This is a technical report detailing the methods and findings for each of the research studies in the LLAMA project.
This presntation addreses 4 research cquestions
Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.
LEAP early algebra curriculum for Grades K-5. Grades 3 and 4 currently available, with the remaining books for Grades K-2, 5 in press.
Blanton, M., Gardiner, A., Stephens, A., & Knuth, E. (2020). LEAP: Learning through an early algebra progression. Didax: Rowley, MA.
Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.
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 instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component.
This study evaluated a portion of our learning trajectory, focusing on the instructional component. We found that the instruction was successful in promoting a progression from one level to the next for 40% of the children, with others developing positive new behaviors (but not sufficient to progress to a new level).
This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks.
This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign.
In this report, authors describe the results of a rigorous two-year study of the impacts of a mathematics initiative called Ongoing Assessment Project (OGAP) on teacher and student learning in grades 3-5 in two Philadelphia area school districts.
This study explored how teachers interpreted and responded to their own student work during the process of formative assessment. The study involved a purposefully selected sample of 32 teachers in grades K-5 who had been trained by the Ongoing Assessment Project (OGAP) to use learning progressions to analyze and respond to evidence in student work.
This study explored how teachers interpreted and responded to their own student work during the process of formative assessment.
Students with learning disabilities display a diverse array of factors that interplay with their mathematical understanding. Our aim in this paper is to discuss the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions. We present analysis and results from multiple sessions conducted during a teaching experiment cast as one-on-one intervention.
This paper discusses the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions.
Dig deeper into classroom artifacts using research-based learning progressions to enhance your analysis and response to student work, even when most students solve a problem correctly.
Ebby, C. B., Hulbert, E. T., and Fletcher, N. (2019). What can we learn from correct answers? Teaching Children Mathematics, 25(6), 346-353.
This article describes how research-based learning progressions can be used to enhance the analysis and response to student work.
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-year-long multisite longitudinal study that studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume).
This monograph is a report on a four-year-long multisite longitudinal study that studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume).
