Photo by Joshua Hoehne

Any parent or educator could get a great elementary algebra book for students and at least one of them would still be prone to so many common errors.

And in an age where the quality of education (or the perceived lack of it) is often a subject of outrage media, this is concerning. Many people have a lot of scapegoats whether it’s teachers, technology, stereotypes about students or schools etc.

What’s overlooked in all of this is just how easy it still is to make errors in elementary algebra. And no, the many advances made in today’s education don’t necessarily prevent it. It’s like the common cold. There’s no actual cure. The human body is just naturally capable of healing itself from it.

Likewise, the best way to address students constantly committing avoidable errors hasn’t much changed. The tricky part is convincing people that a talent for numbers isn’t a magic bullet to these errors.

These mistakes have simpler, more mundane causes.

Inattention to Detail and Bad Shortcuts

Photo by Antoine Dautry

Have you ever found a student who constantly forgets to put a parenthesis at a critical part of the equation? How about accidentally forgetting to mark an integer as a negative and warping the resulting calculation?

Both of these common errors are actually visual errors.

In fact, imagine this: a student solves a problem correctly. But despite the correctness of their calculation, it’s still missing a parenthesis or two. And you, as their teacher, can’t really say they answered correctly on their exam.

The result? You have an otherwise talented student who still fails and still commits a visible error. It’s a typical example of someone doing a calculation in their head yet not properly writing down their solution. They may be often correct. They may even be a genius. But if they don’t know how to write it down, spell it out in detail and show it to their teachers, then they run the risk of committing errors eventually (yes, even in their own brilliant minds).

It’s the same bad habits that lead to bad shortcuts like improper cancellation. By trying to do so much in their head, skipping steps and impatiently wanting to put the answer on paper, the details are sacrificed for perceived efficiency.

Biases and Bad Logic

Some might think that math is never biased. Because, as the saying goes, “Numbers don’t lie.” Unfortunately, that still doesn’t prevent people from making bad leaps in logic and letting their biases result in bad math.

For instance, while it’s common knowledge that dividing by zero is impossible, students still unintentionally try to do it when they make errors in elementary algebra!

This can be the result of them incorrectly applying laws they just learned in the day’s lessons. It could also be because they got the positive and negative integers mixed up. Other errors can result from a false equilavence.

A student can even make the even simpler error of confusing addition and subtraction, all because the numbers on both sides of the equations appeared to be the same. It’s the sign that someone read only one of the many basic laws of algebra and thought that it applied to every problem on their quiz.

Of course, it can be understandable to an extent. Trying to code the basic laws into one’s brain can be tedious and exhausting to a lot of students. And for those who have really low aptitude for mathematics in general, understanding these laws could take even more than a year.

Photo by Jeswin Thomas

Hence, it’s critical for educators to really be patient and look for effective ways to help them grasp such fundamental laws. Don’t be content with placating their desire for shortcuts or quick memorization. Use the laws as a way to help them exercise critical skills in logic and discerning truth. It’s not just about numbers. It’s about teaching them to ensure their own thinking isn’t turning against them.

Influence of Stress, Anxiety and Disinterest

At this point, it’s once again time to face the question: Why do students still want a shortcut?

Why do they still want easy answers only to get snagged by the basic laws of algebra?

Why can’t they just pay attention and follow the rules?

And again, the answers aren’t in the numbers. The answers are in something far more human.

For a number of them, math is a subject that only triggers stress and anxiety. And for those who end up successfully passing, eventually entering the workforce and practicing their skills, they only find more of that same pressure. It doesn’t get any easier for them. Some of the harshest work environments can cause even the most brilliant mathematicians to make errors in elementary algebra.

You also have the students who typically see little use for math in the future they see. It can be laziness. It can be cockiness.

It can also be depression and uncertainty over where they want to be.

Photo by Joice Kelly

Educators should never underestimate the impact of mental health on their students’ ability to study math. It’s why the task of demonstrating algebra’s real-world applications is to be taken very seriously. Paradoxically, it’s also a reason why trying to make the subject fun remains highly effective.

So, the next time you’re wondering why kids these stays still make mistakes in their algebra homework, never forget: Numbers are just one part of that equation.

Need a book that at least helps students better spot their elementary algebra errors? Consider getting Elementary Algebra: With common errors and True-False Drill. It’s now out on Amazon.