Jokes apart, we should look into it. Why is it so important? We use it extensively in Mathematical reasoning- be it algebraic or probabilistic – and problem solving. Moreover, in working out discounts, finding out the proportion of various materials to be added, or drawing and analysing maps, we use fractions widely in our daily life.
Those who have studied fractions might not have skipped the pizza discussion. While it is interesting to look at fractions from the whole-part perspective using the Pizza example, our children need to know more about it.
Scientific American says, “On standard fraction addition, subtraction, multiplication, and division problems with equal denominators (e.g., 3/5+4/5) and unequal denominators (e.g., 3/5+2/3), 6th and 8th graders tend to answer correctly only about 50% of items.”
It is unfortunate that many students struggle with fractions because it is one of the most foundational topics as far as higher studies in Maths or other engineering subjects are concerned.
What makes it so difficult for pupils?
Some of the reasons can be traced to the below.
1. Transition from whole numbers: Students first learn about natural numbers. They familiarize themselves with counting, plotting the numbers on the number line, performing the operations of addition, subtraction, multiplication, addition etc. Once they move to fractions, they are confronted with many questions like:
a. Why is it that there are two whole numbers (numerator and denominator)?
b. What is the “/” connecting these two numbers (as in 2/3)?
c. Beyond the ‘part of a whole’, does each fraction represent one number?
d. Where can I see it on the number line? (Of course they can, but not as easily as natural numbers).
e. Between two natural numbers there is no other natural number. But there is infinity of other rational numbers between any two rational numbers.
f. 2 + 4 = 6, but 1/2 + 1/4 is not equal to 1/6.
g. 2 x 4 = 8, which is bigger than both 2 and 4; however, 10 x ½ = 5 (which is less than 10).
2. Varied meanings: Fraction tends to mean differently in different situations.
a. Ratio: Here it expresses the notional of a comparison between two quantities. For example, five boys for every four girls.
b. Operator: In this category it is a function applied. For example, 3/4th of 60 participants in a meeting.
c. Quotient: Here it refers to the result of a division. For example, 12/3 = 4.
d. Measure: Here they are associated with the measure of an interval. For example, each centimetre represents a length that is one-hundredth of a whole metre.
3. Conceptual and procedural understanding: Procedural knowledge is the knowledge that is needed to work out problems. The various tasks here are performed using the conceptual knowledge. When students try to solve problems without acquiring the required conceptual knowledge, or when they answer questions without knowing what they are doing, it leads to difficulty in learning fractions. In fact the concepts and procedures should stimulate each other.
Teachers and parents should realize:
1. ‘Fractions’ is an important area that children should understand well, and learn thoroughly.
2. There are some inherent factors that make it difficult for most of the students.
3. It is imperative to help and encourage children to learn this foundational topic very well.