| dc.description.abstract | Textbooks continue to play an important role in teaching and learning. Coherence is an assumed feature of all textbooks, but it is ill-defined and rarely examined in detail. In the first study, I developed a framework for examining textbook coherence at three levels: macro-logical coherence, meso-lesson-structure coherence, and micro-example-practice coherence. Then I used this framework to analyze textbook coherence on the topic of equivalent fractions in the three series of mathematics textbooks selected from California, Shanghai, and Singapore, respectively. The findings suggest the feasibility of a framework that can contribute to our understanding of textbook coherence and to the possible improvement of specific topic presentation and organization in textbooks. The second study focused on example-practice coherence by analyzing all problems from the chapters on fractions in the three series of mathematics textbooks. Since problems are important components of school mathematics textbooks, the variation of problems should be in line with students’ cognitive levels. To examine example-practice problem coherence, I developed a conceptual framework for problems’ cognitive requirement in terms of five aspects of variations: response, operation, reasoning, representation, and connection. After comparing the coherence between example and practice problems in terms of these five aspects, the results show that these textbooks have different emphases. California textbooks emphasize the variations of problems in operation and reasoning. Shanghai textbooks emphasize the variations of problems in connection and representation. Singapore textbooks emphasize the variations of problems in reasoning and response. The third study aimed to examine U.S. and Chinese teachers’ knowledge for teaching equivalent fractions. A conceptual framework for instructional coherence was developed based on the MKT model.
his framework includes two aspects: coherence of mathematical content and coherence of mathematical pedagogy. Based on this framework, I designed the interview tasks and interviewed ten U.S. and ten Chinese math teachers, separately. After analyzing and comparing teachers’ responses, the findings reveal the different emphases on teaching between selected U.S. and Chinese teachers and also suggest the feasibility of the framework that can contribute to the understanding of the instructional coherence and improve teachers’ mathematical knowledge for teaching. | en |
