Slope Across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

Abstract

This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property, Real World Situation, and Linear Constant conceptualizations of slope and describe a similar instructional sequence during the middle grades. However, the elementary and high school standards include differences that reflect alternative approaches to covering key prerequisite notions related to slope and in extending ideas of slope to non-linear functions. Both documents are examined in light of their respective purposes, with careful attention to potentially unintended consequences on the treatment of slope across the curriculum. The findings warrant careful consideration of other key mathematical topics to understand the curricular implications of adopting a new set of standards.