Abstract:

While the role of visualization in mathematics learning has long been recognized by researchers, its importance has only begun to draw the strong attention of mathematics teachers in the United States (U.S.) during the past decade. Largely in response to the national Common Core Mathematics Standards initiative, the traditional approach to teaching mathematics by modeling procedures and memorizing rules is undergoing intense scrutiny. It is not surprising, therefore, that pre-service teachers who have matriculated through the American educational system with its emphasis on procedural mathematics learning come to the mathematics methods course - the site where prospective teachers learn to teach math prior to student teaching in U.S. teacher preparation programs - with few if any experiences learning mathematics through reasoning or with visual representations and tools. Prospective teachers are, as researchers like Ball have long pointed out, “unlearning to teach mathematics” in these methods courses. Because the Common Core Mathematics Standards push for students to understand the reasoning behind the mathematical problems that they are working on, prospective teachers must unlearn the memorize-the-rules and copy-the-teacher’s-thinking approach to doing math that most have learned in school.

Transforming prospective teachers’ procedural, rule-based understanding of mathematics into a deep, more meaningful, learning of the mathematical reasons motivating the procedures is the job of mathematics teacher preparation programs. Visualization tasks are a pedagogically sound place for mathematics teacher educators to begin launching the needed shift in pre-service teacher understanding of mathematics and its teaching practices. For as representational theories of mathematics learning suggest, human understanding of abstract mathematical ideas begins with visualization of those ideas through multiple concrete embodiments of them from which learners will eventually generalize the core mathematical notion by being taught to reason spatially across time from the concrete examples to their pictorial counterparts and analogous abstract mathematical symbols.

This poster reports the results of an exploratory teaching experiment in the methods course on the use of spatial-temporal reasoning technology for developing pre-service teachers’ mathematics teaching practices. Digital visualization-learning-sequences (VLS) drawn from the PreK-8 visual instructional program called Spatial Temporal Mathematics (ST Math) provide a novel context for developing pre-service teaching practices. Included are reflections of the pre-service teachers on learning to teach mathematics in this way as well as reflections of the instructor on the rationale and perceived advantages of using the digital ST Math learning sequences to develop pre-service teachers’ ability to 1) use precise terminology to explain the mathematical concepts in the VLS, 2) write learning objectives to fit the VLS, 3) analyze the logical flow and spatial morphing of the VLS, 4) identify how tasks at each level of the VLS move learners’ mathematical thinking forward, and 5) describe how the VLS implement the Common Core Mathematics standards.

Keywords:

Pre-service experiences, mathematics teacher preparation, methods course, spatial-temporal reasoning technology.