, rather than waiting for the changes we can be implementing these questions in our classrooms, ensuring that we are teaching for relational, or conceptual, understanding rather than teaching purely procedures. Take the time to ask the questions that require application in new contexts. Take the time to teach the concepts, the why behind the what. Enrich the curriculum with tasks that involving thinking outside the box and questions framed in a way that the correct method isn’t always immediately obvious, perhaps try some of these puzzles?

Other points in the article

There was a lot early on that I thought I already knew, but it was nice, and useful, to see references and studies to back up some of the ideas.

The MATH taxonomy in this explicit form is new to me and I’m interested to look further into it and see how I can apply it myself.

I was a little purplexed to see that the article stated that questions can change their position on the MATH taxonomy with time, but then have no explanation of how these questions were classified in the research.

All in all a very interesting read that I will re-read and digest in more detail later. I’d love to hear your thoughts on it also.

This post was cross posted to the BetterQs blog here

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