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A Brief History of Algebra in Connected Math

June 24, 2011

Does 8th grade CMP count as Algebra 1?

Short answer: Yes.

But this is a question with a history. Let’s begin in 1989.

1989 NCTM Standards and CMP 1

In 1989, the National Council of Teachers of Mathematics issued Curriculum and Evaluation Standards for School Mathematics. These standards formed the basis for the National Science Foundation funding of the writing of Connected Mathematics and other elementary, middle and high school curricula.

In particular, the Standards called for increased emphasis on algebraic ideas in the middle grades.

One critical transition [between the elementary and the high school curriculum] is that between arithmetic and algebra. It is thus essential that in grades 5—8, students explore algebraic concepts in an informal way to build a foundation for the subsequent formal study of algebra. Such informal exploration should emphasize physical models, data, graphs, and other mathematical representations rather than facility with formal algebraic manipulation. (p. 102)

…by the end of the eighth grade, students should be able to solve linear equations by formal methods and some nonlinear equations by informal means (ibid).

In fact, the authors created algebra units in CMP 1 that addressed all of this and went above and beyond these standards.

Variables and Patterns introduced tables, graphs—and to a lesser extent equations—and relationships between variables in seventh grade. Moving Straight Ahead, also seventh grade, had students working extensively with linear relationships-slope, y-intercept, tables, graphs and equations. At eighth grade, there were four algebra units. Thinking with Mathematical Models revisited linear relationships and introduced (1) modeling and (2) the idea that not all predictable relationships are linear. Growing, Growing, Growing used exponential relationships to strengthen students’ understanding of linearity. Frogs, Fleas and Painted Cubes introduced quadratics and Say It with Symbols summarized the symbolic algebra work in the curriculum.

Taken together, these units created a much more challenging and much richer eighth-grade mathematics curriculum than was typical at the time.

It didn’t take long before the question was being asked.

Does 8th grade CMP count as Algebra 1?

In writing CMP 1, it had not been the intention of the authors to answer this question one way or the other. In the early 1990’s, there was no large scale emphasis on Algebra 1 for eighth graders. Instead, the authors had set out to write a challenging curriculum rich in algebraic ideas.

Principles and Standards 2000, and CMP 2

In 2000, NCTM issued a revised set of standards-Principles and Standards for School Mathematics. These standards also stuck to algebraic ideas and an emphasis on linearity in the middle school curriculum.

Students in the middle grades should learn algebra both as a set of concepts and competencies tied to the representation of quantitative relationships and as a style of mathematical thinking for formalizing patterns, functions, and generalizations … They should connect their experiences with linear functions to their developing understandings of proportionality, and they should learn to distinguish linear relationships from nonlinear ones. In the middle grades, students should also learn to recognize and generate equivalent expressions, solve linear equations, and use simple formulas.

The authors received funding from the National Science Foundation in 2000 to revise the materials from beginning to end, with Principles and Standards as one of the major driving forces. On their own, these standards would not have required a fundamental change in CMP’s algebra strand.

But this time around, they couldn’t ignore the important question of whether eighth-grade CMP is equivalent to Algebra 1. Teachers and district decision-makers had been asking the question, and there had developed a policy environment in which Algebra 1 in eighth grade was being seen as essential for all students.

(For more about this, see a Brookings Institution report, a Washington Post op-ed and a District Administration document. Also, discussions of algebra for eighth graders invariably cite The Algebra Project)

So the authors made a commitment at the beginning of their work creating CMP 2 that eighth-grade CMP 2 would be equivalent to Algebra 1. Now…that said, there is no universal agreement on the definition of Algebra 1. But it was clear that a commitment to aligning CMP2 with Algebra 1 would mean several changes, including (1) more formal symbolic work, especially with respect to the distributive property and quadratic functions, (2) increased attention to algebraic inequalities and (3) some formal work with systems of equations.

In order to address these needs, the existing algebra units were revised and a new unit, Shapes of Algebra was written. Some teachers may have to tweak or supplement in order to meet their idiosyncratic state or district guidelines for Algebra 1, but the eighth-grade CMP 2 algebra units now comprise a principled Algebra 1 course.

Now what? Common Core and Algebra in CMP 3

The present driving force for curriculum and testing is the Common Core State Standards. One of the puzzling things for us is illustrated by this image from the CCSS webpage:

Algebra and Functions are two different standards, while CMP has taken a functions approach to algebra. These different orientations are sure to make alignment challenging in schools.

Eighth-grade Common Core does not comprise a full Algebra 1 course in the standard American curricular sense. We are curious to know how the standing pressures to offer Algebra 1 to all eighth graders will interact with the new pressures of testing in the Common Core era.

We’ll share on this blog the decisions we are making as we work on the algebra strand. But please check in and share your stories from the field. What are the pressures you are working under as you rethink eighth grade in your districts and buildings in light of Common Core?

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From → Grade 7, Grade 8

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