They say you can’t judge a book by its cover, but Peter Appelbaum’s Embracing Mathematics: On Becoming a Teacher and Changing with the Mathematics may be a rare exception. The cover image is bizarre and confusing to me, and from there the book never quite moved back into my favor. The brief table of contents can be found here on MAA Reviews, but in the actual text this is followed by an annotated table of contents, and a preface by David Scott Allen which again summarizes the chapters of the book. This feeling of “too much information” never quite left me as I explored the text. It is a book with many ideas in one place, but the length made me wonder why it felt so dense — it’s not a short book but it still feels a bit rushed.
There are some truly great notions in this book, including the concepts of “embracing mathematics” and “mathematizing” the world around us. A favorite idea I leave this book with is the idea of mathematicians going beyond answering questions and asking their own questions. For example, at the end of Chapter 1 is a series of problems to explore (“MathWorlds”) where a context or parameters are given for consideration; the final question for each item is: “what new questions come to your mind after working on these questions? Choose one of these and begin to explore it.” (p. 49). How do we train ourselves and our students to enjoy the exploration and the loose ends instead of always trying to answer the question and stop? Looking for more questions and possibilities might be one way to develop strong critical thinkers and mathematicians.
Many of the ideas in the book are gathered from other sources, making it a nice collection of citations and resources for mathematics educators. At the end of most chapters is a section called “Action Research” written by K–12 teachers. The one in Chapter 1 is an intriguing project called “numbers on trial” which could be modified for a variety of grade levels. The Action Research sections in Chapters 2 and 3 are brief and strong, and much more traditional as samples of the process of Action Research. The Action Research projects in Chapters 4 and 6 are about mathematics and social justice issues, which are very popular topics for investigation. Chapter 7’s Action Research section was honest and touching; it is a “failed” project that would be informative to teachers just beginning using Action Research in their own classrooms. These brief sections that were not written by Appelbaum were less overwhelming and easier for me to read. They would be more accessible to the pre-service teachers that I am familiar with at my campus.
Overall, the book feels like years of annotated course notes and handouts for a math methods course that Appelbaum finally decided to publish, without actually reading things through for the most usable items. It would take me multiple close reads to really cull my favorites; only then would I know whether the book has enough material to warrant assigning it to students.
Christine Latulippe is assistant professor of mathematics education at California State Polytechnic University, Pomona. Her summer joys are reading, iced coffees, and naps.
Preface: How can I (better) embrace mathematics? David Scott Allen
Prologue Peter Appelbaum
Response to Prologue: Be a student of mathematics learners
Chapter 1: Planning and assessment
Response to Chapter 1: Engage yourself in meaningful observation
Action Research 1 Isaiah Manzella, Numbers on Trial
MathWorlds 1: Reverse answer to questions
Chapter 2: A psychoanalytic perspective
Response to Chapter 2: Ask yourself to change
Action Research 2 Karen Cipriano, Flexible interview project
MathWorlds 2: Multiple answers.
Chapter 3: You are a mathematician
Response to Chapter 3: Explore the vastness of mathematics
Action Research 3 Karen Cipriano, Mathematics journals
MathWorlds 3: Reading and writing mathematics
Chapter 4: Critical thinkers thinking critically
Response to Chapter 4: It is critical to think
Action Research 4 Ada Rocchi, Lesson: world population and wealth
MathWorlds 4: Pitching questions at various levels.
Chapter 5: Consuming culture: commodities and cultural resources
Response to Chapter 5: Emphasize the meaning-making of mathematics
Action Research 5 Colleen Murphy, Problem solving through literature
MathWorlds 5: Turning "puzzles" into "problems" or "exercises"
Chapter 6: Metaphors for the classroom space
Response to Chapter 6: Take ownership of your classroom space
Action Research 6 Kristin Iaccio, Linking mathematics to social issues
MathWorlds 6: Same math, different metaphors
Chapter 7: Places where people learn mathematics
Response to Chapter 7: The classroom is always changing
Action Research 7 Petal Sumner, Empowering students who don’t learn
Chapter 8: When students don’t learn
Response to Chapter 8: We are all students
Epilogue: Becoming a teacher and changing with mathematics
Afterword: What will you write in your chapter?