A Curriculum Project on Incorporating Proofs in Lessons to Deepen Students’ Understanding of Mathematical Concepts

Abstract

This curriculum project provides secondary mathematics teachers with lessons that incorporate proofs to deepen student understanding of mathematical concepts through mathematical reasoning and discourse. The use of proofs in secondary math is essential to prepare students for college mathematics expectations. Mathematical proofs are difficult for students because it is not something that they often see throughout their secondary education. The Constructivist Learning Theory states that students learn by building on prior knowledge to create new understanding, thus each lesson in this curriculum project begins with a review section to connect prior learning to new concepts. Likewise, the use of the Growth Mindset and grit, also used in the curriculum, can encourage students to believe in their mathematical abilities. Encouraging students to attempt questions or proofs without providing immediate support can send a message that they are capable of meeting high expectations. Within the curriculum project there are four lessons: Introduction to Proofs; Quadratic Formula; Properties of Paralellograms; and Remainder Theorem. The last three lessons align with the curriculum for Algebra 1, Geometry, and Algebra 2 respectively. The first lesson was designed to introduce proofs before they are applied in any of these courses.