Teaching Mathematics and its Applications Advance Access published online on April 24, 2008
Teaching Mathematics and its Applications, doi:10.1093/teamat/hrn005
Using technology to facilitate reasoning: lifting the fog from linear algebra
Addresses for Correspondence: John S. Berry, PhD, The Centre for Teaching Mathematics, The University of Plymouth, Plymouth, Devon PL4 8AA, England. Tel: +01752 232772, E-mail: jberry{at}plymouth.ac.uk
Douglas A. Lapp, PhD, Department of Mathematics, Central Michigan University, 214 Pearce Hall, Mount Pleasant, MI 48859, USA. Tel: +989-774-5393, Fax: +989-774-2414, E-mail: lapp1da{at}cmich.edu
Melvin A. Nyman, PhD, Department of Mathematics & Computer Science, Alma College, Alma, MI 48801, USA. Tel: +989-463-7264, Fax: +989-463-7079, E-mail: nyman{at}alma.edu
Submitted March 2008; accepted March 2008
This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological interventions to address these barriers.
John S. Berry is Professor of Mathematics Education at the University of Plymouth, Plymouth, Devon PL48AA, UK. His research interests are in mathematics education, particularly students' development and understanding of key concepts, cooperative learning in mathematics, the use of hand-held technology and symbolic algebra in learning and teaching mathematics. As well as being research active, John is the Mathematics Professor in Residence at Wells Cathedral School, Wells, Somerset, UK working with the able and talented pupils in the School. John is a mathematics education consultant working with gifted and talented students as part of the South West Gifted and Talented Education programme and delivers Professional Development courses for teachers nationally and internationally.
Douglas A. Lapp is Professor of Mathematics and Mathematics Education at Central Michigan University, Mount Pleasant, MI 48859, USA. His research interests are in the use of multiple representations involving technology for teaching mathematics concepts. In particular, he studies the use of computer algebra systems and dynamically connected representations and their connection to student discourse. In addition to his research, he also provides professional development for teachers across the USA on the use of hand-held and computer technologies.
Melvin A. (Mel) Nyman is Professor of Mathematics and Chair of the Department of Mathematics and Computer Science at Alma College, Alma, MI 48801, USA. Recently his primary research interests are in the teaching and learning of undergraduate mathematics. An interest in mathematical modelling, especially as applied to problems in the biological and social sciences grew out of his teaching of undergraduates in liberal arts colleges. He has collaborated with marine botanists in several projects modelling the growth and development of seaweeds.