| Summary: | This study examined teachers‘ knowledge for teaching algebra, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. An embedded mixed methods design was adapted, a design in which the main data set consists of written answers to a questionnaire, while the supportive data set is comprised of the written answers to open-ended questions and follow-up interviews. A structural equation model was adopted to analyze the status and structure of teacher knowledge for teaching algebra in China and the U.S. A qualitative analysis of the answers to the open-ended questions and follow-up interviews is aimed to further illustrate and interpret the quantitative findings.
Three hundred and seventy six Chinese and 115 U.S. prospective middle and high school mathematics teachers participated in this survey. Based on an extensively quantitative and qualitative data analysis, the following conclusions were made. First, the Chinese participants demonstrated a stronger knowledge for teaching algebra when compared with their U.S. counterparts. Second, the structure of knowledge for teaching algebra of the Chinese participants is much more interconnected than that of their U.S. counterparts. Third, the Chinese participants showed flexibility in choosing appropriate perspectives of function concept and in selecting multiple representations in contrast to their U.S. counterparts. Fourth, this flexibility is found to be closely related to school math and teaching math. Finally, the number of college math and math education courses taken impacts teachers‘ knowledge for teaching algebra.
The findings of this study hold several implications for mathematics teacher preparation in general and studies on mathematics teachers‘ knowledge in particular. Theoretically, the complexity of understanding and measuring mathematics teachers‘ knowledge for teaching was examined and discussed. This study also enriches the understanding of mathematics teachers‘ knowledge for teaching at middle and high schools in China and the United States. Specifically, the Chinese practice of developing teachers‘ basic knowledge, skills, and flexibility provides an alternative for U.S. mathematics teacher educators to reflect on their practice. Practically, what we can learn from this study to improve mathematics teacher preparation in China and the U.S. is discussed. Finally, the limitations of this study are discussed and further studies are suggested.
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