A Learning Progression for Elementary Students’ Functional Thinking

Stephens, Ana C.; Fonger, Nicole L.; Strachota, Susanne; Işler, Işıl; Blanton, Maria; Knuth, Eric; Gardiner, Angela Murphy

doi:10.1080/10986065.2017.1328636

Cited by 54 publications

(66 citation statements)

References 26 publications

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“…Functional thinking is a part of algebraic thinking (Blanton & Kaput, 2005), and it is fundamental (Eisenmann, 2009;Kaiser & Willander, 2005;Lichti, 2018;Lichti & Roth, 2019;Stephens et al 2017;Tanıslı, 2011). Functional thinking is generalizing relationships between covarying quantities, expressing those relationships in words, symbols, tables, or graphs, and reasoning with the various representations to analyze function behavior (Blanton et al 2011).…”

Section: Discussionmentioning

confidence: 99%

“…Functional thinking is fundamental to algebra and calculus (Wilkie, 2015). In line with this, functional thinking can serve as an important point of entry into algebra because it involves generalizing relationships between quantities; representing those relationships, or functions, in multiple ways using natural language, formal algebraic notation, tables, and graphs; and reasoning fluently with these representations in order to interpret and predict function behaviour (Stephens et al 2017).…”

Section: Introductionmentioning

confidence: 99%

“…Functional thinking as representational thinking that focuses on the relationship between two (or more) varying quantities, specifically the kinds of thinking that lead from specific relationships (individual incidences) to generalizations of that relationship across instances (Smith, 2008). Functional thinking define as the process of building, describing, and reasoning with and about functions (Stephens et al 2017). Functional thinking is closely related to the function concept (Blanton, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…Three types and ten levels of students sophistication in functional thinking (Stephens et al 2017), (a) type Variational Thinking with Recursive Pattern-Particular (L1), Recursive Pattern-General (L2); (b) type Covariational Thinking with Covariation Relationship (L3) and (c) Type Correspondence Thinking with Single Instantiation (L4), Functional-Particular (L5), Functional-Basic (L6), Functional-Emergent in a variable (L7), Functional-emergent in words (L8), Functional-condensed in variables (L9), and Functional-condensed in words (L10).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Elementary students’ functional thinking: From recursive to correspondence

Syawahid

Purwanto

Sukoriyanto

et al. 2020

Journal for the Education of Gifted Young Scientists

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This study aims to identify elementary students' functional thinking processes in solving pattern problems. Previous studies showed that elementary students' functional thinking still often experience errors in solving pattern problems. The study of the functional thinking process in solving pattern problems is a fundamental key as a solution to find out the strengths and weaknesses of elementary school students, so that they are better prepared in generalizing relationships, representing and analyzing function behavior in advanced algebra classes. This study used a descriptive qualitative approach with a case study method. Participants of study was sixty-five elementary students who had not yet received generalization patterns material. The instruments were tasks and interview guidelines. Based on the task results, students who had correct answers were chosen using purposive sampling to be given an in-depth interview. The finding indicated that elementary students are able to think functionally in different ways. Students' functional thinking begins with recursive thinking in the pre-finding formula in the entry stage. Students find the formula by corresponding thinking in the attack stage. Finally, students use the formula to get inverse in the review stage.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Elementary students’ functional thinking: From recursive to correspondence

Syawahid

Purwanto

Sukoriyanto

et al. 2020

Journal for the Education of Gifted Young Scientists

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“…The papers had one (M2), four (M1) and 25 instances (M3) of the term real-world. In M2,Stephens et al investigated the functional thinking of 100 students, beginning in Grade 3 over three years. The authors draw on literature noting the importance of context in functional thinking, however, 'real-world context' used involved finding a relationship between the number of seats and number of desks being arranged at school for a party.…”

Section: Detailed Analysismentioning

confidence: 99%

Real-World Task Context: Meanings and Roles

Brown

2019

Lines of Inquiry in Mathematical Modelling Research in Education

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This chapter details results of a study intended to increase understanding of the myriad meanings of real-world task context in mathematics education and their relevance to modelling. The research aim was to ascertain how context is viewed within the broader mathematics education community. Data analysis reported here followed an examination of use of the terms: context, task context and real-world in four mathematics education journals. Four samples, one from each journal, two in 2014 and two in 2017 where all papers using the term real-world, comprised the purposive sample used for the in-depth investigation. Whilst, often not defined by the authors, in most papers the context was real-world task context and, in the majority, this played an essential, rather than incidental, role.

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