Math and Math-in-School: Changes in the Treatment of the Function Concept in Twentieth Century Secondary Algebra Textbooks

Abstract

The exercises found in the chapters on function in five American textbooks (each taken from different twenty-year spans of the twentieth century) were analyzed using Mesa's (2000) coding scheme. Problems were analyzed based on the context, the operations needed to solve the problem, the representations used, and the control structures (or checks) available to the students. This analysis allowed for the identification of trends across time. These trends were compared to trends in the concept of function in the mathematics discipline and trends in recommendations for mathematics education. This analysis was undertaken to address three basic research questions. First, is there evidence of change in the treatment of function in school algebra across time? Second, how do any changes that exist in the texts correlate with recommendations for mathematics education? And third, how do changes in the texts correlate with the developments of the function concept in the mathematics discipline?