Lärarnas och elevernas lärande om funktionstänkande: En utbildningsvetenskaplig designstudie i en algebraisk undervisningspraktik

Abstrakt

The overall aim of the thesis is to advance knowledge about algebra teaching in early grades (Grades 1-6). The thesis highlights how teachers’and students’ learning about generalizations and functional relationships in early algebra can change in an algebraic teaching practice. This research focuses on identifying teachers’ and students’ learning about algebra, generalizations and functional relationships and further describes the consequences of such teaching.

Functional thinking consists of three modes: recursive patterning, covariational thinking, and correspondence relationships, and all three are essential in understanding algebraic generalizations. One way to develop students’ learning about functional thinking is to deliberately base the teaching on these three modes of functional thinking. However, such teaching is challenging in the early grades, specifically concerning correspondence relationships, as most often the focus is on recursive patterning.

This project was conducted as an educational design research study, including three consecutive sub-studies that built on each other in terms of both form and content (algebra). The teachers participated in anintervention to develop functional thinking when working with pattern generalizations in their Grades 1 and 6 classes and were involved in all phases of the intervention. The results showed how the understanding of generalizations and functional relationships in algebra changed for both teachers and students. Although, different representations were used the graphs, in particular, developed the students’ functional thinking when working with generalizations in growing patterns. This helped teachers and students visualize and discuss all three modes of functional thinking. Graphs inlinear relations made it possible to visualize covariational thinking, justify different correspondence rules, and enable students to discuss the mathematical structures in generalized formulas.

Due to the fact the teachers participated in all phases of the intervention, it was possible to capture challenges that arose while teaching. Hence, knowledge contribution involved the importance of the teacher being challenged, which required them to develop and alter their teaching practice.