| Summary: | Manipulatives of various kinds are used in elementary schools as part of the mathematics curriculum. They are recognized for their affordances for helping children understand abstract ideas by connecting them to concrete objects, but not all research about the use of manipulatives has been positive. It is sometimes difficult for children to make connections between what they are doing and the ideas the manipulatives embody.
Constructionist research suggests that taking a design approach to learning that involves the learner in constructing not only ideas but also public artifacts facilitates learning particularly well. Further, it suggests that one should design a learning environment that will allow learners to leverage personal and epistemological connections rather than scripting everything that should happen. Additionally, previous research suggests that integrating math with craft and design helps learners engage with math in a personally meaningful manner.
Manipulatives such as pattern tiles and quilt builder tiles are used for design in the classroom, but there is often little to no support for the analysis of designed patterns or other kinds of learning. On the other hand, computerized versions of manipulatives that provide feedback about fractions (or other math concepts) do not offer affordances for design. My goal has been to integrate the best of what computational manipulatives can offer with a design approach to help learners engage with math in a meaningful way.
In this dissertation, I describe the use of a manipulative that combines affordances for design and also links and maintains connections between representations. This gave learners opportunities to see and make connections between symbolic and concrete representations while engaged in designing personally meaningful artifacts. I describe methods that made this constructionist educational experience accessible to a wide range of learners, including aspects of the socio-technical system that seemed to play greater or lesser roles at various times throughout the study. I emphasize roles of the DigiQuilt manipulative and highlight how this software builds on previous work, yet represents a new kind of manipulative one that simultaneously supports design and connecting targeted math concepts with concrete artifacts.
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