Session 2 on 13th August 2013

Concrete, Pictorial and Abstract Approach, Scaffolding and Modelling.

I like the mathematics exercise using the 'Ten Frame' which I can use for instructional. On the other hand, the children get to explore and to conceptualize the number bond in more than only one way to experience whole number.

Another important lesson I learnt through this session is that 'never count the number with different nouns'. I used to think that counting is counting, so why the children in my school were not able to add the sum of boys and girls as the overall number of children in the class. I need to rephrase by asking the children to count as a class then sought the number of girls from the boys. I have to more mindful in the structure of language as not to cause ambiguity that mislead their understanding.

## Sunday, 18 August 2013

Session 2 on 13 August 2013

The five-frame or the ten-frame concrete apparatus for number bond enable children to visualise as they explore and experiment the whole number by counting one by one using manipulative. With concrete manipulative they are developing the computation and internalised the connection of number bond and number sense.

To develop children ability to learn with understanding, teacher support the process by scaffolding, modelling and allow them to explore and to achieve the baby step success. The use of language and the construction is equally important as not to cause confusion and ambiguity.

Thumb of the rule never to count number with different nouns such as to add four apples and two pears.

The five-frame or the ten-frame concrete apparatus for number bond enable children to visualise as they explore and experiment the whole number by counting one by one using manipulative. With concrete manipulative they are developing the computation and internalised the connection of number bond and number sense.

To develop children ability to learn with understanding, teacher support the process by scaffolding, modelling and allow them to explore and to achieve the baby step success. The use of language and the construction is equally important as not to cause confusion and ambiguity.

Thumb of the rule never to count number with different nouns such as to add four apples and two pears.

Session
3 on 14

^{th}August 2013
Something
about the dots on the dice. Knowing the
number without counting is important for all kindergartens. To be able to see and to know the patterned
dots and interpreting the dots on the dice as the number without counting is
known as

*subitizing*. “Subitizing is the fundamental skill in the development of students’ understanding of number”, according to Baroody, p.115 (1987).
Today I get
to know that the standard dice of which both the numbers total sum opposite each
other is seven. Among other practises of number bond of
five-frames or ten-frames, the dice is another method that children learn
number bond.

Curriculum
with mathematics activities had to be focused on the variation for progressive
development and not repetitive of the same contents which stifle learning. Besides having the well-structured and
purposeful curriculum; supported by manipulative for concrete and visualisation
to create model for pictorial to enhance
learning skills.

Session 4 on
15

^{th}August 2013
Incidental
learning is best and well-remembered by children because it is their agenda that
they are interested with a purpose. The
scaffolding to hone children’s developing learning skill with purposeful and
structural curriculum. Drilling and practising
is a regime to reinforce the learning process with children initiated interest. Learning to tell time and numbering are the
examples for incidental learning.

Just
beginning this year 2013, the six years old boy was his first to attend the childcare;
previously he was from a three hour kindergarten program. Every morning he would come teary and
attacked by ‘separation anxiety’ when the mother left for work. Once the mother left the childcare centre, he
would consistently enquire about the time repetitively, “What time is it?” My persistent reply to him is showing him the
clock and telling him the time. The reason for his anxiety to know the time because his mother promised to pick him by six o'clock.

After a month at the childcare centre, he told me that he is can read and tell
the time now. It is a successful story
on his part; learning to tell the time through his purposeful interest.

Session 5 on
16

^{th}August 2013
Dr Yeap walked
us through the memory lane about the characteristics and properties of
triangles namely the isosceles triangle, equilateral triangle, right angled triangle
and scalene triangle. As usual there are
always minimum three methods to find out the angles and to proof the angles of
a triangle, and all the three angles in a triangle is 180

^{0}. The instrument to measure the degree of each angle of a triangle is the protractor.
The mathematics problem:

ABCD is a
parallelogram. CFE is an isosceles
triangle where CE = CF. DF and BE are straight lines. The
sum of Ð CFE
& Ð CBA is 162

^{o}. Find Ð ECF.
This
mathematics is a multi-steps problem which required visual with metacognition piled with number sense
that enable and to s

Method 1: Visualise and generalise through exploring the pattern. Have the characteristics facts of the triangle for student to develop and to improve the required skills.

Method
3: Making conjectures about properties
and compute words or symbols of simplify expressions and equations.

The class
solved the multi-step problem using algebra. We have great fun with all possibility answers but one by one was rejected after much discussion and reasoning. The lesson was interactive and all of us have a share in the contribution of the possible answers. We enjoyed the interaction with laughter and jokes. It was indeed fun!

^{th}August 2013

The planning
of lessons to include differentiation instructions by the objective content, by
process to customise for children who are of low progress, middle progress and
high progress, and by product that the result of the progression content are of
the same with different solutions.

The
follow-up activities are very important that will progress and sustain children’s
learning development abilities from
simple to complex. The activities are hands on like folding and cutting papers, exploring, experimenting and predicting the outcome results after folding and cutting. We also perform a trick which is no trick but base on patterning with reasoning using metacognitive assisted by visualisation with concrete.

## Monday, 12 August 2013

How children learn mathematics?

Interestingly children undertake every mathematics task is problem solving. It is the construction and connection of the existing ideas to the new ideas that link to the meaning of the potential relevant ideas when learning a new concept.

The existing ideas on their prior experience of knowledge with the combination of drill and practicing to reinforce in scaffolding new knowledge from prior knowledge further their conceptual understanding.

Children learn well when they are able to relate with concrete manipulative, pictorial visualise in their brain. Therefore it is concrete before pictorial and pictorial before abstract.

## Thursday, 8 August 2013

### Elementary and Middle School Mathematics, Chapter 1 and 2

Mathematics
is all about Science of Pattern and Order.
“Science is a process of figuring out or making sense, and mathematics
is the science of concepts and processes that have a pattern of regularity and
logical order.”

(Van de Walle, J.A., Karp, K.S., and Bay-Williams,J.M. (2013),

(Van de Walle, J.A., Karp, K.S., and Bay-Williams,J.M. (2013),

*Elementary and middle school mathematics*(8^{t}ed.). USA:Pearson.

Learning mathematics is fun! Children learn better as “doers” when they are involve with mind intriguing verbs such as

*compare, describe, explain, explore, investigate, predict, represent, solve, use and represent.*These mind intriguing verbs definitely will spur them to think further; in addition with encouragement and development opportunities creating higher-level ideas in ‘making sense’ and ‘figuring out’ to a solution.

Children are
empowered to take mathematics ideas to the next level when they are able to
make sense of the mathematics problems and therefore they are capable to solve
the solution. The following are the
mathematics strategies that enable children to believe that they are “doer” of mathematics
(Fillingim & Barlow, 2010) by:-

o connecting to previous material

o responding with info beyond the required response

o conjecturing or predicting

Doing mathematics required effort with the combined collaboration together with the families and the community in order to enhance mathematics learning development, (National Mathematics Advisory Panel, 2008).

In mathematics, the conceptual understanding is when the children apply their previous knowledge, testing ideas, making connections and comparisons. In the process the children take the struggle into their strike and sense their achievement when they are able to solve a solution, (Carter, 2008).

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