The Impact on Algebra vs. Geometry of a Learner's Ability to Develop Reasoning Skills

In this master’s thesis, Dr. Lisa A. Johnson Q.M.E. examines the impact of three reasoning skills—number sense, structure sense, and abstract reasoning—on algebra and geometry. The study concentrates its efforts on data compiled from more than twenty researchers in this area, an extensive annotated bibliography, and work done at fictisciously named Union High School, real school classes consisting of 48 math students and eight math teachers. Through the efforts of this study, Dr. Johnson determined that algebra relies on abstract reasoning and structure sense, while geometry does not. Moreover, Dr. Johnson observed that further instruction needs to be given to teachers on communicating the three reasoning skills, as the teachers studied were not sufficiently knowledgeable in these areas. With teacher improvements, students in non-sufficient school systems could better excel in mathematics.