Applying the CPA approach

Miss Peggy Foo rounded up this module beautifully with the CPA approach that was repeatedly brought up. 

For example, during the Paper Art activity, she introduced to us the “3 What’s”.

1. Basic level: What do you see by using visual to observe and describe. 

2. Higher level of inference: What do you think of the relationship between objects and the ability to reason.

3. Highest level of inference: What do you wonder? The level of inferring increases and builds on my prior knowledge to relate.  Is that Skemp’s theory on relational understanding I wonder…

Lastly, it is important to have differentiated instructions to cater to all children rather than meeting the 60% needs of the bell curve. Instructions can be differentiated by content, by process and by product. 

The double Aces (Art and Angles)

Neither Art nor Angles appeal to me. 

However, the walk through the museum had definitely amazed me lots. I was there for a full 1.5hours before rushing back to class. Back in class, I was introduced to a Greg tang math website which demonstrated how to incorporate art with math lesson. Definitely, in line with the MOE’s move towards being visually literate and to appreciate art. 

Through positive learning experiences in art, students develop visual literacy which enables them to observe and perceive the world with increased awareness and aesthetic sensitivity.  – MOE 

In the parallelogram and isosceles triangle problem, I struggled with it but somehow came out with the correct answer. A correct answer to a problem does not mean anything unless you are able to explain and prove it by showing it. I was able to get the correct answer to the problem yet confused self and was not able to explain my working steps out. 

Lastly, to reiterate, children learn mathematics through;

1. Visualization

2. Looking for Patterns

3. Number Sense

4. Metacognition

5. Communication

It is time to not teach the way we were taught the last time and be updated with the MOE’s pentagon model.  We need to move forward in developing our young learner with the 5 competencies to problem solve not limited by constraints. 



According to Wikipedia, a geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeterarea and the characteristics of triangles and other polygons.


It is a great concrete and open-ended material that young children below the elementary level to calculate area, can learn about shapes, symmetry, array, counting, patterning, rotation and much more.

It made me relate back to the use of Tangram and wondered whether this would be great to ask children, “I wonder how many shapes you can make”, “How many triangles can you see?”, “How many shapes can you make with only a dot inside?”.

As I do not have a geoboard in school, I actually start to make one on my own! 🙂



I wondered aloud why Dr. Yeap was not my Math teacher in my younger days. Perhaps then the fear and dread for Math wouldn’t be what it is like today. I memorized formulas after formulas and eventually mixing up them, followed procedures and did a lot of tedious calculation.

Today, I re-learned about fractions and the importance of a right language used. In fraction, naming of it is very important where it is, “how many parts” in a whole (e.g. 2 thirds rather than 2 over/upon three). Children need to understand that the numerator is used to add, subtract, multiply or for division and the denominator is simply a name or noun.

During the lesson, I was able to understand better, “why children cannot count” as they;

1. Do not possess one-to-one correspondence

2. Are unable to recite in correct sequence

3. Cannot classify (e.g. Count the minions but instead count the number of eyes).

4. Does not understand that the last number uttered represent the total in a set.

This immediately made me understand an encounter with a child in class who was not able to tell me the number of Unifix cubes placed in front of her. It is also highly important to place a unit of an item after a number as a number by itself is useless! (e.g. 1 apples, 3 oranges)

Lastly, while trying to develop a concept using the same objects, the key is in variation.

Learning Whole Number using Ten Frames

The ten frames were introduced today in class and this is the first time I have heard about it and how it have been amazingly used to teach young children about whole numbers.

Benefits that I have learnt using ten frames for children at the stage of learning numbers were;

  1. Concrete – in manipulating one concrete material (the bean) and making ten literally by placing one bean in one frame (one-to-one correspondence)
  2. Visual – children are able to keep track of counting and see that a full ten frame makes 10 and anything less than that is less than 10. Thus cultivating place value (1 in relation to 10).
  3. Arranging and rearranging of the concrete materials will not change the number (quantity) and thus build up children’s number conservation.
  4. As the activity moves on, children can also spot number bonds readily within the ten frames.


Figure 1: Getting children to spot “how many more” to make 10. 



Figure 2: Children can eventually move on to pictorial and making number bonds. 


Concrete, Pictorial, Abstract

Dr. Yeap Ban Har explains the principles of the Concrete Pictorial Abstract approach used in Singapore Maths textbooks. This is an excerpt of a Maths No Problem seminar to an audience of teachers in London. The event was held at Ark Schools headquarters in June 2011.