Learning about Quantity

By Denise Lai, BA, BSocSc (Hons), MEd
This article was first published in Motherhood magazine in May 1995.

Quantity comes in different forms. Consider, for example, pencils, milk and plasticine. You can have eight pencils but one litre of milk. And though you have two sticks of plasticine, one weighs 300 grams and the other 500. How do you teach a child what all these various numbers mean?

Many of the toddlers and preschoolers I have taught can count - "one car, two car, three car…" In fact, the majority of two-year-olds I know can count up to 20! (albeit frequent mix-ups such as 13, 14, 12, 16, 20!). Such consummate skill in counting at so young an age can easily he mistaken for real knowledge. Harsh experience, however, has shown me that I need only turn a Math activity around to show up gaps in what these children understand. Let me explain.

Little Mei Mei has succeeded in counting the sweets in front of her; nine in all. I ask her to "give me four sweets" and she proceeds to pile all nine into my opened palm. Frustrated and not a little puzzled, I ask her to count the sweets again. This she does accurately and quickly. But when I ask her to pass four, only four", she gleefully picks out six for me. I wonder whether she is being cheeky.

Probably not. A few reasons can account for the seeming inconsistency. One relates to memory. The younger a child, the faster he forgets. By the time he has reached counting out the required amount, he has already forgotten what this originally was! And so he carries on counting or stops where he fancies. Children have relatively poor listening skills as well. This may be the result of distractions and inattention or linguistic limitations (for example, between "I want two' and "I want too").

But while these are developmental barriers to learning, the rote methods used by a significant number of teachers and parents to teach Math are not. That a child can say there are "three apples" or "five hats" is not a good enough indicator that he actually understands numbers. Neither is the recognition of written numeral symbols a sign of comprehension.

Rather, it is the knowledge of quantity which is all-important; the fact that spoken or written numerals are merely labels for real amounts in real life. And amounts come in different forms. Consider, for example, pencils, milk and plasticine. I can have eight pencils but one litre of milk. And though I have two sticks of plasticine, one weighs 300 grams and the other 500. How do I teach a child what all these various numbers mean?

Admittedly, young children can only grasp so much. Research has shown that children below the age of seven years are frequently misled by appearances. Do not be aghast, therefore, when your child throws a tantrum and insists on the tall, thin glass of orange juice rather than the short, squat glass of the same drink because the "tall one got more". He has failed to consider the dimension of width where short cups can, in fact, contain more liquid than tall ones!

But while age may force a ceiling on what and how much a child can learn, much must also be said of experience and teaching. These can alter a child's thinking and knowledge capacity. Let me cite a famous example.

Children from around the world before the age of seven usually say that a piece of clay or plasticine is "more" because it is longer or taller than a comparable piece. Mexican children who help their parents in the cottage industry of pottery, however know that an amount of clay does not change regardless of the shape into which it is formed. The essential quantity remains the same.

Which brings me to the point that since the concept behind numbers is more important in the long run than the actual numbers themselves, parents should strive to reinforce the former whenever possible. In this, they will probably find games more useful than a strict, didactic approach. Children, after all, will be children.

Listed below are a few number games but parents should only view these as finite stimuli for further creativity! What they need to keep in mind constantly, however, is the question, "Does my child understand what the numbers mean?"

COUNTABLE OBJECTS

Number threading

1. The child is given a formula to follow to make a necklace or wrist-band (twine/thick thread and large colourful beads are available in educational stores).
2. An adult calls out the sequence while the child finds and threads the correct amount and type of beads, "two blue beads... one square bead... five red beads..."
3. Obviously, this could easily be turned into a competition when there is more than one child. The fun becomes seeing who finishes the sequence correctly and at the fastest speed.
4. To increase the difficulty of the game for older children, the adult can call out blocks of sequences at one go. For younger children, the adult may wish to limit the variations, say "one yellow bead, three green heads, one yellow bead..."

Ravenous rats

1. The aim of the game here is to accumulate as many objects as possible.
2. Two nests of hungry rats face each other from opposite sides of a room. Between them, a large range of different objects of various quantities have been placed - shoes, books, chocolate bars, shirts, crayons...
3. An adult calls out the "food" quantities to be taken; for instance, "12 crayons!" Two single children from each nest then rush out to grab the precious quantity. No snatching is allowed.
4. When every object from the middle has been whittled away, each nest has the obligation to present their hoard - in total and in separate categories. Mistakes cost - a specific number of objects (for example, five) must be forfeited to the other nest.

More, less or equal to?

1. The adult may need to make cards for this game, a variation of "Snap!"
2. Two matching sets of 15 cards (or 10 if the children are young) depicting varying numbers of animals (for example, one horse, two fish, three birds... 14 butterflies, 15 ants) are shuffled and dealt to two players (the adult can be one of them).
3. Cards are revealed singly but simultaneously by each of the players. When there is a discrepancy (for example, four monkeys and eight lions), the player who calls out his relative position first ("more than!" or "less than!") wins the two cards.
4. When there is a match in the cards, the first player who calls out "equal to!" takes the cards.

Apple pie

1. This is a game which teaches grouping and elementary multiplication. Similar-coloured counters of the same size are needed. These represent apples.
2. Each child is given a small cup to hold the counters. At the start of each turn, an adult takes the cups and fills them arbitrarily with counters.
3. The child retrieves his cup and quickly groups the counters into apple pies - each pie requires three counters (three apples).
4. To win a point, the child has to report how many apples he had at the start, how many apple pies he has made and how many apples he has leftover.
5. To increase the complexity of this game, counters of another colour may be introduced into the cups to represent another type of fruit; say, yellow for pineapples. As such, "Pineapple Pies" have to be baked too, each with four counters.
6. To drive the concept across, and if the child appears to be ready for it, the adult can make obvious the fact that "four apple pies of three apples each use the same number of fruit as three pineapple pies of four pineapples each!"

UNCOUNTABLE OBJECTS

Guess more or same?

1. This needs a measuring cylinder (for liquids) and a weighing balance (for substances). The aim is to show the child that the shape of something might change but not necessarily its weight or amount.
2. As such, the adult can ask the child to predict whether there is more or the same amount of water in two differently shaped vases, or whether a long, skinny piece of dough weighs more than a fat, stumpy one.
3. Importantly, the adult must demonstrate and explain -quantity is the result of more than one measuring dimension.
4. As a variation for older children, length can also be taught through this game. The task is to compare two pieces of string - one straight and another squiggly. The squiggly piece should be made to begin and end within the two tails of the straight piece. The child must say which piece is longer, the fact to be borne out by pulling the squiggly piece straight and measuring it against the first piece or a ruler.

MONEY

Playing shop

1. Children can he introduced to the basics of money quantities with coloured counters and a make-believe shop. On a chart, the adult can designate the value of each counter, as shown above.
2. He can also put a price on the shop's goods (the child's own toys). A teddy bear, for example, could cost $3 (that is, three black counters). The fire-engine, however, could be $3.50.
3. Importantly, whenever the child does not have the exact amount of money to buy a desired object, a large opportunity is afforded the adult to teach subtraction, though, of course, younger children need smaller denominations in lesser amounts.

At the end of the day, learning about quantity is really learning about how to think. But in the feverish academic situation that is now prevalent, the tendency for parents and teachers alike may be to achieve performance by static, rote processes. How sad, I feel, and how very wasteful.

If you have found the information in this article useful, please pass it on to your friends.

Wee Care's Bright Starts Preschool Programme helps to develop numeracy skills in young children aged 2-6yo. For more information, please visit our website at www.weecare.com.sg.