Insights into the Teaching of Gradient from an Exploratory Study of Mathematics Textbooks from Germany, Singapore, and South Korea

Textbooks, which form the staples of a teacher’s set of resources, play a critical role in deciding what and how mathematics is taught in classrooms. However, textbooks do not always present concepts in ways that enhance understanding by students, nor are they always comprehensive in the treatment of a topic. In this exploratory study, we analyse three mathematics textbooks from Germany, Singapore, and South Korea to examine how gradient, an important but not well-understood concept, is presented. For each of the textbooks, we characterise the introductory chapter on gradient in terms of contextual (educational factors), content, and instructional variables in relation to the curriculum emphases across the three countries. In addition, we represent these findings using visual representations, which we called textbook signatures. We share insights from our analyses, raise questions, and suggest implications for future research in textbook analyses and ways to represent the findings from such analyses.