Friday, 2 September 2011

My last day in Math class…But DEFINITELY not my last encounter with math!

Today, Dr Yeap shared about assessments. I have always thought that assessment is only in a form of paper and pencil, like those we had during our school times. There was oral but I did not exercise my flexibility to think about doing oral test for math. Why didn’t I think of that??
There are 3 types of assessment tasks:
1.       Paper and pencil test.
2.       Oral test.
3.       Group and individual test.
Another thing that was pointed out was assessing children on the concept to time.

I believe everyone did experience drawing the ‘long’ and ‘short’ hands on the clocks face!!!! Hahaha was that the right thing to do???? DEFINITELY NOT, if your objective is for the children to be able to tell time! It’s more of whether the child can identify the ‘long’ and ‘short’ hands on the clock!

An activity that we did was to come out with a box that fits 15 kidney beans. I find this activity very fun! I saw one small box made by my classmates but it could fit more than 30 kidney beans!  
Thing to note: ** Don’t underestimate the amount of kidney beans a small box can hold!
Let’s go for a trip to…. THE MRT STATION!!!!

Dr Yeap gave us a task of measuring the height of one floor to another in the MRT. Honestly, I was like “WHAT?? Do we really have to do that??? How do we do that with only a ruler measuring 15cm??!!!

But we did it any way…
Here’s how we calculated…
The first set of staircase = 14  steps
The subsequent 3 sets of staircases = 16 x 3 = 48 steps.
The height of 1 step to another = 14.5 cm
THE HEIGHT OF ONE FLOOR TO ANOTHER = (14+48) x 14.5 = 899cm.

Word of the day: Oxymoron (the sound of it is already funny) – two words that contradicts, for example, living dead and awfully beautiful.
A key take-away:
How to make sure the butterfly cannot fly? Go help the butterfly out of its cocoon! Then the butterfly will not be able to fly.
It is the same with children. Give the children freedom to explore and don’t always assume and provide them with answers. They will definitely not survive, just like when you help a butterfly…

I had a great time exploring with Math in Dr Yeap class. I understand that I will be seeing him again in another module. Hope it will be as fun and captivating as this math module
It was an eye opener to discover and learn new things in this math class.

Saturday, 27 August 2011

TGIF - It went well!

 I don’t know why it seems so easy doing math in Dr Yeap’s class. How I wish everyone gets Dr Yeap for their math teacher. Hhhmmmm Dr Yeap…. Quickly go and teach proper math to all the Math teachers out there! I’m sure there will be more children/students liking MATH… And those who like math, will LOVE math! *Just a thought*
Today… I’ve got a new friend, RUSHDA!!! So cute!!! We did chit-chat quite a bit… and break fast together ;) Hope to see you again, Little Rushda! Maybe in our last math lesson?
Today, we started off with fractions. Fractions?? Fraction!!
In 1/5, how many ½ are there?

1)      You can cut the 1/5 into ½ as shown above, to get the answer.
2)      Another way is :
2 fifths ÷ 1 tenth = 4 tenths ÷ 1 tenth
                                               = 4 ÷ 1
                                               = 4
3)      a/b ÷ x/y = a÷x / b÷y
Bloom’s Taxonomy – Describes the cognitive levels and processes when doing different task. We learnt 3 out of 6 levels,
- Knowledge Level
- Comprehension Level (Inferential)
- Application Level
Then we did George Pick’s theorem, the fixed theorem, is rather interesting. We spend quite an amount of time to understand the DOTS diagram.

Hhhmm  in my childcare centre, we did let the children use the geoboards and rubber bands to create different shapes, and then those who were able to create their shapes, will draw on the DOT papers provided. And thats, that.

And it’s very interesting to find out the formula behind the DOT diagram…
Firstly, we did squares of different sizes, then proceeded to create any shape by touching 4 dots (For that, I’ve got 1 peg! Yipeee).


a = p + i – 3 (All thanks to my classmates for trying really hard, we don’t need to stay in the jail to solve this didn’t we?? heheh)
Then, we used graph to document the number of pegs we received since day 1. Our group actually pasted the pegs onto our graph itself… hahahah and WE HAD FUN! Together with Rushda…
Lastly, we received the ‘Monster’ quiz… the quiz that I somehow did with trial and error… oopss heheh. Hope my working is clear!
Teachers act as an external stimulus. When a child does his/her math and approach their teacher for acknowledgement of their answer, be it right or wrong, WITHOUT REALIZING, a teacher acts as a stimulus for their understanding. A teacher will show verbal and non verbal cue to tell children about their answer… NO GOOD NO GOOD (shakes head)…

Children will have a better understanding about the math question itself if he/she uses his/her own internal ability to question whether it is right or wrong.

That’s all for now!!!
See you on our last lesson….!

Thursday, 25 August 2011


We started off with a Mind Reading Game! Doesn’t that sound wacky already??? It is really crazy to see how this trick works. Math is really about number sense and looking out for pattern!

In this activity, we can also provide children with concrete, pictorial and abstract experience.

