Project

Students' conceptions supporting their symbolizations and meanings of function rules

Goal: What is the interplay between students' conceptions of functions and representational fluency in solving problems? What is the nature of students' quantitative reasoning? In this research we explore the bi-directional relationship between students' modes of reasoning in quantitatively rich task situations and their ability to symbolize a function rule (i.e., write an algebraic equation relating two letter-symbolic variables). Students' meanings of functions span both static correspondence views and coordinated change in linked quantities.

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Project log

Nicole L. Fonger
added a research item
This paper argues for creating learning trajectories of children's mathematics by integrating evidence of shifts in the mathematics of students, theory of goal-directed instructional design, and evidence of instructional supports. We networked two theories in support of this stance: a radical constructivist theory of learning, and Duality, Necessity, Repeated Reasoning (DNR)-based instruction. We exemplify how our networking of theories guided methodological choices by drawing on a program of research aimed at understanding and supporting students' ways of understanding quadratic growth as a representation of a constantly changing rate of change. We close by discussing challenges for creating and sharing learning trajectories.
Nicole L. Fonger
added a research item
Understanding function is a critical aspect of algebraic reasoning, and building up functional relationships is an activity increasingly encouraged at the elementary and middle school levels. This study identifies how one group of middle-school students leveraged their rate of change thinking to inform the development and understanding of correspondence rules. Drawing on an analysis of a 15- day teaching experiment with 6 eighth-grade students, we introduce three dependency relations of change concepts – recognition, identification, and translation – and discuss how these concepts support students’ transitions to more formal algebraic expressions.
Nicole L. Fonger
added a research item
This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n=6) emphasizing quadratic growth through covarying quantities. Results indicate four modes of reasoning supportive of students' symbolization of quadratic function rules: (a) correspondence, (b) variation and correspondence, (c) covariation, (d) flexible covariation and correspondence. We discuss implications for research on learning vis-à-vis students' representational fluency, as well as design principles to support quantitative reasoning.
Nicole L. Fonger
added a project goal
What is the interplay between students' conceptions of functions and representational fluency in solving problems? What is the nature of students' quantitative reasoning? In this research we explore the bi-directional relationship between students' modes of reasoning in quantitatively rich task situations and their ability to symbolize a function rule (i.e., write an algebraic equation relating two letter-symbolic variables). Students' meanings of functions span both static correspondence views and coordinated change in linked quantities.