As I continued to think and reflect, think and reflect again....

I realised ...

I realised the reason why I found it hard to teach the basic concept. And that is due to the way I had been taught and also the way I had learnt to conceive my knowledge, concept and skills.

Too much strategies and too much short cuts!

The formulae, the equations, the methods that I was taught and that I had learnt have indeed helped me to score in all my Math exams but it had definitely not equipped with the appropriate knowledge to teach the children.

I could not understand why the boy could not understand simple equation such as 1+1. I could not see that he is not able to visualize and I did not kow that Math concept like this or even simple numbers can be rather abstract for the children to be able to visual it and make meaning of it.

I could not understand that inorder for children to be able to understand, they need concrete materials, they need to make meaning from this concrete materials and that they need to build concept and construct new knowledge from their prior experiences.

I definitely had not rememered to ask and attempt to find out what his prior knowledge were or even conduct discussion on Math.

and I think....

I have been indeed a rather lousy Math Teacher!

## Tuesday, April 9, 2013

### My Reflection I

It seems rather weird not to end off my Blog with a reflection of my thought about the Math module when I had mentioned in my first post that I looked forward to this Math module.

Honestly, it wasn't anything I have expected.

Then again, comes to think about it, I really don't know what to expect!

....hmm...hmm...

or maybe.....

I do expect some 'think I'm so smart' lecturer walking into class throwing us lot of math problems to show how smart he is when everybody in class could not solve the problems.

Well, that is really not the case here.

I think I like the way Dr Yeap, drives us through the math problems. It allows me to truly gain a new understanding of the math problems, through concrete drawings and diagram that make it seems less abstract.

And the questions that he throw our ways prompt us to think and see the problems and solve it by breaking them into the simplest and most basic form that means something for new learners and abit frustrating for 'us' because we know we can solve the problems with the application of some formulae or equations.

Honestly, it wasn't anything I have expected.

Then again, comes to think about it, I really don't know what to expect!

....hmm...hmm...

or maybe.....

I do expect some 'think I'm so smart' lecturer walking into class throwing us lot of math problems to show how smart he is when everybody in class could not solve the problems.

Well, that is really not the case here.

I think I like the way Dr Yeap, drives us through the math problems. It allows me to truly gain a new understanding of the math problems, through concrete drawings and diagram that make it seems less abstract.

And the questions that he throw our ways prompt us to think and see the problems and solve it by breaking them into the simplest and most basic form that means something for new learners and abit frustrating for 'us' because we know we can solve the problems with the application of some formulae or equations.

But I have to say that it is good!

For it allows me to be able to see it from the children's point of view, and have a better understanding of how the perceive information and construct knowledge.

The sharing of theory and information has also allow me to gain better understanding of how children learn and what they really need and how I can better facilitate the children's learning and get them prepared for higher learning as they progress on to Primary school.

## Monday, April 8, 2013

### Well-Prepared II

__How do I Teach to Get Children Ready!__

1) Build New Knowledge from prior knowledge

I understand from Dr. Yeap's lesson that children are able to construct new knowledge only from old knowledge, things they already know. And as educators, it is important for me to make connections between the new information or concept with students' prior experiences.

With this in mind, I also need to understand the need to...

2) Always start with Concrete material that is meaningful to the children

Based on Dr Yeap's explanation, I gathered that learning progresses primarily from prior knowledge and only secondarily from the materials that we presented to the children. Which also explains why the material I used need to be natural and meaningful to the children where they are able to relate and make meaning of it. As math itself is rather abstract and there is a need for teacher to bring in concrete material to help children visualize the concept and construct knowledge from infromation gathered from their experience and exploration of the math problem with the concrete materials.

3) Provide opportunities to talk and 4) Build in opportunities to reflective thought

We are all guilty of hurrying through teaching some concept or skill and not taking time to slow down to allow children the opportunity to talk and discuss math which what Dr. Yeap had done so in his lesson. His way of putting, "I wonder what..." also helps to create an opportunity for us to reflect and be engaged in interesting problems with the use of our prior knowledge as we attempt to search for solutions and create new ideas in the process.

And I think that the most important words that Dr. Yeap used is "Maybe.... We can try!"

5) Treat Errors as opportunities for Learning

It allows us the confident to try. It engages us to attempt to get a solution to the problem. We are not afraid of getting mistakes for we know we will not be let down or put to shame if our answers are not correct.

### My Experience with Zone of Proximal Development

**Gaining a deeper understanding of ZPD**According to Vygotsky's Social Development Theory which Dr Yeap shared, I understand that

Social interaction plays a fundamental role in the process of cognitive development; and every function in a child’s cultural development appears twice: first, on the social level, and later, on the individual level; first, between people (interpsychological) and then inside the child(intrapsychological).” (Vygotsky, 1978).

