For The Love of Logic and Mathematics

By Jamilah Samian

What would you do if your four-year-old throws a tantrum in the middle of a toy shop because you simply refuse to buy a toy that he wants? Depending on your style of parenting and your mood at the time, you might resort to punishing the child, for instance smacking him for what you see as distasteful behaviour. Or, you might want him to learn from the consequences of his actions by ignoring his pleas to tag along the next time you go shopping. Perhaps you might say, “The next time I go shopping, you will have to stay home. I am not happy that you screamed so much just because I refuse to buy the toy that you wanted.”

Of course, this method only works if you follow through with what you said you would do i.e. you actually did not bring him along on the next shopping trip. By explaining the consequences of his less-than-pleasant demeanor and following through, you are helping to nurture his ability to think in a logical manner. In this case, he would quickly learn that his action (throwing a tantrum) causes him to be grounded. Indeed, one way to nurture logical thinking in young children is by letting them learn the consequences of their behaviour. Learning the logical consequences of their own behaviour is a powerful way of instilling discipline among children. Logical thinking, then, is the ability to reason.

Keep in mind, though, that there is a big difference between what is misdemeanor and what is not for younger and older children. It is completely natural for a two-year-old to dip her fingers in a cake mixture out of curiosity if she is left alone with it or for a one-year-old to unravel a ball of thread or pull out tapes out of cassettes if he is allowed to grab hold of them. Any of these behaviours, though, would be unacceptable for a ten-year-old child. It is absolutely essential for us parents to be aware of the kind of behaviour to expect with each developmental stage a child is going through.

The ability to think logically is crucial for a child, not only because it helps to inculcate discipline but also due to the fact that thinking logically is an essential part of science and mathematics. In fact, so entrenched is logical thinking in mathematical concepts that Dr Howard Gardner, the originator of Multiple Intelligences, married these two together as one. In Dr Gardner’s own words, mathematical-logical intelligence is “the ability to detect patterns, reason deductively and think logically”.

When it comes to Mathematics, many of us tend to associate the field with numbers. While it is true that the foundation of Mathematics starts with the introduction of numbers, numbers is only a part of Mathematics. As children progress from preschool through secondary school and consequently to college, a considerable component of Mathematics is intricately linked with problem solving, which is associated in large part with logical thinking. For example, consider this simple mental arithmetic question on fractions that Jee, a ten-year-old, has to solve:

Aminah bought 30 eggs. She used 2/3 of the eggs to bake cakes. How many eggs had she left?

To solve this problem, Jee must be able to reason that the batch of 30 eggs, when divided into three portions, will give ten eggs per portion. Hence, since Aminah used 2/3 of the eggs, she used (2 x 10) eggs = 20 eggs. Notice that the first step Jee has to take is to decide that she needs to tackle the division bit (instead of adding, subtracting or multiplying) before she does anything else.

Mathematics is a subject that steadily builds on previous understanding. Because of this, it is crucial that your child has a solid foundation in Mathematics right from the beginning. Any confusion or misunderstanding will be carried forward to future years and as time passed, this confusion may be difficult to unravel. It is true that some children have a natural affinity for Mathematics, displaying a natural ease when dealing with Mathematical concepts like numbers and geometry and do not need much help. Yet others may need extra help to value similar ideas. Although it is also true that you cannot force your child to appreciate Mathematics, you can encourage him or her to develop a liking for Mathematical and logical thinking from a tender age with the following:

- Encourage your child to explore. An enquiring mind often starts with a passion to explore. Exploration for younger children is synonymous with touching. That is why it is good to let your child lay his hands on as many things as possible. If your child is still a toddler, this is a good time to put away or keep out of reach fragile items especially decorative ones to reduce the number of “No’s” from you! Plus, a child who is consistently told “No” will, after a while, naturally be inclined not to explore. Why try when all you get is a furious glare or a mouthful of scolding?

- Develop a love for problem-solving. Problem-solving starts with asking lots of questions. That is why you should make your best attempt to answer your child’s queries, no matter how trivial they may seem. For example, if you are making play dough and the recipe says to mix two cups of flour with one cup of salt, you might ask your three-and-a-half-year-old to help you find out how much salt you need if you use one cup of flour. The kitchen, by the way, is an excellent venue to start a child on mathematical and logical concepts as cooking and baking need plenty of weighing and measuring, exposing children to scientific paraphernalia like measuring cups, spoons and the weighing scale.

- Engage your child in counting activities. Ask your child, “There are four spoons on the table. We have six guests coming. How many more spoons do we need?” Or count the steps as you walk up and down the stairs. If you want to introduce the concept of multiplication, count in twos, threes, fours and so on. Or say you have just returned home from grocery shopping, you could say something like, “Nina, we have just bought two bottles of Vitagen here and in the fridge there are three bottles of them. How many bottles of Vitagen do we have now?”

- Introduce the concept of measurement. Take an object, for instance, a pencil or a marker pen and start measuring items around the house with it. This will expose your child to the concept of relative length. Change the object with which you do the measuring to make it fun. For shorter items, use smaller objects like erasers, pocket notebooks or a cork.

- Point out the shapes of objects. Geometry is part of Mathematics, and you can draw your child’s attention to the various shapes and sizes that are available around him. For example, let him hold a boiled egg before he eats it for breakfast and say, “The egg is oval in shape. Do you see anything else that’s oval?” Other shapes that are easily recognizable are rectangles, squares, circles and cubes. Compare the different shapes and sizes as you go along.

- Encourage him to play with blocks and structures. Three-dimensional structures figure strongly in Mathematics. Having a hands-on experience with 3-D (three dimensional) structures will help your child to form mental pictures of these items and strengthen his spatial intelligence.

- Help him to understand patterns. This is a concept not limited to Mathematics as it also exists in works of art and literature. Understanding patterns helps prepare your child for the concept of sequencing in Mathematics. For this, you can use a pattern of numbers and/or objects e.g. arrange three spoons followed by one fork followed by two cups. Repeat the pattern all over again.

Last but not least, a love for all things logical and Mathematical begins with the right attitude. Even if you never enjoyed Mathematics, do refrain from making any remarks which might influence your child to develop a dislike for the subject e.g. “Hannah, don’t worry about not being able to do that, dear. I was never good at Mathematics myself.” Or “There are so many people out there who become rich without ever learning Mathematics. So don’t bother!” Just because you never liked Mathematics doesn’t mean that your child is destined to have the same attitude. While your like or dislike towards Mathematics may have been formed by your previous experiences with teachers and other adults, your child deserves a fresh start. If your child thinks that Mathematics is something beyond his reach, he would naturally shy away from anything he sees as remotely associated with Mathematics. And because Mathematics is a big part of everyday living, that would lead to a major loss for him ... You wouldn’t want your child’s cold attitude towards Mathematics to develop into a self-fulfilling prophecy!

As published in Ibu dan Anak (ParenThink) December 2007 issue