Tuesday, 9 April 2013

Day 6

Finally we are done in Day 6

Today is the last day of the module. Although its too much for me to 'absorb' for 6 days but there are some interesting points that I will 'treasure' from this module.

  • Cute numbers - This is a new term that I learnt. 
  • Subitize is actually to be able to tell the number without counting.
  • The term 'diamond' shape that we always use is actually called rombus.
  • Polygons always have straight lines. Examples of polygons are such as triangle, rectangle and square.
  • The correct pronunciation of the word 'area'.
  • The 4 steps when teaching the children : model, scaffold. provide opportunity and explain.
On the whole, it was an 'enriching' week for me.

Day 2

Getting to know the Whole Number in Day 2

I almost fell asleep in the beginning of the lesson but was wide awake when Dr Yeap told us to get in groups and create an addition story using number 8 and 6. Although our group got a bit lost as we are wondering how to start the ideas suddenly came upon seeing the work that one of the groups put up. When all groups put up their work, we realised that the language used in the addition story can interpret a different meaning.

This is what I discovered from the different answers given by each group and after the class discussion to see the differences in the addition story.

Ø  The original version

Lila has 8 pencils, Shanti gives her 6 more pencils.

How many pencils does Lila have now?

Ø  Part whole problem

Jolene has 8 sweets .Tracee has 6 sweets.

How many sweets do they have altogether?

Ø  Comparison

Ali has $8. Mary has $6 more than Ali.

How much do they have altogether?

On the whole, I realised that by using different language in the addition story will give a different meaning to it                                            .



Day 1

Excitement in Day 1

Today is the first lesson for this module. A mixed feeling of excitement and worries, as Maths was never my favourite subject. We started of the lesson with an interesting activity of finding which letter would be in the 99th place in the lecturer’s name. After so much of counting, we found that the third letter in his name is the 99th place. It gets more excited when we are to find out which letter in our name is the 99th place. After most of us completed, we realised the 99th place will be the 3rd letters in our name. We also realised that there is a pattern that of how we can solve this.

In today’s lesson, I learnt that there are four teaching steps to teach children.

·         Teaching by modelling

·         Teaching by scaffolding

·         Teaching by providing opportunity

·         Teaching by explaining

One point that I agree with Vygotsky is that children learn in a social environment. They learn best through social interaction. As such they should be given the opportunities to interact and discussed with their friends. I guess now it is alright if the classroom becomes noisier if the children are busy in their discussion.

At the end of the lesson, knowing about the Concrete-Pictorial-Abstract ( CPA ) gives me a better understanding of how such approach are particularly effective with students who have mathematics difficulties. Through this approach, children are introduce to learning from using concrete objects, then to pictorial and finally to abstract. 
Thanks to Jerome Bruner for introducing such theory :)

Day 5

Connecting with dots in Day 5
We often provide children with Dot to Dot activities such as connecting the dots from 1 to 10 or 1 to 20. Upon completing the all the dots, the children will be amazed to what picture it turn to be. What I’m experiencing today with connecting the dots was a different concept at all. Unlike the other activities for the pass days, I am surprised that I was able to do the activity without any difficulty. This is truly an accomplishment for me.
The first activity that we had was to connect 4 dots to create polygons. I also understand the fact that polygons always have straight lines. From the activities, we also explore the many ways to find the area of the polygons such as:
·         Bisecting
·         Cut and paste
·         Look for half of the rectangle
·         Subtracting
One interesting equation that I learned today to find the area of a polygon
                      Area of polygon ( x + 1)
                        Let x = no of dots  inside
                         A = area of polygon
                        Area = x + y/2
                        y = number of dots on the side

