Learning the concept of function: Guess My Rule activities with Dr. Robert B. Davis.

摘要

A recommendation of the National Council of Teachers of Mathematics and others, including the late Professor Robert B. Davis, New Jersey Distinguished Professor of Mathematics Education, is that algebraic ideas be introduced through meaningful contexts that encourage sense-making by elementary and middle school students, prior to their formal study of algebra. In particular, Davis indicated the importance of understanding the idea of function. In teaching algebra to children, Davis introduced linear and quadratic functions through a Guess My Rule activity. This study analyzes this introduction to 12 sixth-graders over 2 sessions, each 90 minutes, videotaped with 4 cameras. In particular it examines how the activity was used, the interventions made by Davis as teacher/researcher, and students' understanding of linear and quadratic function ideas.; The students were participants in a longitudinal study from the public K-8 school in Kenilworth, New Jersey. They were presented with tables of ordered pairs and asked to write equations. Analysis of the data shows they were able to identify the mathematical ideas of slope and y-intercept in writing equations for linear examples; they retained their use of y-intercept and found second differences in writing equations for quadratic examples; they found patterns, made conjectures, and justified their reasoning.; In analyzing Davis' pedagogy, some important features emerged: he accepted student ideas that were expressed; he facilitated student-to-student talk; and he encouraged investigation based on meaning and thoughtfulness. One effective tool was to introduce the idea of "secret" to motivate students to find solutions and to continue searching for patterns. A resulting benefit was time for others to continue working on the original task. To promote discourse between groups, he invited students to share and discuss their secrets.; Davis' pedagogical approach has important implications for teaching. He created an atmosphere that was conducive to investigation and discovery, used cognitively engaging tasks, and designed lessons to build on the developing understanding of the students. He implemented strategies to address gaps in learning and differences between students. Studying videos of Davis' lessons with early algebra learners could be an effective way of promoting a thoughtful approach to teaching these ideas.