I am intrigued with the question, “How do children relate number and space as they learn mathematics?” I am engaged in research on children’s understanding and strategy development as they learn measurement. I am the principal investigator for a 4-year longitudinal research funded by the Discovery Research K-12 Program at the National Science Foundation. Our project, the Children’s Measurement Project, involves the design, conduct and analysis of data from individual and classroom level teaching experiments for case study children from prekindergarten up into grade 5. These case studies constitute the backbone of our longitudinal data set on children’s developing knowledge of geometric measurement of length, area and volume. We are focusing our investigation on children’s ways of understanding units of measure through varying visual images representing gaps, marks, numerals and line segments as elements of ruler tools to find the interactions among these visual elements. We are interested in students’ ways of conceptualizing motion along a path, their concept of elapsed time during number sequence recitation, and their perception of foreground and background images relating endpoints of unitary segments and the segments themselves. As a complement to this teaching experiment data, we have conducted and analyzed assessments of prekindergarten through grade five students on the concepts of length, area and volume.
Learning Trajectories for Children’s Measurement, PreK to Grade 8
Dr. Barrett is currently Principal Investigator of a four-year project in collaboration with co-PIs Douglas Clements and Julie Sarama at the University of Denver, and Craig Cullen of Illinois State University. This project is part of the DR K-12 program funded by the National Science Foundation. Our project examines two critical issues in the development of trajectories for measurement: we examine outstanding questions from the literature on children’s measurement knowledge during PreKindergarten through Grade 5 and we examine the development of measurement concepts and strategies during the middle school years from Grades 6 through 8. Research teams from Illinois State University and the University of Denver 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 microgenetic analyses of students’ thinking about length, area and volume aspects of the mathematics curriculum in PreK to Grade 5. Secondly, they will develop, test and refine trajectories describing the growth of students’ measurement concepts and strategies in Grades 6, 7 and 8 by following a longitudinal cohort of 16 students. By synthesizing these findings, researchers will improve upon and extend learning trajectories. Such trajectories 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 ten-year span from PreK through Grade 8.
CHILDREN’S MEASUREMENT (2007-2011)
A Longitudinal Examination of Children’s Developing Knowledge of Measurement: Mathematical and Scientific Concept and Strategy Growth from Pre-K to Grade 5
Dr. Barrett is currently Principal Investigator of this four-year project in collaboration with Douglas Clements and Julie Sarama at the University at Buffalo, SUNY. This project is part of the DR K-12 and REESE programs funded by the National Science Foundation. This 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 PreK 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 PreK through Grade 5.
Dr. Barrett was invited to bring a research team from Illinois State University to participate in meetings of this national mini-center for research and development focused on the teaching and learning of measurement. This center, originated at Michigan State University, has been funded by the National Science Foundation to support and strengthen collaborative discussion among research teams from Vanderbilt University, University of Missouri, the Ohio State University, North Carolina State University and the University of Buffalo (SUNY) as well as Illinois State University. The first conference was held September 17-19, 2009. The group met again at Michigan State in 2010, and recently met at Illinois State University (2011).
See notes related to my work on learning progressions and learning trajectories in a Policy Brief from the Consortium for Policy Research in Education (CPRE), RB-52 pdf document: “The Role of Learning Progressions in Standards-Based Education Reform“.
Formative Assessment in Elementary Mathematics Teaching (Illinois Math Science Partnership, Dept. of Education)
This project supports teachers in the Peoria School District (150) as they adopt standards for teaching mathematics (CCSM, 2011), and help them improve their formative assessment knowledge and practices to provide instruction based on students’ levels of understanding and strategies. The project engages teachers and teacher leaders in a professional development program to improve their mathematical content and pedagogical content knowledge about proportional reasoning, and measurement, especially related to number lines. By engaging teachers with these fundamental mathematical ideas from the aspect of children’s thinking rather than from their own perspective as adults and by helping the teachers assess student reasoning on tasks related to these big ideas, we expect to improve their professional practices. Teachers will learn to use a trajectory focused on length measurement to assess student thinking, to categorize student strategies along the trajectory and identify appropriate tasks and instructional moves to support learning at each level of the trajectory. Using trajectories to identify student thinking and to implement specific instructional activities suitable to students’ levels of reasoning and strategies has been successful in promoting student achievement in our own scientific studies implementing learning trajectories for measurement (Barrett et al., 2006; Barrett, et al., in press; Clements & Sarama, 2007). Teachers will develop more connected communities in their school buildings and district by engaging in four sessions of lesson study during the academic year to incorporate formative assessment in their instruction on measurement. Barrett, J. Baek, J. Tobias and C. Cullen are co-Principal Investigators.
A Study of the Struggling Learner’s Knowledge and Development for Number and Operation
In 2009, Dr. Barrett was invited to serve as the external auditor and on the advisory board for this NSF funded (DR K-12 program) project led by John Lannin and Delinda van Garderen of the University of Missouri at Columbia, MO. This three-year project began its funding period on September 1, 2009.
PRIME Mathematics K-5 Project
During the period from 1999 to 2003, Dr. Barrett co-directed a National Science Foundation funded project for systemic K-5 teacher development engaging over 300 teachers learning to teach with the Investigations in Number, Data and Space curriculum. See Reports on this project at: http://pdmathsci.net/findings/memos, a website of Horizons Research, Inc.