Cognitive diagnosis and algorithmic cultural analysis of fourth-grade Yi students’ mathematical skills in China: A case study of several primary schools in Puge county, Liangshan prefecture

The Liangshan Yi Autonomous Prefecture is the largest area in China inhabited by the Yi people, and the original Yi characteristics and culture are well maintained. The Yi also have a high degree of ethnic and cultural intermingling with Tibetans, Han and other ethnic groups. The level of mathematical abilities directly determines the quality of mathematical learning of Yi students. Primary four is the stage of “concrete operations,” and is a critical point in the development of mathematical symbolic awareness. In this study, the geographical location of the school and the financial income of the township in which the school is located were used as the basis for sampling, and the DINA model was used to diagnose the mathematical ability of fourth grade students in three rural Yi primary schools in Puge County. The study found that there was individual variability in the mathematical abilities of fourth grade Yi students, with 21 different types of cognitive error patterns identified, the main ones being five. In addition, the state of knowledge of fourth grade Yi students in arithmetic revealed that their overall level of mathematical ability was low, showing a lag, with none of the knowledge attributes of arithmetic being fully mastered. Cultural differences between the Chinese and Yi languages contribute to the difficulties that Yi students have in learning mathematical operations, including differences in understanding the place value system, zero, decimal expressions, and differences in the perception of multiplication and division. The above research can inform the implementation of targeted remediation for teaching and learning.