Podcast: How to Teach Deep Mathematical Thinking

Narrow, rigid math has “turned students off for generations,” says renowned researcher and Stanford mathematics professor Jo Boaler. 

Yet teachers often don’t have much choice when it comes to math curriculum—what’s mandated by a school or district is what they need to teach.

That’s where *rich tasks* can be transformative, Boaler argues, because they invite the type of reasoning and problem-solving that get kids digging in and taking risks. 

In this episode of School of Practice, we’ll chat with Boaler—who’s spent decades studying math teaching—about how to choose, adapt, and improve math tasks; the power of reasoning and visualizing math questions; and the impact of tiny tweaks, like asking students: “Can you prove it to me visually?”

Related resources:

• 5 Ways to Encourage Deep Mathematical Thinking You can adapt the curriculum you have to create rich tasks that invite reasoning and build students’ problem-solving skills.
• Are We Teaching the Math Kids Need? Every child possesses vast mathematics potential, says Jo Boaler, Stanford University mathematics professor and best-selling author—but for them to access it, we need to rethink how we teach math.
• Rough Draft Thinking Can Make Math Class More Inclusive When math lessons emphasize collaboration and exploration over performance, students become more engaged and confident math thinkers.
• Should More Time Be Spent Learning Math Facts? As schools nationwide contend with declining math scores, some districts are dedicating more time to the practice of foundational skills.
• 7 Ways to Balance Joy With Rigor in Math Class A few straightforward shifts and strategies can help create math classrooms where even the most reticent learners find their footing.
• If You’re Not Failing, You’re Not Learning The learning scientist Manu Kapur, architect of the theory of productive failure, on reframing our notion of failure, and letting kids stumble with purpose.
• Research: Productive Failure in Learning Math (2014) This study found that when students try to solve a hard problem on their own before getting instruction, they build stronger conceptual understanding and are better able to apply their learning to new problems.
• How to Build a Healthy Math Identity (video) When students begin to see themselves as math thinkers, they engage actively, explore creatively, and feel more motivated.
• 6 Unproductive Ways to Learn Math Basics—and What to Do Instead Tune up your math teaching with this review of strategies to avoid, plus alternatives that will challenge, engage, and enlighten your students.
• Math-ish Jo Boaler’s guide to learning math through embracing “joy, understanding, and diversity.”
• YouCubed: Moving from Maths Anxiety (video) A video showing a fourth-grade teacher using a “big ideas” approach to teaching math.
• YouCubed: Math-ish in the Classroom (video) A video showing “ish” thinking in action in a sixth-grade classroom.
• YouCubed: Jo Teaching a Visual Dot Card Number Talk (video) A video showing Jo Boaler teaching a “dot card” number talk.
• YouCubed: Fluency without Fear Co-author Jo Boaler argues that math fluency should come from developing number sense and flexible thinking, not from memorizing facts through drills and timed tests, which can lead to math anxiety in students.
• YouCubed: Wise Investments, Big Returns: Prioritizing Teachers for Districtwide Mathematics Success This case study describes how one California school district improved math achievement by focusing on sustained professional development for teachers, family engagement, and classroom practices that encourage discussion, reflection, and conceptual understanding.