5-Minute Math Instruction Makeovers

Micro PD - The Art of Ambitious Teaching Micro

Overview

Lesson 1. Establish Mathematical Goals

Lesson 2. Tasks that Promote Reasoning and Problem Solving

Lesson 3. Build Procedural Fluency from Conceptual Understanding

Lesson 4. Facilitate Meaningful Mathematical Discourse

Lesson 5. Pose Purposeful Questions

Lesson 6. Use and Connect Mathematical Representations

Lesson 7. Elicit and Use Evidence of Student Thinking

Lesson 8. Support Productive Struggle in Learning Mathematics

Instructional Practices that Promote Students' Mathematical Development and Appreciation of Mathematics
(Overview)

What distinguishes routine instruction from practices that genuinely promote students’ mathematical development and appreciation of the subject?

What do ambitious teachers do differently to bring their instruction to life and create a lasting impact on student learning?

How do teachers move beyond surface-level instruction to teaching that is animated by purpose, passion, and intentional design?

In this micro professional development (PD), we investigate the various components within the art of ambitious teaching. Relying on the eight mathematical practices (NCTM, 2104) as the foundation, we investigate how incorporating these research-based strategies will turn ordinary instruction into extraordinary classroom lessons where students are engaged, confident, and thinking learners.

The connection between purposeful, passionate teaching and students’ meaningful mathematical development lies in designing and implementing lessons that engage them in deep reasoning and sense-making. The eight mathematical practices serve as core habits of mind that nurture students’ growth as mathematical thinkers.

Eight Mathematical Practices

Effective teaching and learning happen when teachers recognize that the eight mathematical practices provide the essential structure. Think of them as the framing of a house—without that framework, the house wouldn’t stand. But what transforms a house into a home is the heart you put inside—the personal touches that give it meaning.

Similarly, ambitious instruction designed within these eight practices elevates teaching beyond mere routines and procedures. The practices form the framework that supports powerful instruction, while your passion and creativity breathe life into the lessons. Together, they allow you to design the kinds of activities and experiences that help students not only make sense of math, but also use it to reason, problem-solve, and see mathematics as meaningful in their own lives.

Let’s start with the very top of the framework: establishing mathematics learning goals to focus learning. Its placement at the top isn’t an accident—it reminds us that setting goals is the starting point for all instructional decision-making. When we write the learning goals or outcomes on the board, they serve as a kind of beacon. They guide us and our students from the very beginning of the lesson all the way through to the end.

Now that the goals are clear, we consider implementing tasks. Tasks are the bridge that moves students from where they are now toward those goals. Depending on the focus, we might choose tasks that promote reasoning and problem-solving, or tasks that build procedural fluency from a strong conceptual foundation.

Key Concept: Building procedural fluency and developing strong conceptual understanding are not in competition. In fact, they work hand in hand, each reinforcing and strengthening the other.

At the center of everything—at the heart of our lessons—is mathematical discourse. Discourse is what makes student thinking visible and what allows the class to reason together. By engaging in rich mathematical conversations, students clarify their own ideas, confront misconceptions, and build deeper conceptual understanding through listening, explaining, and connecting their thinking with others.

And surrounding that discourse are four critical teaching practices. These are:

These four practices all work together. They interact with one another, are grounded in the goals, and advance through the tasks. Together, they create the conditions for meaningful mathematical discourse.

As students work, our role is to use purposeful questions to surface their thinking. That evidence then helps us connect different representations and encourages students to stick with the productive struggle of important mathematical ideas.

For a deeper understanding, continue to the next lesson.

Unit 2. Establishing Mathematical Goals