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A Learning Trajectory in 6-Year-Olds' Thinking about Generalizing Functional Relationships
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Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katie; Newman-Owens, Ashley – Journal for Research in Mathematics Education, 2015
The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…
Descriptors: Young Children, Elementary School Students, Grade 1, Mathematics Instruction
Toward a Theory of Sequencing: An Integrated Program of Research. The Theoretical Model and a Synopsis of the First Two Years of the Research Program
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Heimer, Ralph T.; Lottes, John J. – Journal for Research in Mathematics Education, 1973
A method of organizing studies on sequencing problems in mathematics according to a theoretical model based on characteristics of empirical science is explained. The conceptual framework underlying eight studies that follow this article in JRME (SE 508 022 through SE 508 029) is discussed and a brief overview of each study is given. (DT)
Descriptors: Curriculum, Instruction, Mathematics Education, Models
The Relative Effectiveness of Two Different Instructional Sequences Designed to Teach the Addition and Subtraction Algorithms
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Wiles, Clyde A.; And Others – Journal for Research in Mathematics Education, 1973
Second-grade students were randomly assigned to either an instructional unit within which addition and subtraction of two digit numbers were treated as a single integrated process of regrouping or one which developed the addition and subtractive algorithms sequentially. Periodic assessments favored the sequential approach, but differences were not…
Descriptors: Addition, Algorithms, Elementary School Mathematics, Instruction
Validating Learning Hierarchies for Sequencing Mathematical Tasks in Elementary School Mathematics
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Phillips, E. Ray; Kane, Robert B. – Journal for Research in Mathematics Education, 1973
Seven forms of a programmed booklet based on an eleven-level hierarchy for addition of fractions were developed. One hundred forty-two fourth graders were randomly assigned to treatments; achievement, transfer, retention, and time were compared. No treatment was consistently superior, but developing sequences from hierarchies validated by test…
Descriptors: Elementary School Mathematics, Fractions, Learning Theories, Mathematics Education
Study 3-2: An Exploration of Transitivities Formulated From a Set of Piagetian-Derived Operations and Their Implications in Traversing Learning Hierarchies
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Hopkins, Layne V. – Journal for Research in Mathematics Education, 1973
Descriptors: Curriculum, Elementary School Mathematics, Instruction, Learning Theories
Learning Hierarchies--Numerical Considerations
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Eisenberg, Theodore A.; Walbesser, Henry H. – Journal for Research in Mathematics Education, 1971
The article presents numerical procedures for the validation and comparison of hierarchically organized curricula. Examples of specific hypotheses one should test, and calculations of five statistics for testing these hypotheses are given (consistency ratio, adequacy ratio, inverse consistency ratio, inverse adequacy ratio, and completeness…
Descriptors: Behavioral Objectives, Curriculum, Evaluation Methods, Learning Processes
Study 2-1: An Exploration of the Effect of Selected Sequence Variables on Student Choice in the Use of Algorithms
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Hostetler, Robert P. – Journal for Research in Mathematics Education, 1973
Descriptors: Algorithms, Curriculum, Elementary School Mathematics, Instruction
An Analysis of the Fraction Concept into a Hierarchy of Selected Subconcepts and the Testing of the Hierarchical Dependencies
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Novillis, Carol F. – Journal for Research in Mathematics Education, 1976
The fraction concept was analyzed to yield 16 subconcepts which are hypothesized to be hierarchically ordered. This ordering was tested using subjects in grades 4 through 6, and 18 of 23 dependencies hypothesized were confirmed. (SD)
Descriptors: Concept Formation, Elementary Education, Elementary School Mathematics, Fractions
Research Commentary: Reconceptualizing Procedural Knowledge
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Star, Jon R. – Journal for Research in Mathematics Education, 2005
In this article, I argue for a renewed focus in mathematics education research on procedural knowledge. I make three main points: (1) The development of students' procedural knowledge has not received a great deal of attention in recent research; (2) one possible explanation for this deficiency is that current characterizations of conceptual and…
Descriptors: Mathematics Education, Concept Formation, Scientific Methodology, Sequential Learning