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

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 20 researchers in this area, an extensive annotated bibliography, and work done at fictitiously 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.

Dr. Johnson holds two bachelors in sciences; three master's degrees, one of which is in Math Education Curriculum, and a doctorate degree. She attributes her success to her parents and sisters. This is her second publication.