From Vygotsky's theory, I also learn that interactions with peers is an effective way of developing skills and strategies and how as teacher, I could actually use cooperative learning exercises such as peer learning, where less competent children develop with the help of more skillful peers,which I actually did so to help children to develop in their word recognition and reading skills, but in math learning as I used to think that by doing so the weaker children will not learn as they relied on their peers to solve the sum and come up with the answer.

From Dr Yeap's lesson, I gain a strong interest to know more to how children learn and how as educator I can actually apply this knowledge to help my children to learn better that I read up the text again.

From my reading this time, I noticed that I could better understand the text better this time and I wonder why I have missed out such a useful and important information from my first previous reading.

Guess what!

ZPD!

Using Vygotsky's zone of proximal development, this knowledge is kind of out of reach for me to learn on my own but it becomes accessible to me with the support of my leacturer as he explained in more simplified terms. Through Dr. Yeap's explanation on what children truly need to do well in Primary 1, he has created a symbolic space and culture first, on the social level when I sit in class, listen to the lesson, note take, discuss with coursemates; and later, on the individual level when I sit down going through my note, writing my blog, reflecting on my understanding and experience, reading the text, think, analyse and make meaning; first, between people (interpsychological) and then inside ownself (intrapsychological).

## Wednesday, April 3, 2013

### Well-Prepared I

__Knowing How Children Learn!__What exactly do our preschool children need in order to be well-prepared for Primary school?

Isn't this what all preschool teachers have been working towards?

Isn't this the true and real purpose of a preschool education?

Isn't this the ultimate aim and objective of all preschool curriculum?

What does it really mean to be well-prepared?

That is children are able to receive and take it in stride when they enter their Primary school education.

It means to be able to not just cope with the new environment and curriculum but to cope well.

Yet by asking what do children need to learn well, we could also explore the question on how children actually learn?

__On Sociocultural Theory__Based on Lev, Vygostsky's Sociocultural Theory, we understand that

1)"mental processes exist between and among people in social learning settings, and that from these social settings the learner moves ideas into his or her own psychological realm." (Forman, 2003)

2) "the way in which information is internalized (or learned) depends on whether it was within a learner's zone of proximal development (ZPD), which refers to a range of knowledge that may be out of reach for a person to learn on his or her own, but is accessible if the learner has support from peers or more knowledgeable others." (Van De Walle, Karp, Bay-Williams, 2013, p.20)

It is to my understanding from previous study Vygotsky's ZPD as being the distance between the actual developmental level as determined by independent prblem solving and the level of potential dvelopment as determined through problem under adult guidance, or in collaboration with more capable peers.

Which in layman terms means that children's learning happens in a social context;

Which also implys the importance of being able to socialize in order to learn well;

And socialization requires children to be able to communicate well;

Which means able to speak and listen well and therefore the need to have good language skill.

To explain, I though of some simple math equation.

**Socialization**= social skill + language skill

**Learning**= socialization x new information x prior experience

## Tuesday, April 2, 2013

### Math Never Fails

Once again, I have to say, "Math never fails".

I have enjoyed today's lesson tremendously.

I enjoyed working with my course mates, exploring, attempting, suggesting ideas and solutions to the Math problems.

It is definitely fun and

it definitely makes the long course hours not that long and/or unbearable.

I'm not so sure...

but today's lesson allow me to gain deeper insight and gain better understanding that can put what I know to words on how we could actually teach 'Math'.

I know from my experience that explaining don't work, it’s depressing to attempt to explain the steps or methods over and over again and in the end all you receive is a class of children with blank looks on their faces. Today Dr. Yeap explanation has sheer some lights for me.

He said "Don't try to explain, explanation is not appropriate for young children. It is actually higher level of learning and should be done last. It does not really help children to learn and normally the ones that nodded their head in agreedments are the ones that already understand."

1) Teaching by modelling

Teacher actually demonstrates the steps or solution. This is for teaching new concept

to children or for children who has yet to completely grasp the basic concept and needs a little more

help. By modelling, we are actually providing the necessary guide and assurance.

2) Teaching by scaffolding

Teacher actually prompts children with questions. The questions could serve as a guide to

direct the children as take work towards the solution.

3) Teaching by providing the opportunity

Once children are good and capable, teacher will provide the necessary opportunity for children to

conduct self-exploration where they can applied their learning, skills and prior knowledge.

It is basically just getting the children to do it!

I have enjoyed today's lesson tremendously.

I enjoyed working with my course mates, exploring, attempting, suggesting ideas and solutions to the Math problems.

It is definitely fun and

it definitely makes the long course hours not that long and/or unbearable.

**From the Lesson...****I know something from my past experience with teaching Math but...**I'm not so sure...

but today's lesson allow me to gain deeper insight and gain better understanding that can put what I know to words on how we could actually teach 'Math'.

