A comparative analysis of proficiency ratio and
achievement probability of cognitive attributes related to mathematical
word problem solving in students with mathematical difficulties
and normal students by applying Rule Space Model
Koh, Hye jung (Seoul National Univesity)
Kim, Dong il (Seoul National Univesity)
In order to understand what students with mathematical difficulties are struggling with, in this study, we compared to proficiency ratio and achievement probability of cognitive attributes related to mathematical word problem solving. The participants of this study were 977 4th grade students. Attributes related to mathematical problem solving were extracted and a Qmatrix showing the relationships between the cognitive attributes and the items were developed. RSM analysis was used to find the students’ cognitive attribute type. As a results, a difference of cognitive proficiency ratio and attribute mastery probabilities between normal students and students with mathematical difficulties was significant. Overall, cognitive proficiency ratio and attribute mastery probabilities of students with mathematical difficulties were lower than the normal students, the proficiency ratio of the cognitive attributes of the students with mathematical difficulties were in this order: addition, multiplication, subtraction, and division. Specifically, students with mathematical difficulties showed low cognitive proficiency ratio and achievement probability in most attributes including cognitive attribute(division and arithmetic operation) and cognitive attribute(carrydown) except for the cognitive attribute(addition and arithmetic operation). Considering these results, teachers will be able to determine teaching contents and materials according to hierarchy needs of students with mathematical difficulties. This information can also be applied to educational curriculum and teaching methods for students
with mathematical difficulties.
* Key words : Rule Space Model(RSM), student with mathematical difficulties, word problem solving, cognitive attribute, cognitive proficiency ratio, attribute mastery probabilities
