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What Successful Math Teachers Do, Grades PreK-5: 47 Research-Based Strategies for the Standards-Based Classroom

Edward S. Wall and Alfred S. Posamentier
Corwin Press
Publication Date: 
Number of Pages: 
[Reviewed by
Megan R. Bovill
, on

What Successful Math Teachers Do, Grades, PreK-5  aims to provide a glimpse of some ways to implement the National Council of Teachers of Mathematics’s (NCTM’s) research-based goals for teaching elementary mathematics. The book offers several strategies for incorporating the goals into current classrooms, following examples of teachers who have proven successful. The authors methodically define a strategy that meets a NCTM goal, define the NCTM goal specifically, state the research that supports the goal, and provide a compilation of stories that depict one teacher’s pedagogy that meets the goal.

The premise of this book is great, providing teachers with ideas and motivation for implementing the progressive goals described in Principles and Standards for School Mathematics (PSSM) , but unfortunately the book feels as though it is unfinished. Several aspects of the book are inconsistent. For example, in the first few sections (which are defined by areas in mathematics — algebra, geometry, etc.— the authors provide examples of things parents can do at home to promote sound mathematics learning. This feature disappears beyond the first unit. Although the book is not particularly geared toward parents, the concept of helping parents develop the early foundations was one of my favorite things in the early parts of the book, and I missed it in the latter parts.

The is also inconsistency in the way the authors organize the sections that state the NCTM standards. For the first half of the book the relevant standard is mentioned in statements that differ for each strategy; in the final few units, however, this is done in question form and in the same sequence for each unit.

The sense of incompletion also comes from a lack of analysis. At the end of the vignettes about teachers’ strategies, the authors offer only a few sentences on what the teacher in the sample did that was noteworthy. These sections should be much longer, perhaps offering generalizations for using the same strategies in different situations or suggesting how to vary them depending on how students in individual classes respond. As the work stands, reading the vignettes does not provide enough useful additional information for the reader to know how to apply what the stories teach.

I found the “Potential Problems and Pitfalls” sections very helpful. It was in them that I found the most useful tips for effective teaching. However, while the list of things to avoid is fairly comprehensive and helpful, there are no real tips for how to actually avoid them. Again we are left wanting more from the book.

Finally, there are issue of organization. Several statements are repeated in multiple units (the claim that multiple topics are the cornerstone of mathematics becomes particularly tiresome). Connections are also lacking. In many instances, the vignettes do not clearly follow the strategy they are supposed to illustrate (including better analysis could clear up this concern), and the potential pitfalls do not always relate in an obvious way to the vignettes.

In sum, while the concept of the book is admirable, the content is little more than a simplified, condensed version of PSSM. The book is friendly and easy to read, but in the end it fell short of my hopes for substantial and useful information.

Megan Bovill is a native of Saco, Maine and is a senior Mathematical Sciences and Human Development major at Colby College in Waterville, Maine. Upon graduation, she plans to teach elementary school.


About the Authors
1. Numbers and Operations
Grades PreK-2
1. Encourage young children's exploration and understanding of relationships among numbers.
2. Encourage young children's understanding of addition and subtraction and how they relate to each other.
3. Encourage young children's fluent computation.
Grades 3-5
4. Encourage an understanding of the structure of numbers and relationships among numbers.
5. Encourage an understanding of the meanings of multiplication and division and how they relate to each other.
6. Encourage students to compute fluently and make reasonable estimates.
2. Algebra
Grades PreK-2
7. Encourage young children's systematic sorting and classification as they work with a variety of patterns, geometric shapes, and data.
8. Encourage young children's systematic exploration of the general principles and properties of operations such as addition and subtraction.
Grades 3-5
9. Encourage the expression and generalization of mathematics relationships.
10. Encourage further understanding of multiplicative structures through application and analysis of the distributivity of multiplication over addition.
3. Geometry
Grades PreK-2
11. Encourage young children's exploration of characteristics and properties of two- and three-dimensional shapes.
12. Encourage young children's application of similarity transformations to analyze geometric situations.
13. Encourage young children's use of visualization and spatial reasoning in their exploration of geometric shapes.
Grades 3-5
14. Encourage students' exploration and mathematical analysis of the properties of two-dimensional geometric shapes.
15. Encourage students' use of geometric transformations to analyze mathematical situations.
16. Encourage students' use of visualization, spatial reasoning, and geometric modeling to solve problems.
4. Measurement
Grades PreK-2
17. Encourage young children's exploration and understanding of measurement concepts and relationships.
18. Encourage young children to accurately apply appropriate tools and techniques to linear measurement.
Grades 3-5
19. Encourage students' exploration and understanding of measurement concepts and relationships.
20. Encourage students' appropriate application of conventional measuring tools in varied situations.
5. Data Analysis and Probability
Grades PreK-2
21. Encourage young children's collection, display, and organization of objects and data.
22. Encourage the idea in young children that data, graphs, and charts give information.
23. Encourage young children's informal explorations of probability.
Grades 3-5
24. Encourage students to explore questions they find personally relevant and that can be addressed by data collection and analysis.
25. Encourage students to become more precise in their mathematical descriptions of data.
26. Encourage students to explore and evaluate issues of representativeness and inference.
27. Encourage students' exploration and quantification of simple probabilistic events.
6. Problem Solving
Grades PreK-2
28. Encourage young children to ask mathematical questions and to identify essential mathematical information.
29. Assess young children's abilities to solve problems through examination of student work and conversations.
Grades 3-5
30. Encourage students' development and application of problem-solving strategies.
31. Select rich, appropriate, and challenging problems and orchestrate their use.
7. Reasoning and Proof
Grades PreK-2
32. Encourage young children to explain their thinking by stating their reasons.
33. Ask questions that encourage young children to make conjectures and to justify their thinking.
Grades 3-5
34. Encourage children to reason about the relationships that apply to the numbers, operations, or shapes that they are studying.
35. Focus on general mathematical structures and relationships.
8. Communication
Grades PreK-2
36. Encourage young children's verbal and written communication of mathematics concepts and ideas.
37. Expect young children to explain their thinking and give them opportunities to talk with and listen to their peers.
Grades 3-5
38. Encourage students to share their thinking, to ask questions, and to justify their ideas.
39. Provide models for student dialogue about mathematics.
9. Connections
Grades PreK-2
40. Encourage young children to make connections among mathematical ideas, vocabulary, and representations.
41. Make links between routine school activities and mathematics.
Grades 3-5
42. Encourage students to see that mathematics is a web of closely connected ideas.
43. Select tasks that help students explore and develop increasingly sophisticated mathematical ideas.
10. Representation
Grades PreK-2
44. Encourage young children to represent their mathematical ideas and procedures in varied ways.
45. Create a learning environment that supports and encourages children's use of multiple representations.
Grades 3-5
46. Encourage students to use representations to support, clarify, and extend their mathematical ideas.
47. Choose tasks that embody rich and varied representational structures.