Day 6 – 17/8/2013

Ms Peggy Foo took us through the
last session of this module. She introduced lesson study to us. It is a
teaching improvement process where a group of teachers plan, discuss learning
objectives and design lesson plans based on their discussions. After which, a
teacher conducts the lesson would be observed by other teachers. From the
observation, the teachers would examine their lessons; identify their strengths
and weaknesses, so that they would be able to make changes to their teaching
strategies or lesson plans.

I felt that lesson study is a good
practice as it allows collaboration and peer learning among teachers.

In this lesson, I also learnt about
differentiating learner types during a lesson. In a class, there are different
types of learners. Some might be fast learners and others need more assistance
during teaching. Planning should be based on different needs of the children.

I learnt from Ms Peggy that teachers
can plan:

For the weaker learner, provide them

**with 10 frames and counters**
10
= _ +_

For the advance learner just give
them

**counters****h**
10
= _ +_

For the more advance learner, find
different possible ways to make 10 with

**3 digits****er**
10 = _ +_ + _

I agreed that differentiation instruction would definitely
benefit children with different learning abilities. However, it is not an easy
task for teachers to plan and provide differentiated lessons to cater for the
different needs of the children. The teacher has to be competent enough to
scaffold the advance learners and at the same time, she has to assist the
weaker learners. Therefore, I believe that the teacher must possess good
knowledge of mathematics, perseverance, positive attitude, readiness for change
and have reflective disposition.

Day 5 – 16/8/2013

What
is visualization?

To
get the children’s mind to see difficult things, to make them intelligent.

How
do we make them good in visualization?

Visualization is the most important skill that teachers need to
help children develop in their early years. Writing numerals are an abstract
representation of numbers. Before children are ready to work with writing model
of numbers they need to have experiences with concrete and visual models.

According to ‘Jerome Bruner's CPA Approach’, children develop concepts of the number system in three stages.

They move from working with:

According to ‘Jerome Bruner's CPA Approach’, children develop concepts of the number system in three stages.

They move from working with:

- Concrete representations (blocks,
unifix cubes, tangram)
- Visual representations (pictorial
drawings) and
- Abstract representations (conventional number symbols or models)

The
capable children in the class had developed in
their mind, strong visual images of numbers or models. Children are engaged in
the folding or cutting of paper to develop such models.

They drew shapes, different symbols, then gradually to drawing lines
or circles to representing tens. These symbolic images helped children to
develop mental images.with strong visual image of numbers.

Click on the link to read how
to deepen Mathematics Teaching and Learning through the
Concrete-Pictorial-Abstract Approach

www.ldworldwide.org/.../1096-deepening-mathematics-teaching-and-lea...

Day 4 - 15/8/2013

Geoboard

Today
is the fourth lesson with Dr Yeap, we were given a geoboard to draw different
polygons on it but the polygon can has only one dot inside. It’s astonishing to
find some of them could even draw a large polygon with only one dot inside. After drawing the polygon, we have to find the
area. We used one square as our standard unit of measurement. Some of the
polygons were easy to calculate while others are quite difficult, but we came
up a formula to help us in the calculation.

The children in my centre also get to explore the geoboard, they
form different shapes by attaching the rubber bands and they transfer the
shapes onto geoboard dot paper.

It is not easy to get
children to measure the area of the shapes, but after this lesson I realised
children can learn to measure the area of shapes using geoboard.

There are hundreds of math learning and teaching resources and games organized for you here. Enjoy the math!

There are hundreds of math learning and teaching resources and games organized for you here. Enjoy the math!

http://www.jmathpage.com/JIMSGeometry

**geoboards**.html
Day 3 - 14/8/2013

What would you do when a child in your class cannot count? How would
you inform the parents? Will they be satisfied with just answer from the
teacher saying, “Your child cannot count?”

Dr Yeap got me to realise that I need to find out more about
this child’s learning experience. He reminded me that a child can only count
when he is able to:

- Classify and sort
- Do one-to-one correspondence.
- Role count and lastly
- Understand that the last number
he uses actually represent the thing.

Dr Yeap stated that, ‘Teacher should find out the root cause of
the problem and know the possible strategies to help the child.’

He showed us a dice, and asked us, “How many dots are there on
the dice? Can you tell by looking? Can you tell the number of dots without
counting?” The ability to do so is one
new word that I learnt from Dr Yeap, it is called subitize. It means able to
tell the number without counting. Now I know the children are able to tell the
numbers of objects in a group without counting them. They are subitizing.

Dr
Yeap has been emphasizing on CPA Approach during the lesson. CPA Approach enables
children to learn Maths in a meaningful way and translate mathematical skills
from the concrete to the abstract. During the lesson, we learnt about

**fractions**by folding paper. Each of us was given a piece of paper and to fold it into 4 equal parts (concrete representation). We checked whether they are equal parts (although they are of different shapes) by cutting, matching and overlapping them together. From there it constructs the ideas of equal parts. Thereafter, we could solve problems using pictorial form of the shapes then to abstract representative e.g. 2 1/4 – ½. This is a way of introducing**fractions**to children and also we must teach them to use appropriate terms, for instance, ¾ should be read as “three fourths” and not “three out of four” or “three upon four” or “three over four”.
Day 2 - 13/8/2013

Today
I learnt to use numbers in different ways, and see Mathematics as a natural and
part of everyday activities.

Numbers are
used in four different ways

- Ordinal
numbers:
*1st, 2nd, 3rd* *Cardinal*numbers:*Using numbers for counting purposes Eg: 5 apples*- Norminal numbers:
*Using numbers as identification Eg: Bus No. 174, our IC numbers* - Measurement numbers:
*Using numbers to measure Eg: 5 kilograms*

Dr Yeap mentioned that after each number, there must be a noun
for instance

*1 apple, where 1 is the number and apple is the noun.*This helps children when they learn addition and subtraction. Dr Yeap says “You cannot count things that have different nouns”, for example, you cannot subtract one orange from 3 apples. 2 apples and 5 oranges will never become 7 apple oranges. This can also be shown by 2x + 2y will never become 4xy.Thus we cannot give children different nouns to add and subtract.I get to see what 10 frames is, which is a must in every preschool Maths Learning corner. This 10 frames helps children to understand e.g. 8 is less than 10 by looking at this frame. When I asked the children how many less, the children can easily tell me the answer by looking at the blank box. Children develop number sense by using 10 frames to count. It plays an important role in the development of the children in understanding of numbers, it gives the children the visual cue to count one to one correspondence and learn number conservation. I like the 10 frames method in teaching children to learn about numbers without explicit teaching.

Day 1 - 12/8/2013

After
countless of modules, I liked Dr Yeap’s
style of teaching as he explains the answer clearly, especially when he got us
to stop and ask questions. He also makes the lesson interesting and engaging
with a lot of materials and hands-on activities.

He
started off with the question ‘How do the children learn?’ and ‘How do we help
children to learn?’

From
today’s lesson I learnt that children learn through:

- Exploration, scaffolding from
teachers when they prompt the children by asking questions and then by
teacher modelling.
- Concrete Pictorial Abstract (CPA) approach.

The
Bruner theory emphasises that in learning anything abstract, we need to do
concrete learning first before going to visual and then to the abstract
representation. We explored the different ways of folding the paper to get four
equal parts. It was fun trying to fold it in different ways. While doing the
activity I felt as if I was a child exploring with the concrete materials. Hence,
I agreed that children learn best from exploring concrete materials
followed by pictorials then being exposed to abstracts representations.