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DELTA Project: Diagnostic E-Learning Trajectories Approach for Assessment for Rational Number Reasoning


The DELTA project is one of several projects conducted by GISMO (Generating Increased Science and Math Opportunities) researchers. For more detailed information on any of our projects, please visit our website at http://gismo.fi.ncsu.edu.

Brief Description of the DELTA Project

The DELTA project is designing diagnostic assessments for rational number reasoning (RNR), based on Learning Trajectories synthesized from the rational number reasoning literature.  The key methodological theme of this work is the creation of valid and reliable student-centered assessments that track students’ development over time (within and between grades) in key mathematical ideas of rational number reasoning.  The project’s long-term goal is to develop diagnostic tools, for both individual student and whole class progress, that provide teachers with instructional guidance.  Several strands of work have been pursued so far, in collaboration with the Berkeley Evaluation and Assessment Research Center and the Evaluation team.

The project questions whether the dominant curricular sequence for fractions is the best way to think of RNR.  It has also raised the possibility that division should precede multiplication, and that ratio and proportion should be taught in parallel with fraction-as-number.  This project is closely coupled with our Synthesis of Rational Number Reasoning project, incorporating that project’s extensive research literature base in mathematics education and cognitive psychology. 

Building on the research syntheses, the project has identified the equipartitioning learning trajectory, which we believe forms a major under-recognized cognitive underpinning for rational number reasoning.  Progress Variable are the frameworks of student actions and responses that form the foundation of diagnostic assessments. The equipartitioning progress variable begins with the fair sharing of collections of items, using dealing, proceeds to fair sharing of a single whole, then to fair sharing of multiple wholes.  Within each type of fair sharing, an ordered sequence of the numbers of partitions is used as tasks that draw upon number theoretic qualities and geometry.  Each time students engage in a task, they are expected to solve a problem, use multiple methods, justify their answers, name the results, reverse the process, and, at the highest level of proficiency, demonstrate understanding of the fundamental mathematical properties of compensation, equivalence, and composition.

Additional work is underway to articulate the learning trajectories for division and multiplication and for area and volume.  We are also experimenting with innovative forms of assessment delivery, including video scenarios, and interview data collection on handheld devices.  Graduate students are conducting studies on the use of learning trajectories within instructional practice. We place a high priority on developing assessment settings that leverage dynamic representations, with the aim of aligning the assessment of mathematical reasoning to the skills, environment, and cognitive tools of the types that are standard in modern work settings and increasingly available in schools.

PROJECT TEAM

PARTNERS

  • NSF