________________ CM . . . . Volume XV Number 20 . . . . May 29, 2009

cover Math Memories You Can Count On: A Literature-based Approach to Teaching Mathematics in the Primary Classrooms.

Jo-Anne Lake.
Markham, ON: Pembroke, 2009.
128 pp., pbk., $24.95.
ISBN 978-1-55138-227-2.

Subject Headings:
Mathematics-Study and Teaching (Primary).
Mathematics and literature-Study and Teaching (Primary).


Professional.

Review by Thomas Falkenberg.

**** /4

excerpt:

Using children’s literature to pose a variety of problems drawn from real-life experiences helps teachers move from direct instruction to inquiry-style instruction where students discover properties of numbers and relationships.(p. 14)

Questions naturally emerge from the text and illustrations within each book. Hands-on math activities developed from the literature provide children with experience in using relevant math manipulatives for developing a foundation for learning concepts that are more abstract. (p. 44)

Throughout Math Memories You Can Count On, I have suggested engaging children’s literature as a springboard for developing meaningful mathematical understandings within and across all five mathematics strands. (p. 103)

Math Memories You Can Count On is a professional book for school teachers. It is about teaching rather than a resource for teaching. The focus of the book, as the title and subtitle suggest, is on the teaching of mathematics in the primary grades using literature, fiction as well as nonfiction. The author, Jo-Anne Lake, has 30 years of teaching experience in Kindergarten to Grade 8 and has also worked in teacher education and in-service settings with experienced teachers.

    In Chapter 1, Lake makes the argument that students’ experiences during their learning of mathematics crucially influence their attitude towards mathematics and, as a consequence, their achievement level in mathematics learning. For this argument, Lake draws on mathematics education research that suggests a positive correlation between students’ attitudes towards mathematics and their achievement level in mathematics learning. She also draws at length on one of her teacher candidate’s ‘math autobiography’ in which the teacher candidate writes about his or her ‘math memories,’ illustrating how the different experiences of learning mathematics during different school years have differently influenced his or her attitude toward the subject as well as his or her achievement in mathematics. The title of the book – Math Memories You Can Count On – is derived from the argument Lake makes in this first chapter.

    How then can teachers help their students to build positive math memories? In Chapter 2 Lake addresses this question. In this chapter, she points out that the reform of mathematics teaching proposes “‘problem solving’ and ‘ongoing communication’ as key components of all effective mathematics learning” (p. 13), and that – contrary to this proposal – many primary school teachers opt for a more traditional environment, focusing solely on textbooks and worksheets. Convinced they do not have a strong ‘mathematics background,’ these teachers employ methods many of us may recognize: low-level questioning, fill-in-the-blank activity sheets, and show-and-tell vignettes (p. 13).

    Lake then suggests that, if primary teachers used children’s literature in their mathematics teaching in the way the book will outline in later chapters, those teachers could address problem solving and ongoing communication and they would feel more comfortable teaching for those purposes because the approach allows those teachers who feel uncomfortable with the teaching of mathematics to draw on the area that they generally feel far more comfortable with - language arts. The use of children’s literature in the teaching of mathematics, Lake suggests, “helps teachers move from direct instruction to inquiry-style instruction where students discover properties of numbers and relationships” (p. 14). Lake then argues how the use of children’s literature can promote problem solving as well as communication competencies, and she provides a few examples of children’s books that can be used for one or the other purpose, using a paragraph to introduce each of the nine books.

In Chapter 3 Lake continues her argument for the benefits of a literature-based approach to the teaching of mathematics, and she lists 10 benefits of this approach, listing one children’s book for each of the benefits and describing how each book contributes to the respective benefit of a literature-based approach to the teaching of mathematics.

    Chapter 4 provides teachers with criteria for selecting and organizing children’s literature for their teaching of mathematics. In order to help teachers select quality children’s books for the teaching of mathematics, Lake provides a list of nine criteria, like, ‘Is there accuracy of content in the text and illustrations?’ and ‘Do the illustrations and text imply easy-to-use math manipulatives to help readers benefit from the mathematics knowledge and understanding embedded in the book?’ For each of the criteria, the author names one (often several) children’s book as an exemplary with respect to the respective criterion. Lake also provides four lenses that she suggests teachers can use to organize the children’s books they have selected for their teaching of mathematics: the big (mathematical) ideas lens, the literary genre lens, the author lens, and the mathematical process lens (referring to processes like problem solving and reasoning). For each of the four lenses, she provides a list of titles of children’s books that fall into the respective category. Important in this chapter is also what Lake calls “The Role of the Teacher (in promoting mathematics learning using children’s literature)” (p. 30). In order to help students to inquire into mathematical ideas, concepts and processes using stories, the teacher has to do more than just read the story. In a side panel, Lake provides strategies for the teacher’s role in form of short instructions, like “Provide opportunities to engage in open-ended discussions about the story” (p. 30). At the end of Chapter 4, Lake lists “seven easy steps for implementing the literature-based approach to teaching mathematics” (p. 33).

