Using Graphical Representations to Develop Students’ Correspondence Relationships and Covariational Thinking in Pattern Generalizations in Primary School

Algebra in primary school requires students to engage in functional thinking, including recursive patterning, covariational thinking, and correspondence relationships. However, research suggests that teaching to develop functional thinking is challenging in lower grades, because it risks resulting in discussions solely centered around recursive patterning. This article reports on an intervention where possibilities and limitations were studied when students used different representations to develop functional thinking while working with pattern generalizations. Sixty-nine students in Grade 6 in four different classes worked with graphs and other representations to identify and justify pattern generalizations. The results showed that the graphical representation enabled students to visualize and justify correspondence relationships, thereby developing their functional thinking. Furthermore, the use of graphs helped the students justify their pattern generalizations and shift their conversations from recursive patterning to covariational thinking and correspondence relationships. Consequently, the results emphasize the importance of teacher awareness in developing students’ functional thinking.