As long-time readers of this blog know, I was a fan of Peter Liljedahl’s Thinking Classroom “before it was cool”. (See this post from 2015.) Thus, I was quite pleased to hear from Amanda Cangelosi that the book I co-authored with Robin Pemantle works well as a complement to Liljedahl’s. My book is There Is No One Way to Teach Math — you can read about it on this blog, and see the table of contents here.
Amanda worked briefly at my school many years ago. Later, we collaborated on expanding a couple of lessons of mine into full-on lesson plans (McNuggets, and Cell Phone Plans.) Yet later, she contributed an insightful comment to my blog post Freakonomics Radio on Math Curriculum. Here is what she has to say about the two books.
— Henri
Two Math Education Books
By Amanda Cangelosi (amanda.cangelosi at usu dot edu)
For the past decade, I’ve spent half of my summers facilitating a methods course for pre- and in-service teachers who are seeking to attach a secondary math endorsement to their license in Utah. As it would be unthinkable to fail to incorporate Peter Liljedahl’s Building Thinking Classrooms (BTC) into this course, I make “The Orange Bible” required reading. The 14 practices described in BTC are essential and warmly-welcomed by my teacher-students (and adored by me, possibly to the point of worship). The other required text is Picciotto and Pemantle’s There is No One Way to Teach Math (N1W), which serves as a comprehensive, validating, and uplifting resource for an audience that is overwhelmed by the nature of their careers. My course assigns N1W to be read first, followed by BTC second. Reading N1W first is helpful for several reasons, one of which is that nobody likes to be told what to do.
My course is not exactly voluntary for my teacher-students. State mandates require that those who want to teach secondary math must earn an endorsement, and while there are a handful of pathways for the endorsement to be acquired, taking a 7-week summer course for college credit via Zoom is often the simplest route. Thus, the experience isn’t quite the same as a district-sponsored book club; some people enter the virtual classroom understandably annoyed and skeptical. Are these folks going to endure yet another out-of-touch teacher educator sellout talking at them about the latest fads? The answer would be “yes” if not for N1W. The immediate validation that comes from the book title alone is enough to open hearts and minds, which is a great place to begin a discussion-based class.
Teacher validation is overlooked as a necessary step in inviting large-scale change. We have to meet people where they are, which we seem to understand for children, forgetting that adults are just children who are older. To make complex modes of instruction accessible, we can’t just explain and justify the modes; we need to first say, “I see you, and you bring value to this space,” because that’s the truth. As N1W tells us in the Special Note to Young Teachers, “You are who you are. That is a crucial gift to your students.” When we transition to reading BTC, instead of being overwhelmed by the 14 practices, teachers appreciate remembering that “it cannot be rushed.”
Since our identities include our politics, and since politics intersect with the Math Wars, an important facet of teacher validation is addressing the Math Wars problem. N1W nips the Math Wars problem in the bud, rescuing my class from unproductive debates and false dichotomies. By embracing contraries, N1W fosters a spirit of camaraderie, setting the stage for growth, as opposed to a futile pursuit of “what works.” When teachers hear that whatever instructional modes they are currently practicing have a place, they are being told that they are whole instead of broken. Perhaps ironically, this validation allows teachers to move forward. The polarization spell is broken. Teachers are ready to grow their collection of practices, adding to their instructional repertoire and seeing value in each component.
One powerful excerpt from N1W that clicked with my teacher-students, and dovetails nicely with BTC:
“All of the above”, but not “anything goes!” Our foundational idea is that math teachers should reject shallow either-or stances, and instead learn to combine multiple approaches, even if they superficially seem to contradict each other. There is no one way: we need an eclectic mix of techniques that prioritize student understanding. . . . The main path to student understanding is intellectual engagement [i.e., thinking, as in a Thinking Classroom]. . . . the main vehicle for that engagement: problem solving [e.g., non-curricular tasks].
When my class reads about non-curricular tasks in BTC, it is helpful to have already read about puzzles in N1W. From N1W, we learn that a puzzle is “a relationship between the puzzle constructor and the puzzle solver” and that it must be solvable, fair, challenging, and the solution must be satisfying. Puzzles “help lower the emotional stakes while offering a path to engagement for a wider range of students.” And N1W continues to dive deeper into the characteristics of a good puzzle, providing examples. This made Chapter 1 of BTC a breeze, with minimal panic about non-curricular endeavors.
