Trends of progression of student level of reasoning and generalization in numerical and figural reasoning approaches in pattern generalization

Abstract

This study explored progression of students’ level of reasoning and generalization in numerical and figural reasoning approaches across grades and in different pattern generalization types. An instrument that included four figural patterns was administered to a sample of 1232 students from grades 4 to 11 from five private schools. The findings suggest that there was progressive development in the level of reasoning and generalization in each reasoning approach across clusters of grades. The level of reasoning and generalization in figural approach was higher than that for numerical approach in each grade. In addition, the level of reasoning and generalization for each approach and in each grade was not limited to one level but to several levels. The type of generalization influenced the progression of students’ level of reasoning and generalization in each approach. © 2018, Springer Science+Business Media B.V., part of Springer Nature.