*complex instruction*, an approach to teaching that was refined by a group of teachers in a Bay Area public school nicknamed "Railside", as it sits "on the wrong side of the tracks." My recommendation was based not on reading the books, but on my respect for the Railside math teachers. As I said then, I visit a lot of math classes, in a lot of schools. My visit to Railside stood out, because I witnessed firsthand a pedagogy that was both original and effective. So original and effective, in fact, that math education researchers from both Stanford and Berkeley did quite a bit of work to unravel the ingredients that led to Railside's phenomenal success in engaging students, and having them stick with math and take Calculus at a higher rate than comparable suburban schools.

I am now reading a new book about Railside, this one co-edited by a team consisting of two researchers and two Railside teachers. The book is titled

*Mathematics for Equity*. The title reflects the core values of the authors: math is for everyone, and everyone can do math. It is a collection of papers, some written by academics, some by teachers, some by a combination of both, analyzing the various ingredients that made the Railside approach so effective. One chapter is based on interviews with Railside alumni.

I have only read a few chapters so far, but I am ready to say that you should get this book.

I couldn't help starting near the end, in the chapter titled "Derailed at Railside", which documents how know-nothing administrators destroyed this outstanding program. Periods were shortened from 90 to 60 minutes, teachers were laid off, students were tracked, and class size was increased. The combined effect of these changes made it impossible to continue the practices that made the program successful, and many teachers ended up leaving to seek better conditions elsewhere.

This is infuriating, not least because it is so representative of the way public education is under sustained attack in this country. Luckily, it's only one of 14 chapters, and the others dwell on the positive lessons from this 20-year experiment. Even though my experience is mostly in a private school, with privileged students, I find that many aspects of the Railside approach are in complete agreement with what I learned at my school about teaching to a wide range of students.

Instead of dwelling on what students cannot do, Railside teachers built on the diverse strengths students bring to the classroom. Instead only valuing memorization and speed, they recognize that doing math involves multiple dimensions, including "reasoning and justification, creativity and invention, and use of a variety of strategies and representations." This implies that even the student who is good at memorization and speed can still grow in all those directions, and it opens the door for others. In today's technological age, speed and accuracy in computation are no longer a valid priority.

At the same time, students were encouraged to participate in the work even if they were not sure their approaches were correct. Discussion of each other's ideas and justifications was a key ingredient of classroom discourse. There was some direct instruction, but typically that came

*after*not before students had engaged in "groupworthy" tasks. Those are cognitively demanding problems that "illustrate important mathematical concepts, allow for multiple representations, [...] and have several possible solution paths." Students know to expect that follow-up questions will require them to justify their answers, not merely state them. (Full disclosure: one example of a groupworthy problem that is frequently given by Railside teachers and researchers is a Lab Gear perimeter problem -- this is a genre of problem I invented in the 1990's, using the algebra manipulatives I designed.)

Another feature of the Railside approach is organizing the work around big ideas, rather than lists of microskills. As students grapple with a big idea from multiple points of view, they develop a depth of understanding that is impossible in the traditional model where students are asked to memorize discrete, apparently unrelated techniques. Students are thinking human beings, not programmable machines. Alas, too many math teachers have given up on teaching for understanding, and believe that teaching well means providing students easy-to-memorize techniques to solve a limited range of low-level problems.

*Mathematics for Equity*powerfully presents an alternate point of view, one that is respectful of both students and teachers.

I have only touched on the incredible wealth of ideas in this book, but this post is already too long. Please, get the book!

--Henri

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