Paradigmatic Didactical Mathematical Problematic Situations

In collaboration with Betina Zolkower, Ph.D., Brooklyn College, CUNY.

In the PDMPS project, we designed, implemented, and evaluated an experimental curriculum for pre-service teachers and future education researchers enrolled in graduate-level college courses on mathematics cognition, learning, and instruction. Central to this design are selected ‘paradigmatic didactical-mathematical problematic situations,’ i.e., unique activities evoked as contexts for collaborative inquiry into the epistemology, pedagogy, and practice of mathematics as well as into subject matter content. Our data include rich documentation from both the college classroom and the placement classrooms, where the student teachers tried out the same problems. We investigated the conjecture that the curriculum’s value lies in the authenticity of the multi-disciplinary pragmatic approach it fosters in future teachers. We were also interested in potential tradeoffs inherent to a problem-focused curriculum.

Graduate students and pre-service teachers working on the Pyramid Problem: learning how to “midwife the birth of algebra”

Zolkower, B., & Abrahamson, D. (2009). Studying paradigmatic didactical-mathematical situations: Design and implementation of an experimental graduate level course for pre-service mathematics teachers and doctoral students. Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 13 – 17. 

ABSTRACT: We discuss results from the implementation of an experimental design for pre-service teachers and future education researchers enrolled in graduate-level college courses on mathematics cognition, learning, and instruction. Central to this design are selected ‘paradigmatic didactical-mathematical problematic situations,’ i.e., unique activities evoked as contexts for collaborative inquiry into the epistemology, pedagogy, and practice of mathematics as well as into subject matter content. Our data include rich documentation from both the college classroom and the placement classrooms, where the student teachers tried out the same problems. Building on functional-grammar analysis techniques, we argue that the curriculum’s value lies in the authenticity of the multi-disciplinary pragmatic approach it fosters in future teachers. We discuss potential tradeoffs inherent to a problem-focused curriculum. 

Brar, R., Galpern, A. J., & Abrahamson, D. (2006). Lost in translation: The ‘bean snare’ as a case of the situated-symbolic divide. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), The Twenty-Eighth Conference of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 390-391). Mérida, Yucatán, México: Universidad Pedagógica Nacional.

EXCERPT: …The third author designed the Bean Snare to spark discussion of the complexity of constructivist design, teaching, and learning, i.e., subtle interactions of content and context as well as multi-media, multi-modal, and multi-representational aspects of collaborative reasoning about a situated mathematical problem. Note how the presentation surreptitiously leads us down the garden path to a mathematically incorrect statement….