Monday, 8 April 2013

Reflections after 6th session 6/4/2013

Teachers when you are planning lesson, need to ask yourself the questions:-
1. What do I want the students to learn?
2 How do I know?
3.What if they can't get the idea?
4. What id they already can? ==>go for enrichment

Children achieve metacognition 10-11years old. Teacher must be conscious about teaching independence. Teacher must make concisous effort to develop metacognition in children.

Number sense
Communication through journalling
All these factors contribute towards making a child gifted.

Thank you Dr Yeap for sharing your deep passion for Mathematics. We have been enriched and touched by your passion for children.

Reflections after the 5th session 5/4/2013

In this lesson, Dr Yeap introduced the concept of working with nouns in data handling.
12 can be read as 12 ones (working with 1 noun)
12 can be read as 1 ten 2 ones (working with 2 nouns)

If a teacher wants to teach > 10, she also needs to teach in 2 nouns.
1 ten 1 one
1 ten 2 ones
1 ten 3 ones
1 ten 4 ones

Dr Yeap also constantly reminded us to go for enrichment rather than acceleration. That is to enrich their learning rather than going for more.

For counting, children must learn to count with nouns. (e.g. 1 apple, 2 apples, 3 apples)

Theory of Variability

Zolten Dienes found that in teaching of young children, we must be careful when choosing materials. Things that are closer to real things, it is easier for young minds to perceive. For things further away from real things, it is difficult for young minds to perceive.
It is not advisable to give young children identical things to count. Things in real life does not come in that manner. Manipulatives must be of different colours (e.g. orange square, dark orange square)

Young children only need to identify the shape – circle, triangle, rectangle and square.
A rectangle is any quadrilateral with four right angles. A square is a rectangle.
Carl Friedrich Gauss, a German world top 3 Mathematician found the way to look at numbers through patterns.
M, m+1, m+2, m+3

Number sense, visualization and patterns, strong communication and mental cognition all contribute to the method for raising a gifted child.

Reflections after 4th session 4/4/2013

In designing Numeracy experiences, go for the concept first, then Manipulatives later.
According to Jean Piaget, Intelligence is defined as more refined schema and schema creation.

There are 3 ½ of water in a jar. A thirsty crow drink ¾ of it. How much is left ?
3 ½ - ¾
Method 1
3 ½ - ¾ =
7/2 – ¾ =

Method 2
3 ½ - ½ = 3
1 ¼ = ¾
2 + ¾ = 2 ¾

Method 3
3 ½ - ¾
1 ½ - ¾ = ¾
2 + ¾ = 2 ¾

In teaching Geometry to young children, do not teach kite shape.
For 3D shapes, introduce the shapes as rectangular, circular. Do not introduce words sphere, cylinder as developmentally they may not be able to grasp the concept. Taking a concrete item, refer to the 3D shapes as rectangular, circular.


A good manipulative to introduce is a 2D 7 piece mosaic puzzle that is built on isometric grid.

1. Why shape 1 and 2 are the same size?
2. How many shape 2 are in 5?
3. How many 2 and 1 make 3?
4. Compare 7, 2 and 1.

As an educator, we need to be aware of the games children in other cultures are playing. We need to be constantly asking ourselves what is the concept behind and how does this contribute to their thinking. A tangram is a must in every classroom to build visualization in the minds of children. We learn Maths from the culture around us.

Reflections after 3rd session 3/4/2013

Mathematics concept in Nursery Rhyme

Humpty Dumpty
Lessons in this nursery rhyme
  •  Force
  •  Counting
  •  More man than horses (subtraction)
  •  Fractions


The money concept is a measurement concept. If children have insufficient measuring (length, weight) experiences, it is difficult for them to understand it. Children can learn money concept if they are using it. Money is functional Mathematics.
My colleague once told me that children in Singapore will have no concept of how much money. The joy of counting money has been replaced by cashless initiatives (i.e. EZ link card, Debit card, Credit card). This translated into teachers of young children will potentially mean that we need to introduce more activities that involve counting of money in their Dramatic play centre.

Four equal parts

Origami folding papers are important lesson where young children learn if shapes overlap each other. Through this concrete experience of folding, tearing and cutting paper, young children learn concrete experience on equal shapes.
As the children advance in their learning, they are able to visualize if the shapes can be cut, overlap and rearrange to form desired equal parts.
It is important that young children have adequate paper folding experiences as the paper will be used to introduce Fractions. Paper is a good CPA approach for young children to build their understanding on Fractions. Starting them straight on 3D (apples/oranges) experiences will not help them in understanding the concept.