    Mathematics education research suggests very strongly for primary grades that students generally develop a deeper understanding of mathematical concepts if they are allowed to explore those concepts by manipulating objects which help concretely represent a mathematics idea or concept. Lake draws on this research in Chapter 5 and argues that a literature-based teaching of mathematics needs to draw on stories that provide students the opportunities to explore the mathematical ideas, concepts and processes in the story with concrete manipulatives. Teachers, she argues, need to then make mathematics manipulatives available to students to explore those very ideas, concepts and processes. In the main part of Chapter 5, Lake discusses different types of manipulatives teachers can use in their literature-based teaching of mathematics, and she provides a number of titles and descriptions of children’s books which invite the use of the discussed manipulatives.

    Chapter 6 is about strategies of assessing and evaluating student learning in mathematics. Different assessment methods, like performance assessment and portfolios, are discussed. This chapter is quite different from all the previous ones in the sense that it is not specific to a literature-based approach to teaching mathematics. I also counted only one reference to one children’s book in this chapter.

    Chapter 7, finally, provides a more extensive description of how a literature-based approach to the teaching of mathematics can be implemented for each of the five mathematics strands of the different Canadian mathematics curricula. This chapter is by far the longest, making up almost half of the book. For each curriculum strand, Lake discusses some of its big ideas, links manipulatives and connected children’s literature to one of those big ideas, provides math centre activities around that big idea together with a recommendation of particular assessment methods, and, finally, provides a brief proposal of how 15 particular children’s books can be used to implement the respective strand.

    The book includes three appendices, the first of which is a list of 127 children’s books, which I assume functions as the reference list for the books referenced in the chapters of the book. The second appendix is the reference list of the professional literature referenced in the different chapters, and the third appendix consists of four reproducible graphic organizers that were used in different chapters of the book to support teachers in their planning of their teaching of mathematics using a literature-based approach and in their organizing of the children’s books they want to use with such approach.

    Overall, Math Memories You Can Count On is an excellent professional resource that is well written and that, in its first chapters, explains well why elementary school teachers should use and in its latter chapters how they can use a literature-based approach in their teaching of mathematics. Particularly, I want to emphasize that the author does not just reference 127 children’s books, but that she demonstrates how the different books can be used in literature-based mathematics teaching. The book will be of great value to those teachers who want to move towards a more literature-based approach to their teaching of mathematics. For those teachers who have already been using a literature-based approach to their mathematics teaching, the book will, I expect, provide additional ideas and resources.

    Math Memories You Can Count On makes clear to the reader that a literature-based approach to the teaching of mathematics does not consist of reading a story with some mathematical ideas, terms or concepts in them to students and then moving from the reading of the story to the more traditional way of teaching mathematics (as characterized above). Rather, the book links the reading of well selected children’s literature (selected for the particular purpose) with a more inquiry-based approach to the teaching and learning of mathematics, drawn from the literature on teaching mathematics for deeper understanding. Here, stories provide a context for mathematical problems, and they play the role of a hook for developing mathematical ideas and engaging students in math talk.

    Some elements in the book, though, are unfortunately pointing in a different direction, and I assume that this is done unintentionally. The author uses a language that sometimes seems to suggest that it is indeed the book or the story that is doing the teaching of the mathematics, as for example when the author writes, “the book teaches children the importance of four basic rules in problem solving” (p. 23) or “the book is an outstanding introduction to adding and subtracting small amounts of money” (p. 27). It is how the teacher engages the students with the story that can provide for such learning, not the story itself. The difference is important to emphasize, because the difference lies in the acknowledgment of the crucial role of the teacher in making a well-selected story meaningful for providing an opportunity for students to engage with mathematical ideas and concepts. As mentioned above, the book has sections about what the role of the teacher in a literature-based approach to the teaching of mathematics is, but this role cannot be overemphasized – especially considering how challenging many primary school teachers find an inquiry-based teaching of mathematics. I wished the author had used some of her wording more carefully with respect to this issue, and that she had not just described what the role of the teacher in the literature-based approach is, but also emphasized that it is a crucial role in this approach.

