Toward a Math Pedagogy

November 5th, 2018

There’s that famous yarn about how if someone time traveled from 100 years ago everything would look different except classrooms. That’s not really true. At least, not now. In fact, if this time traveler walked along the hallway of a math department, they’d see all sorts of disparate things. Sure, some classrooms might have desks in rows with the teacher lecturing at the board. But in other rooms students would be working in groups. In other rooms still students would be plugged into a piece of instructional software. This would-be time traveler would have no idea what’s going on!

When I walk down the hallways of a school, I notice these differences. In a 9th-grade Algebra class, students are using physical textbooks, while right across the hall in a 10th-grade Geometry class (or even a different 9th-grade Algebra class), I see hands-on activities. We’ve never had more varying math classroom experiences: project-based learning and instructional software, tracking and de-tracking, group work and packets.

We have so many pedagogies, we don’t have any pedagogy.

So I sought to find a pedagogy. What are the universal elements for a quality math experience? What are the things we as teachers can get better at? What are the things students bring to the table that help or hinder their mathematical identity?

In my work as a traveling instructional coach, I saw three consistent elements in successful math classrooms. The three elements are listed here, with much-too-brief definitions:

  • Academic Safety – the social and self-regard of a student’s mathematical status
  • Quality Tasks – the items that students are working on and toward
  • Effective Facilitation – the short- and long-term moves that allow for learning to occur

We’ll dig into these three elements in my forthcoming book, Necessary Conditions. Each of these elements receive a deep dive individually, with analysis of where these elements interact with one another. These aspects exist in everything students experience: from problem-solving to assessment, from lesson planning to room design. We can create a system that carves the path for our three necessary conditions, or we can create a system that works against them.

Combining research, classroom observations, and student voices, the book contains practical examples of how to assess and improve each of these conditions in your classroom and how you can imbue them in every lesson.

You can check out a preview of the book here. You can read stories of students who have been lifted up by incredible math teachers. You can see concrete examples of lessons and routines that yield deep mathematical learning. You can gawk at the ridiculous number of appendices.

So give it a look and see if we can really make that time traveler have something to marvel at.

This blog post was written by Geoff Krall, educator and author of the new title, Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation.

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