Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook

Given the significance of functional thinking as one of the main routes to foster early algebraic thinking, in this paper we describe how a current elementary mathematics textbook's unit titled "Pattern and Correspondence" was developed in the Korean context. The following four key instructional elements for fostering functional thinking were extracted from the literature review: (a) correspondence relationships in real-life contexts; (b) various pattern tasks; (c) exploration for a correspondence relationship; and (d) symbol variables to represent a correspondence relationship. These elements were employed to analyze the strengths and weaknesses of the unit covering pattern and correspondence in the previous mathematics textbook. Based on this analysis, a new draft for the pattern and correspondence unit was designed and implemented in an elementary school to test its appropriateness and ability to enhance students' functional thinking. Students' responses using the new draft were analyzed in terms of the four elements. Performance between the students with the new draft and their counterparts with the previous textbook was compared. The students with the new draft were more successful than their counterparts in exploring and representing the relationship between two quantities. The final version of the unit was developed and has been applied to all schools. The whole process of developing the unit can be an example of how to foster functional thinking through changes to curricular resources.