2025 MidSchoolMath National Conference

This session will begin with a short introduction to conceptual metaphor as a lens for thinking about mathematics teaching and learning. For example, our spatial understanding of up and down, along with our experiential understanding of stacks of objects, leads to a metaphor “up is more”, which we see in phrases like “above average” or “higher test score.” Drawing from this work, I will share some examples suggesting that metaphor is a normal part of teacher language in a math classroom, and that we can use metaphors strategically to improve student understanding.

Following the conceptual overview, we will play several counting games to find different patterns, leading to metaphors for variables, evaluating expressions and solving equations. During the games, specific teacher moves and mathematical extensions will be discussed, ensuring you can envision how this story and games can develop foundational algebraic ideas. You'll leave with an understanding of how to use this game with students, how elements of the game become metaphors for mathematical concepts, and how to involve game concepts into future math lessons.

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.