The second edition of Learning and Teaching Early Math: The Learning Trajectories Approach by Clements and Sarama is the quintessential book about mathematics instruction for educators who teach children aged 3 to 8.
It is comprehensive, informative and practical – designed for classroom use. Its 380 pages may seem daunting, but you just need to read chapters 1 and 14 to 16 before beginning to use it to assess the mathematical thinking of your students.
The book is organized by chapter into fundamental mathematical concepts and processes. For example, there are chapters on Quantity, Number, Verbal and Object Counting, Early Addition and Subtraction, Place Value, Spatial Thinking, Composition and Decomposition of Shapes and four aspects of Geometric Measurement.
The first section of each chapter is frequently cross-referenced with other parts of the book. The middle provides links to the US common core math curriculum, which is somewhat useful though not ideal when trying to locate these concepts in the Ontario grades 1 to 3 and kindergarten math strands for report card writing.
The last section is a t-chart of learning trajectories – the typical developmental stages and progression of mathematical sub-concepts by approximate age. It includes instructional tasks designed to foster them.
Armed with learning trajectories, it is easy to assess any student’s thinking via pedagogical documentation, locate the student on a trajectory, determine the next step in the child’s learning, provide feedback that fosters it and program relevant instructional tasks.
Try it yourself. Read the obligatory four chapters and begin using it in your classroom. With 28 pages of references listing 70 research articles by the authors, it is impossible to find fault with the book’s content. My only quibble is that the publisher reduced the font size of the learning trajectory sections. They were a trial for my 58-year-old, bespectacled eyes.
Edward Schroeter is a member of the Kawartha Pine Ridge Teacher local.