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Volume 28, Number 3
May/June 2012

The Algebra Problem

How to elicit algebraic thinking in students before eighth grade


Introducing letters to represent quantities, as in these first-grade math problems, helps students prepare for algebra. (Source: Curriculum Research and Development Group, Univ. of Hawaii)

It’s Crazy Hair Day at Marshall Elementary School in Boston’s Dorchester neighborhood—which is perfect, because Tufts University researcher Bárbara Brizuela has brought a hat.

In the stovepipe style and made from oaktag paper, the hat is one foot tall. Brizuela then asks, “If I’m five and a half feet tall, how tall will I be with the hat on?” Second-grader Jasmine, smiley in a pink sweatsuit, answers, “Six and a half feet.” Rather than say, “Right!” Brizuela offers another question: “How do you know?”

Thus begins a math conversation that researchers like Brizuela believe may hold the key to tackling one of our biggest school bugaboos: algebra. As they talk, Jasmine uses words, bar graphs, and a table to describe how tall each person they discuss will be if they put on the hat. Jasmine creates a rule—“add one foot to the number you already had”—and applies it to an imaginary person 100 feet tall.

This is an excerpt from the Harvard Education Letter. Subscribers can click here to continue reading this article.


For Further Information

For Further Information

J. Babcock et al. Breaking the Cycle: An Inter­national ­Comparison of U.S. Mathematics Teacher Preparation. East Lansing, MI: Center for Research in Mathematics and Science Edu­cation, 2010.

D. Chazan. “The Shifting Landscape of School Algebra in the United States: No Child Left Behind, High School Graduation Requirements, Principles and Standards, and Technology.” In Algebra and Algebraic Thinking in School Mathematics, edited by C. Greenes and R. Rubenstein, 19–33. Reston, VA: National Council of Teachers of Mathematics, 2008.

J. R. Star and B. Rittle-Johnson. “Making Algebra Work: Instructional Strategies That Deepen Student Understanding, Within and Between Algebraic Representations.” ERS Spectrum 27, no. 2 (2009), 1–18.

T. Williams et al. Improving Middle Grades Math Performance: A Closer Look at District and School Policies and Practices, Course Placements, and Student Outcomes in California. Mountain View, CA: EdSource, 2011.