CM . . .
. Volume XXIV Number 27. . . .March 16, 2018
Moving Math: How to Use Thinking Skills to Help Students Make Sense of Mathematical Concepts and Support Numeracy Development.
Mary Fiore & Maria Luisa Lebar.
Markham, ON: Pembroke, 2017.
122 pp., trade pbk. & pdf, $24.95 (pbk.), $21.95 (pdf).
ISBN 978-1-55138-325-5 (pbk.), ISBN 978-1-55138-925-7 (pdf).
Mathematics-Study and teaching (Elementary).
Numeracy-Study and teaching (Elementary).
Critical thinking-Study and teaching (Elementary).
Review by Thomas Falkenberg.
Numerate learners use their knowledge and understanding of mathematics to make sense of the world around them so they can participate as reflective and competent citizens in a rapidly changing world. To help us make sense of what this means for the teaching and learning of mathematics, we reflected on how we support literacy development. We soon realized that effective mathematics instruction is closely linked to effective literacy instruction.” (p. 22)
Teachers often refer to the big ideas in mathematics, but we offer an innovative variation on that. The big ideas are those statements that link mathematical concepts between various math topics or strands . . . . We are proposing that teachers consider the Bigger ideas: the mental actions or processes associated with the thinking skills noted. As we have designed them, the Bigger ideas can help teachers and students make connections between the thinking skills to support mathematical thinking and the development of numerate learners.” (p. 11)
Moving Math is a professional development book for school teachers in the area of mathematics teaching. While the examples are chosen for K-8 teachers, the approach to mathematics teaching that the authors propose in their book can – and should – be seriously considered by mathematics high school teachers as well. As the first quote above suggests, the authors build their approach to mathematics teaching on their understanding of literacy teaching. This idea goes back to their earlier book, The Four Roles of the Numerate Learner, in which they derive four clusters of competencies of numerate learners from the four clusters of competencies they have identified for literate learners. A numerate learner is: a sense maker; a skill user; a thought communicator; and a critical interpreter. What the current book complementarily adds to this understanding of a numerate learner is reflected in the second quotation above: the capability of using thinking skills when engaging mathematically with problems. The authors introduce seven such thinking skills: inferring and interpreting; making connections, analyzing; evaluating; synthesizing; reasoning and proving; and reflecting. The book is then all about explaining and illustrating how engaging students in and developing further these thinking skills can help students “make sense of mathematical concepts and support numeracy developments,” as the book’s subtitles suggests.
The first three chapters of the book provide the conceptual and theoretical framework for the development of the seven thinking skills in mathematics teaching. Here, the authors discuss the “transformative role” (p. 16) of professional learning (chapter 1), a vision for mathematics teaching and learning which is grounded in a concept of the numerate learner and the development of thinking skills (chapter 2), and different approaches that help create “learning experiences that allow for sense making” (p. 33), like responsive instruction and inquiry-based learning (chapter 3). The remaining seven chapters deal each with one of the seven thinking skills. In each of these seven chapters, the authors introduce first what they call the bigger ideas linked to the respective thinking skill, like the bigger idea that “combining and integrating ideas will lead to the creation of a new understanding” (p. 79) in the chapter on synthesizing. Then they link the bigger idea to the teaching and learning of mathematics, provide suggestions on how students can be helped in engaging and developing the respective thinking skill, and then provide criteria to help teachers know when their students engage the respective thinking skill. The remainder of each chapter is filled with concrete examples how the respective thinking skill can be used and developed in grades 1-3, 4-6, and 7-8, respectively. The book’s chapters are enveloped by an introduction and a conclusion section.
In Moving Math, the authors expand on their earlier work to include the development of thinking skills that are of a subject-area-transcendent nature into their understanding of a numerate learner and, thus, into the teaching and learning of mathematics. The conceptual and theoretical framework for professional development of teachers of mathematics that the book provides is well-developed. The authors provide a substantial reference list that demonstrates how the framework is grounded in scholarship and research, and that list can be beneficial to professional developers and teachers of mathematics if they choose to read further on ideas presented in the book. In line with their earlier book, in Moving Math, the authors provide again an approach to the teaching and learning of mathematics that is guided by a rich understanding of what it means for a learner to be numerate, or, as others call it, mathematically literate. While this rich vision of the numerate learner can be found in the front parts of Canadian mathematics school curricula, where the goals and visions of school mathematics are explicated, it is – unfortunately – too rare the case that this vision guides the teaching and learning of mathematics education in the times of PISA and PCAP outcome anxiety. Moving Math, as its predecessor, The Four Roles of the Numerate Learner, provides a conceptual and theoretical framework that stands against a narrow vision of success in school mathematics and holds against it a rich and complex vision of the numerate learner that fits much better with a vision of school education as citizen(ship) education. The practical nature of the book, with concrete examples for learning activities, teaching and assessment practices, makes the book a very valuable resource for teachers and teacher educators who want to develop a rich(er) vision of numerate learners and the practical competencies to support their development.
Thomas Falkenberg, a professor in the Faculty of Education at the University of Manitoba, teaches mathematics education courses in the faculty’s initial teacher education program.
© CM Association
University of Manitoba
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