Sunday, 7 April 2013

Day 6 (6th April 2013)

Today marks the end of the module. There are basically 5 main core values of the module:
1) Visualisation
2) Number sense
3) Pattern
4) Communication
5) Meta cognition
Concrete Pictorial Abstract Approach were the main gees of it. The approach were supported by theorists Jean Piaget - theory of Assimilation and Accommodation, Vygotsy - Scaffolding, Jerome Bruner - three modes of representation and Dienes  - theory of variability.
I learnt there are 3 questions we should always ask ourselves when planning a lesson:
1) What do you want children to learn? Focus on the learning instead of what you want children to do.
2) How do I know if the children understand what is being taught? (Based on assessments)
3) What if they can? What if they cant?
There are 4 teaching strategies which we should always remember:
Stage 1 - Demonstration. We model, we show examples.
Stage 2- We scaffold.
If the child is unable to understand, then we move back to stage one which is demonstrate.
Stage 3 - We allow children to do it by themselves. 
Stage 4 - If the children could not do it independently, we scaffold their learning again till they are able to do it independently.
Lastly, if the child is able to understand and do the concepts independently, we further extend their learning by moving to enrichment.
Why we do we have to do enrichment?
1) For learners who can do the concept taught independently
2) For struggling learners, who are almost there.
3) For weaker children to be exposed in a stimulating environment.
Children who are weaker will eventually go a step further when placed in a stimulating environment, learning from peers.
Thank you Dr. Yeap for the past 6 days. It had been an inspiring and enriching experiences. Looking forward to the next module in July. Take care! :)

Saturday, 6 April 2013

Day 5 (5th April 2013)

I was very motivated to do such activity since young. Looking for patterns and solving the mystery.
How many different ways of making sure that the numbers placed in the boxes add up equally for both directions? How do you know you which number to place in the middle? Why does it have to be an odd number? Why does it have to be an even number?
I was impressed by the different ways of solving the problems and felt good unravelling the mystery behind.
I was once again reminded of this question which I had encountered many years backs, when I was still in my Primary school days.
“What is the sum of the first one hundred numbers beginning from one?” 
1+2+3+ ... + 100 = ?

Today, I discovered how this question came about.
In the late 18th century, a classroom teacher asked this question, the class, which was full of young kids, fell into complete silence. A few students were stunned by the seemingly-impossible challenge and readily gave up; most students began scribbling on the paper, trying to add all the numbers one by one, from the very beginning. What a difficult question! They thought.

But there was one kid in the class did it differently. He thought about it for a few minutes, did some simple calculation, and raised his hand.

“I am finished,” the student said.

“How is it possible,” the teacher said to himself as he walked toward the student, “the problem would take one at least an hour to do!” Indeed, if he had solve the problem himself, he would just sum up all the one hundred numbers one by one as well – as a matter of fact, he presented the problem to the class just to kill some time. But after he examined his student’s answer, he was shocked. 

The student was no other than Johann Carl Friedrich Gauss, one of the most famous and important mathematicians of all time.
So, how did young Gauss do the calculation?
First, he wrote the sum twice, one in an ordinary order and the other in a reverse order:
1+2+3... 99+100
100+99+ ... 3+2+1

By adding vertically, each pair of numbers adds up to 101:
. . .
. . .

. . .
Since there are 100 of these sums of 101, the total is 100 x 101 = 10,100. Because this sum 10,100 is twice the sum of numbers 1 through 100, we hence have:
1+2+3... 99+100 = 100 x 101 divide by 2 = 5050!!
This is also one of the way we used to solve our problem of finding the total number altogether. I am totally amazed by it.

Day 4 (4th April 2013)

Have you ever experienced the process of categorizing information in order to learn something new? What kinds of things that you know now do you think you had to use assimilation or accommodation to learn?
While you may never have seriously thought about these things, a man named Jean Piaget is famous for having researched and pondered them. 
Assimilation and Accommodation always go together, we cannot have one without the other.
Assimilation is the process by which a person takes material into their mind from the environment, which may mean changing the evidence of their senses to make it fit. Whereas for accommodation, it is the difference made to one's mind or concepts by the process of assimilation. It is a process of modifying what we already know. We improve and construct the schema.
Today, we covered topics on area, division and multiplication. One takeaway was I realised when we do on division or multiplication word problems, sharing things among people should not be considered. Why? Because people often refers to a person, not a group.
The "Group" have to be a concrete item. We should first  teach young children on sharing concrete items such as paper plates, bowls, and goodies bag.
For example, we should say:
Mother has 24 sweets. She pack the sweets equally into 6 goodie bags. How many sweets are there in each goodie bag?
Instead of:
Father bought 4 apples. He shared it equally with 2 children. How many apples did each child get?
I also enjoyed playing with Tangrams today! I find that Tangrams seemed to be an overlooked educational tool in the preschools settings. Like building blocks, Tangrams can teach children about geometry and foster problem solving skills.
In addition, I learnt that we can use Tangrams to calculate areas! How nice if I have been exposed to such strategies back then during my school days.


