Lost in translation: comparing the mathematics in high school physics and mathematics textbooks

Mathematics courses should prepare students to use mathematics in a range of contexts, including science. However, students often struggle in applying mathematics in physics courses, even when they understand the mathematical content (Rebello et al., 2007). Often the root of this struggle is attributed to the student or the teaching; rarely is the form and function of the mathematics itself considered. Yet some have suggested that mathematics is used differently by physicists and mathematicians resulting in two different “languages” of mathematics (e.g., Redish & Kuo, 2015). This curriculum study identifies and describes differences in mathematics, specifically right triangle trigonometry, as manifested across high school physics and mathematics textbooks. Textbooks with different curricular approaches were selected for physics (i.e., Holt McDougal Physics, Active Physics) and mathematics (i.e., Holt McDougal Geometry and Algebra 2, Geometry Connections and Algebra 2 Connections). Since differences between these textbooks could come in a variety of ways, a broad definition of mathematics, including mathematical content, practices, and language, was used. Analysis included developing a coding scheme for understandings of trigonometry content using an iterative emergent process, coding tasks for opportunities for mathematical practices as described in the Common Core State Standards, and writing lesson memos to capture salient features of mathematical content, practice, and language. Findings expose significant differences in how right triangle trigonometry is used, the features of right triangle diagrams, and the opportunities provided for mathematical practices across physics and mathematics textbooks. In mathematics textbooks, sine, cosine and tangent ratios are used to find unknown measurements in a right triangle and tangent is also used to describe a slope. In physics textbooks, trigonometric ratios have more specialized uses, with tangent being used to find the direction of a vector and sine and cosine used to calculate the components of a vector. Right triangle diagrams in mathematics textbooks may be provided by tasks and are used to model static scenarios involving lengths in application tasks. In contrast, tasks in physics textbooks prompt a reader to generate their own right triangle diagram to model dynamic scenarios involving more abstract quantities (e.g., force, velocity) represented as vectors. Tasks in physics textbooks that involve the analysis of forces acting on an object provide different and specific opportunities for mathematical practices not found in mathematics textbooks. This study reveals that students may be experiencing mathematics differently between their physics and mathematics courses, which may explain why students struggle to use mathematics in physics class. Furthermore, this study demonstrates the value of comparing the mathematics situated in textbooks from different disciplines (i.e., not only mathematics textbooks) and opens new avenues for future research