Developmental Math Workshop

January 20, 2005 (held at UW Fox Valley)

Perspectives from a First Year Faculty

Assistant Professor Yongjun Yang, UW Barron County

Professor Yang shared some of his thoughts on common student difficulties in algebra. He emphasized the importance of correct use of parentheses in algebra.

Examples of some common errors in algebra:

-5² = (-5)² = 25 (Incorrect order operations)

(x + y)² = x² + y² (“Everything is distributive”)

(Undistributed cancellations)

(Invisible parentheses)

Does 1/2x mean or (Ambiguous notation)

Professor Yang offered these suggestions for help in avoiding common errors like those above:

Building algebraic expressions: know what you are working with.

· View numbers and variables as building blocks: x, y, 1, 2, …

· View operations as links between the building blocks: +, -, *, /, exponents, roots, …

· Continually emphasize that order matters!

1 – 2x²

(1 – 2)x²

(1 – 2x)²

Understand and use the parentheses

· The priority of parentheses (both visible and invisible ones)

· Use parentheses at the right place and the right time

· Know when you have “free” parentheses; e.g.

· Good by-product: students will be better at function composition when they get to it; e.g.

Given f(x) = x² and g(x) = x+ 1, then