On the last day of class, I came across Du Four's theory of Professional Learning Community and the factors to consider when planning a lesson plan. As a teacher, it is essential for me to know the learning goal of every lesson, to assess each child and the steps that I can take to help the child when he/she can reach the goal or cannot reach the goal.

For a child who is clueless in their learning, the peers play an important part. It is important not to isolate the child but to create the opportunity for the child to see his/her friends modelling in their learning. This child nees to be stimulated to enable further brain development.

I would have to identify the children in my class who are the average learners, struggling learners and advance learners.

I am reminded of how I can assist children in their learning through modelling, scaffolding and allowing children to do things independently. As teachers, we need to cater to the needs of each child in our classroom.

## Tuesday, 9 April 2013

### Reflection - 6 April 2013

Today we learnt about graphing. Graphing helps us to collate, group, present and analyze data.

To make graphing more meaningful for children, we need to reflect real things and get them personally involved. I have come to realise that the objectives on doing graphs should be focused on analysis and communication rather than the technique. (pg 441).

In the graph that we did in class, we collated information of our various ages. We created a picture graph, using tiles with a range of ages, made up of the following:

a) between the ages of 20 -29 = 14 students

b) between the ages of 30-39 = 10 students

c) between the ages of 40-49 = 16 students

d) between the ages of 50-59 = 5 students

Here I learnt that continuous data is converted to discreet data. An example of this is the range of the ages of people.

The limitation in deriving this kind of information is that although a majority of us fall under the 40-49 age group, we could not tell for certain which was the average age amongst us and which is the exact number of people for each age.

To make graphing more meaningful for children, we need to reflect real things and get them personally involved. I have come to realise that the objectives on doing graphs should be focused on analysis and communication rather than the technique. (pg 441).

In the graph that we did in class, we collated information of our various ages. We created a picture graph, using tiles with a range of ages, made up of the following:

a) between the ages of 20 -29 = 14 students

b) between the ages of 30-39 = 10 students

c) between the ages of 40-49 = 16 students

d) between the ages of 50-59 = 5 students

Here I learnt that continuous data is converted to discreet data. An example of this is the range of the ages of people.

The limitation in deriving this kind of information is that although a majority of us fall under the 40-49 age group, we could not tell for certain which was the average age amongst us and which is the exact number of people for each age.

## Friday, 5 April 2013

### Reflection _ 5 apr 2013

As teachers, we are continually reflecting on our learning and teaching by assimilating and accomodating new information ourselves. We retrieve the existing information stored in the filing cabinet of our mind,make the decision of putting away incorrect perceptions taught to us when we were students, after getting clarity in understanding in the principals and ideas behind formulas and seeing things in a bigger perspective.

I am beginning to see maths as observing patterns, generalising these patterns into mathematical expressions to cause a deeper thinking through the initial stage of visualization.

I appreciate the use of geoboards and dots in helping us to make sense of abstract concepts through the exploration of shapes and their properties.

I am beginning to see maths as observing patterns, generalising these patterns into mathematical expressions to cause a deeper thinking through the initial stage of visualization.

I appreciate the use of geoboards and dots in helping us to make sense of abstract concepts through the exploration of shapes and their properties.

## Thursday, 4 April 2013

### Reflection for 4 April 2013

As a teacher, I have to provide experiences for young children to be involved in problem solving. They need to have sufficient schema to enable them to build on their prior knowledge, to accomodate and assimilate information in their learning process.

I have discovered van's Hiele theory of geometric thought which is made up of 5 levels:

1) Level 0 -visualization

2) Level 1 - analysis

3) Level 2 - informal deduction

4) Level 3 - deduction

5) Level 4 - rigor

At the same time, it is important that I need to teach at the student's level of thought, encouraging them to move on to the next level and adapting activities accordingly.

I have discovered van's Hiele theory of geometric thought which is made up of 5 levels:

1) Level 0 -visualization

2) Level 1 - analysis

3) Level 2 - informal deduction

4) Level 3 - deduction

5) Level 4 - rigor

At the same time, it is important that I need to teach at the student's level of thought, encouraging them to move on to the next level and adapting activities accordingly.

### Make up work for absentees - 3 April 2013

Most fundamental idea about fractions

1) Fractions show the relationship between the part and the whole.

2)Sharing tasks are beginning steps to development of fractions.

3)Help students to use the words halves, thirds, fourths, fifths, whole, one whole or one.

How to teach equivalent fractions?

We can use the following area models in the teaching of equivalent fractions:

a) Filling in regions with fraction pieces

b) Grid paper

c) Paper folding

d) Dot paper

Quiz 1

12-4

1)Mary had 12 balloons. She gave away 4 balloons. How many balloons did she have left after giving away the 4 balloons?

2) Ahmad's father has 12 mangoes in his shop. Four mangoes were sold. How many mangoes were not sold?

