For today's lesson, we went back to working with Tangrams. This time round, we were asked to form a square instead of a rectangle. It was pretty challenging trying to fix the pieces together. These were some of the photos taken during our session.

We managed to find the the following solutions to squares of different sizes.

Besides that, we were also asked to head to the nearest museum to find some artpieces that we can use for our group assignment! We visited the National Museum and found some pretty nice works under the "William Farquar" section where there were a few artpieces of the nature and sights in Singapore, a long time ago.

We also went to the Peranakan Museum. I have always wanted to head there but did not have the time to. This visit to the Peranakan Museum was a whole new familiar experience for me. During this moment of loss, it felt good to visit and read about my grandmother's past. The similar things she would have experienced when she was a young nyonya. Looking at the kebaya exhibits and jewelry brings back good memories of my beloved grandmother. Yes, grandma had some of the similar jewelry and ornaments found at the exhibition. :) The visit to the Peranakan Museum was definitely heart warming. :)

## Friday, 27 September 2013

### Lesson Four - 26th September 2013

We did a discussion in class today regarding how children actually look at the solutions to a math problem.

Eg: 15 - 9

I also listed one of the solution where children can make use of a number line to work out the math problem.

Attached is a video of how children can make use of the number line not only to derive at the answer but they can also learn how if given the equation: 4 + __ = 10 they are able to fill in the blank with the correct answer.Dr Yeap also included the following statement:

"Memorizing Math = Robbing children from the ability to reason/figuring out"

This sentence really stood out because all along, my mentality of Math has been about memorizing and remembering of formulas. I reflect upon how when i was younger and mum would always buy a stack of Math assessment books and make me do every one of it. She would say, "Practice, practice and you will get good results. Better remember all the formulas and use it on your paper!" I guess that is probably the reason why i felt that Math is a difficult subject to handle and never quite fancy it.

Perhaps, it is about time i begin to look at Math differently.. :)

## Tuesday, 24 September 2013

### Lesson Two - 24th September 2013

Today's lesson was rather interesting. I like the pointers on

There are 3 main points:

1) Model - To be a model and set an example for the children (Children tend to learn by imitating)

2) Scaffold - "A scaffold is temporarily and not supposed to be part of the structure"

3) Independence - Children need to be given time to explore and learn independently

1) To classify

2) Ability to rote count in sequence from 1-5 or 1-10

3) One-to-one correspondence

4) Conceptual understanding of cardinal numbers

Definition: To perceive at a glance the number of items presented

(the limit for humans being about seven)

Example: We can't count 2 apples and 4 oranges together unless the question states, "How many fruits are there altogether?"

We need to rename the noun to "fruits"

It's odd how we are so used to speaking that we often overlook how counting should take place. I think we ought to define in clearer terms when the children are asked to execute a particular instruction.

One thing I enjoyed most is trying to figure out the problem where we did the activity on the red beans. (This is for two players. Select any number less than 20. Take turns to subtract either 1 or 2. The winner is the player who gets to zero. Think about the strategy to win the game.)

We found out that the "Bad" numbers are 3, 6 and 9

*I will play this game with my parents/sibling some time soon and see if there are other "bad" numbers! :)

**.**__how children learn Math__There are 3 main points:

1) Model - To be a model and set an example for the children (Children tend to learn by imitating)

2) Scaffold - "A scaffold is temporarily and not supposed to be part of the structure"

3) Independence - Children need to be given time to explore and learn independently

__4 main things that children need to have in order to do rote counting:__1) To classify

2) Ability to rote count in sequence from 1-5 or 1-10

3) One-to-one correspondence

4) Conceptual understanding of cardinal numbers

**-**__A new word for the day: Subitize__Definition: To perceive at a glance the number of items presented

(the limit for humans being about seven)

**-**__"We cannot count things that have different nouns"__Example: We can't count 2 apples and 4 oranges together unless the question states, "How many fruits are there altogether?"

We need to rename the noun to "fruits"

It's odd how we are so used to speaking that we often overlook how counting should take place. I think we ought to define in clearer terms when the children are asked to execute a particular instruction.

