Transforming instruction about functions: One veteran teacher's experience with an innovative secondary mathematics curriculum.

Abstract

The purpose of this study was to understand how reform recommendations are incorporated into secondary mathematics teachers' instruction when implementing innovative curricula. The constructs of mathematical and pedagogical content conceptions guided the investigation of one high school teacher's experience implementing Core-Plus Mathematics Project (CPMP) curriculum materials. Mr. Allen voluntarily implemented the ninth grade materials during the 1994-95 and 1995-96 school years. Primary attention was on his conceptions and instruction about mathematical functions. CPMP's Patterns of Change unit treats functions as dependence relationships using; student-centered, contextualized activities with focus on exploring and connecting multiple representations. Mr. Allen participated in 15 interviews during his two years of implementation. Interviews were audio-recorded and transcribed. In both years, daily observations of the Patterns of Change unit were video-recorded. In year 2, lessons from additional CPMP units and several of Mr. Allen's traditional courses were observed. Major analytic categories were developed using Spradley's taxonomic and thematic strategies. Mr. Allen's dialogues with students consistently enacted the robust and integrated understandings of function that he communicated prior to teaching the unit for the first time. In particular, his graphical proficiency and personal focus on patterns of covariation empowered him to effectively utilize the CPMP materials. During year 2, he even more explicitly and frequently emphasized the importance of recognizing and describing the nature of covariation relationships, and understanding that relationships can be represented in multiple ways. He also displayed evidence in year 2 of having developed new pedagogical content conceptions (e.g., more equal treatment of non-graphical representations). When concerns about familiarity with new activities were alleviated by a year's experience, Mr. Allen was able to contemplate and experiment more directly with pedagogical struggles (e.g., how to organize small groups). This study illustrates how flexible, connected, and comprehensive content conceptions can support the implementation of novel approaches to subject matter. Moreover, Mr. Allen's experiences demonstrate how strong content conceptions contribute in pivotal ways to facilitating the gradual development of new pedagogical content conceptions. The subtle content-related differences displayed by Mr. Allen in year 2 contribute meaningful information about how instruction with a novel curriculum changes over time.