Preschool - Mathematics

In mainstream education, the Ministry of Education detailed the syllabus for a child's learning. For preschoolers, the MCYS do not provide the answers on what preschoolers should learn. The preschools are free to provide their own syllabus.

I have done a comparison of the syllabus of a few preschools, references and primary school textbooks and this is my list of 'must learn' for Primary 1 readiness on Mathematics.

1. Counting 1 to 150
2. Spelling the numbers in words 1 to 100
3. Patterns
4. Addition
5. Subtraction
6. Multiplication 1 to 50
7. Clock
8. Dollars and Cents

I am in favour of the Kumon workbook, available in Popular bookstore at $10.90 each. I like their techniques on imparting the Mathematics skills to preschoolers. The workbooks are also printed on quality papers and the layouts are attactive. However, I find the workbooks voluminous for a young child. There are many repetition to allow sufficient practices of each topic. My child takes advantage of these repetition and choose to copy the answers instead. So, I used the workbooks selectively to sustain a child's interest on the subject.

Additional Mathematics - Combinations and Permutations (no repetition)

Questions on Combinations and Permutations gives the stories and requires you to provide the solutions. Comparison and studying the reverse gives better understanding of combinations and Permutations. Read on. It helps.

Eg A, B, C
1. Combination: 3C2 = 3 = AB, AC, BC
The order is not important. It does not matter who comes first. The order is interchangeable ie AB = BA, AC = CA, BC = CB

2. Permutation: 3P2 = 6 = AB, BA, AC, CA, BC, CB
The order is important. It shows who comes first and who is next.

3. Factorial:
2! = 2P2 = 2 = AB, BA
3! = 3P3 = 6 = ABC, ACB, BAC, BCA, CAB, CBA
The order is important.

(1), (2) and (3) above looks at 1 group of object only. They look simple. Complication comes in when there are 2 or more groups of objects. When this happens, we need to use a mixture of the above 3 rules. The following scenarios are important as they are the trends of GCE 'O' Level examination questions.

4. Multiplication of Permutation and Factorial
Group 1: A, B, C
Group 2: 1

3P2(Group 1) = 6 = AB, AC, BC, BA, CA, CB
2! (both groups) = 2 = G1G2 or G2G1
3P2(Group 1) x 2!(both groups) = 6 x 2 = 12
= AB1, 1AB, AC1, 1AC, BC1, 1BC, BA1, 1BA, CA1, 1CA, CB1, 1CB

5. Multiplication of Permutation with Permutation and Factorial
Group 1: A, B, C
Group 2: 1, 2, 3, 4

3P2(Group 1) = 6 = AB, AC, BC, BA, CA, CB
4P2(Group 2) = 12 = 12, 21, 13, 31, 14, 41, 23, 32, 24, 42, 34, 43
2!(Group 1 & Group 2) = 2 = G1G2, G2G1

3P2(Group 1) x 4P2(Group 2) x 2!(Group 1 & Group 2) = 6 x 12 x 2 = 144

AB12 12AB AB21 21AB AB13 31AB AB14 14AB AB41 AB41 AB23 23BA AB32 32AB AB24 24AB
AC12 12AC AC21 21AC AC13 31AC AC14 14AC AC41 AC41 AC23 23AC AC32 32AC AC24 24AC
BC12 12BC BC21 21BC BC13 31BC BC14 14CB BC41 41BC BC23 23BC BC32 32BC BC24 24BC
BA12 12BA BA21 21BA BA13 31BA BA14 14AB BA41 41BA BA23 23BA BA32 32BA BA24 24BA
CA12 12CA CA21 21CA CA13 31CA CA14 14CA CA41 41CA CA23 23CA CA32 32CA CA24 24CA
CB12 12CB CB21 21CB CB13 31CB CB14 14CB CB41 41CB CB23 23CB CB32 32CB CB24 24CB

AB42 42AB AB34 34AB AB43 43AB AB31 31AB
AC42 42AC AC34 34AC AC43 43AC AC31 31AC
BC42 42BC BC34 34BC BC43 43BC BC31 31BC
BA42 42BA BA34 34BA BA43 43BA BA31 31BA
CA42 42CA AC34 34AC AC43 43AC AC31 31AC
CB42 42CB CB34 34CB CB43 43CB CB31 31CB Phew!

Now that you have mastered the patterns and properties of Combination, Permutation and Factorial and their multiplication. The challenges lies with the identification on what are the groups. Practice makes perfect.

If you like the above or you have any comments, pls let me know at SwallowTuition@gmail.com. I would like to hear from you. Thank You.

Preschool - Phonics

During my childhood, I was not exposed to phonics. Today, phonics is a popular topic for pre-schoolers. The lower primary schools textbooks cover the advanced level of phonics too.

So, what is phonics?
Phonics is a step by step guide to help preschoolers read and spell.

My child's pre-school introduced phonics at the age of 4. Her teacher was always complaining to me that she was unable to remember the phonics sound. I tried to coach her myself, and I faced the same problem as the pre-school teacher. One day, when I have a chance to talk to some parents of my child's classmates, I realised that my child was not alone.

I searched for books and internet to learn ways and means to help my child. I have a good friend who helped me on this too. I took more than a year to master the correct techniques on teaching phonics.

Looking back, I tried to analyse my child's problems. Firstly, she may not be ready to learn phonics at 4 year-old. All of us are good at something and poor at others, we are simply not perfect. Also, the child is not to blame for her weaknesses, the teacher played a part too. Her teacher was unable to develop her interest in the subject and helping her learn. Just like adults, when we have get over the basic, we will be motivated to go deeper into the subject.