**-**__Red Bean Game__One thing I enjoyed most is trying to figure out the problem where we did the activity on the red beans. (This is for two players. Select any number less than 20. Take turns to subtract either 1 or 2. The winner is the player who gets to zero. Think about the strategy to win the game.)

We found out that the "Bad" numbers are 3, 6 and 9

*I will play this game with my parents/sibling some time soon and see if there are other "bad" numbers! :)

### Lesson One - 23 September 2013

We did a couple of problems during lesson time. It's a rather mind-blowing session. I didn't realize that math would seem so much more interesting than i imagined it to be. I was strictly brought up with the:

Upon reflection, i agree how math should be taught through the wonders of play in free exploration! I also agree on Broner's belief on having concrete materials/tools. The problems such as the Card Trick and Tangram really got me amazed and interested! :)

It was certainly a tricky tricky problem to solve but my team and I managed to solve it on our second attempt! This is our solution: We started by listing the numbers 1-10 on the top of the paper. There after we spelt the number word, "one"

1 2 3 4 5 6 7 8 9 10

"O" "N" "E" 1

"T" "W" "O" 2

"T" "H"

"R" "E" "E" 3 "F" "O" "U" "R" 4

.....................................................................................................................

Our final answer for the cards in sequence:

The next problem I enjoyed most was the tangram! It's odd how i have seen it so many times but haven't quite have the time and motivation to explore/work on it. Today we had some time to try to use this particular formation - of a square and have it transformed into a rectangle..

This was what we were asked to start with - A square

Solution 2:

*Remember this formula and practice a lot! Do a zillion sums in your TEN-YEAR-SERIES and you'll score "A"s!"*After today's lesson, i realize that...maybe, like what Dr Yeap has mentioned: You were taught Math in the wrong method.Upon reflection, i agree how math should be taught through the wonders of play in free exploration! I also agree on Broner's belief on having concrete materials/tools. The problems such as the Card Trick and Tangram really got me amazed and interested! :)

__Card Trick__It was certainly a tricky tricky problem to solve but my team and I managed to solve it on our second attempt! This is our solution: We started by listing the numbers 1-10 on the top of the paper. There after we spelt the number word, "one"

1 2 3 4 5 6 7 8 9 10

"O" "N" "E" 1

"T" "W" "O" 2

"T" "H"

"R" "E" "E" 3 "F" "O" "U" "R" 4

.....................................................................................................................

Our final answer for the cards in sequence:

**Tangram**The next problem I enjoyed most was the tangram! It's odd how i have seen it so many times but haven't quite have the time and motivation to explore/work on it. Today we had some time to try to use this particular formation - of a square and have it transformed into a rectangle..

This was what we were asked to start with - A square

After which, we came u with our own solutions:

Solution 1:

Solution 1:

Solution 2:

As much as i am seriously afraid of Math, i realized..there isn't anything to be afraid of!

Math is fun and there are a lot of exploration needed to find out similarities or patterns of a particular problem. Certainly cannot wait to learn how i can translate or modify all these ideas learnt in class to help my younger ones in school! :)

Math is fun and there are a lot of exploration needed to find out similarities or patterns of a particular problem. Certainly cannot wait to learn how i can translate or modify all these ideas learnt in class to help my younger ones in school! :)

## Sunday, 22 September 2013

### The Art of Mathematics (Pre-assignment Readings on Chapt 1 & 2)

(See bottom picture) This is me..and yes, i struggle with math. all the time. from primary school till my secondary days (i am not sure why but i was in a class with e-math and a-math). the only reason why I've got "B"s for my 'O' levels was probably due to the fact that i had an awesome teacher who refused to give up on me even when i was happy with an "E8" grade. You see..this is how i perceive math..(See right picture). While I was growing up, my mum asked, "Why won't you be an accountant?" I replied, "I don't like the idea of counting other peoples' money. Unless, it's MY money."

Nevertheless, I grew up and became a preschool teacher! And now that Math is part of my job, I shiver at the thought of how i can actively teach and shower the children with sufficient assistance to master the art of mathematics.

