Teaching Mathematics Through Inquiry and Sense-Making Microcredential

Mathematics learning deepens when students explore problems, apply strategies, explain their thinking, and make sense of mathematical relationships. When instruction focuses primarily on procedures, students may learn how to perform calculations but may not develop strong conceptual understanding.

Inquiry-based mathematics instruction invites students to engage in reasoning, problem solving, and discussion about mathematical ideas. In inquiry-centered classrooms, students investigate problems, represent their thinking in multiple ways, compare strategies, and build understanding through discussion and reflection.

This microcredential supports educators in strengthening mathematics instruction by making student thinking visible and supporting meaningful mathematical discussion. Participants analyze lessons with attention to the mathematical goal of the lesson, anticipate how students may reason about the mathematics, and design questions that reveal and extend student thinking.

Participants work with 2–3 lessons from their own teaching context. Lessons may come from a published curriculum such as Illustrative Mathematics, Eureka, EnVision, or another program, or they may be lessons participants have designed themselves.

This course is designed to help teachers work thoughtfully within their existing curriculum materials. Participants analyze and enhance lessons to strengthen opportunities for mathematical reasoning, representation, and discussion. Teachers focus on anticipating student strategies, interpreting student work, and making instructional decisions based on evidence of student thinking.

By the end of the course, participants will have analyzed, implemented, and refined lessons that strengthen opportunities for student reasoning, discussion, and mathematical sense making.

Microcourse 1: Designing Mathematical Tasks

This microcourse focuses on how mathematical task design shapes student thinking. It distinguishes between tasks that rely on procedures versus those that promote exploration, strategy, and reasoning. Participants analyze and improve tasks from their own curriculum, anticipate student approaches, then implement and observe the tasks in their classrooms.

Microcourse 2: Facilitating Mathematical Discourse

This microcourse emphasizes using classroom discussion to deepen students' mathematical understanding. When students share and respond to each other's reasoning, they strengthen their thinking and arguments. Participants learn to facilitate inquiry-based discussions, plan thoughtful questions, and reflect on how dialogue makes student thinking visible and supports mathematical exploration.

Microcourse 3: Analyzing Student Thinking

This microcourse focuses on using student work as a tool for informing teaching. By examining student solutions, teachers can identify patterns in reasoning and common misconceptions. Participants use these insights to make better instructional decisions and support students' continued mathematical growth.

Microcourse 4: Refining Instruction for Mathematical Sense Making

This microcourse helps teachers improve their practice by reflecting on patterns across past lessons — including student reasoning, discussions, and task engagement. Participants use these observations to refine key instructional moves like task design, questioning, and discussion structures, with the goal of developing sustainable teaching practices that consistently support student reasoning and mathematical sense-making.