Research Foundation

The LMR project provided strong empirical grounding for the design of our lesson sequence and our Lesson Guides through interview, tutorial, and classroom studies. In the last phase of the project, we conducted an efficacy study that involved 21 classrooms.

Study Types Used to Develop and Evaluate LMR

Interview studies. Interview studies provided us information on children’s mathematical thinking related to key LMR topics - for example, how students conceptualize points on the number line. We were particularly concerned with identifying mathematical ideas that are difficult for students to learn.
Tutorial studies. Tutorial studies enabled us to explore ways that teachers might use number lines (and other representations) to support student learning. Tutorial studies built on findings from our interview studies as we investigated learning trajectories in a particular domain, the hurdles that students encounter, and the benefits of particular instructional approaches.
Classroom studies. There were two purposes to our classroom studies. The first was development and formative refinement of LMR lesson design in collaboration with teachers. Findings from the interview and tutorial studies provided the research base for lesson design, and studies in the classroom allowed us to refine the design. The second purpose was an empirical investigation of the ’travel of ideas’ as students learn from mathematical tasks, representations, and discussions. We investigated ways that mathematical ideas emerge, are taken up or resisted, are built upon, and are transformed in classroom communities.

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Efficacy studies. In the final phase of the LMR project, we conducted an evaluation of the curriculum unit in an experimental study that documented lesson implementation and student learning. We contrasted the learning gains in 11 LMR and 10 matched comparison classrooms. The performance of both groups was identical at pretest, and all students made strong gains over the academic year; however, the gains of LMR students were 75% greater than the gains of comparison students on assessments given both directly after LMR and at the end of the academic year. These findings provide support for the efficacy of the LMR curriculum in strengthening 4th and 5th grade student's understandings of integers and fractions. Importantly, we found that English Learners and English Proficient students progressed at similar rates of gain.

See publication page for articles that report on student gains as well as case studies of LMR classrooms.

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