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Most Recent Funded Project:
Learning Trajectories to Support the Growth of Measurement Knowledge:
Pre-K through Middle School
NSF: DRK12
funding period: 2012-2016
This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children’s knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8.
The project employs a form of microgenetic studies (Siegler et al., 2006) with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate of all components of each learning trajectory—goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis.
To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments (Steffe & Thompson, 2000); this design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards—issued by CCSSO/NGA, NCTM, NSTA, AAAS, and NRC—with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.
This project provides a longitudinal account of pre-K to Grade 8 children’s ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art—integrated, interdisciplinary, theoretically- and empirically-based—descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children’s development of reasoning from short-term analyses of learning or cross-sectional studies; there are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway.
Work on this project was supported by the National Science Foundation under Grant No. DRL-1222944. The opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K through Middle School
Award Number:1222944;
Principal Investigator:Jeffrey Barrett; Co-Principal Investigator:Douglas Clements, Julie Sarama, Craig Cullen; Organization:Board of Trustees of Illinois State University;NSF Organization:DRL Start Date:08/01/2012; Award Amount:$2,092,005.00
Learning Trajectories to Support the Growth of Measurement Knowledge:
Pre-K through Middle School
NSF: DRK12
funding period: 2012-2016
This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children’s knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8.
The project employs a form of microgenetic studies (Siegler et al., 2006) with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate of all components of each learning trajectory—goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis.
To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments (Steffe & Thompson, 2000); this design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards—issued by CCSSO/NGA, NCTM, NSTA, AAAS, and NRC—with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.
This project provides a longitudinal account of pre-K to Grade 8 children’s ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art—integrated, interdisciplinary, theoretically- and empirically-based—descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children’s development of reasoning from short-term analyses of learning or cross-sectional studies; there are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway.
Work on this project was supported by the National Science Foundation under Grant No. DRL-1222944. The opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K through Middle School
Award Number:1222944;
Principal Investigator:Jeffrey Barrett; Co-Principal Investigator:Douglas Clements, Julie Sarama, Craig Cullen; Organization:Board of Trustees of Illinois State University;NSF Organization:DRL Start Date:08/01/2012; Award Amount:$2,092,005.00
PRIOR PROJECT:
A Longitudinal Examination of Children's Developing Knowledge of Measurement: Mathematical and Scientific Concept and Strategy Growth from pre-K to Grade 5
Project Summary for a Preliminary Proposal: Discovery Research K-12 Program
Category: Applied Research
Sub-category: Studies of Student Learning Progressions
This four-year longitudinal study will produce research-based developmental progressions in measurement across a seven-year span. Research teams from Illinois State University and the University at Buffalo, SUNY will examine the mathematical and scientific concept growth of 24 students learning measurement between pre-K and Grade 5. The researchers will coordinate cognitive literature on learning measurement with standards for curriculum, instruction and assessment issued by NCTM, NSTA, AAAS and NRC as they design and implement teaching experiments in clinical and classroom contexts. They will develop, test and refine trajectories describing the growth of students measurement concepts and strategies, coordinating their analyses and findings across two overlapping studies. By synthesizing these findings, researchers will generate developmental progressions. These progressions constitute successively more complex ways of thinking about an idea that enable learners to achieve increasingly substantive tasks. Finally, researchers will characterize learning trajectories (Clements & Sarama, 2004), which include the learning progressions and instructional tasks corresponding to each level. These are designed to engender the mental processes or actions hypothesized to move children through the learning progression for key concepts of measurement found in mathematics and science along the entire seven-year span from pre-K through Grade 5.
The Intellectual Merit of the proposed work is its development of a comprehensive, longitudinal account of children's ways of thinking about and understanding mathematical and scientific concepts of measurement through empirical analysis. This longitudinal study will help check hypothetical accounts of the growth and development of children's reasoning about elementary science and mathematics that have been developed through short-term analyses of learning or cross-sectional studies; there are no integrative longitudinal studies describing this cognitive domain. The proposed work is well-situated in research we have conducted using teaching experiments and clinical interview methods to examine children's understanding of linear measurement during the last ten years. Furthermore, the study will help synthesize two disconnected aspects of the literature: (1) research on mathematical and scientific standards from NCTM, NSTA, AAAS and NRC, and (2) research on children's learning of mathematical and scientific reasoning about measurement and proportion (Smith, Wiser, Anderson, & Krajcik, 2006).
The Project's Broader Impact: The investigators believe the project will establish a productive research base regarding trajectories for measurement for use in curriculum development, professional development and assessment, as called for in the NCTM's Curriculum Focal Points (2006). The learning trajectories will inform designers of large-scale and classroom assessment instruments, and developers of curricular materials addressing science and math topics related to measurement. This is a critical need, given that international studies identify measurement as the domain of least relative competence for U.S. students.
A Longitudinal Examination of Children's Developing Knowledge of Measurement: Mathematical and Scientific Concept and Strategy Growth from Pre-K through Grade 5
Award Number: DRL 0732217; The opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
Principal Investigator:Jeffrey Barrett; Co-Principal Investigator:Douglas Clements; Organization:Board of Trustees of Illinois State University;NSF Organization:DRL Start Date: 08/15/2007; Award Amount:$1,594,532.00;