How to train yourself out of making “silly mistakes” in mathematics

Do you sometimes lose marks on your maths tests due to “silly mistakes”? Algebraic errors? Forgetting to write a negative sign? Even errors with basic arithmetic?

Losing marks due to simple mistakes can be frustrating. When you put in the work to understand a topic but still don’t end up with a good mark, it can be dispiriting.

If “silly mistakes” are affecting your maths results, you are not alone. When I go over tests with my clients, I often find most of the marks they lost were due to exactly those sorts of silly errors. Often, I don’t even need to point out which step went wrong. The student can spot the mistakes themselves once they know the answer is wrong.

You may have been advised to “check your answers”, “be careful” or given other such vague recommendations to help avoid the types of mistakes we a talking about. Here are some strategies my clients have found helpful that, hopefully, you will find more “actionable” than the advice you have been given so far.

Strategy 1: Clearly show your working

A common cause of errors is trying to save time by doing several steps in your head. This is asking for trouble. First, if you have not shown sufficient working, you may lose marks even if the final answer is correct. Second, you are less likely to arrive at the correct answer if you do too much in your head.

Strategy 2: Redo questions if you make a silly mistake

Most silly mistakes occur outside your conscious awareness. This is because, almost by definition, these are mistakes with tasks that you know so well you don’t really need to think about them. (Like like basic arithmetic or algebra.)

To bring these mistakes into your conscious awareness, it important to redo questions when you make such mistakes. This includes test questions (when you get the tests back), textbook questions and practice test questions.

It may be tempting not to redo questions when the reason you got them wrong was “just” a silly mistake. Especially if it is a long question and you just made a little slip near the end, right?

You may think: “I get that now, I’ll just fix it up and move on”. If you do that, the mistake you made only briefly enters your conscious awareness. In contrast, if you redo the entire question from the start, this has much more impact.

You will probably be thinking “I know, I know, I should done ______” the whole time you redo the question. This is good. You are training yourself to notice and avoid similar mistakes next time. You are also rehearsing the correct working out that you want to replace the mistake with.

In case I have not convinced you yet, consider this analogy . . .

A tennis player hires a coach to watch her play a match, observe her form and find opportunities to improve. So, the coach watches the player and notices she is taking her eye off the ball a fraction too early when serving.

What should the player do with this information?

(a) Say to herself “Oh, I get that. I’ll remember not to do that next time I play a game.” Or;

(b)Practice serving, with the coach watching to check the error has been corrected, until the new form feels as natural as the old method of serving.

Of course, you know option (a) would be futile. In the heat of a tennis match, the player will fall back into the form they habitually use to serve.

Option (b) is the only way the player has a hope of changing her form. Even then she is likely to backslide a few times before the new serve is natural and automatic. Same with your maths.

Strategy 3: Practice under test conditions before your actual test

Sometimes a student does not have much trouble with silly mistakes unless they are doing a test. It is important to replicate the conditions you will be examined under as closely as possible when revising.

At a minimum, do a practice test in one sitting with someone else keeping time. Ideally, seated in an area where you don’t usually study.

(For instance, sitting at the kitchen table if you usually study at a desk in your room.)

Of course, you should then redo any questions that you get wrong as previously described!

Strategy 4: Develop methods to cross check your answers

When teachers advise students to “check your answers”, many students simply reread their working out.

You may spot some mistakes this way, but it is not efficient. To do it properly you would need to essentially redo the entire test in your head as you check each line of working.

Also, because you know what you meant to write, it can be hard to spot mistakes.

(This is like the difficultly people have spotting their own typographical errors.)

Instead, develop methods of cross checking your answers. . .

For example: substituting the solution to an equation back into the original equation, considering the graphical interpretation of an algebraic solution, or using a different method to solve the question to check you get the same answer.I hope these strategies help you to improve your marks in mathematics!