Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.
Filling Vases and Making Tanks
Crack the Code
Karen Zwanch and Bridget Broome
This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.
Discovering Area Models: The Giant Sicilian Pizza Task
Corinne Thatcher Day
This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from Principles to Actions, this article describes the task’s setup and implementation.
GPS: Perceiving Variability in Graphs
Linda L. Cooper
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.
Growing TTULPs through Your Lessons
Jonathan D. Bostic, Brooks Vostal, and Timothy Folger
All students have strengths that can be leveraged through universally designed instruction.
Odd Shape Out
big solutions to little problems
Jo Ann Cady and Pamela Wells
Solutions to a previous Solve It problem are discussed, and the procedures used with problem solving are explored.
Hook and Hold
Jennifer R. Brown
Set sail to explore powerful ways to use anchor charts in mathematics teaching and learning.
Difference Not Deficit: Reconceptualizing Mathematical Learning Disabilities
Katherine E. Lewis
Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.
Calculator Programming Engages Visual and Kinesthetic Learners
A programming activity helps students give meaning to the abstract concept of slope.
Differentiated Instruction in Shared Mathematical Contexts
Maryl Gearhart and Geoffrey B. Saxe
Try these methods for integrating diverse learners.