A novel approach to teaching Algebra

A novel approach to teaching Algebra


Photo by Kathy F. Atkinson | Illustration courtesy of Teo Paoletti

Unlike other primary and secondary school math courses, algebra is beginning to introduce relationships and abstract ideas. While textbooks try to provide students with real-world illustrations of these new concepts, many students struggle to combine what they are learning in the classroom with concrete experiences.

For students struggling to master these fundamental concepts, the challenges of algebra can have long-term economic and social impacts. Algebra often serves as the guardian of future math and science, technology, engineering, and math (STEM) courses. How can K-12 educators help their students develop this critical algebraic knowledge?

Teo Paoletti of the University of Delaware, who is an assistant professor in the School of Education (SOE) at the Faculty of Education and Human Development (CEHD), said he thought the answer might be to help students develop covariate reasoning or the ability to reason about relationships as quantities change together. He has received a considerable grant from the National Science Foundation (NSF) that can help advance his research. Through the Covariate and Algebraic Reasoning Project: A New Path to Algebra (CARe Project), Paoletti will create and test digital instructional tasks designed to support high school students’ covariate reasoning through a free educational technology platform. He hopes to integrate education and research to create a new path to learning algebra for high school students.

In support of this new approach to teaching and learning algebra, Paoletti received a nearly $ 885,000 NSF CAREER award, one of the organization’s most prestigious awards. These awards support beginning-of-career professors who have the potential to serve as academic role models in research and education and to lead advancements in their organization’s mission.

“Part of what makes school algebra so difficult for students is that it can feel really abstract and different from what they experience in their day-to-day lives,” Paoletti said. “When they learn to add, subtract, multiply and divide numbers, students have concrete experiences in which they can draw. However, algebra is more complex than arithmetic. By designing opportunities for students to see and experience changing quantities in context, they can begin to represent the relationships between these changing quantities. My goal is for students to see how they can use algebraic graphs and expressions as representations of the specific relationships they conceive in a situation. This approach can not only provide a more accessible way to enter algebra, but also better connect with how algebra is used in the fields of science and engineering. “

What is Project CARe?

In the CARe Project, Paoletti will explore how the ability of high school students to reason covariateally can help them develop an understanding of ideas that are critical to learning algebra. Specifically, it will investigate how students’ covariate reasoning can serve as a basis for the development of algebraic reasoning and identify instructional pathways — or what teachers can do in the classroom — to support their reasoning.

A series of new digital instructional tasks, designed and piloted by Paoletti, serve as the basis for this project. Using the free and publicly available Desmos platform, Paoletti will create a sequence of research-based teaching activities, including teacher support materials, that have been effective in supporting students ’algebraic and covariate reasoning.

For example, the tap task, which asks students to make predictions about water flow and temperature changes as they adjust the hot and cold buttons on a digital faucet, is designed to help students develop the tap. understanding of graphic representation. After playing with the buttons and observing the animated changes in flow and temperature (indicated by color changes), students are asked to make predictions about how specific actions, such as turning on the cold button slowly, will affect the flow and water temperature. Students then practice drawing these relationships.



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