Understanding the value of eclecticism from N1W, ahead of reading BTC, is fruitful. We must remember that research is a thing because variability exists. It is soothing for my teacher-students to hear—from a published source—that just because a study concludes that certain practices are optimal doesn’t mean it’s what they, as individuals, should be doing (and certainly not all the time). Rather, the study provides really good information for them to add to their arsenal. Once any given practice becomes mass-normalized, it may lose its power; the key is to have an ever-growing collection of ideas at your disposal to shake things up. I admit that I’m guilty of rolling my eyes and disengaging at professional development meetings whenever the giant post-its, accompanied by smaller post-its and markers come out. The post-its-atop-post-its got old, and I don’t want to play that game anymore, because too much routine begins to feel patronizing after a while. According to N1W, “It is a mistake to put all one’s pedagogical eggs in one basket. . . . Students do appreciate some predictable routines, but too much of that can take the life out of a class. Switching modes can contribute to welcome changes of pace, and bring some variety to the program.” When my teacher-students know this, they are more open to taking risks, because they don’t feel locked-in to playing one game all year.
There are five comprehensive chapters in N1W that address modes of instruction, including many examples of multiple representations and manipulatives. Each of these can be incorporated in BTC-style tasks, and my teacher-students appreciate having seen so many examples when they read The Orange Bible. In addition to fleshed-out examples of Thinking Classroom tasks, N1W addresses homework, planning, assessment, teacher joy, philosophical underpinnings, and professional development.
Regarding teacher joy and self-care, an important intersection of BTC and N1W is that of giving teachers permission to teach in ways that are consistent with their values. In BTC, Liljedahl says, “We need to start evaluating what we value,” where what we value is not only content knowledge but, crucially, habits of mind such as perseverance and collaboration. In N1W, Picciotto and Pemantle include strategies for “participation quizzes,” and further invite teachers to, more generally, “…trust your intuition, avoid dogma, be flexible, be kind. . . . even if your intuition is `wrong’, at least it is yours. Your students deserve to get the real you, not a poor imitation.”
“The real you,” as a teacher, is more than the tasks you choose, the way you arrange your classroom, the modes you choose to facilitate activities, and the way you evaluate students. The fullness of N1W helps my teacher-students in ways beyond what the main title suggests: It is packed with concrete, usable ideas that reflect the lived experiences of the authors. It is comforting to read a book that is non-academic, personal, and steeped in the wisdom built from decades of the authors’ classroom experience. Let us consider the subtitles of BTC and N1W, respectively: “14 Teaching Practices for Enhancing Learning” and “Actionable Ideas for Grades 6-12.” I don’t know about you, but to me the word “practices” signals something research-based (e.g., 5 Practices; Standards for Mathematical Practice; Principles to Actions’s eight “Effective Mathematics Teaching Practices”), while the gentle word “ideas” feels personal and anecdotal, signaling a conversation with trusted colleagues. Obviously, both are important, which is why utilizing both books is wonderful.
I shall attempt to wrap things up by way of a poor metaphor. When I was a child, I attended many birthday parties at Aladdin’s Castle, an arcade at my local mall. The best game was Ms. Pac-Man (duh), so I played that the most. But other games were great, too; I wasn’t about to put all of my tokens in one machine, no matter how much I loved Ms. Pac-Man on a spiritual level. There are a lot of great games to play as a math teacher. You can play Building Thinking Classrooms (Ms. Pac-Man), 5 Practices (Pac-Man), Complex Instruction (Mega Man), and so on. If instructional frameworks are games to play, then There is No One Way to Teach Math pours you a hot coffee, double-checks your seat belt, drives you to the arcade, suggests winning strategies, reminds you that you don’t have to play any of the games, and then ensures you make it home safely.
Teaching is more complex than playing a game, even when the game is complex; teaching demands the teacher’s whole self. In an alarmist culture of math education, it’s important to have cutting-edge research-based resources like BTC and also a comprehensive home base from experienced colleagues that validates and uplifts our individuality and supplies a wide range of tools and activities, such as N1W. I enthusiastically utilize both.
Henri's Math Education Blog 