Michael Pedersen From Arithmetic to Algebra

Michael Pedersen’s Literature Review

Title: From Arithmetic to Algebra

Authors: Leanne R. Ketterlin-Geller, Kathleen Jungjohann, David J. Chard and Scott Baker

Source: Leanne R. Ketterlin-Geller, Kathleen Jungjohann, David J. Chard and Scott (2007, Nov.). From Arithmetic to Algebra. Making Math Count, 66-71.

Summary:

This article discussed key components needed to teach algebra. It also talked about how teachers can move from just teaching arithmetic to combining arithmetic and Algebra.

1.      Variables and Constants: The same rules apply for constants and variables.

a.       For example, the distributive property 4 x (3 +2) = 4 x 3+ 4 x 2. Then do the same problem but replace constant with a variable and solve.

2.      Represent and Decompose word problems algebraically.

a.       “Start by identifying the unknown” (p 69). What they are solving for is the variable.

b.      Write out the steps you need to find the unknown as Math expressions.

c.       “Check the problem using different Constants to verify the equation” (p 69).

3.      Symbol Manipulation

a.       Help students understand the equal (=) sign does not mean solve, but to balance each side

4.      Functions

a.       Find patterns

b.      “Sort and classify objects on the basis of unique properties” (p 69). For example all students wearing a blue shirt is a function or rule for sorting students.

Analysis:

Students need to start learning algebra, problem solving skills, and math concepts starting in Kindergarten. Students need to be explicitly taught these concepts and how to verbalize these concepts. In class teachers need to explicitly teach concepts using the algorithm, as well as, bringing in pictures and models to help students understand why the algorithm works. A teacher can use think-a-louds to verbalize how they are thinking about the problem and working through problem. After modeling and talking through the problem, students need to be given a chance not only to solve the problem with pen and paper but also be able to verbally discuss the problem. Students should be able to orally share what the problem is and the steps they will use to solve it. Students need to see and understand that problem solving is more than filling in a formula. Problem solving is creating math expressions and solving them using math properties.