GRAFEN – EN VÄG TILL FUNKTIONSTÄNKANDE : En algebraisk undervisningspraktik med möjligheter till lärande om funktionssamband genom mönstergeneraliseringar
Sammanfattning: Learning and developing functional thinking is essential in understanding algebraic generalizations in early algebra. However, research shows that teaching functional thinking is challenging in lower grades. One challenging aspect is to teach from all three perspectives of functional thinking: recursive patterning, covariational thinking, and correspondence relationships. Research indicates that it is specifically difficult to teach based on correspondence relationships. At the same time, research also shows that there is a risk that teaching about functional thinking ends up merely discussing recursive patterning. One way to develop students’ learning about functional thinking is to deliberately teach based on all three modes of functional thinking using graph representations. This study was conducted as an educational design research, an intervention theory guided by design principles. This research highlights how the three teachers and their students learning about generalizations and functional relationships changed in an algebraic teaching practice. During a nine-month period, three teachers participated in an intervention to develop functional thinking when working with pattern generalizations in their Grade 1 and 6 classes. Based on the chosen methodological framework, the teachers were actors in all the intervention phases. They used different representations; the graph was one means to develop the students’ functional thinking when working with arithmetic growing patterns. The results showed that the graph representation helped the teachers and the students to visualize and discuss all three modes of functional thinking. The graph made it possible to visualize covariational thinking, justify different correspondence rules, and enable the students to discuss the mathematical structures in generalized formulas. Due to the fact that the teachers participated in all phases of the intervention, it was possible to capture challenges that occurred in teaching, and the intervention was able to take on new, unforeseen directions
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