Three Elements of a Successful Secondary Math Classroom

This is the first in a series of posts where we take a deep dive into the three elements of a successful classroom from the upcoming book, Necessary Conditions by Geoff Krall.

We want kids to like math. We want kids to be mathematical thinkers. So why is it that math is often the barrier that prevents students from having a rich secondary or post-secondary experience? That is the question author and educator, Geoff Krall, tackles in his new book, Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation.

“As challenging as it is to teach math, a high-quality mathematical school experience can unlock a person’s academic identity…I’ve found that the biggest drivers of a high-quality math experience are teachers dedicated to their craft and to their students.” ~Geoff Krall

In his research visiting schools across the country, Krall found secondary mathematical ecosystems where learning is thriving; students are confident in mathematics and demonstrate high achievement. He found that all the classrooms he visited had a common thread: the teachers are implementing high-quality mathematical tasks, facilitating effectively, and attending to the students’ social and emotional well-being and self-regard in math. In Necessary Conditions, Krall explores these three elements of a successful math classroom. Here’s a brief description. We will go into more detail in subsequent blog posts.

Academic Safety

Academic Safety exists when students are in a safe environment where they have the allowance to ask questions, make mistakes, and try something new. Being proactive about academic safety is especially crucial in mathematics because students often arrive with negative prior experiences and already-low self-esteem. It is the teacher’s responsibility to create and maintain an environment that invites all students into challenging mathematics. Through real classroom stories and thoughtful analysis, Krall describes specific teacher moves and routines we can use to create academic safety.

Quality Tasks

For students to build and develop their own mathematical identity they need to hone it with quality tasks. Tasks are what you see students working on in the classroom. A quality task is one that is intrinsically interesting and allows all students to access it. Students cannot realize their mathematical potential without being provided opportunities to grapple with and successfully solve quality tasks.

Effective Facilitation

Effective facilitation involves the series of teacher moves that guide students to construct, enhance, and communicate their mathematical insight in a quality task. It is the launch of a rich task that captures all students’ interest; the question that pushes a collaborative group of students to think more deeply; the framing of the whole-class discussion afterward to promote sense making. Facilitation appears as singular moments in a classroom and as structures and norms that develop over months.

If a student enters post-secondary education requiring remediation (most typically in math), that student is much less likely to graduate. Of students who require remedial courses at four-year universities, only 35 percent go on to graduate within six years (Complete College America 2012). Let’s work to change this statistic by giving our secondary students a better math experience.

Click HERE to see a preview of Geoff Krall’s new book, Necessary Conditions.

Add comment November 12th, 2018

Toward a Math Pedagogy

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.

Add comment November 5th, 2018


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