Developing a learning progression for number sense based on the rule space model in China

Abstract

The current study focuses on developing the learning progression of number sense for primary school students, and it applies a cognitive diagnostic model, the rule space model, to data analysis. The rule space model analysis firstly extracted nine cognitive attributes and their hierarchy model from the analysis of previous research and the mathematics textbook used in Beijing. A cognitive diagnostic test for number sense was then developed based upon the cognitive attributes. Finally, the model was used to analyse a sample of 1207 Chinese primary school students’ observed item responses to identify their knowledge states and to validate and modify the hypothesised learning progression. The results showed that the test was of good psychometric quality, and that the hypothesised learning progression was generally validated. By applying the rule space model, the hypothesised learning progression was modified at each level. The results also showed that students in grade 3, grade 4 and grade 5 were mainly classified into level 1 and level 2, level 2–level 4 and level 5 of the modified learning progression, respectively. These results suggest the feasibility and benefits of using cognitive diagnostic models to develop learning progressions.

Keywords:

• Number sense
• learning progression
• rule space model
• cognitive diagnostic model
• learning path

Acknowledgements

We would like to thank the students, teachers and experts for participating in and assisting with the present research.