I know from my experience that explaining don't work, it’s depressing to attempt to explain the steps or methods over and over again and in the end all you receive is a class of children with blank looks on their faces. Today Dr. Yeap explanation has sheer some lights for me.

He said "Don't try to explain, explanation is not appropriate for young children. It is actually higher level of learning and should be done last. It does not really help children to learn and normally the ones that nodded their head in agreedments are the ones that already understand."

**My take away from today's lesson:****There are different forms of teaching or rather steps to teaching.**1) Teaching by modelling

Teacher actually demonstrates the steps or solution. This is for teaching new concept

to children or for children who has yet to completely grasp the basic concept and needs a little more

help. By modelling, we are actually providing the necessary guide and assurance.

2) Teaching by scaffolding

Teacher actually prompts children with questions. The questions could serve as a guide to

direct the children as take work towards the solution.

3) Teaching by providing the opportunity

Once children are good and capable, teacher will provide the necessary opportunity for children to

conduct self-exploration where they can applied their learning, skills and prior knowledge.

It is basically just getting the children to do it!

## Sunday, March 31, 2013

### Reflection From My Reading of Chapter 1 and 2

I particularly like a statement and hold the same believe as was mentioned in the book, where it

stated that "students learn about mathematics depends almost entirely on the experience

that teachers provide every day in the classroom." (Van De Walle, Karp, Bay-Williams, 2013, p.3)

From my experiences gained from teaching, I believe that the best way to

bring a concept across to young children is not how well you explain or

teaches a concept but rather how well a teacher create opportunities for

children to explore and applied the concept. And from their exploration

highlight the learning point to the children. Children learns better from

hands-on and they understand better from their experiences, just like us.

Our experiences are the best teacher and learning opportunity for us.

Math is definitely not a theoretical subject, it should not consist mainly

words or the copying of steps written on the board by the teacher.

It is a subject that requires self exploration, it requires self application to

gain understanding.

For the child who could not understand why 1 + 1 is 2 then do something

that really affect him. Take away 1 of his favourite toys for two consecutive

days and asked him how many of his favourite toys have you taken.

(I'm just kidding!)

Or

Give him a sticker for two consecutive days and asked him to count the

number of stickers he has.

Minus the abstract and add in the concrete for them to be able to visualize and feel.

stated that "students learn about mathematics depends almost entirely on the experience

that teachers provide every day in the classroom." (Van De Walle, Karp, Bay-Williams, 2013, p.3)

From my experiences gained from teaching, I believe that the best way to

bring a concept across to young children is not how well you explain or

teaches a concept but rather how well a teacher create opportunities for

children to explore and applied the concept. And from their exploration

highlight the learning point to the children. Children learns better from

hands-on and they understand better from their experiences, just like us.

Our experiences are the best teacher and learning opportunity for us.

Math is definitely not a theoretical subject, it should not consist mainly

words or the copying of steps written on the board by the teacher.

It is a subject that requires self exploration, it requires self application to

gain understanding.

For the child who could not understand why 1 + 1 is 2 then do something

that really affect him. Take away 1 of his favourite toys for two consecutive

days and asked him how many of his favourite toys have you taken.

(I'm just kidding!)

Or

Give him a sticker for two consecutive days and asked him to count the

number of stickers he has.

Minus the abstract and add in the concrete for them to be able to visualize and feel.

### Math in My Life

**My relationship with Math**

I enjoyed math, I would say from young. I think mainly because I am truly

not much of a language person. If I need to be at least something than I

would say I am a Math person.

Since young I have not much issue with math though not always the first in

class but definitely a subject that I can always count on.

It has never failed me.

I like the idea of applying the appropriate strategies to solve a problem

and I like the process of burying my whole self into solving a sum or two.

I like the feeling of being totally engaged in something;

The satisfaction of obtaining the solution to the problems;

The feeling of accomplishment is...

I would say 'Absolutely Wonderful'.

At least it helps to will away the boring hours in school.

When I am working on the math problems;

Everything seems to be at a standstill.

Everything seems not to matter.

Math! At least it makes more sense to me than English, which does not even have a definite rule.

But for math, 1 + 1 will definitely be 2, regardless of what others say,

I can count on that!

**My Experience with Teaching Math**

Have you ever encounter teaching Math to a student who just could not

understand why 1 + 1 is equal to 2, no matter how hard you tried, even with

the use of concrete object such as 'sweet', 'cookies', 'toys' etc.

You name it I believed I had used it.

Well, I met one such student and it almost did me in.

Though I enjoy mathematics and am good in it but I realised that it does

not necessary makes me a good teacher to teach mathematics.

Yes, I have inspired many students to like and enjoy mathematics,

Yes, I have encouraged many to persist on even when they feel like giving up.

Yes, I have taught many students and guide them to solve challenging sums.

But I realised that the most difficult is teaching the simplest, the most basic

concept of math.

I'm looking forward to this module!

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