# An Account of 20 Common Math Misconceptions And How to Curb Them (PART-2)

### 5. Nonrecognition of regular common shapes when they aren’t drawn upright

This misconception can be curbed if the teachers practice drawing regular common shapes for the students in any other position other than the upright normal position. This would make the students more acclimatized to the shapes and they would be able to recognize those specific shapes at a glance. Teachers can sometimes draw shapes upside-down, tilted on one side or in another direction to make students more accustomed to those type of problems where students are required to count the number of a certain figure (say a rectangle, square, triangle) in a compound figure. Hence, they would be able to recognize those figures irrespective of their positions. It’s a common problem among students to misinterpret figures if they are placed in unusual positions. This misconception can be solved to a certain extent through the solutions mentioned above.

### 6. Multiplication by 10 can be done by just adding a 0

It’s a very common concept. This one is taught to all elementary grade students by teachers or parents. This concept is considered a thumb rule by many students. Now we are not saying that it’s wrong. We are saying that it’s “partially correct”. Hence, this misconception can be deemed “partial misconception”. This rule works but there are several exceptions. We are pointing out one with an example and you’ll get our point. For example:

23.7 *10

The answer is 237. Point this out to your students. That will make them aware of the fact that this concept will not work all the time. Soon afterwards, ask them to solve these sums:

5/7 *10

0.66*10.

### 7. Misconception on proportions

This point is not for elementary grade Math education. This misconception is based on the topic of ratio and proportion. Say for example, a student is given a problem that has 3 red balls and 5 blue balls in a basket. The student is asked to find out the proportion of the balls that are red. You should not be surprised if you get the answer as “3/5”. This is a very common misconception where the student makes the comparison between red and blue. You should state clearly that proportions are counted as a “part of the whole” which in this case is the total number of balls (8). The correct answer to that problem is “3/8”.

### 8. Misconception on representation of any number in an expanded form

We’ll give you a simple example to illuminate this point. Pick any number, say 52. A student reads this number as ‘fifty two’ and knows the numerical representation as “52”. That’s expected from him/her but a minor misconception arises when they have to expand the number into tens and units. You can ask him/her to expand the digit. You may see him/her doing it like “5+2”. It’s a common misconception. Tell him to multiply the tens digit with 10 and the unit one with 1 like,

5*10 +2*1.

The student should understand this easily and will rectify that misconception. Similarly, the same concept can be used on three, four five digit numbers where the position of digits can be based on unit, tenth, hundredth, thousandth position and so on.

### 9. Subtractions are commutative

It’s a very common problem where the student understands the ways through which a subtraction calculation works but doesn’t understand the way through which a commutative property works for subtraction. It’s necessary to explain a commutative theory before explaining the fact that subtractions are not commutative. The brief explanation of commutative theory can be found here. We are just showing an example to illuminate commutative theory. Commutative means “move around”. Simple arithmetic operations like addition, multiplication are commutative. This means that:

3+2=2+3.

3 *2 = 2*3

Both the above operations will give you the same result. But operations like subtraction and division are non-commutative, meaning:

3-4 ≠ 4-3

3/4 ≠ 4/3

Generally, the misconception on “commutative or non-commutative properties” doesn’t happen a lot in division because students generally know about the numerator and denominator concept of division and learn to think along that line. It happens a lot in subtraction where students feel that “2-3 =3-2”. This is a misconception that should be curbed at the budding stage. It’s therefore necessary to make them aware of the fact that subtractions are non-commutative.

### 10. Misapplication of the subtraction concept :“A smaller number should always be subtracted from a larger number”

This concept is taught to each and every student in elementary grades. For subtraction, the smaller number should be subtracted from the larger. But this rule becomes a problem in subtractions involving bigger numbers having more number of digits. The student remembers this concept and applies this on every digit present in the number rather than using the concept on the number as a whole. Several examples of such mistakes are found like:

You’ll see that the student has subtracted each smaller digit from the larger digit. The answer is wrong. This misconception can be curbed by telling him/her to subtract the smaller “number” from the bigger “number” with the addition of this statement that numbers and digits are not the same thing.  You should also explain the difference between numbers and digits to the student, so that he doesn’t repeat the same mistake in future. Digits are present in a number e.g. 65 is a number, 6 and 5 are two individual digits that are present in the number 65.