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Journal Article
The String Task: Not Just for High School
2014
Overview
The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and \"Principles and Standards for School Mathematics\" (National Council of Teachers of Mathematics [NCTM] 2000). However, the growing acceptance of algebra as a K-grade 12 strand of thinking by math education researchers and in standards documents, along with the view that the study of functions is an important route into learning algebra (Carraher and Schliemann 2007), raises the importance of developing children's understanding of functions in the elementary grades. What might it look like to engage students in functional thinking in the elementary grades? Elementary school curricula often include a focus on simple patterning activities (e.g., recursive number sequences, such as 2, 4, 6, 8, …) in which only one variable is observed. However, an exclusive focus on this type of activity might hinder the development of students' reasoning about how two or more quantities vary simultaneously (Blanton and Kaput 2004), a key component of functional thinking. Blanton and her colleagues argue that elementary school students are in fact capable of engaging in this type of thinking (Blanton et al. 2011, p. 47). Furthermore, they point out that focusing on functional thinking provides a context for students to understand the role of variable as varying quantity. This article supports Blanton and her colleagues' (2011) argument by sharing a classroom episode as well as pre-instruction and post-instruction data from a yearlong teaching experiment. The authors discuss some of the crucial elements they believe contributed to students' growing abilities to engage in functional thinking. They also discuss connections made among various representations, another important benefit of having students engage in functional thinking.
Publisher
National Council of Teachers of Mathematics
