Teaching Math With Examples

Some teachers think that there’s little to say about teaching with examples – after all, everyone uses them. But here are just some of the questions you might have about teaching with worked examples: How do we introduce an example? What do we ask students to do when studying a solution? Should a solution be presented all at once or revealed step-by-step? After we study an example, what comes next? Does it matter if the solution is presented as if from a fictional student, a real student in class, or from the teacher? How do we help students move from understanding someone else’s ideas towards using it on their own to solve problems? How do we write a solution in a clear way, that students can learn from? When is a good time to offer a worked example? When is it better to let students try a problem? Are worked examples more useful for some mathematical content than others? This book will answer all of these questions. In some cases, research offers answers. Other questions represent gaps in the research literature and the book offers solutions arrived at through experience and trial-and-error and the author’s own process of classroom problem solving. Welcome to the world of teaching with examples!

About the Author :
Michael Pershan began his career in 2010 at a high school in New York City where he taught mathematics and computer science. Since then he has taught at St Ann’s School in Brooklyn, where he teaches math to elementary, middle, and high school students, and at Bridge to Enter Advanced Mathematics’s summer camp for underserved students. He has taught a course for teachers at Math for America, organized math education conferences, and helped create research-informed curriculum for Mathalicious, Amplify Education and M.I.T.’s Teaching Systems Lab. He and his family live in NYC.

Review :
Of all the changes I have made to my teaching since I began engaging with educational research five years ago, my use of worked examples has been the most significant. I now have a structure and routine for worked examples that takes less time, my students enjoy and – most importantly of all – seems to lead to greater understanding. I thought my worked examples had peaked, and finally I could stop thinking about them. Then I read Michael's book, and my world has fallen apart again. What I find fascinating is that Michael has read much the same research as me, and yet we have reached contrasting conclusions. His worked examples look very different to mine, and yet I spent the entire book nodding in agreement. Michael makes the point that ‘some of the dullest teaching on the planet comes courtesy of worked example abusers’. This is so true. If students stare blankly at a teacher's squiggles, nod their heads on cue, don't ask any awkward questions, and then frantically copy down what is on the board into their books, then maths is at risk of becoming the boring, incomprehensible subject many label it as. But the approach Michael presents is interactive, thought-provoking and interesting. There is support scaffolded in for those who initially struggle, and no ceiling imposed for those who grasp the concept more quickly. Above all, the approach has the potential to lay the foundations to enable our students to become the creative, knowledgeable, problem solvers we all want them to be. Rammed full of practical ideas – all of which are beautifully articulated and backed by research – this is a truly wonderful book. So often, books about education float high above the work of teaching, with nods to the ways that big ideas and values might look in practice – but without getting much into the muck of the classroom itself. It’s such a pleasure as an educator to come across a book that dives deep into instruction, while situating a very specific body of practices (in this case, teaching with worked examples) within a much broader literature on cognitive science and equitable mathematics teaching. Michael Pershan makes a compelling argument for educators to shift their focus from mathematical problem-solving to mathematical understanding – and describes the many ways that exploring and analyzing worked examples can democratize the math classroom, engage learners in rich thinking tasks, and provide targeted, thoughtful scaffolding towards the problem-solving work that math educators (rightfully) value. The book is rich with specific strategies and tools for implementing worked examples – and the theoretical grounding for those ideas, making it a wonderful resource for educators who want something ‘they can enact on Monday’ and something that strengthens and extends their schema about how math learning (and learning in general) works. As a bonus, it is also a human, funny, and real book about teaching stuff to kids – which is a rarity in itself and makes each chapter a pleasure to read. What do you get when you cross a teacher's generosity, a scientist's precision, and a philosopher's dogged pursuit of the truth? Two words: Michael Pershan. Michael Pershan hears the quiet moments that make education work. Reading this book, I felt he was teaching me how to listen. He takes up the humblest parts of teaching, and he makes them shine. An exemplary book, in every sense. If you could visit the classroom of a friendly colleague engaging in research-informed practice, while he conversationally whispers in your ear the what, how, and why, it would be something like reading Teaching Math with Examples. I can’t recommend highly enough this very do-able and high-leverage approach to any math teacher or curriculum developer who wants to level up their task design, or just try out something new.