The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.
Charles F. Marion
Michelle T. Chamberlin and Robert A. Powers
Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.
Eric Cordero-Siy and Hala Ghousseini
Three deliberate teaching practices can help students strengthen multiple connections to a unifying concept.
Examining the covariation of triangle dimensions and area offers a geometric context that makes analyzing a piecewise function easier for students.
Lori Burch, Erik S. Tillema, and Andrew M. Gatza
Use this approach to developing algebraic identities as a generalization of combinatorial and quantitative reasoning. Secondary school students reason about important ideas in the instructional sequence, and teachers consider newfound implications for and extensions of this generalization in secondary algebra curricula.
Lessons that focus on a conceptual understanding offer an opportunity for students to learn about mathematical structure, not just computation.
William DeLeeuw, Samuel Otten, and Ruveyda Karaman Dundar
The planful use of boardspace can help move the structure and regularity to the visual realm and make it more readily perceivable by students.
Caroline Byrd Hornburg, Heather Brletic-Shipley, Julia M. Matthews, and Nicole M. McNeil
Modify arithmetic problem formats to make the relational equation structure more transparent. We describe this practice and three additional evidence-based practices: (1) introducing the equal sign outside of arithmetic, (2) concreteness fading activities, and (3) comparing and explaining different problem formats and problem-solving strategies.
S. Asli Özgün-Koca and Matt Enlow
In this month’s Growing Problem Solvers, we aimed to help students explore patterns where they pay attention to the mathematical structures behind those patterns.
This poem starts with the question in the trunk of the tree, where we imagine that we are deciding to do or not to do something. Each level represents steps in making the decision, with the top indicating a resolution in the future. Phrases wander and change direction, leading to different results. How many paths to a resolution do you see?