Sequencing learning with multiple representations of rational numbers (Aleven, Rummel, & Rau)

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Sequencing learning with multiple representations of rational numbers

Vincent Aleven, Nikol Rummel, and Martina Rau'

Summary Table

Study 1

PIs Vincent Aleven & Nikol Rummel
Other Contributers Graduate Students: Martina Rau (CMU HCII)
Study Start Date September 1st, 2008
Study End Date August 31st, 2009
Number of Students ~350
Total Participant Hours ~2100
DataShop Log data is uploaded and available in the DataShop


We investigate a key issue in coordinative learning, namely, how learning with multiple external representations (MERs) should be sequenced to effectively support students’ conceptual understanding. In order to benefit from MERs, learners must attain some level of fluency in interpreting and manipulating the individual representations, and must also engage in sense making across the representations to relate them and abstract underlying concepts. The question arises how tasks involving different representations should be sequenced so that both these aspects of robust learning are realized. In particular, how frequently should students switch between representations? We focus on fractions as a challenging topic area for students in which multiple representations are often used and likely to support robust learning. This research will contribute to the literature on early mathematics learning, learning with multiple representations, and learning with intelligent tutoring systems. It will also add to the portfolio of studies in the PSLC’s coordinative learning cluster.

Background & Significance


  • Conceptual knowledge: knowledge about the rationale of a solution procedure
  • Procedural knowledge: knowledge of the components of a correct procedure involving knowledge about step-by-step actions for solving problems

Research questions


Dependent variables

Independent Variables



Further Information


Annotated Bibliography