Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education
Date
2018-01-01
Author
Fonger, Nicole L.
Stephens, Ana
Blanton, Maria
İşler Baykal, Işıl
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
172
views
0
downloads
Cite This
Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.
Subject Keywords
Equivalence
,
Algebra and algebraic thinking
,
Mathematics
,
Learning
,
Instruction
,
Curriculum
,
learning progressions
URI
https://hdl.handle.net/11511/42127
Journal
COGNITION AND INSTRUCTION
DOI
https://doi.org/10.1080/07370008.2017.1392965
Collections
Department of Mathematics and Science Education, Article
Suggestions
OpenMETU
Core
Investigating fifth-grade students' functional thinking processes through a game-based learning activity
Arslandaş, Tuba; İşler Baykal, Işıl; Department of Mathematics Education (2022-9)
The aim of this study was to investigate fifth-grade students' generalization and representation processes of functional relationships through a game-based learning activity. This study was carried out with four students selected from the fifth grade in a state village middle school in Mardin. In this school, where the researcher worked as a teacher, a Functional Thinking Test was applied to two classes, and participants were selected based on pre-test responses and the ability to express themselves. A pre-...
Analyzing generalizations through discourse
Strachota, Susanne; İşler Baykal, Işıl; Fonger, Nicole; Blanton, Maria; Gardiner, Angela Murphy (null; 2016-11-03)
Although generalizing is “intrinsic to mathematical activity and thinking” (Kaput, 1999, p. 137), students struggle to generalize, often make weak generalizations, and rarely justify their generalizations. Supporting generalizing in the mathematics classroom requires a better understanding of the source of students’ generalizing. What are the mechanisms that encourage students’ generalizing? This question is central to our research, which seeks to understand the nature of the discourse that supports student...
Developing prospective mathematics teachers’ knowledge for teaching quadrilaterals through a video case-based learning environment
Ulusoy, Fadime; Çakıroğlu, Erdinç; Department of Elementary Education (2016)
The aim of this study was to examine the developments in prospective middle school mathematics teachers’ subject matter knowledge and pedagogical content knowledge about quadrilaterals as they attended to a teaching experiment that was designed in a video case-based learning environment. Data was collected from eight prospective teachers during the fall semester of 2014-2015 in the scope of an elective course. In data collection process, multiple data sources were utilized such as clinical individual pre- a...
Teachers' Knowledge about Ninth Grade Students' Ways of Algebraic Thinking
Bas, Sinem; Erbaş, Ayhan Kürşat; Çetinkaya, Bülent (2011-01-01)
The purpose of this study is to describe teachers' knowledge about their students' algebraic thinking and to determine to what extent this knowledge essentially reflects students' ways of thinking. Three mathematics teachers and their 49 ninth grade students were selected as participants. In this study, students' algebraic thinking was determined through a generalization activity and then the teachers' knowledge and expectations were investigated. The data were comprised of students' worksheets and the inte...
Implementing a Framework for Early Algebra
Blanton, Maria; Brizuela, Barbara M.; Stephens, Ana; Knuth, Eric; İşler Baykal, Işıl; Gardiner, Angela Murphy; Stroud, Rena; Fonger, Nicole L.; Stylianou, Despina (2018-01-01)
In this chapter, we discuss the algebra framework that guides our work and how this framework was enacted in the design of a curricular approach for systematically developing elementary-aged students' algebraic thinking. We provide evidence that, using this approach, students in elementary grades can engage in sophisticated practices of algebraic thinking based on generalizing, representing, justifying, and reasoning with mathematical structure and relationships. Moreover, they can engage in these practices...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
N. L. Fonger, A. Stephens, M. Blanton, I. İşler Baykal, E. Knuth, and A. M. Gardiner, “Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education,”
COGNITION AND INSTRUCTION
, pp. 30–55, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42127.