Anyway, here is my Pre-assignment from what I have read and learnt in Chapter 1 and Chapter 2 readings:

Dear Parents,

In this following write-up, I am going to introduce the following key points to you:

The 6 principals and standards are: Equity, Curriculum, Teaching, Learning, Assessment and Technology. All factors are inter-connected. Children given the opportunity for adequate support to learn mathematics, they will require appropriate curriculum and teaching. This result to a much more effective learning. In order to enhance a productive learning, the use of assessments and technology are necessary to gauge and assist the children's learning.

How does the children acquire and use their mathematical knowledge?

- Problem solving: Children should be given the opportunity/time to problem solve.

- Reasoning and proof: Children should learn the value of justifying ideas through a logical argument.

- Communication: By actively communicating with their peers, it fosters interaction and exploration of ideas.

- Connections: Children will have to draw connections to see how some ideas/solution are inter-connected and intergate math with other discipline areas.

- Representation: Symbolism in math with visual aids such as charts/graph help to reinforce the understanding of math

Piaget VS Vygotsky? Who's who? Does your child apply either, both or none?

Piaget - The father of Constructivism. He believed that learners are not blank slates but rather creators (constructors) of their own learning. He also explained how it is linked to Assimilation (new concept fits with prior knowledge) and Accommodation (New knowledge does not "fit" with existing network of knowledge).

Vygotsky - He believes that each and every child has their own zone of proximal development (ZPD) where individual learners learn at different stages and phrases in their life.

Regardless of whichever theorist your child is "practicing", it is vital that maximized opportunities to construct ideas and room for ample discussion is given for children to "wire-in" thoughts and experiences to solve math.

With encouragement and endurance to engage in mathematical sums, children will be in a better position of mastering the art of mathematics. The children will experience an effective learning of new concepts and procedures. They will learn to enjoy math as there will be less to remember, it aids an increase in retention and recalling and enhances problem-solving abilities (which they can also relate to problems and source out solutions). Lastly, there will be an improvement in the child's attitudes and beliefs where he/she is positive enough to know how his/her problems can be solved to feel an utter sense of accomplishment.

Dear Parents,

In this following write-up, I am going to introduce the following key points to you:

__1) The 6 Principals and standards for school mathematics__The 6 principals and standards are: Equity, Curriculum, Teaching, Learning, Assessment and Technology. All factors are inter-connected. Children given the opportunity for adequate support to learn mathematics, they will require appropriate curriculum and teaching. This result to a much more effective learning. In order to enhance a productive learning, the use of assessments and technology are necessary to gauge and assist the children's learning.

__2) The 5 Process standards__How does the children acquire and use their mathematical knowledge?

- Problem solving: Children should be given the opportunity/time to problem solve.

- Reasoning and proof: Children should learn the value of justifying ideas through a logical argument.

- Communication: By actively communicating with their peers, it fosters interaction and exploration of ideas.

- Connections: Children will have to draw connections to see how some ideas/solution are inter-connected and intergate math with other discipline areas.

- Representation: Symbolism in math with visual aids such as charts/graph help to reinforce the understanding of math

__3) The wise words of Piaget and Vygotsky__Piaget VS Vygotsky? Who's who? Does your child apply either, both or none?

Piaget - The father of Constructivism. He believed that learners are not blank slates but rather creators (constructors) of their own learning. He also explained how it is linked to Assimilation (new concept fits with prior knowledge) and Accommodation (New knowledge does not "fit" with existing network of knowledge).

Vygotsky - He believes that each and every child has their own zone of proximal development (ZPD) where individual learners learn at different stages and phrases in their life.

Regardless of whichever theorist your child is "practicing", it is vital that maximized opportunities to construct ideas and room for ample discussion is given for children to "wire-in" thoughts and experiences to solve math.

**4) Benefits of developing Mathematical Proficiency**With encouragement and endurance to engage in mathematical sums, children will be in a better position of mastering the art of mathematics. The children will experience an effective learning of new concepts and procedures. They will learn to enjoy math as there will be less to remember, it aids an increase in retention and recalling and enhances problem-solving abilities (which they can also relate to problems and source out solutions). Lastly, there will be an improvement in the child's attitudes and beliefs where he/she is positive enough to know how his/her problems can be solved to feel an utter sense of accomplishment.

Therefore,

go forth & may the power of math be imparted to our future ones...

go forth & may the power of math be imparted to our future ones...

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