30/06/2020 by Dina Grimes 0 Comments
How Fraction Misconceptions Can Stop You from Getting that Top Mark
So what is stopping pupils from achieving better grades than what they are currently getting? Misconceptions are surely one of them. In this blog, I will be talking about common misconceptions which I have encountered so many times in my teaching career ... on Fractions!
I was once asked to help my very first A level pupil who was predicted to get an A-A* in his exams but somehow never really managed to nail it. He was getting frustrated as all he could muster was a C on his mocks and eventually the same on his Maths Cores 1 and 2 exams. His mum decided to hire a private tutor to help her son out. I was referred to them by their family friend whose child I was tutoring at the time.
I met the young lad, who was very eager to learn, hard worker, determined to secure that grade he was predicted. He seemed to me a little bit frustrated and by then had lost a bit of his confidence too. As we worked through various topics for Cores 3 and 4, I found a consistent mistake in his Algebraic Fractions. He had a misconception which he had been carrying along with him over time which somehow remained unchecked.
Fractions: Well, what can I say about fractions except that as I consider this a very important topic. It is usually one of the first topics I tend to go over with new pupils.
The misconception below is common in almost all levels from KS2 right up to GCSE level.
Let us start with the basics: (Note: All illustrations are found below this blog)
A common misconception in adding or subtracting fractions is pupils treating the numerators and denominators as whole numbers so end up adding or subtracting the denominators as well
(see Illustration 1).
Illustration 2 shows the right way to add fractions with different denominators. First find a common denominator before you can add the numerators then just copy the common denominator. Simplify the answer if you can.
The same goes with subtracting fractions. The misconception is to subtract the denominators as you would the numerators as shown on Illustration 3. Put this misconception right by finding a common denominator before subtracting the numerators then just copying the denominators. Simplify the answer.
Another common mistake made by pupils is the tendency to divide the bigger value by the smaller value notwithstanding the bigger value being the denominator as shown on illustration 4.
When my pupil and I got to the topic on Algebraic Fractions, a misconception was uncovered which remained uncorrected until we got into it
(illustration 5). There is a set of invisible brackets on both the numerator and denominator which means you cannot just cancel like terms unless if it was factorised first (illustrations 6).
It was this misconception that stopped my pupil from achieving that targeted grade! When this was sorted out, he was getting much better marks on the work set out by school. He regained his confidence and much to my surprise decided to take on not just Cores 3 and 4 exams he was due to take but also resat his Cores 1 and 2! But he did it and to my amazement got A's on all of them! And all these were due mainly to a misconception sorted! (He did work so hard as well). After this, I made fractions one of the most important topics which I made sure all my pupils do well from the onset.