The big question being addressed in this project is, "How can technology support the teaching and learning of mathematical argumentation?" This EAGER proposal focuses on the first steps in moving towards the vision of helping youngsters learn mathematical/algebraic argumentation. The project has two complementary goals: to better define the technological tools needed to support elementary students learning about proof and argumentation and to understand better how elementary school students learn to make and defend mathematical claims when such tools are available. The PIs envision and are developing an animation tool to be implemented on tablet computers (so each child has his/her own electronic notebook) that provides infrastructure for sharing and refining arguments in small groups and across the class and for promoting concrete math discussions. A big challenge is providing the right tools for expression; for sharing to happen, learners need to first be able to express their understanding, and much research shows that a concrete "written" (sharable) expression of understanding provides better foundations for promoting concrete discussion than do expressions of understanding that are simply verbal. The particular advance in expression that is being made in this project is providing tools for dynamic representations; that is, they are able to animate what happens when mathematical operations are carried out. These concrete expressions of understanding can then be played back, paused, and so on. Students create animations by drawing, erasing, duplicating, moving, and grouping objects. They can edit each others' animations, and the teacher will also be able to create animations for students to view and edit. They record and save their oral explanations along with the animations and play them back together, thus making their verbal descriptions concrete, examinable, and sharable.
The ability to prepare and present a mathematical argument is a key component of the mathematical competence students need to achieve in upper elementary school (grades 3 through 5). Many students struggle with the subject matter and therefore struggle as well with making mathematical arguments. The PIs envision a computational tool set that young students will use to construct and share mathematical arguments, in the service of learning to be competent algebraic reasoners. In this EAGER project, they focus on first steps in developing that tool set and on investigating how young learners make and defend mathematical arguments when they have such tools available. This project represents work in its early states on an untested but potentially transformative idea and is likely to catalyze rapid and innovative advances in helping young learners become mathematical reasoners.
