Mathematics textbooks for teaching

Abstract

An analysis of content knowledge and pedagogical content knowledge concerning algebra in mathematics textbooks in Swedish upper secondary education

How to solve quadratic equations is a common teaching topic in upper secondary school algebra. This study has the interest in analyzing algebra content knowledge related to quadratic equations and factorization in mathematics textbooks at upper secondary level. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. On the other hand, what is missing from the textbook may not be presented by the teacher. Textbooks contain both subject knowledge and pedagogical knowledge.

This thesis is about analyzing the algebra content related to factorization and quadratic equations from a teaching perspective, as presented in mathematics textbooks at Swedish upper secondary schools. The analysis focuses on algebra content related to factorization and quadratic equations as subject matter content knowledge (CK) and the embedded pedagogical content knowledge (PCK) in the textbooks. The main aim is to explore what pedagogical content knowledge regarding quadratic equations–is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom.

The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The analysis contains four rounds of analyses. The results of the first three rounds of analyses have set up a basis for the deep analysis of one selected textbook.

The results show that there is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula; the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models traced back to algebra history. These four geometrical models are applied for illustrating algebra rules and construct five embedded hypothetical teaching trajectories and an overall teaching trajectory. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the embedded pedagogical content knowledge related to quadratic equations.