Graphing formulas by hand to promote symbol sense

Graphing formulas by hand to promote symbol sense. Becoming friends with algebraic formulas

Proefschrift van Peter Kop, Universiteit Leiden Verdediging op woensdag 18 november 2020, 11:15 uur

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Abstract

Many students in secondary school continue to have serious problems with algebra formulas which are very abstract for them (e.g. Kieran, 2006). Often these students lack symbol sense, that is, they have trouble with reading through formulas, recognizing its structure, and making sense of them. Symbol sense is a very broad concept, which was described by Arcavi as “an intuitive feel for when to call on symbols in the process of solving a problem, and controversy, when to abandon a symbolic treatment for better tools” (Arcavi, 1994). Drijvers, Goddijn and Kindt (2011) see symbol sense as complementary to basic skills: it is about taking a global view, algebraic reasoning, and adopting a strategic approach, and, in this way, it forms a compass for basic skills. In many curricula the importance of symbol sense is acknowledged (e.g., NCTM, 2000), However, it is not clear how to teach this symbol sense in a systematic way (Arcavi, Drijvers, & Stacey, 2017; Hoch & Dreyfus, 2005). In our research, we investigated how teaching graphing formulas by hand could promote students’ symbol sense. Based on expert research, we formulated the GQR-design (Graphing based on Qualitative reasoning and Recognition), a series of lessons with five whole tasks, with help-questions and with reflection, and “questioning the formula” as a leading meta-heuristic. In this seminar, first, I will show some results that suggest that through these lessons students improved their insight into formulas and their symbol sense to solve non-routine algebra problems, and then will discuss some issues about teaching symbol sense.