Kindergarteners must have visualization skills. 
To build visual literacy,
  •           Children must have done things using their gross motor skills (e.g. throw and catch) 
  •       When they are older, they handle fine motor skills (E.g. Lego blocks)
  •       Children play with sand, tied things, hold scissors.
  •       Children should be running around a lot and doing art.
  •       They should be going to museums with notebooks.
  •       Children should be exposed to drawing, visualization. (Observation, processing through the hands of the child, visible evidence contributes towards the visualization of the mind)

Reflections after 2nd session 2/4/2013

Observation of a K2 boy

Tim, a K2 child cannot tell the teacher the correct number of eggs in the photo. What information can you provide to Tim’s parents?
The child needs to practice more on:-
  •      Count using concrete materials.
  •          One-to-one correspondence
  •           Rote counting

Young learners must do counting, matching to determine Cardinal numbers.  The teaching of Mathematics to children must follow the CPA approach (concrete, pictorial and abstract) to align with the development of young children, nurturing them in the process of becoming capable thinking adults.

Shaking can experiment

If this is 3, I wonder how much is this?  Teacher shakes the can. In the process continuously refer back to “benchmark” sound. This process gives a reference yardstick for students to guess the subsequent number of paper clips in the can.

This experiment gives an initial lesson on comparison. Richard Skemp (1978) introduced the theory on Relational Understanding where he found that understanding is a measure of the quality and quantity of connections that a new idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding. 

I’ve never thought of using sound to teach the number concept. When teaching number concept, preschool teacher have to engage the senses of the young child. Through this experiment, we are also teaching the young minds to perceive Maths using their listening skills.  On the other hand, introduce the “guess” element that keeps the young minds in suspense. By having this fun element in lessons, children will be engaged in their learning and using their sense of hearing, other than sight, to help them solve this Maths problem. Good experiment to try with my students!

7 + 6 =
This addition equation can be read in 2 ways
  •       Double of something add on 1
  •       Double of something less of 1

Kindergarten Basics
First 6 years of child’s life must learn :-
  •       Language (at least 1 language learnt well)
  •         Concrete experiences
  •         Visualization
  •       Number Sense
  •        Patterns
  •        Social skills  

Friday, 5 April 2013

Reflections after the 1st session 1/4/2013

The professor pointed out that all teachers is to follow the steps below to explain mathematical concept to children.

Teaching is to follow 4 basic steps below:-
1. Modelling
2. Scaffolding
3. Providing opportunity for children to do it
4. Explaining

How does children learn Mathematics?
The answer lie sin the learning theory and research on how people learn. 2 important theories (constructivism and sociocultural theory).

Construtivism is the notion that learners are creators of their own learning (Cognitive schemas). This is the work of Jean Piaget. When children created knowledge, they go through a process of assimilation and accommodation.

Socialcultural  is when learners come together and they learn from one another. The learner moves ideas into his own psychological realm, together with peers, he get to learn a range of knowledge, stretching his knowledge beyond what he can learn himself. With social interaction, the learners get to exchange ideas and learn more as a community.

The Professor also stressed on the importance of looking into the theories from Jerome Bruner (CPA approach - Concrete, Pictorial, Abstract approach)

Different Uses of Numbers
Number is being referred to having the below uses:-
1. Rational number - simply means ratio number.
2.Cardinal number - simply means it is used to count things.
3. Ordinal number - refers to the position / order of something
4. Nominal number - refers to number being used as name / label. (for e.g. Bus no.2,12,33,130, IC number, Handphone number)
5. Measurement number - refers to quantifying a thing. (e.g. teacher to say 1 apple, 2 apples, 3 apples and not simply 1,2,3)

In Early Childhood, it is important that the child masters sorting, one-to-one correspondence and rote-counting. This is the summary for our first session.

Jia You!

Sunday, 31 March 2013

Elementary Mathematics_A Pre-course reading

Elementary Mathematics (a Pre-course reading )

Chapter 1

Reading through some of the standards on teaching Mathematics, I found that some of it is a bit difficult to understand. My next reaction is "Will we have a similar standard in Singapore"? The KCG (Kindergarten Curriculum Guide) does not have enough content to enforce similar standards like in the US. 

Learning Mathematics should start once the baby is born. Mothers should be singing nursery rhymes that has Maths content to their children. It gives a personal touch to the child.

Becoming a teacher of Mathematics is for the teacher to persist, have a positive attitude and always ready for change. Most importantly, ask yourself if you love the children and what do you want to do for children under your care. 

Chapter 2

The learning theory

The importance of having opportunities for children to try out their thoughts using physical materials / manipulatives and to solve the problem through social interaction and reflection.

Children are taking out some unifix cubes from the feely bag. They are to fix and count the cubes. Afterwhich, they are to record in their papers. They then ask their friend next door how many cubes they have god and record down in their papers.

Respect the children and give them time to experiment for themselves. Let them talk to their friends asking them their experiences. 

Relational Knowledge

In designing the teaching, teachers need to plan and design instruction on how to elicit prior knowledge to challenge the students to think critically and creatively. In the process, engaging the students to share their ideas to one another, taking into account their social and cultural background.

Developing Mathematics Proficiency

Should young children develop their Mathematics proficiency at a young age, they need to remember less as they proceed on in school. They could spend their time on other learning. In order for us to reach this goal, the lessons must be carefully crafted and more time to be given to children to construct their knowledge on Maths. If school time is not enough, I think we should ask parents to work with their child and suggest for some bonding time to increase their contact time on Maths.