Abstract
Design research studies provide significant opportunities to study new innovations and approaches and how they affect the forms of learning in complex classroom ecologies. This paper reports on a two-week long design research study with twelve 2nd through 4th graders using curricular materials and a tablet-based diagnostic assessment system, both designed around a learning trajectory on equipartitioning. A learning trajectory is a conceptual model of how students move from naïve to more sophisticated understandings as they engage with a carefully sequenced set of tasks. The equipartitioning construct describes how students come to understand the ideas involved in sharing fairly an evenly divisible collection, a single shape or multiple shapes. The paper is organized around the three phases of design research: planning, conduct, and retrospective analysis Cobb et al. (Educ Res 32(1):9–13, 2003). It illustrates how the conjectures of the study are subjected to testing and revision, based on the students’ and teachers’ behaviors during the study, and how interpretations and theories evolve during the different phases.
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Notes
Learning progress profiles synchronized for networked wireless devices.
For family reasons, a 3rd- and two 4th-grade boys left the program after week 1; their work during week 1 is reflected in the study data.
Some students struggled with the precision of the physical task; many said they had never tried to share make fair shares from single shapes.
Only late in the study was it discovered that the internal software criteria for accepting equipartitioned areas as correct was inappropriately stringent: student responses had been scored incorrect for only minor variations in the sizes of partitions. This resulted in mis-scoring and denying students opportunities to answer most of single-whole naming and reassembly questions.
Prior research has shown that individualized instruction has uneven and limited benefits (Erlwanger 1975).
Figure 5 shows correct scores for equipartitioning tasks, based on replaying recorded student on-screen actions, circumventing the software scoring defect (see footnote 4).
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This material is based upon work supported by the National Science Foundation (DRL-0758151) and Qualcomm. Opinions, findings, conclusions, or recommendations are those of the authors and do not necessarily reflect views of the funders.
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Confrey, J., Maloney, A. A design research study of a curriculum and diagnostic assessment system for a learning trajectory on equipartitioning. ZDM Mathematics Education 47, 919–932 (2015). https://doi.org/10.1007/s11858-015-0699-y
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DOI: https://doi.org/10.1007/s11858-015-0699-y