Friday, June 21, 2013

Book review: Computer Aided Assessment of Mathematics by Chris Sangwin

The book coverChris is the brains behind the STACK online assessment system for maths, and he has been thinking about how best to use computers in maths teaching for well over ten years. This book is the distillation what he has learned about the subject.

While the book focusses specifically on online maths assessment, it takes a very broad view of that topic. Chris starts by asking what we are really trying to achive when teaching and assessing maths, before considering how computers can help with that. There are broadly two areas of mathematics: solving problems and proving theorems. Computer assessment tools can cope with the former, where the student performs a calculation that the computer can check. Getting computers to teach the student to prove theorems is an outstanding research problem, which is touched on briefly at the end of the book.

So the bulk of the book is about how computers can help students master the parts of maths that are about performing calculations. As Chris says, learning and practising these routine techniques is the un-sexy part of maths education. It does not get talked about very much, but it is important for students to master these skills. Doing this requires several problems to be addressed. We want randomly generated questions, so we have to ask what it means for two maths questions to be basically the same, and equally difficult. We have to solve the problem of how students can type maths into the computer, since traditional mathematics notation is two dimensional, but it is easier to type a single line of characters. Chris precedes this with a fascinating digression into where modern maths notation came from, something I had not previously considered. It is more recent than you probably think.

Example of how STACK handles maths input

If we are going to get the computer to automatically assess mathematics, we have to work out what it is we are looking for in students' work. We also need to think about the outcomes we want, namely feedback for the student to help them learn; numerical grades to get a measure of how much the student has learned; and diagnostic output for the teacher, identifying which types of mistakes the students made, which may inform subsequent teaching decisions. Having discussed all the issues, Chris them brings them together by describing STACK. This is an opportune moment for me to add the dislaimer that I worked with Chris for much of 2012 to re-write STACK as a Moodle question type. That was one of the most enjoyable projects I have ever worked on, so I am probably biassed. If you are interested, you can try out a demo of STACK here.

Chris rounds off the book with a review of other computer-assissted assessment systems for maths that have notable features.

In summary, this is a facinating book for anyone who is interested in this topic. Computers will never replace teachers. They can only automate some of the more routine things that teachers do. (They can also be more available than teachers, making feedback on their work available to students even when the teacher is not around.) To automate anything via a computer you really have to understand that thing. Hence this book about computer-assessted assessment gives a range of great insights into maths education. Highly recommended. Buy it here!