It is highly unusual to teach multiplication at Kindergartens. If a kindergartener can memorise multiplication tables, they are simply memorizing them just as a 3-year old does if she or he can remember 4-letter word such as “love”.

Does it make sense?

If adults were to pressurize children to learn a subject hard by memory work, they will rob their child of one learning opportunity – that is the ability to make sense. It is very important that children:

1. Learn to make sense

2. Have a belief system in themselves that they can learn to figure things out by their own abilities. They will become less reliant on adults and reduce their feeling of helplessness when handling challenging mathematical tasks.

The ideas embedded within a multiplication content, however, can be explored at the kindergarten level. Jerome Bruner’s theory about free play before structural learning can be applied to introduce multiplication to kindergarteners.

For examples:

Use of concrete materials

Supply 6 cups to a child with 2 candies placed in each cup. Let child counts how many candies are there altogether in the 6 cups.

Use of pictorial cards

Show picture of 5 stems. On each stem, two leaves branch out from it. Let child counts and tell how many leaves are there altogether on all 5 stems.

Parents who wish to prepare their children for multiplication work at the primary level will benefit from Dr Yeap’s sharing about the 4 basic meanings to multiplication.

1. Equal Groups

Example:

There are 5 plates of 4 cookies. How many cookies are there altogether?

2. Multiplicative Comparison

Example:

I have 2 time as many apples than you have 3. So how many apples

do I have?

Dr Yeap highlighted on a common error used in verbalising “4 times as many”. It is wrong and confusing to say “four times more than” because it doesn’t imply the function of “comparing”.

3. Area Measurement

Example:

There are 7 squares in a row and there are 4 rows. What is the area

of this rectangle?

To get the answer, the child may count to add the 4 rows of squares or the child may multiply them (4 rows x 7 squares). This is also known as the Array Model where the arrangement of content is placed in a rectangular array.

4. Combination

Example:

An outfit for a teddy bear consists of a jacket and a pair of pants. I have 4 different pairs of pants and 3 jackets. How many ways can I dress up a teddy bear? All in all, there are 4 times 3 ways of dressing up the teddy bear.

So have we made some sense into our thinking when we ponder over the meanings of multiplication? Do children really need to learn multiplication tables by hard? Here is a video where Ms Emma McCrea gives her children the time to figure out different ways of working out counting by adding in groups.

I might not have answered all the quiz questions perfectly, however, I appreciate myself for my persistence and my attempts to bring out my creative juices to tackle the questions within the constraint of time.

Perhaps, it has been all those positive problem solving experiences created by Dr Yeap which has led to this good feeling about the self. So, the key to enable your child to enjoy quizzes and tests is to prepare your child well during the process of his or her learning experiences.

It will never be emphasized enough by Dr Yeap that we have to acquaint ourselves with the theories and apply them in our teaching. The four theories emphasized throughout the course on how children learn by:

Zoltan Dienes

1. Free Play

2. Structured Learning to play by rules

3. Practice

Lev Vygotsky

Give children experiences that were within their zones of proximal development to scaffold their learning.

Jerome Bruner

Apply the Concrete-Pictorial-Abstract approach for children to be engaged actively in their own process of learning.

Howard Gardner

Each child differs in how each learns. Children should not be restricted to any one specific way of learning. For example, for kinesthetic children, the teaching approach should be based on movement and games through which these children learn best.

My mind has not been trained to be stretched in that way……….a brain which I would describe as long being “stagnant” for any kind of numeracy work.

A negative habitual tendency resurfaced as I begun to shut off to yet another problem solving experience today. I waited for answers to be provided. I looked around the classroom and my classmates were busily engaged in problem solving. I recollected myself and continued to confront the challenge ahead. In my mind, I saw a child…. just like me….got stuck….still trying to work hard but not knowing how to proceed. What was that stumbling block?