    The author argues well why an approach to the teaching of mathematics that draws on children’s books to engage students with mathematical ideas, concepts and processes is a very meaningful approach. What I find less convincing, though, is the argument that the use of literature will – almost by default - support the development of positive math memories for students, even if the literature is used to teach mathematics in the way suggested in the book. As many other approaches to the teaching of mathematics, a literature-based approach has the potential to contribute to students’ positive math memories but will not do so by default. It all depends on how a teacher actually implements the ideas for teaching mathematics. Even in a literature-based approach as suggested in the book, students can get frustrated with their struggle to understand mathematical concepts, with the way in which the teacher has them practice mathematical procedures, which a literature-based approach also does not get away from. The long quotation from a student teacher’s math memories in Chapter 1 illustrate quite well the importance of the personal relationship between teacher and student for the type of memories the student’s will have about the subject itself. A high quality literature-based approach to mathematics teaching probably compensates very poorly for a problematic personal relationship between teacher and student with its impact on the student’s math memory. In my view, what should be said on the issue is that a literature-based approach to teaching mathematics as suggested in the book has a better chance than more traditional ways of teaching mathematics to provide students with positive math memories, but that the quality of those memories depends ultimately on many other factors.

    What I find also less convincing in the book’s line of argumentation is the argument that a literature-based approach to the teaching of mathematics will have two advantages for those primary school teachers who have a strong language arts background but do not feel strong enough in the teaching of mathematics or do not use inquiry-focused math instructions. The first advantage, Lake argues, is that such teachers will be able to draw on their strong language arts background to help students with their numeracy skills (Chapter 3). The second advantage that Lake describes is that “using children’s literature to pose a variety of problems drawn from real-life experiences helps teachers move from direct instruction [in their teaching of mathematics] to inquiry-style instruction” (p. 14). It seems to me that Lake underestimates the need of a deeper understanding of the mathematical concepts, ideas and processes required for teachers to teach in the way suggested in the book. A strong language arts background does not diminish that need. Lake writes (p. 13) that it is often teachers’ own experiences of learning mathematics that has them use “low-level questioning, fill-in-the-blank activity sheets, and show-and-tell vignettes” (p. 13), but these approaches to teaching mathematics also provide a more secure way for insecure teachers of mathematics than a more open-ended inquiry approach. The former is far more predictable with respect to what assessment and evaluation of student responses look like than the latter approach. A literature-based approach that engages students in talking and thinking about mathematical ideas in a more inquiry-based approach belongs to the latter rather than the former approaches, and, as such, makes it more likely that teachers who feel they do not have a sufficiently deep understanding of the underlying mathematical concepts and ideas as well as of students’ mathematical thinking around those ideas will feel even more insecure using this approach to teaching mathematics. Nothing removes the need for developing a deeper understanding of mathematical ideas, concepts and processes for teaching mathematics using a more inquiry-based approach, not even a strong background in language arts and the use of children’s literature. For that reason, I want to emphasize that the use of the teaching approach suggested in Math Memories You Can Count On has requirements for the mathematical and mathematics education background of the teacher using the book. For some teachers, that might mean that the book can be only one component in their professional development towards a literature-based approach to their teaching of mathematics.

    Let me mention one other thought that I had when reading Memories You Can Count On. The book is published in Canada and reviewed for Canadian teachers. With the Canadian education system becoming more and more considerate of the language and cultural diversity in Canadian schools, a book that promotes literature-based teaching particularly touches the need to consider English-as-an-additional-language (EAL) and cultural diversity issues. Memories You Can Count On gives consideration to neither of the two.

    The critical points I raised about the book reviewed here should not distract from my view that Memories You Can Count On is an excellent professional book for primary school teachers that I can only highly recommend. It provides an excellent resource for those who want to give consideration to a more integrated approach in their teaching of mathematics and to those who want to take seriously the recommendation from research into teaching mathematics in the early years that says that helping students to make sense of mathematical ideas, concepts and processes depends in those years crucially on helping students anchor those ideas, concepts and processes into concrete contexts. Stories provide an excellent context for mathematical sense making, whether those contexts are ‘real-life’ contexts or imagined contexts.

Highly Recommended.

Thomas Falkenberg is a mathematics teacher educator in the Faculty of Education at the University of Manitoba.

To comment on this title or this review, send mail to cm@umanitoba.ca.

Copyright © the Manitoba Library Association. Reproduction for personal use is permitted only if this copyright notice is maintained. Any other reproduction is prohibited without permission.

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The Manitoba Library Association
ISSN 1201-9364
Hosted by the University of Manitoba.
 

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