Last Day review

Well, we have reached the finale! And here's a short review of what I have learnt in the past week.

1. Division

I learnt that the 'old skool' method of division that I have been using for years is the wrong method. Not convinced, I went home to ask my 9-year old which method did her teacher taught her and showed her the slides by Dr Yeap. Without a blink of her eye, she pointed to the 2nd method and asked me why there were so many '0's in the last working (the one that I have been using).

The method that my daughter used in school

The 'old skool' method that I learnt (the one at the bottom). The top method is another way that schools taught children to divide. 

Hence, the verdict.....

I am wrong.

 2. Quiz No. 2

We were asked to write problem sums based on the following number sentences:
a. 8 divided by 4
b. 4 divided by 8
c. 3 divided by 2 thirds
d. 2 thirds divided by 3

After attempting this quiz, I realized how difficult it was to write a story problem. There were a lot of factors involved to make sure that the question is understandable and easy for the students to grasp.

3. Salute Game
Objective of the game: To train your child's (and yourself) mental skills by calculating without the use of paper and pen or a calculator!

Play this game with your child.You need 3 or more players (but I would suggest starting with 3 players). Basically, use a set of poker cards (removing the Kings, Queens, Jack and Jokers). One person will be the commander while the other two take a card each (without peeking at their own cards) and place it on their forehead. The commander has to multiply the number that he/she sees from the other two players and call out the answer. Using the answer, the other two players have to guess what number card do they have.

Other options: Use addition, subtraction or add more players in (making it more difficult)
jective of the game: To train your child's (and yourself) mental skills by calculating without the use of paper and pen or a calculator!

Well, in all, I felt that I have learnt a lot more about Math, let's just say, a new found respect to teachers who specialise in teaching Math. So, thank you for all that you have done, Dr Yeap, you have indeed, made my eyes WIDE OPEN!

Back to Tangrams

Make Squares!

Encourage your child to make as many squares as he/she can with a set of tangrams. Challenge your child to make different kinds of squares using the least amount or the most amount of pieces and draw it out on a piece of paper. Ask her if using the most amount of pieces makes the biggest square or the least amount of pieces to make a bigger square. 

Here are some suggestions to help you along: 

To end it off, here's a short video on how to make a square using all 7 pieces!

Have fun exploring with shapes!!

Fractions, Multiplications and Geometry

Lesson on Fractions, multiplications and geometry had me stumped today. I did not know that there were so many methods in learning multiplications and something new that I learnt today made me wondered whether I had taught my child the right way.

"Learning the times tables by heart restricts your child from understanding the number pattern and their exploration in learning Math." 

Somehow, after hearing that statement, it made me feel like I have been a DICTATOR in teaching and guiding children in Math as that was what I had learnt when I was a child. Hence, I posed a question to Dr Yeap,

"If the child has a teacher who allows him/her to explore with the concepts of Mathematics just like how he is doing with us in class, and in the next year, he/she gets a teacher that sticks to the old traditional method of teaching, how then, can we help the child?"

Points taken from Dr Yeap answers:
Teachers these days have been trained with a certain guidelines of how to teach children Math and they also have ongoing professional development to help them observe other teachers teach (teachers being in position of students)

However, there are 3 factors that might hinder this ~
1. Training
2. Previous learning - being exposed to not very good models of learning
3. Ethical - teachers taking a short cut in teaching or doing it the right way

To sum it off, it is very hard for a parent to judge if the teacher is teaching math the right way or not. But on a whole, I guess we can only have faith and trust that the Singapore school system has sufficient quality checks and ongoing professional development for these teachers to ensure standards and the right teaching methods are in place.


To end, I have found two interesting videos on how to teach children multiplications of 2 and 8

as well as how to use a geoboard to teach various concepts. 

Have a great day! 

Fractions and more....

