In working with schools and parents, we do notice that there are some very common misconceptions when students attempt questions involving fractions when it comes to PSLE Math papers. This is the number 1 reason why students are unable to obtain the correct answer in PSLE Math papers. More often than not, if the students’ understanding is not strong, chances are that they will be unable to complete the question itself. Either that, or they will employ a wrong method in obtaining the answer. If we are able to pinpoint the errors and nip the problem in the bud, then the student will be able to gain the invaluable marks, which will help them in obtaining a good score for PSLE.
Common Misconceptions In Solving PSLE Fraction Questions
After speaking to the parents as well as teachers, we managed to illicit from them the main problem that usually surface when they try to understand and correct their child or students’ errors in fractions. These common misconceptions in solving PSLE fraction questions are so fundamental, that it perplexes educators and parents alike.
1. Treating Numerators And Denominators As Whole Numbers
This is one of the most common mistakes that students make. I would classify this as a conceptual error. Students often think that they can treat the numerators and denominators of the fractions as a whole. For example, students are asked to answer the following question.
Find the sum of 1⁄3 + 2⁄7.
Students who make the conceptual error will add the numerators together and likewise for the denominators.
1⁄3 + 2⁄7
= 3⁄10 .
If you look at the answer generated, the student added the numerator together, and obtained 3. Likewise, they added the denominator together to obtain 10. This is wrong. However, students do not really understand this. Some parents commented that they are at a loss of how to explain the concept to their child.
1.1 Why Is This Mistake Being Made
This mistake can occur due to 2 reasons.
First, students can be confused with the concept of fractions. The student failed to understand that they will need to ensure that the fractions need to have a common denominator before adding or subtracting them. Secondly, the problem is then exacerbated by the fact that the numerators and denominators are treated as whole numbers when doing multiplication. For multiplication of fractions, the fractions are not required to have the common denominator.
1.2 How To Solve This Misconception
When presented with this fundamental misconception, you can structure a real life problem to the child. Get the student to relate real life problem to math. For example, ask your child this question: “You have 2⁄3 of a pizza and you gave 1⁄2 of it away. How much pizza do you have left?”. If your child subtracts the numerator and denominator together, they will obtain 1⁄1. You should then ask your child if it is possible to obtain a whole pizza when they have only 2⁄3 to start with.
2. Not Multiplying Denominators When Multiplying Fractions
There are some students who will forget to multiply the denominators together when they attempt questions involving multiplying fractions together. The problem is more obvious when the question involves two fractions with the same denominator. Here is an example of the error made.
Multiply 1⁄3 and 2⁄3 together
Students who make the conceptual error will not multiply the denominators together.
1⁄3 x 2⁄3
= 2⁄3 .
If you look at the answer generated, the student multiplied the numerators together, which is correct. However, they failed to multiply the denominator together, resulting in a wrong answer.
2.1 Why Is This Mistake Being Made
This conceptual error occurs when the students get confused between the addition operator and the multiplication operator. They are applying the procedure for addition questions onto multiplication problems, which is completely incorrect.
2.2 How To Solve This Misconception
One of the best ways to address this problem, is to illustrate to the students in the form of an example. Take for example a question 1⁄2 x 1⁄2 .
The teacher can explain that this question is asking for the “half of a half”. Proceed then to draw half of a circle, and ask the student what is the half of a half of a circle. Visually, it will be a quarter. Once the context is being laid out to the student, the teacher can then proceed to teach the student the mathematical way of getting the answer. Also, the teacher can point out to the student that if you multiply two proper fractions together, the resulting fraction will always be smaller.
3. Incorrect Application Of The Invert-And-Multiply Procedure For Division Problems.
We have addressed the problem for addition and multiplication problems. There is another common conceptual error that student commit, and it is in relation to the division of fractions. The concept that students need to understand is the inverting of the 2nd or later fraction when faced with a divisional problem. Here is an example of the conceptual error being made.
Find the answer to the following question
1⁄3 ÷ 2⁄3 = ?
Students who make the conceptual error will invert the 1st fraction instead of the 2nd fraction.
1⁄3 ÷ 2⁄3 = ?
= 3⁄1 x 2⁄3
If you look at the answer generated, the student applied the concept of inverting a fraction, which is technically correct. However, they inverted the wrong fraction, which is conceptually wrong. They should have inverted the 2nd fraction (2⁄3).
3.1 Why Is This Mistake Being Made
This conceptual error occurs when the students are not familiar with the invert-and-multiply procedure when faced with a divisional problem.
3.2 How To Solve This Misconception
There is no hard and fast rule in solving this conceptual error. The best way to eliminate this error is to have ample practice. When students start to have enough practice, they will get familiarized with the technique needed to solve this type of question. Perhaps you would want to have a closer guidance during the first few questions. This will ensure that the child is doing things right. Imagine the student practicing using the wrong method right at the beginning. The latter is a problem , as the wrong concept will be too ingrained into the child.
As you can see, there are many conceptual errors that students will make when computing fractions. If these conceptual error are not addressed at the fundamental levels, students will face tougher problems when doing fraction questions in the PSLE math paper.
What other problems do your child face when it comes to PSLE fraction questions? Input them in the comments below!