Computer Aided Assessment of Mathematics

Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.

Chris Sangwin is a Senior Lecturer in the School of Mathematics at the University of Birmingham in the United Kingdom. From 2000-2011 he was seconded half time to the UK Higher Education Academy "Maths Stats and OR Network" to promote learning and teaching of university mathematics. In 2006 he was awarded a National Teaching Fellowship. His learning and teaching interests include (i) automatic assessment of mathematics using computer algebra, and (ii) problem solving using Moore method and similar student-centred approaches. Chris Sangwin is the author of a number of books, including How Round is Your Circle (Princeton University Press, 2011), which illustrates and investigates many links between mathematics and engineering using physical models.