Saturday, April 23, 2011

Algebra in Elementary School

Most students in the United States do not study algebra until high school. The reasons why algebra instruction has been postponed are varied, but some of the most popular ones include:
  • it is assumed that younger children aren't developmentally ready for the type of abstract thinking that algebra introduces
  • even teenagers have trouble with algebra, so introducing it earlier doesn't make sense
  • the current curricula in most schools do not emphasize the need for or benefits of introducing algebra in elementary school

In their paper, Arithmetic and Algebra in Early Mathematics Education [1],  David W. Carraher, Analúcia D. Schliemann and Bárbara M. Brizuela describe their research indicating that algebraic concepts could quite easily be introduced at an earlier age and may even be beneficial to students' mathematical learning processes.

The authors conducted a 30-month study of second through fourth graders in which they introduced activities designed to emphasize the algebraic nature of arithmetic, including addition, subtraction, multiplication, and division.

By exploring the commonality between arithmetic and algebra, both flavors of mathematics can be enhanced for pre-teens if the parent or teacher is aware of the overlaps. Some examples of opportunities for exploring both arithmetic and algebra at the same time include:
  • arithmetic can be thought of as a part of algebra - the part that deals with numerical concepts, number lines, as well as functions involving numbers
  • arithmetic operations can be described as functions in an algebraic sense 
  • many concepts in algebra can be thought of as a generalization of arithmetic operations
Number lines, for example, can be used to describe the most basic algebraic concepts, like additive linear functions. The authors used number lines to help the children in the study start internalizing algebraic concepts and thinking at an earlier age than thought possible.

Word problems can also be used to bridge the divide between teaching pure arithmetic and algebraic concepts. Replacing a number in a word problem with a symbol helps teachers reinforce the generalizations that algebra introduces. Tufts University provides a lot of great resources on their Early Algebra site, including creative ways to use word problems to introduce algebraic functions for third graders [2].

The National Council of Mathematics Teachers (NCTM) supports the authors' research findings and encourages teachers to find ways to integrate more algebraic reasoning when possible in elementary school. "As a collection of mathematical understandings develops over time, students must encounter algebraic ideas across the pre-K–12 curriculum. At the elementary school level, teachers help students be proficient with numbers, identify relationships, and use a variety of representations to describe and generalize patterns and solve equations." [3]

Because Peaksmart's curricula for pre-K through third grade are based on NCTM standards and recommendations, our students naturally encounter many of the overlapping concepts described in this post, like number lines and word problems. In fact, you'll see a specific algebra topic in each grade - starting in Kindergarten - that builds on the idea that introducing algebraic concepts in elementary school is a natural way to reinforce mathematics learning.


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