What if one of the most common terms in math education — conceptual understanding in math — isn’t actually understood the same way across schools, systems, or even math classrooms?

A recent podcast sparked a big question: is conceptual understanding in math poorly defined? The challenge wasn’t just the definition itself, but the claim that conceptual understanding in math may be getting in the way of math fluency. In this episode, Jon Orr, Yvette Lehman, and Beth Curran unpack that tension and wrestle with a deeper issue: maybe conceptual understanding in math is not poorly defined in research, but poorly understood and inconsistently implemented in practice.

In this episode, you’ll learn:

• Why conceptual understanding in math and math fluency should not be framed as opposing goals
• How conceptual understanding in math supports retention, reasoning, and equitable access to math learning
• Why poor implementation of conceptual understanding in math can create confusion and pushback
• How overemphasizing one part of math instruction can unintentionally crowd out purposeful math practice and explicit math instruction
• Why dips in math data should not automatically trigger a rejection of conceptual understanding in math
• How math leaders can build coherence around what conceptual understanding in math actually looks like in math classrooms

Ask yourself: when your team says “conceptual understanding in math,” do you all mean the same thing? If not, that may be the real math improvement work ahead.

Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/

Math coordinators and leaders – Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com

Looking to supplement your curriculum with problem-based lessons and units? Make Math Moments Problem Based Lessons & Units

Show Notes Page

Love the show? Text us your big takeaway!

Get a Customized Math Improvement Plan For Your District.

Are you district leader for mathematics? Take the 12 minute assessment and you’ll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.

Take the assessment

Are you wondering how to create K-12 math lesson plans that leave students so engaged they don’t want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.

Some math teachers insist students must always show their math thinking. Others argue that if the math answer is correct, that should be enough. When math grading practices don’t align with math learning goals, frustration grows — for math students and parents alike. The real issue isn’t compliance in math. It’s clarity about what we are assessing in math.

In this episode, we explore:

• The difference between assessing math fluency and assessing math understanding
• Why getting the right answer in math doesn’t always prove deep math understanding
• When requiring students to show their math thinking strengthens math learning
• When over-requiring explanation in math can harm math confidence and math identity
• How math leaders can support math teachers in aligning math learning goals, math success criteria, and math grading practices

Before grading the next math assessment, ask:
What was I trying to measure in math — accuracy or reasoning?

Your answer should determine whether students need to show their math thinking.

Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/

Math coordinators and leaders – Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com

Looking to supplement your curriculum with problem-based lessons and units? Make Math Moments Problem Based Lessons & Units

Show Notes Page

Love the show? Text us your big takeaway!

Get a Customized Math Improvement Plan For Your District.

Are you district leader for mathematics? Take the 12 minute assessment and you’ll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.

Take the assessment

Are you wondering how to create K-12 math lesson plans that leave students so engaged they don’t want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.

You’re teaching math to 34 students. You slow math pacing to support the middle, but you can feel yourself losing students who are ready to move.

A listener emailed us after our episode on rigorous Tier 1 math instruction: they don’t want to create opportunity gaps by slowing math down—but they also don’t know how to actually run small group math instruction after the main lesson. We also connect this to a real conversation with a district math team wrestling with Tier 2 math and Tier 3 math supports.

In This Episode, You’ll Learn

• Why “high/middle/low” labels get in the way of effective math small grouping
• How CRA math (concrete–pictorial/representational–abstract) can guide flexible math groups after the lesson
• Why CRA in math is not a ladder—and why abstract math isn’t automatically the “top group”
• How to use formative math assessment (including exit tickets) to identify what students need next in math
• How to structure math class so random groups drive discourse, then targeted math groups drive practice and support
• A coaching/leadership math move: “live the math work” in a classroom for a full unit before scaling the strategy
• Why sustained math coaching support (not one-off math PD) builds coherence in math instruction across a system

If you’re a math leader or math coach, ask: What’s one unit where we can co-teach, gather formative math assessment daily, and build CRA-informed math small groups—so we can scale what actually works in real math classrooms?

Not sure what matters most when designing math improvement plans? Take this assessment and get a free customized report: https://makemathmoments.com/grow/

Math coordinators and leaders – Ready to design your math improvement plan with guidance, support and using structure? Learn how to follow our 4 stage process. https://growyourmathprogram.com

Looking to supplement your curriculum with problem-based lessons and units? Make Math Moments Problem Based Lessons & Units

Show Notes Page

Love the show? Text us your big takeaway!

Get a Customized Math Improvement Plan For Your District.

Are you district leader for mathematics? Take the 12 minute assessment and you’ll get a free, customized improvement plan to shape and grow the 6 parts of any strong mathematics program.

Take the assessment

Are you wondering how to create K-12 math lesson plans that leave students so engaged they don’t want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.