Then we did subtraction using 37 - 19. We came out with a variety of word problems using 39 – 17. We saw different kinds of word problems.
Discrete quantities: can be presented one by one
Continuous quantities: For example, dollars
Tips to teach children word problems from simple to complex
1.       Give a join problem; any of the three quantities can be unknown (result, change, initial unknown)
2.       Then part-part whole problems; either whole unknown or part unknown
3.       Then compare problems; difference, larger, smaller unknown
Try to guess which category this word problem belongs to, 1, 2, or 3…
Jamie has 5 fewer marbles than Sarah. Jamie has 9 marbles. How many marbles does Sarah have?

“Children don’t learn well through repetition, they learn well when we provide them with variation of the same idea.”
                                                                                 -   Zoltan Dienes

Next, paper folding time!!!
Try folding square and rectangle papers into equal parts…

Being EQUAL doesn’t mean IDENTICAL.

Again, from concrete, to pictorial and then to abstract...

Let’s reflect…(This is interesting..)
Why didn’t we question our math teachers as to why the divisions are done this way??? Hhhhmmmmmmmmmm

Till then....

Wednesday, 24 August 2011

Case Study With Ms Peggy! Oh it rhymes!

Today, we were given 3 case studies on Lesson Study. Two of which was on a teacher teaching concept of “more than” and “less than”.  The second lesson, the teacher did much better taking into consideration some of the pointers given during post lesson discussion.
After watching the videos, we had to come out with a strength and an area of which she has to improve on. From our findings, we categorized them into different aspects of lesson implementation:
1)      Sitting arrangement
2)      Level of engagement / involvement
3)      Use of materials / manipulative
4)      Flow / sequence of lesson
5)      Classroom management
6)      Communication (teacher:pupil, pupil:pupil)
7)      Questioning techniques (no. of qn,types of qn, waiting time given)
8)      Disposition
9)      Differentiation
Case study 2 was Ms Peggy herself who did number conservation with the K1 children. Impressive I might say, for a first timer teaching the younger ones! She looked so enthusiastic and animated, trying to capture the children’s attention and digging out the answers to match her objective. Hehe
My key take-away for these case studies was the fruitful sharing of how we can create differentiated learning for children with higher or lower ability. It is truly difficult for teachers to come out with differentiated lessons to meet individual needs of children. So, I feel that this is a good way to create the awareness of coming out with differentiated learning in a lesson itself.
We had BRAIN GAME with 5 unifix cubes.

Each group was supposed to create as many unique structures with 5 unifix cubes. Competition was tight!!! Everyone had the pegs in mind! Haha. Anyway, my group did our best, but did not quite get the most number. We were very close to getting the highest number, 25. Nonetheless, we had fun! Really!
Ms Peggy also talked about how lesson study is important and aligned with some SPARK criterion. How great! With this implementations going on, it’s like killing two birds with one stone;
helping the teachers to be engaged in examining their practices to provide the best for the children and also meeting the SPARK criterion.
Lastly, we got our quiz! Super challenging! It is easy when the question is posted to you….. But when you are the one creating the word problem with the given sum, that’s the
BIG PROBLEM. However, I tried, so we will see! HAHA
Homework of the day: Activity for Visualization using Tangram.

Good luck to me in figuring out!

Tuesday, 23 August 2011

Math - It's not about what you teach... It's HOW you teach

I personally like the way my title sounds! A teacher needs to know what his/her objective is when he/she is teaching. His/her main focus or objective is about teaching mathematics children. If we want children to learn, we let them correct their own mistakes, correcting the mistakes for them. In this way, we help children to feel and understand what they are doing and with this understanding, they are able to remember it.

"People won't remember what you tell them. But people can remember how you make them feel."
                                                                  -Dr Yeap Ban Har

I feel that this is a great statement to make. I didn't realize this until Dr Yeap mentioned it just now. This is really true. I thought that by memorizing, I am able to understand and learn. Initally, I depend very much on memorizing as I want to remember things quickly. But the fact is that I can't memorize and remember for nuts!

Even in Howard Gardner's theory, there is no such thing as "MEMORY INTELLIGENCE"! hahahaha If there is, I will be a GENIUS! Everyone will be too!

I also want to share something that I discovered. I have always thought that Math is somehow close-ended apart from the word problems (one definite answer) that we had to solve. But when Dr Yeap provided us with the above, I can see that there is no one definite answer and children can actually put in different numbers and get the answer 5. How cool is that?

It is really about how I make connections to things or prior knowledge, find patterns, reasoning as well as communicate my thoughts that I learn better.

This brings me to the 5 things we teach to develop thinking skills and problem solving.
1. Generalization
2. Meta cognition
3. Communication
4. Visualization
5. Developing number sense

Theorist Jerome Bruner uses the CPA Approach (concrete,pictorial,abstract) in learning things. By providing the concrete materials, children will be better able to do trial and error, understand and reason out why things are arranged in a certain manner. Then they move on to pictorial (2D) and proceed to look at abstract things. This is also true as in my childcare centre, we believe and also practice providing children with the opportunity to interact with materials as they learn. INTERESTING!

