PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Students’ Understanding of Quadratic Equations
Page: 1721
Action–Process–Object–Schema theory (APOS) was applied to study student understanding of quadratic equations with one variable. This requires proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may use to understand quadratic equations. The genetic decomposition, which was proposed, can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data was obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.