Representation of Problem Solving in Canadian and Chinese Elementary Mathematics Textbooks: A Comparative International Study

• In Event: 41.021 - Approaches to Cross-Cultural Reciprocal Learning Between Mathematics Educators: Collaborations Between Districts, Schools, and Teachers

Abstract

Mathematics textbooks play a fundamental and pervasive role in mathematics classrooms including serving as a vehicle for change in the curriculum, exposition of mathematics content, presentation of problems, positionof mathematics course as the centerpiece, transmission of an ideal curriculum, definition of mathematics branches as a subject in students’ minds, and vehicle for learning mathematics (Usiskin, 2013). Undoubtedly, mathematics textbooks shape the way we teach and learn mathematics.
Problem solving has long been a crucial component of school mathematics, and the issue of how problem solving is represented in school mathematics textbooks has recently received considerable attention from researchers (Fan & Zhu, 2007; Peng & Song, 2015). Results from these research studies suggest that the varied weightings or values attached to overall mathematics education in different educational systems may influence the representation of problem-solving procedures, and accordingly, the impacts on students’ learning of problem solving in specific educational systems (Fan & Zhu, 2007).
Under a broader seven-year Reciprocal Learning Partnership Project in teacher education and school education between Canada and China (Xu & Connelly, 2014), this study aims to investigate how problem solving procedures are represented in elementary mathematics textbooks in Canada and China - two countries with distinctly different educational systems and varied mathematical educational values - so as to see how the representation of problem solving procedures in textbooks can be improved upon in both countries.
The chosen mathematics textbooks from each country are widely used textbooks in each respective country, state, or province. The Chinese textbook is published by the People’s Education Press and is written in accordance with the curriculum standard issued by the Chinese Ministry of Education. It is called The Compulsory Education Textbooks-Mathematics. The Canadian textbook is Math Makes Sense and it meets the Ontario provincial math curriculum standards as stipulated by the Ontario Ministry of Education at the specified grade level/s. We examined the problem solving procedures by analysing the problems introduced in the main text parts of the textbooks. The specific analysis of problem-solving procedures is carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model (Polya, 1971), and specific strategies, which consisted of different problem-solving heuristics such as ‘acting it out,’ ‘looking for a pattern,’ ‘working backwards,’ etc., adapted from Fan and Zhu (2007).
Our results indicate that, at the general strategies layer, the Chinese textbook exhibits a more explicit presentation than the Canadian textbook because it gives clear labels at each problem solving stage, so it is easier for the readers to distinguish and identify the different stages involved. At the specific strategies layer, both the Canadian and Chinese textbooks introduces a considerable number of problem-solving heuristics through the representation of problem solutions, but the frequency of using specific heuristics in both textbooks differ. We explored the possible reasons for the similarities and especially for the differences. We end with suggestions on problem-solving heuristics employed in elementary school classrooms in Canada and Chinaand suggested improvements on the representation of problem solving in mathematics textbooks in both countries.


Authors

• Aihui Peng, Southwest University

• Anthony Ezeife, University of Windsor

• Bo Yu, Southwest University