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Teaching Mathematics and its Applications Advance Access originally published online on January 30, 2009
Teaching Mathematics and its Applications 2009 28(1):21-31; doi:10.1093/teamat/hrn023
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© The Author 2009. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Open-start mathematics problems: an approach to assessing problem solving

John Monaghan{dagger}

Centre for Studies in Science and Mathematics Education, School of Education, University of Leeds, Leeds, UK

Peter Pool

Centre for Studies in Science and Mathematics Education, School of Education, University of Leeds, Leeds, UK

Tom Roper

Centre for Studies in Science and Mathematics Education, School of Education, University of Leeds, Leeds, UK

John Threlfall

Centre for Studies in Science and Mathematics Education, School of Education, University of Leeds, Leeds, UK

{dagger}Email: J.D.Monaghan{at}education.leeds.ac.uk

Submitted October 2008; accepted November 2008

This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics teaching. The article provides a brief review of problem solving and describes open-start problems in detail. The article then considers how open-start problems could address some important concerns in the teaching and assessment of mathematics and raises issues with regard to the future use of open-start problems in assessment.

John Monaghan is Professor of Mathematics Education in the School of Education, University of Leeds. John enjoys both research and teaching and aspires to research that is of eventual use to both learners and teachers of mathematics.

Peter Pool is Senior Research Fellow in the School of Education at the University of Leeds. After many years teaching and teacher training, he is now involved in assessment and specializes in mathematics test development.

Tom Roper is a senior lecturer in mathematics education and Head of the School of Education. Tom wishes he had more time for the former.

John Threlfall is Senior Lecturer in Primary Mathematics at the School of Education, University of Leeds, and also Director of the School's Assessment and Evaluation Unit. His teaching and research spans both mathematics education in schools and the field of educational assessment.


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