Algebra for All in Eighth Grade: What's the Rush?
Lynn Arthur Steen, St. Olaf College
Appeared in Middle Matters, the newsletter of the National Association of Elementary School Principals, Vol 8, No. 1, Fall 1999, pp. 1, 6-7.
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Not so long ago, high school algebra served as an effective filter to separate college-bound students from their work-bound classmates. Then advocates for educational standards began demanding "algebra for all," a significant challenge for a nation accustomed to the notion that only some could learn algebra well. More recently, notably in California--the center for start-up educational movements--this demand escalated to "algebra in eighth grade for all" or what one skeptic described as "algebra before acne."

Is algebra--especially early algebra--really that important for all students? How can a subject that for many adults serves as a metaphor for frustration suddenly be the top priority for soccer moms and internet dads? And why do so many parents suddenly demand of their schools and their children something they themselves neither mastered nor loved?

One answer is that algebra is, in Robert Moses' apt phrase, "the new civil right" (Moses, 1995). Algebra means access. It unlocks doors to productive careers and democratizes access to big ideas. As an alternative to dead-end courses in general and commercial mathematics, algebra serves as an invaluable engine of equity. The notion that by identifying relationships we can discover things that are unknown--"that we can find out what we want to know"--is a very powerful and liberating idea (Malcolm, 1997).

Another answer is that algebra is the language of mathematics, which itself is the language of the information age. The language of algebra is the Rosetta Stone of nature and the passport to advanced mathematics (Usiskin, 1995). It is the logical structure of algebra, not the solutions of its equations, that made algebra a central component of classical education. And as a language, algebra is better learned earlier and harder when learned later.

Parents' views of algebra are both more mundane and more inconsistent. Some see algebra primarily as the mark of a rigorous education, others see it as the key to lucrative careers. Some see algebra as a motivator for high performance, others as a reminder of their worst memories of school mathematics. ("Word problems" still cause many adults to grimace.) Parents with more favorable experiences recall algebra as an embalmed memory of their bygone school days. Many others see algebra as a metaphor for authority--for rules and regulations, for the discipline of following procedures and getting correct results. For them, rigorous algebra that only future leaders can master is essential to preserve our nation's economic and social stability.

In the Middle Ages, algebra meant calculating by rules (algorithms). During the Renaissance, it came to mean calculation with signs and symbols--using x's and y's instead of numbers. (Even today, lay persons tend to judge algebra books by the symbols they contain: they believe that more symbols mean more algebra, more words, less.) In subsequent centuries, algebra came to be primarily about solving equations and determining unknowns. School algebra still focuses on these three aspects: employing letters, following procedures, and solving equations.

However, in the twentieth century algebra moved rapidly and powerfully beyond its historical roots. First it became what we might call the science of arithmetic--the abstract study of the operations of arithmetic (addition, subtraction, multiplication, etc.). As the power of this "abstract algebra" became evident in such diverse fields as economics and quantum mechanics, algebra evolved into the study of all operations, not just the four found in arithmetic. Thus did it become truly the language of mathematics and, for that reason, the key to access in our technological society.

No doubt about it: algebra for all is a wise educational goal. The challenge for educators is to find means of achieving this goal that are equally wise (Steen, 1992). Algebra for all in eighth grade is clearly not one of them--at least not at this time, in this nation, under these circumstances. The impediments are virtually insurmountable:

  • Relatively few students finish seventh grade prepared to study algebra. At this age students' readiness for algebra--their maturity, motivation, and preparation--is as varied as their height, weight, and sexual maturity. Premature immersion in the abstraction of algebra is a leading source of math anxiety among adults.
  • Even fewer eighth grade teachers are prepared to teach algebra. Most eighth grade teachers, having migrated upwards from an elementary license, are barely qualified to teach the mix of advanced arithmetic and pre-algebra topics found in traditional eighth grade mathematics. Practically nothing is worse for students' mathematical growth than instruction by a teacher who is uncomfortable with algebra and insecure about mathematics.
  • Few algebra courses or textbooks offer sufficient immersion in the kind of concrete, authentic problems that many students require as a bridge from numbers to variables and from arithmetic to algebra. Indeed, despite revolutionary changes in technology and in the practice of mathematics, most algebra courses are still filled with mindless exercises in symbol manipulation that require extraordinary motivation to master.
  • Most teachers don't believe that all students can learn algebra in eighth grade. Many studies show that teachers' beliefs about children and about mathematics significantly influence student learning. Algebra in eighth grade cannot succeed unless teachers believe that all their students can learn it.

Any middle school principal who contemplates requiring algebra in eighth grade must address these practical issues. Are all the students ready? Are all the teachers prepared? Does the textbook serve all students well? Do the teachers believe the program can succeed?

But behind these concerns lies a crucial policy question: What's the rush? The goal of mathematics education is not speed but understanding. Nothing in high school requires mastery of algebra so early. Worse, much valuable mathematics will necessarily be neglected in a thoughtless stampede to early algebra, notably data analysis, elementary statistics, geometry (in two and three dimensions), discrete (computer) mathematics, risk analysis, and financial mathematics. All these topics are more valuable than algebra for citizenship and employment (Forman and Steen, 1997), most are also more concrete (thus easier to learn at an early age), and all would help students build a firm foundation for later study of algebra.

Algebra in eighth grade should pass the same tests of quality that mathematicians and mathematics educators have consistently recommended for calculus in high school. Such "early" courses should be offered only by well-prepared teachers to well-prepared and highly motivated students under circumstances that will enable every student who works hard to master the course at the same level as those who take it a year later. The most effective way to make "algebra for all" a reality is for strudents to take it when they are ready--some in eighth grade, some in ninth, and some in tenth. What matters is not when students study algebra but that they learn it well.

References

Forman, Susan L. and Steen, Lynn Arthur. "Mathematics for Work and Life." In Seventy-Five Years of Progress: Prospects for School Mathematics, Iris Carl, Editor. Reston, VA: National Council of Teachers of Mathematics, 1995, pp. 219-241.

Malcom, Shirley. "Making Mathematics the Great Equalizer." In Why Numbers Count: Quantitative Literacy for Tomorrow's America, Lynn Arthur Steen, Editor. New York, NY: The College Board, 1997, pp. 30-35.

Moses, Robert. "Algebra, The New Civil Right." In The Algebra Initiative Colloquium, Vol. II. Carol Lacampagne, et al., Editors. Washington, DC: U. S. Department of Education, Office of Educational Research and Improvement, 1995, pp. 53-67.

Steen, Lynn Arthur. "Does Everybody Need to Study Algebra?" Mathematics Teacher, 85:4 (April 1992) 258-260. Also appeared in Basic Education, 37 (January 1992) 9-13.

Usiskin, Zalman. "Why is Algebra Important to Learn?" American Educator, (Spring 1995) 30-37.

 

 


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