Balance Board Math

Series of three photographs of a woman sitting on a wooden balance board against a blue background. A number line is overlaid over each image. In the first image, the woman (Sofia)’s hands are together at her midline, and the point where they meet is labelled 0 on the number line. In the second image, the right hand remains in the middle at 0 while the left has moved left by about a foot to a point labelled -4. The movement of the left hand has resulted in a slight leftward tilt of the balance board. In the third image, the right hand remains in the middle at 0 and the left has moved even further left by another 6 inches or so to a point labelled -6, and the board is tilted further left as a result.

Balance Board Math (BBM) aims to explore what kinds of learning become possible when the balance system participates directly in mathematical activity. In BBM, learners rock on a wooden balance board to explore a range of mathematical concepts including absolute value, angles, and functions. This project reimagines human-computer interactions in math instructional design to accommodate … Continue Reading »


Learning is Moving in New Ways UCB Committee on Research: Faculty Research Grants, 2008-2011 The Mathematics Imagery Trainer for Proportion: Make the screen green!


Signs of mathematics: Fostering the development of conceptual gestures among deaf students

Metaphor Retheorized

Mathematics learning as grounded in developing new sensorimotor perceptual structures.

Magical Musical Mat

A communicative platform that surfaces the embodied interactions of students in Special Education.

Special Education Embodied Design (SpEED)

Special Education Embodied Design (SpEED) sets out to develop guiding principles for building and running embodied design for special education students’ learning of mathematics.

Fractal Village

Dissertation Project, Sneha Veeragoudar Harrell Design-based research utilizing a critical and constructionist pedagogical philosophy in an alternative high school setting to study mathematical agency, computational literacy, and identity. Publications Veeragoudar Harrell, S., & Abrahamson, D. (2010). Second Life Unplugged: A design for fostering at-risk students’ STEM agency. In H. Gazit, D. L. Garcia, G. LeMasers, & … Continue Reading »

The Three M’s: Imagination, Embodiment, and Mathematics

Research into the mechanisms and potential role of imagination in mathematical reasoning. Abrahamson, D. (2006, June). The three M’s: Imagination, embodiment, and mathematics. Paper presented at the annual conference of the Jean Piaget Society, June 1-3, Baltimore, MD. ABSTRACT: The objective of this paper is to call for research into the mechanisms and potential agency of imagination … Continue Reading »

Distributed Learning in Practice and Theory

At the Center for Connected Learning and Computer-Based Modeling (Uri Wilensky, Director), we were: (a) building agent-based computer models as learning tools for students to simulate scientific, mathematical, and social phenomena; and (b) analyzing emprical data from our design experiments to develop theoretical models of cognition, teaching, and learning. These theoretical models were by and large expressed … Continue Reading »

Handing Down Mathematics: The Roles of Gesture in the Design, Teaching, and Learning of Ratio and Proportion

Analyzing videotaped classroom interactions to understand the roles of gesture in the design, teaching, and learning of mathematics. Publications Abrahamson, D. (2007). Handling problems: Embodied reasoning in situated mathematics. In T. Lamberg & L. Wiest (Eds.), Proceedings of the Twenty Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics … Continue Reading »

The Real World as a Trick Question: Mathematical Modeling, Knowledge, and Assessment

UCB Committee on Research: Junior Faculty Research Grant, 2006-7 [$6k] This research direction, part of the Seeing Chance project, consisted of conducting and analyzing probability-related clinical interviews with college students majoring in statistics to explore issues of intuitive reasoning. Abrahamson, D. (2007, April). The real world as a trick question: Undergraduate statistics majors’ construction-based modeling … Continue Reading »

Paradigmatic Didactical Mathematical Problematic Situations

In collaboration with Betina Zolkower, Ph.D., Brooklyn College, CUNY. In the PDMPS project, we designed, implemented, and evaluated an experimental curriculum for pre-service teachers and future education researchers enrolled in graduate-level college courses on mathematics cognition, learning, and instruction. Central to this design are selected ‘paradigmatic didactical-mathematical problematic situations,’ i.e., unique activities evoked as contexts for … Continue Reading »

Defining Practice

Overview Defining, a central practice in mathematics, is different from the daily practice of clarifying the meaning of words. Mathematics students often have trouble formulating definitions, interpreting new definitions, and using definitions in proof and problem solving. And whereas students may be able to state many mathematical definitions, these are often presented and received as … Continue Reading »

Giant Steps for Algebra

Overview Giant Steps for Algebra (GS4A) is the dissertation project of Kiera Chase. GS4A is a design-based research project investigating the cognition, teaching, and learning of early algebra. The project is centered on a technology-based activity, in which students use computer-interface resources so as to model a narrative about a giant burying stolen treasure on a … Continue Reading »

Seeing Chance

Bridging Informal and Formal Visualizations of Probability Experiments Seed funding: National Academy of Education/Spencer Foundation postdoctoral fellowship to Abrahamson, 2005-6 ($65k) The Marbles Scooper (design: Dor Abrahamson; engineering & production: Paulo Blikstein). Random sampling of four marbles. The Combinations Tower, the sample space of this probability experiment. An outcome distribution from a computer-based simulation of the … Continue Reading »


Create an engaging environment in which learners can have a collaborative, embodied experience of geometry.