Mathematics is frustrating when you’re trying to learn it, and even worse when you’re trying to teach it. You know how children sometimes end up in tears? Well that’s how I used to end up. No, not as a student, as a person trying to teach simple subtraction. Time, experience, and a ton of advice from expert tutors have since fixed that. Now I know there are three main stumbling blocks to remove:
Inability to translate word problems into number based problems
This is the most common obstacle many children (and even adults) face. It’s not easy to convert words (let’s call them stories) into numbers, or vice versa.
It’s actually quite amazing that we can do it at all – architects, for example, need years of training to see that durian shaped Esplanade as a series of numbers. In short, converting words to numbers is a different skill set from mere calculation, and it is very difficult.
As an example of “converting” word problems:
Sam had nine marbles. He dropped one on the way from school, and then gave two of them to Susan. He had ______ marbles left.
The numerical expression of this would be: 9 – 1 – 2 = 6
Many children can solve the problem easily once it’s expressed as above. The problem is when it’s expressed as a story, instead of directly giving those numbers.
There are two solutions to this:
The first is to demonstrate the problem in a physical and tangible way (e.g. actually moving the marbles around in front of your child). But as this is sometimes not possible, you may also consider teaching your child the model method.
This system uses a simple visualisation technique, in which rectangular boxes are drawn to indicate sets of numbers. This helps to ease the conversion from words into numerical expressions.
The following is a basic subtraction model from modelmethod.com, which depicts the problem “7 – 3”.
In the question 7 – 3, draw two boxes, one to represent 7 and the other to represent 3. For this model, there are a few ways to draw it. They are presented below. You may choose the one that you like most.
From the model, we arrived at the conclusion that the unknown value (?) can be calculated by taking away the value of the shorter box (3) from the value of the longer box (7). Hence, we formulate the number sentence ======> 7 – 3 = ?
Problem with arithmetic, not mathematics in general
You know how sometimes, you know the right formula to use but you get the answer wrong anyway? I don’t know about you, but this happens to me at work all the time. Tallying stock is a simple matter of addition and subtraction; but all it takes is one minor distraction and suddenly nothing adds up.
In math, and most parts of life, it doesn’t matter that we know what to do if we’re doing it wrong. This is where the gap between mathematical knowledge and arithmetic comes in.
Arithmetic refers to the basic calculations of numbers (addition, subtraction, division, finding the square root, etc.) as opposed to the broader concept of mathematics (e.g. knowing which formula to use to calculate the surface area of a sphere)
It’s possible for some children to have a good grasp of mathematics, but still arrive at wrong answers due to problems with arithmetic.
For example, a child approaches this problem:
Judy was 13 years older than Sam, and Sam was 10 years older than his brother. If Sam’s brother is 7, how old is Judy?
A child may correctly convert this to 7 + 10 + 13, but then erroneously conclude that the answer is 28. Such a child understands the how to solve the problem, but fails to execute the calculation.
This problem is easy to spot. Your child’s workings may show the correct process and application of formulas, but end in the wrong answer regardless.
Arithmetic issues boil down to concentration and practice. Repeated calculations, or learning to use an abacus, are good ways to overcome this problem.
Unfamiliarity with mathematical language
Math uses words in a very specific context, which may conflict with conventional use.
A simple example of this is when children confuse the use of the term “difference”. Mathematically, the difference between four and three is one; but a child may not equate “difference” with “subtraction”.
During English lessons, for example, a child may be asked the difference between a dog and a cat. Once this usage is learned, it may be counter-intuitive to associate it with the process of subtraction.
Some of the words used in math, such as divisors, volume, binomial, etc. have broad meanings outside the field of mathematics. For example, a volume is also one part of a book series. For children who are still developing their vocabulary, all this can be confusing.
Fortunately this is easy to correct. A good tutor can explain the common terms in just a few short lessons.
If your child has problems with the language however (down to an actual inability to read the problem), tuition may be needed for language skills as well.
A note on dyscalculia
If your child has persistent and extreme difficulties with mathematics, you may want to consider testing for dyscalculia. This is a condition similar to dyslexia, but which affects numeracy rather than literacy.
The Dyslexia Association of Singapore (DAS) can be approached for further assistance. A standardised screening test is available to detect dyscalculia.
In most cases however, problems with maths will stem from one of the three factors described here. These are simple enough to remedy with the help of a patient teacher.
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