DescriptionResearcher Maria Steffero conducts an interview with Romina as an adult, who recently completed her M.B.A., and asks her to reflect on her participation in a long-term study on development of mathematical thinking and reasoning in students. Interview questions include: "What does it mean to you to know something really well? How would you define math now? What would be something you know really well?"
For Romina, knowing something really well has three components: understanding the concept, recalling meaning after a long passage of time, and being able to explain the concept to others. She asserts that performing a procedure like calculating a derivative would not constitute knowledge of calculus. Romina states that even today she would be able to “explain” for others both background and computation of “the fundamental theorem of calculus” – specifically, “how all these things happened and worked.” Romina continues to distinguish between the conceptual “understanding how slope works” versus the procedural “actually figuring out the slope.” She describes the “understanding” as “much more higher level,” whereas “figuring out” computations is “basic” and “number crunching” with which tools like Excel help. Romina implies a lack of appreciation for knowing only a procedure – what she calls the “mechanics – just moving numbers around.” She admits frustration in the past that she “couldn’t do the mechanical part” of mathematics, but that since she does “understand” the ideas behind concepts, she will “get through life just fine.” As a problem-solver, Romina states she is “pretty good” at a process that includes: “getting a lot of information,” “organizing” the information to “see” the problem, and finally “working to find the solution.”
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes Romina interview reflections (M.B.A. graduate): Understanding the ideas Date: 2010 Author: Steffero, Maria (Rutgers, the State University of New Jersey)