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doi:10.7282/t3-rykn-3x55

Authors: Jianene Meola, Christian Orr-Woods

In her 2007 dissertation, Mayansky conducted a study of Robert B. Davis’ pedagogy, drawing on data from Davis’ own writing and video footage of his teaching. Her goal was to gain a deeper insight into the philosophies of a renowned mathematics educator and engaging mathematics teacher, to see how his classroom practices connected to his views about teaching mathematics, and to identify what student outcomes could be associated with those practices. This resulted in Mayansky’s creation of two frameworks that were created to explain Davis’ teaching moves in terms of his own ideas on mathematics learning, and also to categorize the observable effects of those moves. Mayansky summarizes these results in the following quote:

"We can observe from Professor Davis’ writing and practice the following: a strong focus on each individual student; primary concern for how a student is thinking; listening to students; cooperative problem solving (students frequently working together in small groups); students working on tasks that are interesting and clearly understood and where it is the students’ responsibility to invent methods of solution; concern for nonverbal forms of communication; mental representations; naming the method after the student; responding to student errors; responding to a student initiative; recognition of student potential; recognition of complex thought processes; deliberate creation of assimilation paradigms; discovery learning; and encouragement of student decision making." (pg. 91, Mayansky 2007)

Underlying Mayansky’s research is a strong belief that Davis is a figure worthy of detailed study. Indeed, she writes in one of her closing sections that “Robert B. Davis’ name and work should be made known to the deeper layer of the community of educators” (pg. 159, Mayansky, 2007). We share this belief and consider Mayansky’s dissertation to be a thoughtful analysis of a man who had powerful ideas concerning mathematics education. We also believe that a full appreciation of his philosophies and teaching practices is difficult to capture and convey in text alone. The Video Mosaic Collaborative (VMC) has enabled researchers to share and make use of video records in order to advance their claims with visual data that their audience can see. We have used video narratives in the hopes to strengthen Mayansky’s work by juxtaposing elements of her framework of Davis’ teaching alongside actual footage of his teaching. In this way, viewers will achieve a deeper understanding of how Mayansky’s framework is supported by her data and see for themselves how Davis’ philosophies shine through his pedagogical style. This analytic focuses on Professor Davis’ pedagogical behaviors during multiple lessons that challenge students to create a closed form for the Tower of Hanoi problem, a central data source of Mayansky’s study. Following a description of the legend behind the problem, the students are first asked to formulate results regarding the number of moves required for transferring one through seven disks. The lesson progresses by having the students extend these results to the situation of the number of moves for 100 disks. With increased difficulty, the students successfully meet the challenge and subsequently work to calculate the amount of time until the “end of the world,” a consequence of solving the Tower of Hanoi problem that is alluded to in the legend. The video clips from these events highlight the various moves which are noted and analyzed in Mayansky’s dissertation. We explain how these clips relate to the framework that Mayansky has created, using some of her analysis as well as original work of our own.

In addition to the analysis of Professor Davis’ teaching moves, we also attempt to note a multitude of positive student outcomes that emerge. These outcomes (e.g., students taking great pride and responsibility in their work as a result of Professor Davis’ acknowledgement of their potential) are mentioned in the descriptions of the events in which they can be observed.

References

Davis, R. B. & Maher, C. A. (1997). How students think: The role of representations. In L. English (Ed.), Mathematical Reasoning: Analogies, Metaphors, and Images (pp.93-115). Hillsdale, NJ: Lawrence E. Erlbaum Associates.

Mayansky, E. (2007). An analysis of the pedagogy of Robert B. Davis: Young children working on the Tower of Hanoi problem (Doctoral Dissertation), Rutgers University, New Brunswick, NJ.

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