Jeffrey Barrett

Illinois State University | ISU · Department of Mathematics

We report on the process of children’s construction of a volume calculation algorithm for rectangular prisms. We provided third- and fourth-grade students with traditional volume tasks and a dynamic virtual manipulative to support their three-dimensional reasoning and use of unit cubes to structure space. We investigated the challenges faced, evolv...

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instruction...

We present our findings with respect to our two research questions: 1) How well do children at the ICS and ARCS levels of the LT for area measurement estimate areas of rectangles and what is the nature of their estimates? And 2) To what extent can ICS and ARCS level children’s area estimation performance be quantitatively improved through targeted...

Designed to strengthen the teaching of mathematics in the elementary grades, this chapter focuses on helping teachers engage in instruction based on learning trajectories (LTs). We explain our experiences and key research-based findings working with teacher educators in which we created effective professional development around LTs for geometric me...

In this article, we describe how students structured 2-dimensional space with square and nonsquare units. We employed a cross-sectional design, interviewing 5 students from each of 4 different grade groups: Grades 1, 3, 5, and 7 (ages 7, 9, 11, and 13) in structured, task-based interviews. Our findings about students’ ways of measuring area fit a h...

We examine the effects of 3 interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways. We employed the microge-netic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to childre...

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on corre...

Quantitative reasoning and measurement competencies support the development of mathematical and scientific thinking in children in the early and middle grades and are fundamental to science, technology, engineering, and mathematics (STEM) education. The sixteenth Journal for Research in Mathematics Education (JRME) monograph is a report on a four-y...

This monograph is a report on a 4-year-long multisite longitudinal study in which we studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume). The Children’s Measurement research team, as funded by the National Science Foundation between 2007 and 2012, completed the research reported in this monograph. D...

This study investigated the ways in which four middle grades teachers developed mathematical knowledge for teaching (MKT) geometry as they implemented dynamic geometry software in their classrooms with the assistance of a coach. Teachers developed various components of MKT by observing coaches teach, by dynamic discourse with students, which is dis...

In Reconceptualizing Early Mathematics Learning , editors Lyn English and Joanne Mulligan present a widely varying collection of research and initiatives within the field of early mathematics education research, providing a thoughtful argument for further investment and work in this developing field of study. Among the diverse contributions to this...

We examined children's estimation performance, ages 9-10, to find the area of rectangular regions given a unit square for visual comparison. We found children generally underestimated, with approximately 40 percent error. We relied on prior research to establish a starting point of approximately 14 percent as the boundary beyond which it proved too...

http://www.amazon.com/Learning-Progressions-Geospatial-Technology-Thinking/dp/1443874272

http://www.amazon.com/Learning-Progressions-Geospatial-Technology-Thinking/dp/1443874272

In this paper we report on five Grade 6 students’ responses to a proportional reasoning task. We conducted pair interviews within a longitudinal study focused on extending a hypothetical learning trajectory for length measurement. Results suggest that there exists a link between children’s level of conceptual and procedural knowledge for length mea...

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics—how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings—and how to use these insights to improve instruction and student learning. In this book,...

This report describes the longitudinal development of one student, Drew, in terms of his unit concepts in area and volume measurement situations across Grades 2 through 5. Data were collected during individual interviews and an open-response assessment within the context of a four-year longitudinal teaching experiment. Results indicate that Drew's...

We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical s...

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited, especially compared to topics such as number and operations. To contribute to the establishment of a research base for instruction in measurement, we evaluated and refined a previously developed learning trajectory in e...

We examined ways of improving students’ unit concepts across spatial measurement situations. We report data from our teaching experiment during a six-semester longitudinal study from grade 2 through grade 5. Data include instructional task sequences designed to help children (a) integrate multiple representations of unit, (b) coordinate and group u...

The purpose of this report is to compare three different unit eliciting task structures for measurement comparison tasks. Twelve students ranging from grade 2-4 were presented length, area, and volume tasks. Student responses were coded for correctness and comparison type. The results indicated that students were most successful with task structure...

Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction aims to provide: A useful introduction to current work and thinking about learning trajectories for mathematics education An explanation for why we should care about these questions A strategy for how to think about what is being attempted in t...

The purpose of this report is to compare the effects of presentation mode based on y use in measurement tasks. The same treatment was presented, either with a paper-and-pencil environment to 36 students (21 aged 4-5 years, and 15 aged 7-8 years. Changes in student strategy use were tracked by following a microgenetic method over 18 trials. The non-...

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of...

This article describes how children build increasingly abstract knowledge of linear measurement, emphasizing ways they relate space and number. Assessments indicate children struggle to understand measurement, especially concepts related to complex paths as in perimeter tasks. This article draws on developmental accounts of children's knowledge of...

Japanese lesson study, in various adapted forms, is becoming increasingly significant in professional development of mathematics teachers in the USA. Our goal in the research reported in this paper was to investigate, in a three-tiered teaching experiment, the cycles of learning of two researchers, six teachers, and the students in three grade 4 cl...

This study examined the classroom practice and beliefs of two novice teachers, Anne and Rachel, during their first year of teaching and during the first year of their involvement in Project PRIME, a district-wide professional development project. The research also analysed the challenges faced by the novice teachers and the professional developer w...