An Account of 20 Common Math Misconceptions And How to Curb Them (PART-1)

Conceptual understanding is an important aspect of Mathematics. This means that students have to grasp and understand clearly certain basic concepts of mathematics before engaging in sums in a procedure-oriented fashion. It’s essential for teachers to understand this before teaching any math topic to a student. The teacher should find out whether the very basic math concepts like certain concepts related to arithmetic operations (addition, subtraction, multiplication, division), number system etc.  of that specific student is clear or not before teaching a more complex topic like algebra, fractions, percentage, trigonometry, geometry and so on. The main problem behind certain misconceptions is certain concepts that seemingly look very paradoxical in nature. An easy example is a concept that finds out the biggest number among a list of numbers on the basis of the amount of digits present in the numbers. Students have the belief that if a number has more digits than another number, it’s greater than the other one. Isn’t this concept a paradox? We are not denying the fact that this concept is entirely false. But there are some exceptions. What happens if the two numbers are 4.678 and 234? The first number has more digits than the second one. But does it make 4.678 greater than 234? You can judge it yourself. Similarly, there are many other misconceptions in students. All these misconceptions are based on the very basics of mathematics but sadly, these small mistakes can prove to be a problem at the later stage of their education. This article will throw light on some very common Math misconceptions in students that should be curbed at the budding stage. We have divided the complete article into 3 parts.

1. A number having “4” digit must always be greater than a number having “3” digits

We already explained this just before with an example. This is a very common misconception in students.” 4” and “3” mentioned in this sub-heading is just a figure of speech. You can substitute “4” with “7” and “3” with “5” but the result will be the same. To curb this problem, children should clearly understand the concept of fractions and decimals. For e.g.:

4.678= 4678/1000.

Now ask them their opinion on this. Do they still find 4.678 to be the greater number among 4.678 and 234? Surely the answer should be “no”. Urge them to use the same tactic in relevant sums as per requirement.

2. Multiplication of 2 numbers would give an answer that’s always greater than both the initial numbers used in calculation

This misconception is common among many students. They develop their mentality to think in this pattern. This is a very basic mistake that needs to be curbed at its roots. To curb this problem, you should show them various examples involving decimal numbers and fractions. For example, a problem that involves the multiplication of 0.2 and 0.3. The result is 0.06. Now ask them whether this number is greater than 0.2 or 0.3. They should say ‘no’. If they still say ‘yes’, refer to the above point. You can show them the same example with fractions.

3. Misconception on fractions

Consider these 2 fractions ½ and ¼. How many of your students will have the opinion that ¼ is greater than ½? If all of your students disagree on the fact, you can skip this point and go to the next one. But you would generally see at least some of them agreeing to the fact that ¼ is greater than ½. The main reason behind this is the numbers 4 and 2. 4 is always greater than 2, which is absolutely correct and all students have this idea. But when the numbers are placed as denominators, the entire concept changes. The best way to curb this practice is to ask them to convert the fraction into decimals like 0.25(¼) and 0.5(½). After that ask them to compare the two decimal numbers. Which number is greater? They should say 0.5 is greater than 0.25 and simultaneously, they would come to know that the equivalent respective fraction ½ is greater than ¼. If they say that 0.5 is lesser than 0.25, refer to point

4. Misconception on Addition of decimals and fractions

This is a pretty common misconception among students but this problem can be easily curbed. Let’s provide you with an example of this misconception. Consider this image shown below of a problem sum based on simple addition of decimals. The student has provided an answer in the box.

The student has misplaced the decimal point and provided a wrong answer. It’s not that he misunderstood the problem. S/He knew that it’ll be a simple addition. Unfortunately s/he might have developed a wrong concept as to how two decimal numbers are added. The misconception is based on “carryover of decimal number additions”. Try to clarify the same with the student as to how the carryover is done in which the number “1” is shifted to the left of the decimal point from the student’s perspective. Another way to curb this is to change the decimal numbers to fractions but for that the students should know how to transform a decimal number to fractions and vice versa.

0.9= 9/10.

0.3= 3/10.

9/10+3/10= 12/10= 1.2.

This can solve the problem to a certain extent. Once this misconception is curbed, the student will be hugely benefited in the long run.

That’s it for now. Refer to part-2 and part-3 for more information.

Sudipto Das

Sudipto writes technical and educational content periodically for wizert.com and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got a B.Tech in Electronics and Instrumentation.