Utilizing Conceptual Anchors in Mathematics to Promote Enduring Conceptual Knowledge and Procedural Skills

Abstract

Conceptual understanding and procedural knowledge in mathematics are at the core of what enables high school mathematics student to transfer successfully learning from one mathematical content area to another. While procedural knowledge, at its base level, can be memorized in a rote, mechanical manner, conceptual understanding requires an ability to connect a mathematical concept to multiple representations (e.g. algebraic, geometric, numerical). Mathematics educators aim to develop lasting mathematical understanding in their students so as to minimize misconceptions and prepare students for future studies. This thesis evaluated whether a student exploration could serve as a conceptual anchor designed to promote long-term understanding and enduring procedural mastery. Limited data from the research did not demonstrate benefits of the student exploration that served as a conceptual anchor. There is a possibility that the students who practiced rote procedures retained facility with those procedures better than the students who spent time with a mathematical exploration. However, there is no conclusive evidence that the students who demonstrated an enduring procedural mastery had a better conceptual understanding. Additionally, the students enrolled in honors level courses tended to outperform the students enrolled in non-honors-level courses on questions pertaining to both procedural skills and conceptual understanding, but they did not retain those skills or that understanding any better than the students enrolled in non honors-level courses. More research needs to be conducted to explore further the question of how to promote enduring mathematical understanding in high school students.