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 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.
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 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.