I want to share the different lessons we had today... It is really so difficult to choose one lesson as all the lessons are taught interestingly... But I personally like Lesson 7: Largest Even Number

There will be 4 number spinners and a 4 row of squares. The number spinner will be spinned one at a time. You will have to decide where you want to put the number. You have to bear in mind that you are to make the LARGEST EVEN NUMBER. So exciting! We played it a few times and guess what! I did got one right and got a peg for myself!!! This game really gives me the adrenaline rush! hahaha I guess we were so noisy that my friend from the class next door texted me and said, "What are you guys doing? Why so noisy!" hahahah

Word of the day: Subitize - counting a small number by looking

I would also like to thank Dr Yeap for pointing out on what I wrote on my first entry about math which was "Either you get it or you don't". Now I am going to do some corrections to it. It is "Either you have the opportunity to receive QUALITY INSTRUCTIONS or you don't".

Happy thinking!
Looking forward to another day of Math!

Monday, 22 August 2011

Awesome Monday Math!

WoW! I never thought maths will be this fun...! To be frank, I was super sleepy today and could not concentrate during my whole day course in the morning. I was thinking to myself, "I am so tired and sleepy... How can I survive my first math class today?"
Indeed, I survived! I was wide awake!

I feel we can do wonders with math!!! It can be magical and interesting. It is how the teacher introduce the different math concepts and provide us with the opportunity to really think of the solutions!

Today's math class was awesomely interesting! Initially, I was sharing with Liana, saying, "Is he (Mr Yeap) speaking math to us? It seems that everything he writes, he links it to math (e.g date, lesson number, his name)" I came to conclude that INDEED he is... He also provides us with the foundation and the correct terms to use to teach math.

One interestingly funny example Mr Yeap shared was about the difference between ordinal number with respect to time and ordinal number with respect to space.
A teacher has to be carefully with the way he/she asks a math question. Let's look at the two questions and see which makes sense....
Question 1: Who is third in the race? (ordinal number with respect to time)
Question 2:  Who is third from the finishing line? (ordinal number with respect to space)

Let's ponder for a moment....

Alright... Let me share with you... How can a child answer question 1 when the teacher only shows the picture??? A child may be able to tell who is third in the race if he/she is given a video and to see the ordinal number with respect to TIME.....
BUT the child can definitely find out the answer to question 2, which is "Who is third from the finishing line?" from the picture... GET IT?? hahhahah

I didn't know that POKER CARDS can be a good resource for math... Believe it or not, just now Mr Yeap shared a MAGIC!!! And Liana and I could actually figure out how he did that! AMAZING!!!!

The objective of the game is to call out the number and make sure the card you show is the number you call out. You have cards Ace to 9.  Arrange the cards in a way that you spell the numbers out, one to nine. Place the cards facing down .After spelling each number, say out the number and put the card away .... For example, o,n,e,1. put away the card "1" that you call out. Then continue with the rest of the numbers.
Try it... It's Fun!

"Mathematics is an excellent vehicle for the development and improvement of a
person’s intellectual competence in logical reasoning, spatial visualisation, analysis
and abstract thought. Students develop numeracy, reasoning, thinking skills, and
problem solving skills through the learning and application of mathematics."
                                                                                    -MOE Mathematics Syllabus

Just something to share before come to an end:

Prerequisite of counting (The fundamentals of counting)
1st: Is to classify.
2nd: Is to rote count.
3rd: Is to count with one to one correspondence
4th: is to appreciate the last number you utter in the group.

Happy thinking about math!!!
Looking forward to my next and many many math lessons!!

Saturday, 13 August 2011

Are we teachers ready for maths??

                                                              by Irène Marcovici     

I have always been having a love-hate relationship with maths. What I remember about maths was to memorise, memorise and memorise the various formulas for the different concepts that was taught. It was all about equations and problem solving.

                                             by Irène Marcovic

Maths is magical. It's either you get it or not.

I agreed with the text that PREVIOUSLY we learn maths through teacher's demonstrating the methods and then we practice the procedures.

                                   by Prof. Jorge Joaquin Delgado Gomez 

You memorized the formulas and if you remember it, you are lucky, if not, then you will get a X on your paper. How sad isn't it? I just do maths for the sake of doing and try my best to get it right.

Now, I believe that the teaching of maths has gone to a new level. To be a math teacher, it consists of understanding what it means to know and do Maths. Having the ability to think and reasoning it out is essential. 

But firstly to teach math, teachers must first love maths. Teachers must be persistent and has to show positive attitude towards the subject of maths.

"Teachers with  positive attitudes teach math in more successful ways that results in their students liking math more." (Karp,1991)

Teachers have to be aware and create that awareness for children and their families that maths is not inherited and that anyone can learn maths. I agree with the Curriculum Principle that maths is not a subject on its own. It is an integrated whole and not a subject in isolation. 

Another way for teachers to make the children feel comfortable with maths is to provide them with a classroom environment that 

1. allows them to express their ideas
2. allows them to have the autonomy with respect to the methods used to
    problem solve  

3. allows them to appreciate mistakes as opportunities to learn
4. allows them to rationalize their solutions to problems

I hope to make maths fun for my children and from this module, I will gain knowledge to create a fun and lively environment, and learn captivating methods on how to teach maths. :)