3 different types of Mathematics:

Dr Yeap shares that children habitually copy steps demonstrated by their teacher at the level of procedural understanding and not gain a conceptual understanding when they learnt Mathematics. When teaching, teachers need to be aware of the 3 different types of Mathematics:

1. Conceptual (e.g. understanding cardinality).

2. Procedural (able to do something in steps to show the working of a sum for

example, as in a division sum)

3. Conventional (e.g. if a we don’t rote count in Thai, it is not an issue about our

cognition development because Thai is a foreign language to us).

How should a teacher teach Math?

Understand and follow what theories say – do not skip steps when teaching children.

What does theory say?

– Help young children input knowledge through songs, music and movement, etc.

– Counting is nothing innate about it. It’s about interacting with the society-

interacting with supportive peers and adults.

– Allow children’s constant practice by allowing them to interact with their

environment to make sense and meaning to what they learn to help build a

Dr Yeap says that no one is to be blamed if we were not taught well. So do I have to sulk over my misfortune? I see my fortune coming my way as Dr Yeap continues to share his wealth of knowledge in Mathematics. He turns me into a fortune maker who is going to transform the fortune for the better of those children under my care. I am asked to take a lead in the Math Curriculum Planning at my Kindergarten! “Am I ready?” Dr Yeap says that I will need a master degree for that. I agree!

What have I not been taught before?

Do not count things that have different nouns.

Two class mates who sat beside me stuck out their tongue in guilt as Dr Yeap explained that teachers should not take any objects randomly of different nouns to teach counting. I didn’t know that too.

For example, 1 apple + 3 oranges = 4 apples

Proper use of Mathematical language

Never say 2 is lesser than 8. Reason? 2 will be insulted!

I could now identify the 4 abilities a child needs to have in order to count. They need to know how to classify, rote count, do one-to-one correspondence counting and to use cardinal number. Huh….the cause is known and teacher becomes less frustrated and stress-free!

Reflecting now……..

why didn’t these basic understanding being shared and explained to us by our former teachers?

My thoughts? A quote to share from Brian Tracy:

“Those people who develop the ability to continuously acquire new and better forms of knowledge that they can apply to their work and to their lives will be the movers and shakers in our society for the indefinite future.”

During my 3 years of teaching preschoolers, I have never been given a Mathematics Lesson to teach. So it is a real wonder if I don’t feel anxiety and stress when I stepped into Dr Yeap’s class on the first day. Surprisingly, it is a module which one doesn’t feel stressed out from it anymore but enjoys in wonderment of what Mathematics is all about!

Why did I enjoy it?

There is never a “one right answer” to anything! And Dr Yeap has modeled it well.

– He allows plenty of time for our exploration and reflection

– He allows discussion and then he illustrates the different methods one could apply to

problem solve.

During the class sharing session on ways to find out “which alphabet will 99 stop at BAN HAR”, one classmate had shared her method but it was not substantiated with evidence. Dr Yeap smilingly responded: ” Although we can’t find the answer (through the method shared by the classmate), it may be useful in the future.” Isn’t this being very encouraging to spur on one’s courage and enthusiasm to persevere in more future challenges!

In schools, children are not given enough time for exploration; teachers practically rushed them through their work to meet the day’s prescheduled timetable. Teachers start to take over children’s work in order to do a “quick fix”.

So, NEVER, NEVER, EVER tell a child “No, that’s not the right answer” and create fear in wanting to try again.

Now let us create a positive learning environment in the classroom

Be bold to put in place practices of what is important for the children. Let children explore enough before introducing conceptual learning. When I was manipulating with the tan gram pieces, I was told that no matter what shapes you were given, any 7 pieces of tan gram pieces will allow you to make a rectangle. At the end of the session, I still could not get a rectangle. However, I felt an innate need to want to persist further. I begin to realize that any child who may be struggling like me to make the rectangle will probably need more time to figure how this is to be done and that innate desire to want to master that ability is to be addressed.

I experience encouragement in a positive learning environment – I truly realize how it feels to confront a challenge but not feeling stress from this challenge.