A Learning Progression for Elementary Students' Functional Thinking

Date

2017-01-01

Author

Stephens, Ana C.
Fonger, Nicole
Strachota, Susanne
İşler Baykal, Işıl
Blanton, Maria
Knuth, Eric
Gardiner, Angela Murphy

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

196
views

0
downloads

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an instructional sequence, written assessments, and levels of sophistication describing students' algebraic thinking. After detailing this approach, we focus on what we have learned about the development of students' abilities to generalize and represent functional relationships in a grades 3-5 early algebra intervention by sharing the levels of responses we observed in students' written work over time. We found that the sophistication of students' responses increased over the course of the intervention from recursive patterning to correspondence and in some cases covariation relationships between variables. Students' responses at times differed by the particular tasks that were posed. We discuss implications for research and practice.

Subject Keywords

Education, General Mathematics, Developmental and Educational Psychology

URI

https://hdl.handle.net/11511/42907

Journal

MATHEMATICAL THINKING AND LEARNING

DOI

https://doi.org/10.1080/10986065.2017.1328636

Collections

Department of Mathematics and Science Education, Article

Suggestions

OpenMETU
Core

Growth in children's understanding of generalizing and representing mathematical structure and relationships Blanton, Maria; İşler Baykal, Işıl; Stroud, Rena; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy (Springer Science and Business Media LLC, 2019-10-01) We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3-5. Analyses showed that, while there were no significant differences between experimental and control students on a grade 3 pre-assessment measuring students' capacity for generalizing and representing generalizations, experi...
Effect of conceptual change approach accompanied with concept mapping on understanding of solution concepts Kondakçı, Esen; Geban, Ömer (Springer Science and Business Media LLC, 2005-07-01) The purpose of this study was to investigate the effect of conceptual change texts accompanied with concept mapping instruction, compared to traditional instruction (TI), on 8th grade students' understanding of solution concepts and their attitudes toward science as a school subject. Solution Concept Test was developed as a result of examination of related literature and interviews with teachers regarding their observations of students' difficulties. The test was administered to a total of 64 eighth grade s...
Promoting students' learning in genetics with the learning cycle Dogru-Atay, Pinar; Öztekin, Ceren (Informa UK Limited, 2008-03-01) The authors investigated the comparative effect of the learning cycle and expository instruction on 8th-grade students' achievement in genetics. They adopted the nonequivalent control group design as a type of quasiexperimental design. The experimental group (N = 104) received learning cycle instruction, and the control group (N = 109) received expository instruction. The 2-way analysis of covariance indicated a statistically significant posttreatment difference between the experimental and control groups i...
A multilevel analysis of home and classroom literacy environments in relation to preschoolers' early literacy development Altun, Dilek; Erden, Feyza; Snow, Catherine E (Wiley, 2018-11-01) This study aimed to investigate the characteristics of preschoolers' home and classroom literacy environments and the relationships between receptive and expressive vocabulary, phonological awareness, and concepts about print (CAP) development. The participants were 168 parents and their children from five private preschools in a large suburban area. Two waves of data were collected. Multilevel linear modeling was used to analyze the two-level data set. The findings of the study revealed that children have ...
THE THINKING-ABOUT-DERIVATIVE TEST FOR UNDERGRADUATE STUDENTS: DEVELOPMENT AND VALIDATION UBUZ, BEHİYE; Ubuz, Behiye (Springer Science and Business Media LLC, 2015-12-01) Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises...

Citation Formats

A. C. Stephens et al., “A Learning Progression for Elementary Students’ Functional Thinking,” MATHEMATICAL THINKING AND LEARNING, pp. 143–166, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42907.