BLOOMINGTON, Ind. – Algebra students could soon have an innovative new learning tool, and teachers the ability to track step-by-step progress, using technology developed at Indiana University. The technology allows static math problems to be manipulated by hand.
Students use the technology to engage with digital algebraic expressions. They open a browser on their electronic device and follow a URL link to a page with a set of algebraic expressions. These appear on the device’s screen in black handwritten text on a white background. Students touch the screen to move the terms around. Users can drag terms to solve equations or to simplify or rearrange expressions.
The researchers who developed the technology have launched Graspable Inc. to make sure their innovation gets into the hands of students and teachers who can benefit from their creation. The company was founded by Erik Weitnauer, president; David Landy, research and product leader; and Erin Ottmar, teacher outreach and content leader.
Weitnauer said that today, teachers have to spend a lot of their time practicing mathematical procedures with their students. This is because doing math on paper requires students to master the rules of algebra first. Yet by the time they do, there often is little time left to learn about the concepts behind the rules and how to flexibly apply them.
“Graspable Math, our flagship technology, creates a safe space for students to explore rules, concepts and applications at the same time,” he said. “It also provides immediate feedback on every algebraic step in a derivation.”
Weitnauer said Graspable Math has features and benefits for teachers that conventional mathematics learning and assessment systems lack. A video about Graspable Math is available online.
“Those systems are based on typing in solutions via an on-screen keyboard, which takes time and leads to typos. They don’t provide access to students’ work or outline step-by-step feedback,” he said. “Graspable Math tracks the steps a student takes so a derivation can be shared with the teacher or classroom. It also has tools that help make sense of an existing derivation.”
Weitnauer said Graspable’s founders want to improve algebra instruction by bringing recent findings in cognitive science into classrooms. They initially created the software as a tool to support their research.
“David has been researching for over 10 years how our brains allow us to reason with formal notations like algebra. The first prototypes of Graspable Math were created to test a hypothesis about how perception and motor systems are involved in doing algebra,” he said. “Erin has run studies in classrooms to look at student motivation and learning gains with our interventions compared to traditional methods. David and Erin are conducting further research into how using Graspable Math will influence classroom discourse and the language and gestures that teachers use.”
Graspable’s user interface is embedded into the Graspable Math canvas, a web application that resembles a digital whiteboard; the Graspable Math sidebar, an extension that allows users to change static math pages into dynamic expressions; and From Here to There, a game in which students solve math puzzles to gain points, unlock challenges and advance through levels.
“In the next year, we are focusing on content development, including lesson materials and assessments that use the benefits of Graspable Math; a second math game; and an online tool for teachers to build math problems,” Weitnauer said. “We are also talking to education technology companies about partnerships.”