Are better teaching methods the answer to improved math proficiency or are we simply barking up the wrong tree?

Abstract

The Organization for Economic Cooperation and Development (OECD) administers its Program for International Student Assessment (PISA) study once every three years to assess the scholastic performance of fifteen-year-old students in the field of mathematics, science and reading. This study is conducted among OECD member nations and select non-member nations. Results from the PISA study consistently show that, on average, the United States ranks poorly in mathematics when compared against most of the other OECD member nations. While disparity in math proficiency may exist between states and opinions may differ on the way samples were collected from each nation for the study, the generally poor proficiency in mathematics among students at the K-12 level has serious implications as they advance into undergraduate studies, especially in STEM fields. Students who lack strong fundamentals in mathematics at the K-12 level will find themselves struggling to overcome the steep learning curve in courses discussing the concepts of calculus and differential equations when they are also already grappling with simpler concepts such as basic trigonometry and linear algebra. This constant struggle could lead to demotivation among students and retention issues in STEM colleges. Various literature highlights the difficulties that students face when learning mathematics, and numerous pedagogical discussions were made with the hope that the teaching of mathematics can be done more efficiently and more effectively. Yet the fact that the United States, as a whole, shows little improvement, if any, in the PISA rankings for math proficiency in the past decade indicates that there are underlying problems which may not be solved by just proposing new teaching methods. In this paper, we inspect the merits of emphasizing the fundamentals of mathematics and how a solid grounding in mathematics can be founded on "trivial" methods, as well as how they can be invaluable to help students segue into developing their computational thinking skills. The factors that lead to an apparent stagnation in math proficiency among students are identified and discussed to ascertain whether new teaching methods are the answer to improving math proficiency among students. We consider the observations made by instructors from Texas Tech University about the apparently poor mastery of basic mathematical skills among freshmen engineering students. These instructors teach an introductory course that covers mathematical methods to solve problems on trigonometry, systems of linear equations, quadratic equations, sample statistics, vectors, etc. These observations, coupled with higher expectations by universities on their students, provide the motivation for the discussion that will follow in this paper. Finally, we discuss a path forward for engineering undergraduate students who are struggling to keep up with the mastery of pre-college mathematical skills needed prior to pursuing their engineering core courses.