The Algebraic Thinking of Mathematics Teachers in China and the U.S.

The purpose of this study was to examine U. S. and Chinese secondary mathematics teachers’ knowledge and beliefs. To give insights into cross-national differences in student achievement, this study investigated teachers’ content knowledge about quadratic equations and functions, teachers’ knowledge of students’ errors about quadratic equations and functions as well as teachers’ beliefs about students’ mathematical learning abilities.

Twenty Chinese high school teachers and twenty U.S. high school teachers participated in the study and finished the specific designed survey. The teachers’ responses were analyzed quantitatively and qualitatively. Analysis results revealed that more Chinese teachers than U.S. teachers correctly employed a quadratic function to represent a real-world situation and obtained two solutions for a quadratic equation. In terms of translation among various representations of quadratic functions, all the teachers in the two groups showed their proficiency. The two groups of teachers mostly employed procedural-based explanations in obtaining their solutions.

With respect to teachers’ knowledge of students’ errors, the Chinese teachers provided more negative evaluations toward students’ errors and identified more students’ errors than the U.S. teachers did. Responding to students’ errors, the two groups of teachers were more likely to focus on procedural knowledge if students were not able to finish problems. When students finished solving problems, the two groups of teachers highlighted conceptual explanations targeting students’ mistakes. The U.S. teachers were more likely to provide general knowledge guidance while the Chinese teachers tended to go back to basic knowledge.

Concerning teachers’ beliefs about students’ mathematical learning abilities, the Chinese teachers tended to believe that students’ mathematical abilities are fixed and the focus of students’ learning is to obtain positive evaluations. However, most of the U.S. teachers believed that students’ mathematical abilities are not fixed and the goal of students’ learning is to improve their mathematical proficiency. Although the two groups of teachers agreed on setting up different expectations for high-level and low-level students, they held that students could achieve a behavior pattern of seeking opportunities to solve challenging problems. Implications for teachers, teacher educators, mathematics education researchers as well as policy makers have been discussed in accordance with the findings.