University of Illinois Urbana-Champaign

Supporting children’s conceptual understanding of fractions with manipulatives and gesture

Beilstein, Shereen Oca

Content Files
BEILSTEIN-DISSERTATION-2019.pdf

Permalink

https://hdl.handle.net/2142/104770

Description

Title
Supporting children’s conceptual understanding of fractions with manipulatives and gesture
Author(s)
Beilstein, Shereen Oca
Issue Date
2019-04-03
Director of Research (if dissertation) or Advisor (if thesis)
Perry, Michelle
Doctoral Committee Chair(s)
Perry, Michelle
Committee Member(s)
  • Alibali, Martha
  • González, Gloriana
  • Lindgren, Robb
Department of Study
Educational Psychology
Discipline
Educational Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2019-08-23T19:51:38Z
Keyword(s)
  • cognitive development
  • mathematics learning
Abstract
Fractions—their concepts, procedures, and symbolic notation—are well-known for the difficulty they present children, beginning in elementary school, and often, persisting long after. However, promoting children’s development of flexible and robust conceptual knowledge in this content area is critical for their success both in and out of school. The overarching goal of this project is to investigate the tools that support elementary school-aged children’s fraction learning by focusing on two different, yet related areas in cognitive science: physical action on objects (i.e., working with concrete manipulatives) and gesture. The first study identifies the specific mental models about fractions children develop and express through their speech and gesture. The second paper presents a comparative case study that examines how two children’s coordination of speech, gesture, and manipulatives reveals their fraction knowledge. By honing in on how children use gesture and/or manipulatives at times to their advantage and, at others, to their disadvantage, these two studies explore children’s existing knowledge to understand the nature of their fraction concepts, and ultimately, to inform the design of educational interventions that foster learning. The third, and final, study experimentally tests how variations in tools across an instructional intervention affect children’s learning of fraction notation and magnitude estimation. Preliminary results suggest that three of the four conditions—a gesture-based lesson, a manipulatives and gesture-based lesson, as well as a pencil and paper-based control, but not the manipulative-based lesson—led to learning gains from pre- to posttest on magnitude-estimation problems. None of the conditions, however, were successful at promoting transfer to problems, which included area-model estimation and fraction-magnitude comparison, beyond the intervention’s purview. Taken together, these three studies lend further insight into the affordances and constraints of using manipulatives and gesture to support the development of flexible and generalizable mathematics knowledge, concentrating specifically on a topic that challenges children as well as adults—fractions.
Graduation Semester
2019-05
Type of Resource
text
Permalink
http://hdl.handle.net/2142/104770
Copyright and License Information
© 2019 Shereen Oca Beilstein ALL RIGHTS RESERVED

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Education
Dissertations and Theses from the College of Education