Advanced mathematics knowledge of senior secondary school teachers in China and its influence on classroom teaching

Abstract

Results of international studies suggest East Asian students’ outstanding mathematics achievement can be partially attributed to their teachers’ high levels of competence in mathematics knowledge. Also, the image of the mathematics teacher in East Asian tradition is that of an expert scholar in mathematics. These phenomena suggest a consensus that teachers should possess sufficient advanced mathematics knowledge (AMK) to become, in the school context, a mathematician or mathematics expert. However, evidence for this is still lacking, and the relevance of AMK to the quality of classroom teaching is ambiguous. This research developed a test of teachers’ AMK on the topic complex numbers. Four teachers with different performances in the AMK test were selected from 243 in-service senior secondary school teachers in China who completed that test. A series of lessons taught by these four teachers on the same topic, complex numbers, were videotaped and analyzed using the Mathematical Quality of Instruction (MQI) video analysis protocol. In addition, the classroom teachings of the four teachers were compared in a more detailed manner, by means of case study. The results of the AMK test indicate that a large percentage of teachers failed to reach the crucial “advanced standpoint” in school mathematics, although some teachers got excellent scores. Moreover, we found that teachers’ first degree major, gender, and the level of the schools in which they taught were three influential factors in their AMK competence. The findings also suggest that although some contextual factors, such as students’ or school characteristics, might mediate the expression of AMK in teaching senior secondary school mathematics, AMK was still strongly positively related to the quality of classroom teaching. This study confirms that AMK occupies a significant place in the knowledge system of senior secondary school teachers, and is indispensable for the high-quality teaching of senior secondary school mathematics. Recommendations are offered for mathematics teacher education programs, the professional development of mathematics teachers, and teacher recruitment criteria.