Airing my doubts
I had my doubts cleared about my daughter's math development when I asked if it is normal for a 5 year old child to not know rote counting beyond 10 even after different methods of exposure. Dr Yeap reassured me that my child is normally developing and that she just might have trouble remembering the names of the numbers or have trouble pronouncing it as it has multiple syllabus. For her, I would have to just keep practicing with her and expose her to counting beyond 10 as much as I can during our daily activities. ~Phew!

What struck me today was Problem 11 & 12 - All about fractions!

These were the questions and the various way I came about to dividing the paper to equal parts. 

Problem 11 - Sharing a rectangular piece of paper into 4 equal parts. 
Basically, how many ways can you divide the paper into four equal parts. Dr Yeap went a bit further by challenging us to divide it equally into 4 different shapes and this was what I did.

1st attempt: Three different shapes with one not joined but all divided equally. 

2nd attempt: Four different equal shapes

Problem 12 taught me that how to say Fractions in the right way:
For example, 1/4,  It's not said as....

• 1 upon 4
• 1 over 4
• I out of 4 (unless you are talking about probability)

You say it as 1 FOURTH! So, all these years, I have been saying it wrongly, and now, even teaching my children and students the wrong way of saying it. Better start making changes now!!!!

Cardinal, Nominal, Ordinal and Measurement Numbers! What?!!!

WooHoo ~! A day on numbers! I did not know that there were so many different names for numbers that functions differently.

A few things that struck me in this lesson was the 4 contributing factors for children who are unable to count. They are:
1. Ability to classify
2. Ability to do rote counting
3. Ablilty to do one-to-one correspondent counting
4. Conceptual understanding of cardinal number

These are basically four stages of counting, and if your child has issues with any of the factor stated above, he/she may not move on to the next stage. For example, if your child is unable to do rote-counting, he or she will not be able to understand one-to-one correspondent counting until he/she understands the concept of rote counting. There are no issues with your child if they are unable to meet a certain stage as each child takes different time to reach it. No one child is alike to another!

Yet, HOW DO WE INSTRUCT CHILDREN IN MATH?

Well, using this method of "I do, We do, You do" theory.

1. I do - Let the children learn through a role-model (best example, YOU!)

2. We do - Scaffold the child 

3. You do - Let the children be independent in their exploration with the concepts. 

It sounds so simple yet many parents and educators tend to neglect the "You do" where we allow the child to freely explore. Rather, we tend to give them a certain way of answering mathematic questions. 

Highlighted Problem of the Day: Problem 6 "Beans"

This game reminds me of the "31 Game" played in Running Man (a Korean variety show). Basically, the rules of the games are simple. You take a set amount of beans, in this case, we were asked to take a maximum of 20. Between 2 players, you are only allowed to removed 1 or 2 beans per turn, the last player who takes the last bean wins (In Running Man, the last person with the last dish loses). 

This game is connected to subtraction and it allows you to introduce the idea of subtraction without mentioning to the children that they are actually doing it! This is how the "play stage"  by Dienes that I had mentioned in my previous entry should be carried out. 

Throughout the game, my strategy was to take control of the situation by ensuring that I have either 5 or 3 beans left so that it will be to my advantage that I could win. My team even tried playing with all the beans that were given - 66 in all and removing to a maximum of 3 beans among 3 players. It was harder to strategise in the beginning but after the first round, we could come up with ways to ensure that we were the winners by counting the number of minimum or maximum beans that a person could take away and ensuring that we are left with the last bean! 

Try the game and let me know how it works for you and your child!

Fun with Problem Solving!

Wow! The first night of EDU 330 Elementary Mathematics have been great and I have been met with a few surprises myself:

1. The lecturer looks really young despite his years of teaching!
2. I enjoy the lessons more than I had expected.
3. I am NO GOOD in math!

There were many memorable problems that were given to us that I had thought was useful for children to learn how to acquire their problem-solving skills.

Problem #1 - Name

First problem of the day was titled, 'NAME'. What is so special about this problem, you'll asked? Well, it requires your child's name and their ability to rote count. Take for example, my name, CLARE. Which letter will be the 99th letter if I were to start counting my name this way....

