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Graspable Math: Making Algebra Notation Accessible (and Even Fun!) to Every Student

Explore and create
Pre-registration required

Explore and create : BYOD

Monday, June 24, 4:30–5:30 pm
Location: 118A

Taylyn Hulse   Katie Sawrey   Dr. Erik Weitnauer  
Students struggle with line-by-line problem-solving on paper. Make algebra hands-on by using learning technologies that utilize motion and digital notation. Learn how to use Graspable Math, utilize its data and leave with a set of playful, inquisitive activities that encourage exploration of algebraic patterns and concepts.

Audience: Coaches, Teachers, Technology coordinators/facilitators
Skill level: Beginner
Attendee devices: Devices required
Attendee device specification: Laptop: Chromebook, Mac, PC
Tablet: Android, iOS, Windows
Participant accounts, software and other materials: The attendees will need a Google account in order to save the digital materials they create.
While other devices and browsers might work, the ideal setup will be a laptop with a Chrome browser.
Focus: Digital age teaching & learning
Topic: Online tools, apps and resources
Grade level: 6-12
Subject area: Math
ISTE Standards: For Educators:
  • Design authentic learning activities that align with content area standards and use digital tools and resources to maximize active, deep learning.
  • Model and nurture creativity and creative expression to communicate ideas, knowledge or connections.
  • Provide alternative ways for students to demonstrate competency and reflect on their learning using technology.
Disclosure: The submitter of this session has been supported by a company whose product is being included in the session

Proposal summary

Purpose & objective

Students struggle with line-by-line problem solving on paper. To improve this, classrooms can make algebra more engaging and hands-on by using learning technologies that utilize physical manipulation and digital notation. In this session, participants will learn how to use Graspable Math, utilize its data, and leave with a set of playful, inquisitive activities that encourage exploration of algebraic patterns, rules, and concepts.

First, they will learn how to use the free Graspable Math ( system in terms of manipulating algebraic expressions and equations. This key skill cuts across many areas of mathematics content, especially number and equation properties, order of operations, linear and quadratic equations, and application areas including physics, chemistry, and other STEM disciplines.

Second, participants will learn how to use existing GM-based activities, and how to create their own. Participants will also learn how to use the teacher tools to effectively implement GM in their current curricula and classrooms. Participants will leave the workshop with all they need to implement a dynamic algebra based lesson in their classroom.


5 min
Introduction, get to know the audience, and objectives

10 min
Hands-on introduction to GM's work space and gesture-based algebra transformations Participants play a GM-based algebra game using their devices:

15 min
Research and examples of how to facilitate and integrate dynamic algebras into classroom context
Participants explore two GM-based classroom activities
Algebra Maze:
Linking Equations and Graphs:

10 min
Introduction of teacher Canvas tool to design lessons
Participants work through the demo with the presenters to create a lesson
Turning this:
Into this:

10 min
Walk-through of GM data through teacher dashboards.
Participants learn how to interpret, analyze, and apply data to inform instruction

10 min
Group discussion and recap of session objectives

Supporting research

Chazan, D., & Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions of curricular change. In (Eds.), A research companion to Principles and Standards for school mathematics, p. 123 – 135. Reston, VA: NCTM.
Goldstone, R. L., Landy, D. H., & Son, J. Y. (2010). The education of perception. Topics in Cognitive Science, 2(2), 265–284.
Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. H. (2017). Adapting Perception, Action, and Technology for Mathematical Reasoning. Current Directions in Psychological Science, 26(5), 434–441.
Kaput, J. J. (1999). Teaching and Learning a New Algebra. In Mathematics Classrooms that Promote Understanding (pp. 133–155).
Kaput, J. J., Noss, R., & Hoyles, C. (2002). Developing New Notations for a Learnable Mathematics in the Computational Era 1. In Handbook of international research in mathematics education (pp. 1–43).
Ke, F. (2016). Designing and integrating purposeful learning in game play: a systematic review. Educational Technology Research and Development, 64(2), 219–244.
Kirshner, D., & Awtry, T. (2004). Visual salience of algebraic transformations. Journal for Research in Mathematics Education, 35(4), p. 224 – 257.
Landy, D., Allen, C., & Zednik, C. (2014). A perceptual account of symbolic reasoning. Frontiers in Psychology, 5(April), 1–10.
Landy, D. H., & Goldstone. (2007). Formal notations are diagrams: Evidence from a production task. Memory & Cognition, 35(8), 2033–2040.
Weitnauer, E., Landy, D., & Ottmar, E. (2016, December). Graspable math: Towards dynamic algebra notations that support learners better than paper. In Future Technologies Conference (FTC) (pp. 406-414). IEEE.
Martin, T. (2009). A Theory of Physically Distributed Learning : How External Environments and Internal States Interact in Mathematics Learning. Child Development Perspectives, 3(3), 140–144.
Sarama, J., & Clements, D. H. (2009). “Concrete” Computer Manipulatives in Mathematics Education. Child Development Perspectives, 3(3), 145–150.
Sedig, K. (2008). From Play to Thoughtful Learning: A Design Strategy to Engage Children With Mathematical Representations. The Journal of Computers in Mathematics and Science Teaching, 27(1), p. 65–101.

More [+]


Taylyn Hulse, Worcester Polytechnic Institute
Katie Sawrey, Worcester Polytechnic Institute
Dr. Erik Weitnauer, Graspable Inc.

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