Mathematical thinking in the intended curriculum in China and three case studies in the implemented curriculum

Abstract

Mathematical thinking, as a process of mathematics, is much more important than mathematics as a product. Developing students’ process skills can benefit to them in problem solving in school education and in society. Mathematical thinking has been one of the most prominent teaching and learning goals in mathematics education and is, for example, one of the “Four Basics” in Chinese mathematics education. However, although the extant literature suggests that significant scholarly attention is being paid to mathematical thinking, a common definition has not yet been reached and relatively few empirical studies exist on the teaching of mathematical thinking in the classroom. This study aims to first explore from a historical perspective the various descriptions of “mathematical thinking (Shuxuesixiang)” provided by Chinese official documents and researchers in the intended curriculum. To consider the implemented curriculum level, three case studies are undertaken with three teachers who have the same amount of teaching experience but are teaching different lessons at different schools. Their interpretations of mathematical thinking are investigated through interviews, with thematic analysis of the collected data. The enactment of mathematical thinking in the teachers’ lesson planning and classroom teaching are explored through collecting the textbooks, lesson plans, PowerPoint slides and lesson videos they use and then developing an analytical framework containing eight types of mathematical thinking, with reference to the literature for the analysis. The findings reveal that the mathematical method is always involved in mathematical thinking, both in the explanations of the intended curriculum and in the views of the three teachers studied. When students think about how to select, determine and apply mathematical methods in problem solving, the process can be seen as their mathematical thinking. The major findings from studying the teachers’ practice include that (i) they aim to raise the level of thinking demanded in the tasks designed in the textbooks but usually adapted in their lesson plans; (ii) they use questioning as the main way to prompt students’ mathematical thinking; and (iii) most of the questions and oral statements they use to prompt mathematical thinking provided or followed obvious answers and explanations. Overall, mathematical thinking as one of the “Four Basics” in the new Curriculum Standard 2011 can be accepted by the teachers, but they may not implement it in their teaching due to various factors, such as the students’ quality and limited lesson time. This study has both theoretical and practical significance. Theoretically, this research provides a comprehensive understanding on mathematical thinking as Shuxuesixiang in a Chinese context, which can broaden researchers’ views on mathematical thinking, particularly the understanding of it embedment in intended and the implemented curriculum. This study also carries practical implications that in-service teachers should pay attention to their questions if they want to prompt students’ mathematical thinking and that relevant training programmes should be provided for teachers.