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CM . . .
. Volume XV Number 20 . . . . May 29, 2009
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 – How then can teachers help their students to build 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 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,
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 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 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 Let me mention one other thought that I had when reading The critical points I raised about the book reviewed here should not distract from my view that
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