Multiplicative Reasoning as a Foundation for Stochastic Reasoning (NSF Grant No. REC-9811879)

Project Overview


This 40-month project aims to investigate two highly related areas. They are: (1) What high school students learn and the difficulties they have as they participate in sustained, quantitatively-oriented, scheme-based instruction in probabilistic and statistical reasoning; (2) How we might effectively engage teachers so they can teach for students' abilities to reason stochastically.

The project will have two overlapping phases. The first will focus on college-bound humanities-oriented high school students' participation in a semester-long course on probability and statistics using specially-designed activities and instruction, and on describing aspects of instructional actions and interactions which might be key to what they learned. The second phase will use products and insights from the first phase to engage a group of high school Algebra II teachers in rethinking what they hope students learn from statistics instruction and in reflecting on ways variations in their instruction can variously affect students' learning. The site of the second phase will be a three-week workshop, with follow-up visits, for 10 Algebra II teachers. The workshop's ostensive aim will be that they design instructional activities and materials to use in teaching probability or statistics in their regular Algebra II classes. The workshop and follow-up's research aim will be to provide occasions for teachers to grapple with issues of their personal understandings of probability/statistics and of mathematics teaching and learning that are central to their instruction, all so that they may be analyzed and understood.

Data will be collected from a number of sources, including videotaped instruction, individual interviews with students and teachers, students' and teachers' written work, draft and final documents from the workshop, and videotaped discussions of issues surrounding the documents. Student data will be analyzed in terms of the mental actions, operations and schemes and concomitant imagery that might be expressed in their visible actions ("the sense they make of instruction"). Teacher data will be analyzed similarly, but with added attention to institutional and self-imposed constraints under which they may feel compelled to operate, and with special attention given to changes in their conceptions of aims, objectives, and content.