Day 4

Theories and More Theories in Day 4
We discussed two of Piaget’s theory today. According to Piaget :
v  Assimilation happens when a child responds to a new event. In this process, new information is added to the existing knowledge.
v  Accomodation is the process when a child responds to a conflict and the child modifies an existing schema or form another new schema to solve the problem.
Today, we also discussed about van Hiele’s theory.
·         Level 1: Analysis (drawing and verbal skills)
           Children at the analysis level think in terms of properties.
          They can list all of the properties of a figure but don’t see any relationships between
          the properties, and don’t realize that some properties imply others.
·         Level 2:  Informal Deductive (verbal skills)
            Children at the informal deduction level not only think about properties but also are
            able to notice relationships within and between figures.
·         Level 3: Deduction
Children at the formal deductive level think about relationships between properties of
            shapes and also understand relationships between axioms, definitions, theorems,
            corollaries, and postulates. They understand how to do a formal proof and understand   
            why it is needed.
We had several activities using tangrams. Using the tangrams provided, we are supposed to make a bigger shape using the smaller ones. It was a challenged in the beginning, but after a few attempts, we had fun J

Day 3

Breaking into parts with Fraction in Day 3

When we introduce fraction as whole and half, we often used apple as an example. Today, I discover that using apple is not appropriate as it may not be exactly half when we cut it into two. So, no more using apples as an example when we want to introduce whole and halve.

We normally use rhymes to develop children’s language and creativity. Today, I realised that rhymes can be used to stimulate mathematical activities with the children. Dr Yeap, began the lesson with our old time favourite rhyme ‘Humpty Dumpty’. He then asked us to think of what numeracy concept that we can teach the children using the rhyme. After a minute of brainstorming, we came up with a few ideas :

v  Counting the number of horses and men

v  One to one correspondence such as counting the men to the horses

v  Using height to measure how high should we place the egg to make it cracked.

Sunday, 31 March 2013

Teaching and Exploring Mathematics

Mathematics’ – The Subject that I love to hate. 
 Mathematics is one of the subjects that I love to hate during my school days. I totally lost my interest in the subject when I failed all my exams during my secondary school.However, my perception changed just a little, when I started working as a pre-school teacher. I realise that there are many interest ways and approaches of how we can introduced mathematical concepts in early childhood.

Upon reading Chapter 1, I am glad to know that for more than two decades the mathematics education has been going through changes gradually. I strongly agree that as teacher, we should boost the children’s interest with mathematics, base on our beliefs about what it means to know and do mathematics and how the children understands about mathematics will effects  how we teach.

With the introduction of the six principles which is equity, curriculum, teaching, learning, assessment and technology indicates that excellence in mathematics education involves more than listing the content objectives. Base on the six principles, I do agree that each child should be given opportunity and support to learn mathematics. We should also focus the importance of mathematics in our curriculum. To make the teaching of mathematics more effective, we need to understand what the children know and need to learn. This will also depends on what we provide in the children’s learning base on the daily lesson that we provide. In the process of learning mathematics, the children must understand and can understand what they learn. It is also important to have a continuous assessment to see the children’s progress in learning mathematics. The children now are fortunate as they are exposed with multi media. Using modern technology such as computers, calculators and other media technologies is also essential in teaching mathematics to the children.

Back then in the 70s, my first experience of learning mathematics was basically rote counting, memorising the tables and to understand the concepts of addition, subtractions, multiplication and division. The ‘all time favourite’ instructions that I heard from my teacher was count, memorise, copy and listen. In chapter 2, I realised that my traditional ways of learning mathematics are considered lower-level thinking activities which do not adequately prepare the children for the real act of doing mathematics.

As a pre-school teacher, I often used simple instructions such as find out, see the difference and think when teaching mathematics. Upon reading the text, I agree that by using such verbs such as explore, investigate, solve, compare and predict will stimulate children’s thinking about mathematical ideas. Using such verbs as instructions may not only develop a higher-level thinking but also develop their vocabulary.

In this chapter, I simply love the term ‘productive struggle’. It gives me a good interpretation of how we should teach and how children should learn mathematics. Children should have the prior knowledge and tools of how to solve a problem which they are able to achieve. Simple and straightforward tasks may not give them an energetic attempt to achieve the mathematical ideas. Thus, they must know that they need to go through the ‘struggling processes before achieving the success.

Hopefully, upon completing this module, although I may still not fall in love with mathematics, but I hope that I will be able to make the children love the subject.