Why These Eight Practices Should Ground Every Math Classroom (And Coaching Conversation)
- Shannon Olson
- Oct 27
- 5 min read
If you’ve ever stood at the board wondering how to make today’s math lesson click for every student, you’re not alone. No matter the grade level or curriculum, math teachers everywhere share that same challenge—making math meaningful for every student.
With new programs and shifting expectations, it’s easy to feel like the target is always moving. So where should teachers focus their energy? What’s steady and worth getting really good at, no matter what changes around us?
For us, the answer is simple: focus on the eight Effective Mathematics Teaching Practices from Principles to Actions (NCTM, 2014). Why? These practices help teachers see themselves not merely as implementers of lessons, but as architects of meaningful mathematical experiences. At the same time, students begin to view themselves not just as learners completing tasks, but as confident, capable mathematicians.
The Eight Effective Mathematics Teaching Practices
What are the eight Effective Mathematics Teaching Practices?
These aren’t abstract research ideas or a new curriculum you have to weave into what you’re already using. They’re practical moves that great teachers use everyday to make math meaningful.
Establish mathematics goals to focus learning
Start with a clear purpose. What mathematical ideas should students understand? How will these goals build on each other over the course of the lesson, unit, and school year to ensure that students are learning along progressions and gaining deep mathematical knowledge? That focus guides every decision that follows.
Implement tasks that promote reasoning and problem solving
Once a clear goal is established, teachers choose or adapt tasks that encourage students to engage deeply with that specific mathematical concept. These tasks connect to students’ lives, making math more meaningful and engaging. They provide opportunities for students to explore the content in ways that make sense to them, while still uncovering and mastering both the “why” and the “how” behind the mathematics.
Build procedural fluency from conceptual understanding
Using these tasks over time helps students build procedural fluency grounded in a deep understanding of mathematical concepts.
Pose purposeful questions
During math tasks and class discussions, teachers ask purposeful questions that draw out reasoning, press for clarity, and help students make connections. Purposeful questioning allows students to bridge the gap from exploring math to making meaning, connecting, and applying mathematics across domains.
Facilitate meaningful mathematical discourse
Purposeful questions need a space to live and breathe. When teachers build in moments for students to share, compare, and connect ideas—whether through individual reflection, partner talk, small groups, or whole-class discussion—students have the chance to learn from one another’s thinking.
Use and connect mathematical representations
Without multiple representations, there is little for students to discuss! Encouraging different ways of showing thinking helps students see how various representations tell the same story, and how different real-life situations may call for different approaches.
Support productive struggle in learning mathematics
Let students wrestle with ideas long enough to learn from the process. The struggle itself is where learning happens.
Elicit and use evidence of student thinking
Listen for understanding, not just answers. Use what students say and show to make instructional decisions in the moment.
Although each of these practices is powerful on its own, they are not meant to be separated—they work together as a system. Each one supports and strengthens the others. A clear goal guides the task you choose. The task shapes the kinds of representations and questions that emerge. Those representations and questions fuel meaningful discourse and reveal evidence of student thinking. When we view the practices as interconnected rather than separate steps, our teaching becomes more intentional, flexible, and responsive to students’ needs. Grounded in these practices, students don’t just do math—they understand it, talk about it, and see themselves as mathematicians. When teachers learn about and more fully utilize these practices as a lens for math instruction, student learning deepens.*
What These Practices Look Like in Action
Imagine a teacher preparing for a lesson on multiplication. Before students arrive, they select a clear learning goal: by the end of the lesson, students will understand what multiplication really means. They chose a task that encourages reasoning and anticipate the types of strategies and representations students might use—drawings, counters, arrays, or equations. They also think through ways to highlight student strategies during discussion, moving from concrete to abstract while remaining flexible, knowing students may surprise them with valuable approaches.
When the lesson begins, the teacher doesn’t reveal the goal. Instead, they ask students to explore something relevant to them: “If a group of 6 players each collects 9 diamond blocks in Minecraft, how many diamond blocks do they have in total?” Students immediately start reasoning, drawing Minecraft characters with blocks, arranging counters, or creating arrays. One student adds repeatedly, “9 + 9 + 9 + 9 + 9 + 9,” while another counts using an array, seeing six groups of nine blocks at once.
As students work, the teacher monitors their strategies and encourages productive struggle, posing guiding questions such as:
“How does your picture show the total number of diamond blocks?”
“Can you explain how your equation matches your drawing?”
“If we already knew there were 54 blocks, how could we figure out how many each player collected?”
The teacher also selects strategies to share during whole-class discussion to highlight what multiplication is—groups of a certain size collected to find a total.
During discussion, student-generated examples illustrate the concept, and strategies are sequenced dynamically, often starting with physical representations like drawings or counters, then moving to arrays, and finally to equations. This sequencing helps students make connections across representations and see the underlying concept.
The teacher facilitates discourse, prompting students to share strategies, compare ideas, ask questions, and listen to peers. Throughout the lesson, the teacher continually draws attention to the goal: understanding multiplication. Student work is used to make learning visible, questions guide reasoning, and answers are not given upfront, allowing students to construct understanding. At the end, the teacher explicitly restates the goal, connecting it back to student-generated strategies and reinforcing the meaning of multiplication.
Over time, through similar experiences, students begin to see connections to division—like dividing 54 blocks into 6 players to find how many each player collected—and notice patterns, such as realizing 9 × 6 can be decomposed as 9 × 5 + 9 × 1, supporting flexible thinking and mental calculation.
In this lesson, the teacher sets a clear goal for students, uses a task that encourages reasoning and problem solving, and supports multiple representations—drawings, counters, arrays, and equations. Purposeful questions, rich discourse, highlighting student strategies, and attention to productive struggle help students connect representations, explore patterns, and build procedural fluency grounded in conceptual understanding. These practices together help students see multiplication as a connected system rather than isolated facts.
How These Practices Ground Our Professional Learning
At Olson Educational Services, all workshops, walk-throughs, learning labs, and coaching cycles are grounded in the eight Effective Mathematics Teaching Practices, providing a shared framework for lesson design, reflection, and growth. When we visit classrooms, we’re not just looking at the task on the board—we’re looking for evidence of student reasoning, how teacher questions guide thinking, and how discourse moves ideas forward.
As teachers engage in learning labs or coaching cycles, they begin to see how the practices fit together: a clear goal shapes the tasks we choose, anticipating student representations informs the discourse, and purposeful questions turn a routine lesson into a rich conversation. Experiencing these connections builds confidence, enabling teachers to adapt any curriculum to make lessons engaging, meaningful, and responsive to students’ needs. Teachers leave feeling empowered to become not just deliverers of curriculum, but facilitators of meaningful mathematical experiences for all students.
Looking Ahead
These eight practices go beyond steps to follow—they shape how teachers think about, plan, and lead mathematics learning. In the coming weeks, we’ll take a closer look at each practice—what it looks like in real classrooms, how to get started, and small shifts that make a big difference. Follow along to learn about these amazing practices that transform teaching.
*Source: Bognar, B., Horvat, A., & Matić, L. (2025). Characteristics of effective elementary mathematics instruction: A scoping review of experimental studies. Education Sciences, 15(1), 76. https://doi.org/10.3390/educsci15010076
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