Fraction Fundas

What fraction of the children in the following group are GIRLS ?

No. of students: 8314

Option		Percent Chosen
A.		18 %
B		26.90 %
C		43.20 %
D		9.30 %

Option B (coloured green) represents the correct answer.
Option C (coloured red) represents maximum chosen answer by students

This is a question tested in class 4 on 8314 students nationwide. Since the basic concepts of fractions like equal parts of whole, numerator, denominator etc. are being introduced in class 3 in majority of school boards, class 4 students were expected to answer this simple question testing the basic understanding of fractions.

The question tests the basic understanding of fractions, especially the concept of ‘whole’ or ‘group’ of which the parts form a fraction. Here, the students are asked to name the fraction that represents the girls in the group. Girls and boys are represented using pictures and are defined in the key present alongside. Since there are only two girls in the group of five children, the answer is B (2/5). However, only 27% of the 8314 have got it correct. The data also shows that around 43% of the students are going for the wrong option C (3/2) and hence it turns out to be the most common wrong answer.

To know the reason why the students are selecting the wrong option C, students of class 4 and 5 were interviewed at a school. As expected, the students who were interviewed and had selected the wrong option C gave the reason that they had answered 3/2 just by looking at the figure. Since there were three boys up and two girls down, they selected 3/2 as the answer. This fact was also seen in the written responses that these students were asked to write before interviewing them.

“My answer is (number) C because there are three boys (up) and two girls down. And in (number) C there is three on top and two down.” – a student of Class 4

A clear pattern coming from the responses and the interviews is that the figure dominates the thinking of some of the children. They do not seem to have properly understood the concept of fractions. One thing they seem to know well is how to write fractions. And since the figure seems to be dominating, children jump to the conclusion that the correct answer will be a number where 3 is on top and 2 at the bottom.

Another interesting point that was discovered in this group during the interviews was that students tend to give unnecessary importance to the form of proper fractions while reasoning about fractions. Kids who had answered 2/3 when asked to reason why they selected that option said that they saw two girls and three boys and since the answer has to be a proper fraction, 2/3 will be the correct answer.