A Comparative Study of Creative Solution Reasoning in Chinese and Canadian Math Tests

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

Abstract

Creative mathematically founded reasoning (CMR) is a creative solution reasoning to a problem, which creates new ideas or new strategies when solving mathematical problems. Creative mathematically founded reasoning is usually applied to solve math tasks that have low relatedness to the textbooks. It is more likely that students will be able to solve math tasks having low relatedness to textbooks by creative mathematically founded reasoning rather than other techniques. CMR is also likely to help students develop better conceptual understanding and creativity.
Under the direction of the Reciprocal Learning between Canada and China Partnership Grant in teacher education and school education, we investigate the requirements of creative mathematically founded reasoning in Chinese and Canadian math tests. In this study, we follow the framework from Palm, Boesen, & Lithner (2011), who devide reasoning type into imitative reasoning (IR) and CMR. They argue that imitative reasoning is applied to solve mathematical tasks successfully in most cases, however, when some mathematical tasks are not similar to tasks in the textbook, CMR could be needed that includes three conditions: novelty, plausibility and mathematical foundation (Palm, Boesen, & Lithner, 2011). Novelty means that a new sequence of solution reasoning is created, or a forgotten sequence is recreated. Plausibility means that there are arguments supporting the strategy choice and strategy implementation, motivating why the conclusions are true or plausible. Mathematical foundation means that arguments are anchored in intrinsic mathematical properties of the components involved in the reasoning.
As CMR requirements are closely related with low relatedness task to the textbook, we investigate the creative solution reasoning requirement through analyzing the mathematical tasks of the tests and the mathematics textbooks in China and Canada and calculate the proportion of low relatedness task in the math test. The Chinese textbook is published by the People’s Education Press and written in accordance with the curriculum standard issued by the Chinese Ministry of Education. The Canadian textbook is Math Make Sense and it meets the Ontario provincial math curriculum standards as stipulated by the Ontario Ministry of Education at the specified grade level/s. The chosen math tests from each country are representative final exams.
The results show that there are only a small number of creative solution reasoning requirement in the Chinese and Canadian math tests. It suggests that creative mathematically founded reasoning requirements in math tests should be increased to develop students’ ability. It is also suggested that additional low relatedness tasks are needed in math tests. We argue that, in both Chinese and Canadian school education, the importance of knowledge is over-emphasized while the cultivation of students’ abilities is less likely to receive attention. We have some suggestions on how we might cultivate the student’s abilities in problem solving.

Authors

• Xie Dan, Southwest University - China

• Aihui Peng, Southwest University

• Zhang lingling