Session 6 – 17 August

Miss Peggy Foo has introduced many activites to teach patterning, number sense and visualisation (card trick, paper cutting,using stories).

I am keen to try out the activity on the card trick in my classroom as it is interesting due to the presence of entertainment and mystery. Children may perceive it to be a magic performance when teachers perform it. Hence, I believe that it will develop an interest in them to find out how the teacher actually do it. Besides having fun, this activity provides opportunities for children to use patterning in order to do the trick.

In addition, I found this link to be useful too as they provides a variety of activties using cards as a mathematical tool

The next part of this session is on professional development. This term is not unfamiliar to me as there is a module that we are taking concurrently that emphazises on this term as well. Indeed, professional development is important as it helps teachers to engage in to examine their teaching practices systematically.

Session 5- 16 August 2013

In this session, the lesson is focused on solving problems on angles. A test paper question on angles was given for us to solve. It took us a while to come up with as many as ways as we can to solve the question.

This question highlights the importance of the skill which is VISUALISATION. Children need to be able to visualise in order to solve mathematical questions. Besides learning functional mathematics where they learn mathematical concepts which is useful in real life such as money,time or counting, children also need to grasp mathematical concepts which is not used in real life eg. angles.

The question is “But WHY?”

” Mathematics is an excellent vehicle for development and improvement of a person’s INTELLECTUAL COMPETENCE…” (MOE)

In order for children to develop into intellectually competent learners, they need these abilites :
1) Visualisation
2) Matacognition
3) Generalisation/ Patterns
4) Number senses
5) Communication

Session 4- 15 August 2013

Some learning points from this session
1) Different semantics for addition, subtraction,multiplication and division.

2) Skemp’s theory on instrumental understanding,relational understanding and conventional understanding.

When a child has difficulty in learning a concept, ponder upon these questions:
What can the child do?
Can the child understand what he or she do?
Can the child understand the convention use?

The answers to this question will be CPA( Concrete, Pictorai and Abstract) approach by Bruner, as well as the three understanding theory by Skemp, and Dienes’s theory on variation of activity. In addition,the role of teacher to scaffold,model and allowing children to explore is esssential too.

Another material used in this session is Geobaord which is effective to teach area and geometry. Below are some of the videos which I found useful in using Geoboard as a tool to teach these concepts

Session 3 – 14 August 2013

After going through this session, teaching fractions is not as complicated to me now as what I have preceived prior today. Teaching fractions is similar to teaching whole numbers where CPA (Concrete,Pictorial,Abstract) approach is one of the ways to teach fractions to children.

In addition, the use of language in how teachers name fractions is important. For example, I learnt that saying 1 out of 10 or 1 upon 10 is the incorrect way of naming fractions. Teachers should use the correct naming for children to model and that will be saying one tenth. I also realise that once the language has been instilled, it is also easier for children to solve questions on fractions.

Below are some links which I found useful as there are many concrete materials that teachers could use when they introduce fractions to children. For example, using candy bars,pies or cakes.


Concrete materials help children to visualise and once children are able to understand, the concrete materials can be replaced with the use of pictures and the last stage will be abstract.
The quote learnt from the session today :” Children need to go through the JOURNEY to get to the DESTINATION. JOURNEY is more important than DESTINATION”

Session 2- 13 August 2013

This session is on the concept of whole numbers. I will share about the use of ten frame in teaching children this concept.

I feel that ten frame is an effective material that children can use to learn about tens & ones, more, less and number bonds. My past experience of teaching children this concept was the use of unifix cubes in most of my teaching. Hence. I discovered that ten frame can be another useful material which can be used as well.

I found this link a useful one as there are games which children can play using the ten frame.

In addition, ten frame need not be a commerialised item as it can be made by children. I feel that getting children to decorate and make their own ten frame makes them more interested and captivated in learning with the material that they have made. (eg. decorating of egg carton ten frame)


Ten frame enables children to visualise what they are doing and I believe that it will be most effective for children who are visual learners. In addition, children can understand that quantity is the same even though they are displayed in different arrangement. These concepts are very important as taken from the quote by Dr Yeap that ” children cannot imagine well what they have never experience”. In this session, I discovered that experiences with ten frame is useful for children to create their own learning experiences.

Session 1 – 12 August 2013

The first class session was fun and interesting as there were many hands-on activites with tangrams. The other 2 problems were given later in the session which I feel that it was a tough challenge to think of as many ways as possible to solve the problems.

I enjoyed the process of solving the first problem of using tangrams the most. It brought back memories of my childhood where I played with tangrams to form the animal using the shapes given. It was really fun to be able to explore and think of ways to create a rectangle using a required number of pieces which was instructed. I found it extremely hard to create a rectangle using all the pieces given. Our group had an intensive discussion in trying to get as many ways to create a rectangle. Below are some of the ways that my group had come up with…

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The other 2 problems were on the 99th letter position of names and getting equal parts from a rectangle.
Upon hearing the question, I was at a loss of what to do. This made me recall the schoolin years again. Thankfully this time round, I could seek help from my classmates and discuss with them on solving these problems.

Pre Reading on Ch 1 and 2

These readings recalled the learning during my school years where I had to solve tons of maths problems and sums. It was rare for me to score good grades in this subject during the first two years in my secondary education. It was the teacher which impacted me to change and develop a liking for maths for the next two years. Therefore,  I believe being a teacher, I need to create a positive attitude in children to learn mathematics.

Ch 1

I learnt about the six principles and five content  standards for school mathematics.  There are also five  process standards and the common core standards. I feel that the common core standards are familiar  as they are similar to what is written in the MOE curriculum framework.

In addition, I do agree the the knowledge,skills and attitude in the teacher affect the learning of children. Children role-model the  teacher. When the teacher shows a dislike in mathematics, the children shows the same likewise. Hence, in order for children to learn well, the interest must be present in them. This interest  has to be cultivated by the teacher. I like the quote by Steve  Leinward the most in this chapter which states that ” If you don’t feel inadequate,  you’re probably not doing the job” (p.10)

Ch 2

In this chapter, I came across the names of the theorists again.They are  Piaget and Vvgotsky. No matter what subject the teacher is teaching, it is  always important to understand and know the theory which supported the children’s learning.

This chapter stresses me after reading as there are many examples of sums that keeps me thinking.  Honestly, it took me some time to understand the solution given in some of the questions stated. 

This leads me to recall a question that a K2 boy has asked me before during the maths lesson. He asked  me why he had to draw model even though he knew the equation of getting the answer. I was surprised to hear this question from him and I realised that I did not know how to answer him.

Is model drawing really important if the child knows the number equation and gets the answer of  the  question?  I am clueless about this as most of my K2 children are struggling with model drawing.

Just like what this chapter has stated, there are many ways to understand mathematics. I feel that time needs to be given for children to pick up mathematical concepts. In order to understand it,  it takes persistance and effort by the children. Therefore, I believe in giving time to children to grasp the mathematical concepts because “childhood is a journey,not a race”. However, I feel that some parents do not seem to understand this.