C   L  A  R  E

1    2   3   4  5

9    8   7   6

     10  11  12  13

17  16  15  14       so on and so forth.....

A sample look of the various methods used in class.... 

The answer does not matter, but the different methods of how your child derived the answers other than using the traditional method of counting all the way to 99. You can try it yourself too and see what are the different strategies that you can come up with! 

Problem #2 - Card Trick

Another memorable problem that we were given was the 'Card Trick'. I'm still in awed at how this came about and never mind the fact that Dr Yeap seem to win the women over with his 'magic' trick! I showed my 9-year-old the trick and her mouth was wide open throughout! Imagine what you can do in class with your students too!

The method my team used was 'trial and error'. This card trick not only teach numbers, but the spelling of the numbers. I'm not going to reveal the answers of how you are supposed to arrange the cards BUT, I will gladly show you the video of what I meant! You can even try this trick using shapes!

First video demo by Dr Yeap

Second demo by our very beautiful Shirley

To end it off, Dr Yeap mentioned that what your elders used to say, "Practice makes perfect" but if you are not practicing the right thing, you are practicing the wrong thing perfectly, So, in other words, "I have been to a clinic many times, does that make me a doctor?"

This is so true, hence parents, help your child by ensuring that they understand Mathematics using the one of the learning theory from Dienes

Play - let your children explore with Mathematics through play where they derive their own knowledge, thinking skills. 

Only through their own explorations, will they be able to make sense of what they are learning. Sharing and discussing their ideas with their peers or with an adult enable them to see that there are many methods to solve a problem. Solving a problem means that the way that you obtain your answers must be explainable and make logical sense!

Have a great day! 

Introductory to Mathematics - What Parents need to know!

Mathematics had always been a main concern for parents. But, what exactly is Mathematics? How do we go about teaching children about Mathematics? And, how can we, as parents support my child in their mathematics development?

Being a parent myself, I often ask these questions as my child grew. Now that she's in Primary 3, I had left the job of coaching her in Math to a more experience tuition teacher who is able to answer her doubts and questions. Guilt sets in as I realised how incapable I am as a mother. 

Being a preschool teacher, it dawns on me that I need to teach these children mathematics as it is an important element in their growth. From numbers, to shapes, to patterning, these help them to get about their daily life in future. To ensure that each child is able to learn the concepts at their own pace, I have to plan for differentiated lessons so as to ensure that No child is left behind. 

So, what is mathematics and how do we go about teaching children the various concepts?

Mathematics is not just a subject, but according to Van De Walle Karp Bay-Williams, it is a child's ability to "generate strategies for solving problems, applying these approaches. seeing if they lead to solutions and checking to see whether their answers make sense (p.13)". There are no set way of teaching the concepts as it depends on the teachers' or parents' personal beliefs in teaching and understanding Mathematics. However, by encouraging your children to share their ideas or knowledge of the concepts, you are encouraging them to think of different strategies to help connect their thinking. 

How can we as parents, support my child in their Mathematics development?

Well, there are a few things that you can do to help:

1. Be a source of support and not a source of fear - Each child have a different way of understanding mathematical concepts. It might take a child to understand that 1 + 2 = 3 very easily but not for another child who is not able to understand the concept of addition. 

2. Don't confuse your child by teaching them new concepts that they have not learnt in school - Many years back when I was in secondary school, my younger sister (who was in Primary school then) asked me for help in her math paper. I solved the problem for her by using algebra (she had not learnt it then) and got her into serious trouble. 

3. Time and practice - Your child might need more time and practice to understand certain mathematical concepts. Through this, they will be able to generate their own understanding, build connections and see if their answers makes sense to them. 

It does not take a magician to conjure up mathematical formulations, all you need is time, love and patience. With that formula, your child will be able to excel in Mathematics with your support. 

Sources: 

Elementary and Middle School Mathematics Teaching Developmentally by Van De Walle Karp Bay-Williams