TY - JOUR
T1 - A quadratic growth learning trajectory
AU - Fonger, Nicole L.
AU - Ellis, Amy B.
AU - Dogan, Muhammed F.
N1 - Funding Information:
Support for this research was provided in part by the U.S. Department of Education IES Research Training Programs in the Education Sciences under grant no. R305B130007 , and the National Science Foundation under Award REC 0952415. Any opinions, findings, and conclusions expressed in this material are those of the authors, not the funding agencies.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/9
Y1 - 2020/9
N2 - This paper introduces a quadratic growth learning trajectory, a series of transitions in students’ ways of thinking (WoT) and ways of understanding (WoU) quadratic growth in response to instructional supports emphasizing change in linked quantities. We studied middle grade (ages 12–13) students’ conceptions during a small-scale teaching experiment aimed at fostering an understanding of quadratic growth as phenomenon of constantly-changing rate of change. We elaborate the duality, necessity, repeated reasoning framework, and methods of creating learning trajectories. We report five WoT: Variation, Early Coordinated Change, Explicitly Quantified Coordinated Change, Dependency Relations of Change, and Correspondence. We also articulate instructional supports that engendered transitions across these WoT: teacher moves, norms, and task design features. Our integration of instructional supports and transitions in students’ WoT extend current research on quadratic function. A visual metaphor is leveraged to discuss the role of learning trajectories research in unifying research on teaching and learning.
AB - This paper introduces a quadratic growth learning trajectory, a series of transitions in students’ ways of thinking (WoT) and ways of understanding (WoU) quadratic growth in response to instructional supports emphasizing change in linked quantities. We studied middle grade (ages 12–13) students’ conceptions during a small-scale teaching experiment aimed at fostering an understanding of quadratic growth as phenomenon of constantly-changing rate of change. We elaborate the duality, necessity, repeated reasoning framework, and methods of creating learning trajectories. We report five WoT: Variation, Early Coordinated Change, Explicitly Quantified Coordinated Change, Dependency Relations of Change, and Correspondence. We also articulate instructional supports that engendered transitions across these WoT: teacher moves, norms, and task design features. Our integration of instructional supports and transitions in students’ WoT extend current research on quadratic function. A visual metaphor is leveraged to discuss the role of learning trajectories research in unifying research on teaching and learning.
KW - DNR
KW - Instructional supports
KW - Learning trajectory
KW - Quadratic function
KW - Quantitative reasoning
KW - Representational fluency
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U2 - 10.1016/j.jmathb.2020.100795
DO - 10.1016/j.jmathb.2020.100795
M3 - Article
AN - SCOPUS:85086907872
SN - 0732-3123
VL - 59
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
M1 - 100795
ER -