When you are learning a new skill, do you do it perfectly the very first time? Do you know all the answers before you even begin? Of course not! The same is true of math. Learning math requires practice, and making mistakes is part of the process. But as I’ve shared before, making mistakes in math is a good thing, and can help kids learn and understand more deeply. Today I want to dive a little deeper, because all mistakes are not equal. There are different types of math errors that students make, and understanding how to prevent them and how to learn from them is essential.
3 Types of Math Errors:
As I’ve thought about the different mistakes students of all ages make as they solve math problems, I’ve narrowed them down to 3 categories:
• Careless Errors
• Computational Errors
• Conceptual Errors
Careless errors occur simply because they are not paying attention, or are working too fast. Some examples might be:
• Copying the problem wrong to begin with
• Writing a wrong number
• Dropping a negative sign
• Sloppy handwriting
• Not following the directions
• Typing it wrong into their calculator
Here are some simple ways to help kids prevent making careless mistakes:
• Slow down
This seems obvious, but students are often in a rush to finish so that they can move on to something else. Rushing is the easiest way to ensure careless mistakes. Encourage kids to take it slow and pay attention to what they’re doing.
• Circle important information
Whether it’s a worksheet or word problems, circling important information will help students know what to do. Circling something in the directions will help them follow them correctly. Circling key information in a word problem will help them think through their strategy and make sure they don’t forget anything.
• Use graph paper
Using a sheet of graph paper to work out problems can be a really simple fix for kids who struggle with neatness. Graph paper allows kids to line up the numbers correctly and prevent sloppy mix ups.
The second type of mistake is computational. This means somewhere in the process they incorrectly added, subtracted, multiplied or divided.
Making one computational mistake in a multi-step problem means the rest of their work will be wrong and the final solution wrong.
As a classroom teacher, I always required students to show all their steps because if they used the correct procedure and showed me that they understood the concept, I was not too concerned about a small computational error.
Yes, that may have meant the “whole problem” was wrong, but to me, the final solution is not as important as understanding the concept and the process.
Still, we never want to encourage carelessness in computation.
Here are some ways to help students prevent computational errors:
• Slow down
• Check the answer after solving
• Use a calculator
Conceptual errors occur because kids have misunderstood the underlying concepts or have used incorrect logic. This is the most difficult type of error to identify at first glance. This is also the most difficult type of error for students to recognize, but it is the most important to catch and correct.
When students make conceptual errors, it’s possible that all the math computations are correct. If they’ve misunderstood a concept and thus used an incorrect method to solve, they can work out each step meticulously and correctly but still get the wrong answer.
Ways to prevent and correct conceptual errors:
Obviously preventing conceptual errors is not as easy or straightforward as careless or computational errors. And of course, all students will have varying degrees of understanding, and will struggle with different concepts
But here are a few things you can do to try and encourage conceptual understanding and prevent future conceptual mistakes.
• Introduce concepts in hands-on, conceptual ways
• Teach a concept more than one way
• Have math talks
• Use math journals