Algebra: Teach the Instructions

Have you noticed this when teaching Algebra?

I’ve found that when my algebra students are struggling, the cause is often not the math, but the instructions and vocabulary.

For example, if the instructions say “factor the polynomial completely”, students often write solutions as if solving an equation.  As shown below, the student knows how to factor, but goes beyond that due to misunderstanding how an expression and equation are different. 

Often it seems as though students are understanding the material, yet they don’t perform well on assessments.  The example above shows one reason why this may happen.

Here is another example: “Find the zeros to the quadratic function.” or “Find the roots to the quadratic function.”  (Hands go up … “What are zeros?”  or What are roots?”)

The issue is the vocabulary term.  My students may have mastered using the quadratic formula, yet not have a clue how to begin to answer this question.

How can we fix this you ask? 

When you begin the quadratics unit, teach the vocabulary including terms students may see in instructions.  Stress that “answers, solutions, roots, zeros, and x-intercepts” are all synonyms.  Because you know what?  It is confusing!  Although you may not typically consider these to be vocabulary terms for the unit, being familiar with these synonyms is critical to success.

My advice is to make a conscious effort to teach students about not just the algebra, but about the most common errors they are likely to make and how to understand instructions.  You may think it is common sense, but kids don’t have the experience teachers do.  After completing high school and college, we’ve solved so many problems similar to the one above that we naturally do what we should because we have learned.  Students are still learning!