2021 Research in Undergraduate Mathematics Education Reports
2021
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Making Connections: Advanced Perspectives on School Algebra
Page: 386
Fostering conceptual understanding is a main goal of mathematics education. Yet, students do not often see connections between topics. The recognition of connections can be fostered by making them explicit in instruction and by encouraging students to struggle with the relevant mathematics. Instances in which knowledge from one domain is brought to bear in another domain are examples of transfer; in particular, backward transfer describes the ways in which learning new information influences prior knowledge. We solicited narratives from individuals with a strong mathematics background describing instances during which they recognized a connection between two mathematics topics. We present two of these narratives which contain instances of backward transfer connecting advanced mathematics to the binomial theorem. These narratives suggest that backward transfer is also facilitated by explicit instruction and productive struggle. We discuss implications for education of backward transfer that is induced by learning advanced mathematics, particularly for pre-service teachers.