Research highlights power of interactive, gesture-based lessons when teaching abstract math concepts

Colorado State University researchers are exploring how nonverbal communication can be leveraged by faculty to reach educational goals and support individualized learning around abstract mathematical concepts.

The work is led by Professor Hortensia Soto and is described in a new paper. published I Issues, Resources, and Issues in Undergraduate Studies in Mathematics (PRIMUS). This paper shows how gestures and body language can be used to explain abstract algebraic ideas that may be difficult for students to engage with in formal teaching methods.

This work extends Soto’s research into embodied cognition. Mathematics educationUsing body gestures with speech to help students develop meaning and communicate. To explore this imagining In the paper, Soto and his team studied teachers’ practices. Undergraduate students Communicated in an abstract algebra classroom setting that prioritized two-way participation and nonverbal communication.

The paper examines how the resulting organic interactions in the classroom focused on key concepts while also promoting equity and supporting diverse learning needs.

“Part of this experiment was to give students a space to feel free to comment with gestures — not just in writing or speaking, but through their bodies,” said Soto, who is part of the math department. “This was already happening in an organic way, but this work shows how teachers can interact with and re-enforce this instinct in students to support learning through multiple senses. can.”

To illustrate this concept, Soto notes that many children are often taught that counting on their fingers is not the “correct” way to do math. However, using fingers or other types of body movements can reduce the cognitive load required to learn something new, and this benefits students, teachers, and even mathematicians. Likewise, incorporating physical materials into lessons can provide another resource for students who have difficulty verbalizing ideas.

The paper documents and explores these types of activities as the instructor invites students to participate through gestures or reuse of a student’s organics. Body language To help the lesson progress. Soto said there is no single “right way” to integrate these types of activities into the classroom, but that they can be powerful tools to aid learning and communicate concepts.

He said that we convey information to others through our body before speaking. It is not until much later that we find symbols to write down our thoughts and words. “Often we start with a very formal way of teaching these concepts because that’s how we’re taught, and students may not be ready for that.”

Students learning under this method may or may not have a better understanding of the material in the assessment setting, Soto said. Instead, he said, this type of approach aims to support fluency around abstract concepts and better prepare students to engage with subsequent formal definitions, theories, and proofs. .

Alyssa Romero, a co-author on the paper and a graduate student at CSU, said the work had practical implications for teachers at any grade level and wasn’t limited to gestures.

“For example, before introducing a formal mathematical definition or theory, a teacher can also develop a mathematical idea in terms of everyday experiences,” he said.

Jesse Lajos is also a co-author on it. Paper and Assistant Professor at Utah State University. Lajos said the instructor’s focus on classroom activities and the use of embodiment not only supported students’ abstract thinking, but also brought play and joy to the classroom.

Research shows that evidence of learning in the classroom doesn’t have to look like something procedural or formal, Soto said.

“Not everyone is ready for formality, and teachers can create activities in their own way that nurture what students are saying with the body,” she said.

“It requires creativity and rethinking how we teach abstract math concepts, but you can start by telling them, ‘Your clue told me something about what You got it.'”