Broadening the Scope of Research on Mathematical Problem Solving

This extensive volume, appearing in Springer’s Research in Mathematics Education Series, is a welcome addition to the field of research in mathematical problem-solving. The 25 chapters of the book were solicited from participants of an international conference held in 2014 and a few additional invited contributors. The conference, organized by the University of Algarve and the Institute of Education of the University of Lisbon, to share the work and research results of the Problem@Web Project along with emerging research in the areas of technology, creativity, and affect and aesthetics in problem-solving. The purpose of the conference was to shine a light on these three strands of research, which the organizers felt needed more attention from the problem-solving research community. While the Problem@Web Project studied extra-curricular mathematical problem-solving in the context of inclusive internet-based mathematical competitions, this collection includes classroom-based studies, as well.

 

The introduction by the editors provides a brief, yet thorough overview of the research “shoulders” upon which research in technology, creativity, and affect in problem-solving sits and a foreshadowing of the contents of the main text. The book is naturally divided into three main sections, focusing on Technology, Creativity, and Affect and Aesthetics – each beginning with introductory chapters emerging from the conference keynote addresses – and conclude with a chapter (by Arthur Powell, Pietro Di Martino, and

Roza Leikin, respectively) reflecting on the work presented and pointing out directions for future work. The final chapter provides a synthesis by Viktor Freiman, tying together the three strands of this collection through the historical context of recreational puzzles, including a fascinating glimpse at years of correspondence between Gauss and the astronomer H.C. Schumacher on the Eight Queens Puzzle.

 

This collection is a valuable resource for researchers and non-researchers alike – researchers will find insights on which to build further inquiry and just about all mathematicians and mathematics educators (regardless of research area) will find many problem-solving gems that will tantalize students and professionals alike. If the experience of this reviewer is any indication, readers will find themselves continually sidetracked by the urge to work on the plethora of well-crafted activities, themselves, and to marvel at the approaches taken by students.

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Steve Benson is a Professor of Mathematics at Lesley University and co-Director of the Master of Science for Teachers program at the University of New Hampshire. Dr. Benson received his Ph.D. in Mathematics from the University of Illinois under the supervision of Dr. Leon R. McCulloh.  Initially “trained” in Algebraic Number Theory, his scholarly pursuits have ranged from elementary group theory and number theory to problem solving and mathematics education, especially the preparation of teachers.