2025 MidSchoolMath National Conference

Middle school students are natural pattern-finders and exception-finders. In a mathematics classroom built on thinking and reasoning, we want students doing both! Come and participate as we walk through two mini-lessons meant to harness both the generalization- and snark-making machines that are middle schoolers.

The session will start with a Problem String, an instructional routine developed by Pam Harris that exposes students to high-dose patterning as they reason about adding integers. Problem Strings ask a series of intentionally-sequenced, easily understood questions and allow students to see a relationship made visible through teacher modeling, repeated in ways that are similar enough to encourage generalization and different enough to keep the interest of students coming from all levels of experience. As teachers we want to ask more of what Peter Liljedahl calls “keep-thinking questions” to help students reason about relationships without overgeneralizing. With this in mind, the second portion of this session will look closely at how exception-finding emerges as a natural and powerful extension of pattern-finding in mathematics, specifically through the lens of geometric “prove or disprove” statements.

Throughout the session, you'll have the opportunity to share strategies and ideas with each other, in partners, small groups, and as a whole group. Together, you'll learn from one another's perspectives and strategies as we do math by experiencing what one aspect of the mathematics of thinking classes could look like.