Sunday, 18 August 2013

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.

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.

Session 3  on 14th 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 15th 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 16th 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 1800.  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 162o.   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 2:  Develop the ability to visualise the patterns, relations and functions.

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!


 Session 6 on 17th August 2013

  The key words of solving mathematics problems are patterning, generalisation, visualisation, reasoning, and inferring.

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

Session One

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), Elementary and middle school mathematics (8ted.). 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).