The Critical Position of Algebra II

Our high schools face a new and imposing standard: how will we provide access to high quality, challenging and advanced course work in mathematics and the sciences not just for the few but for all students? In the past the argument has been that students must earn the right to learn (at one time) algebra and (presently still) calculus. But we now know that, just as in learning to read, the ability of students to learn and master mathematics depends primarily upon the quality of instruction. Instructional innovations over the past twenty years indicate that the same is true even for supposedly advanced topics such as the calculus. In a knowledge-based economy access to advanced study in mathematics and the sciences for all students is effectively a redistribution of privilege and opportunity.

Algebra II is located in a critical position in the secondary school mathematics curriculum. Because US school systems presently endorse a minimum of three years of secondary mathematics ( typically Algebra I, Geometry, and Algebra II ) as part of the requirements for graduation, Algebra II now stands as the benchmark in quantitative literacy for all students successfully passing through the public school system. The content of Algebra II constitutes the level of quantitative knowledge and skill that all students completing high school are expected to attain. In turn for college-intending students, Algebra II functions as the gateway course to higher mathematics in general and Advanced Placement Calculus in particular.

General mathematics requirements
Algebra I	Geometry	Algebra II	Trigonometry	AP Calculus
	College-preparatory courses

There is a way to raise the level of quantitative literacy for all students taking Algebra II and at the same time better prepare students for advanced study in mathematics &ndash the Polynomial Calculus. The Polynomial Calculus, from a mathematical standpoint, is nothing more than the Analytic Geometry of size and shape applied to polynomial and rational functions. With respect to content it is simply a thematic reorganization of the standard material of Algebra II. As part of the secondary mathematics curriculum Algebra I and Geometry are the only pre-requisites. The Polynomial Calculus establishes a basic level of competence in quantitative reasoning - the ability to reason in terms of quantity and rate - for all high school students completing three years of secondary mathematics. It allows all students to develop a deep understanding of the conceptual foundations of the calculus and in so doing it strengthens and broadens the pool of college-intending students targeting Advanced Placement Calculus by the end of their high school careers. The Polynomial Calculus lays the conceptual foundations for Advanced Placement Calculus by separating the conceptual issues of slope and area (derivative and integral) from the technical intricacies of analysis (approximations and limits). By strategically setting the Polynomial Calculus as the key organizing theme within Algebra II we ensure a higher level of quantitative literacy for all students and simultaneously strengthen the preparation and increase the pool of students moving on to advanced study in mathematics.