Mid Sweden University

For many students, algebra is one of the most difficult areas of mathematics, and limited algebra knowledge, particularly concerning algebraic symbols, can hinder students’ successin other areas, such as physics (Pospiech, et.al., 2019). In a Swedish context, algebra and algebraic symbols are usually introduced in grades 7-9 (age 13-15), and are then taken for granted in grades 10-12, also in physics. Thus, it is important to identify similarities and differences in how algebra is taught and used in the different contexts of mathematics and physics. This pilot study, focusing on the use of algebraic symbols, is part of a larger project contributing to a more holistic view of students’ algebraic knowledge in different parts of the educational system. We take a discourse perspective, where the algebraic discourse is characterized by the word-use and visual mediators (e.g., symbols), among other things (Sfard, 2008).

We analysed common Swedish textbooks for the first physics course and the first mathematics course at upper secondary level (grade 10). Content of both textbooks was categorized with respect to, for example, symbols that were used (e.g., Latin or Greek letters), number of different and similar symbols in symbolic expressions, words used to address (part of) symbolic expressions, and overall mathematical context of the symbolic expression (e.g., calculation with a fixed value or derivation of one expression from another). Preliminary results, here delimited to differences, show that on average it is a greater number of different symbols in expressions in the physics textbook compared to mathematics. Calculations with specific values are more common in physics, whereas it is more common that algebraic entities relate to each other in mathematics. In mathematics, more than half of the symbolic expressions are never referred to using words, while the same is true in physics for 18% ofthe expressions. Commonly used physics words in the mathematics textbook were time and distance, while time was not common in the physics textbook, when referring to symbolic expressions. These differences imply that students meet different algebra discourses in mathematics and physics. Thus, it can be hard for them to identify these discourses as “the same mathematics”. By being aware of these differences, teachers can facilitate students’ use of algebra, and in the long run, students’ learning in both mathematics and physics.

References

Pospiech, G., Michelini, M., & Eylon, B-S. (Eds.). (2019). Mathematics in physics education.Springer. https://doi.org/10.1007/978-3-030-04627-9.

Sfard, A. (2008). Thinking as communicating: Human development, the growth of discoursesand mathematizing. Cambridge University Press.