Thursday, 4 April 2013

Day 3 ( 3rd April 2013)

The takeaway thought for today lesson was "If an abstract idea cannot be seen in the concrete material, it is not CPA Approach."

Concrete Pictorial Abstract Approach is similar and orginally based on the work of Jerome Bruner in the 1960s.
1) Concrete components include manipulatives, measuring tools, or other objects the students can handle during the lesson.
2)  Pictorial representations include drawings, diagrams, charts, or graphs that are drawn by the students or are provided for the students to read and interpret.
3) Abstract refers to symbolic representations such as numbers or letters that the student writes or interprets to demonstrate understanding of a task.

The concrete material should contain the concept we want to teach. It should be emboided the abstract idea to be considered as a concrete material. E.g. Checking for equals parts on a piece of paper. The equal part is the abstract idea, while the paper is the concrete material.

The Pictured relationships show visual  representations of the concrete manipulatives and help children visualize mathematical operations during problem solving.
Hence, it is important that children should be familiar with visuals (visual literacy), observing and processing through mental images and are provided opportunities for them to develop their motor skills development. This can be done through art, music and movement and other activities that promotes visual literacy and physical development.

A visual representation Multi-Sensory & Multiple Intelligences (© Joseph Aquilina 2011)

The second take away was "fraction means equal parts." As easy as it may sounds, how well do you know the meaing of equal? Have you ever use an apple to teach fraction? If you do, please discontinued using apple as an example to teach fraction. Why? Simply becuase no matter how precise you cut the apple, the halves would not be equal. And you know it very well, fraction means having equal parts.

When the parts are equal, we can actually name them. The denomination is a name and in this case (3/4),  the nominal number 4 has a name call "fourth". Hence we can call it three fourth, or 3 out of 4. 



Wednesday, 3 April 2013

Day 2 (2 April 2013)

I understood why we have been practising the "estimating/predicting" and "checking our prediction" kind of activities with our children from today lesson.

"Benchmark" is the key to it. Let's take a look at this question:

1) Can you tell me if this circle ( O ) is big or small?

Now think again. How do you find if the question is phrased in this way:
1) Can you tell me which circle is bigger? ( O or o )

Interesting isn't it? From this activity, i learnt that the concept of how big or how small will only make sense when we know the "benchmark" of the sizes.

Children relate to what they already know. They  learn by constructing their own knowledge. We start teaching new knowledge from something that is realistic.
E.g. First we learn that this is a big cat, this is a small cat.
Then we move on to teaching children about a big animal and a small animal.
Finally we moved on to a more abstract thinking when the big cat is now a small animal when we compared it with a lion.

I realised there are many methods we can introduced to the children to teach the concept of "Who has more?" It all depends on teaching which methods will help the child to relate and see the idea of it. However, one question that has been bothering me is  "How do we teach children about more than and less than. How many more? less by how many?" I understand the concept of using realistic concrete materials. The children are able to tell me who has more, who has less but when asked the question "How many more?" they gave me a puzzled look.

It maybe because they do not have the language to comprehend the meaning of my questions, or i have asked the question inappropriately. I do not know. Lastly, i like the "10 Frames" method in teaching children to learn about numbers without explicit teaching.

                                                                10 Frames

Tuesday, 2 April 2013

Cardinal, Ordinal, Nominal and the list goes on...

I am pretty excited and looking forward in attending this module. As i myself is weak in math, I have the urge to learn whatever concepts is being taught and transfer the best information to children under my care. I must say i have enjoyed the first math lesson! I realised there are different methods to solve a problem instead of just one solution to a problem.

I am overwhelmed by the number of mathematical terms we used in math. Cardinal, Ordinal, Nominal, Rational, Irrational. All the "nal". Pretty confusing isn't it?

Basically Cardinal answer the question "How many?", Ordinal tells the "Position" of something in a list and Nominal is a number used to identify something or as a "Name".
Here's what I figured on how we can remember these mathematical terms:
  • Cardinal is Counting
  • Ordinal is what Orders things are in
  • Nominal is a Name