How Textbooks Influence Students’ Algebra Learning: A Comparative Study on the initial treatment of the concept of function

To give insights into cross national differences in schooling this study analyzed the initial treatment of the concept of function in three curricula: a US standards-based text--Connected Mathematic 2: Variables and Patterns, a US conventional text--Glencoe: Mathematics Applications and Concepts: Course 2, and a Chinese reform text--Shu Xue: Grade 8, first volume.

This study examined content organization and problem features in the three textbooks. For content analysis, this study explored how the concept of function was introduced, defined, and developed. The results indicated both of the US textbooks introduce this concept at grade 7 whereas the Chinese text does so at grade 8. Connected Mathematics devotes more lessons than the Chinese text and Glencoe in the initial treatment of the concept of function. Connected Mathematics defines function as rule while Glencoe addresses it as relationship; the Chinese text introduces the concept of function as correspondence. Connected Mathematics pays equal an amount of attention to the four representations including tables, graphs, verbal descriptions, and equations examined in this study. In contrast, Glencoe employs the representations of tables, graphs, and equations and it focuses on the representation of graphs; the Chinese text also employs the representations of tables, graphs, and equations but it focuses on the representation of equation. The Chinese text provides many explanations and illuminations in worked-out examples to tell how the solutions are derived.

Problems were then analyzed extensively with respect to three criteria: (1) contextual feature, (2) response type, and (3) cognitive expectation. Analysis results showed that all the three texts emphasize the cognitive expectation of representation. Connected Mathematics provides more real-world problems than other texts; and the problems aim at cultivating students’ mathematical reasoning. Most of the problems in Glencoe are embedded in pure math contexts to help students do procedure practice. The problems in the Chinese text emphasize problem solving. Implications for curriculum developers, teachers, and researchers have been discussed in accordance with the findings.