12:4

1) There are altogether 12 oranges. Mrs Lim has to pack them equally into 4 boxes. How many oranges will there be in each box?

2) Share 12 toys among 4 children. How many toys will each child receive?

Ways to find value of 12-7

1) Count down-Using a number line, drawing the arrow backwards from 12 to 7, count the number of spaces.

2) Set up a stack of 12 cubes. On another set, stack up 7 cubes. Ask the question " how many more cubes do we need to match the 12 cubes?"

3) Draw 12 chairs. Cross out 7 of them. How may chairs are left not crossed out.

1) Fractions show the relationship between the part and the whole.

2)Sharing tasks are beginning steps to development of fractions.

3)Help students to use the words halves, thirds, fourths, fifths, whole, one whole or one.

How to teach equivalent fractions?

We can use the following area models in the teaching of equivalent fractions:

a) Filling in regions with fraction pieces

b) Grid paper

c) Paper folding

d) Dot paper

Quiz 1

12-4

1)Mary had 12 balloons. She gave away 4 balloons. How many balloons did she have left after giving away the 4 balloons?

2) Ahmad's father has 12 mangoes in his shop. Four mangoes were sold. How many mangoes were not sold?

12:4

1) There are altogether 12 oranges. Mrs Lim has to pack them equally into 4 boxes. How many oranges will there be in each box?

2) Share 12 toys among 4 children. How many toys will each child receive?

Ways to find value of 12-7

1) Count down-Using a number line, drawing the arrow backwards from 12 to 7, count the number of spaces.

2) Set up a stack of 12 cubes. On another set, stack up 7 cubes. Ask the question " how many more cubes do we need to match the 12 cubes?"

3) Draw 12 chairs. Cross out 7 of them. How may chairs are left not crossed out.

## Tuesday, 2 April 2013

I have discovered the use of 10 frames. They help young children to have good number sense. At the same time, children are encouraged to count in 10s rather than in 1s. There are 3 different ways in doing addition - counting on, counting all, and moving counters between 2 frames to make 10. The concept of number bonds is also reflected in the use of 10 frames.

We can encourage a higher level of thinking for the advance learners in our classrooms. Getting them to think of ways of doing something in other ways encourages their creativity.

In our lesson planning, teachers would have to carefully think through of what we use- be it the kind of concrete experiences or the terms , as well consider what is the teaching goal- the concept to be learnt.

We can encourage a higher level of thinking for the advance learners in our classrooms. Getting them to think of ways of doing something in other ways encourages their creativity.

In our lesson planning, teachers would have to carefully think through of what we use- be it the kind of concrete experiences or the terms , as well consider what is the teaching goal- the concept to be learnt.

### Reflection - 1 April 2013

Cute numbers is a new concept for me. As I googled the term, I discovered that 4 and 10 are cute numbers. The use of diagram help me to understand the concept better.

There is a large square divided into 4 quarters. Two of these quarters are subdivided into eight smaller squares. These 8 smaller squares together with the last two bigger quadrants make up 10 squares.

Richard Skemp (1978)'s theory on the continuum from relational understanding to instrumental is also new to me. Children need to understand concepts, conventions and procedures.

There is a large square divided into 4 quarters. Two of these quarters are subdivided into eight smaller squares. These 8 smaller squares together with the last two bigger quadrants make up 10 squares.

Richard Skemp (1978)'s theory on the continuum from relational understanding to instrumental is also new to me. Children need to understand concepts, conventions and procedures.

## Sunday, 31 March 2013

### reflections on chap 1 and 2

**Reflection on Chapter 1 and 2**

My own personal experience with the learning of Maths in primary school had been quite unpleasant – low grades in red marks was a consistent feature in my report card. My interest in Maths plummeted as I could not grasp the concepts which seem to be difficult. I struggled with problem solving and algebra. The turning point in my life was when I was in lower secondary. I had a very good Maths teacher, Mrs Wong who helped me see Maths in a new light. She helped me make connections between the mathematical concepts and daily life and that Maths can be fun! I can now understand how important it is to have a good foundation in Maths.

At the same time, I need to be familiar with the documents that influence state policy and teacher practice and curriculum guidelines to stay relevant in my profession. I believe that as a teacher of Maths, I must also know the learning continuum for Maths and the focus at each level of a child’s learning. Making connections, an integral part of learning, the linking of one idea to another helps children to remain focused in their learning. Each concept builds on another – pieces of a jigsaw equally important for the whole picture to be in place. My familiarity with the Common Core standards for Maths and the Curriculum Framework is essential in charting the progress of children in their understanding of Maths. Reading such material with understanding of how these pieces of information fit together to form a bigger picture of things is crucial.

I believe that children must be given the opportunity and time to explore Maths, to identify patterns in their learning environment and solve problems. Experiential learning and personal reflection is an integral part of building up of Maths concepts. Letting children to struggle through their problems will help them to reflect what they know and how they can apply what they know. Helping children not to give up easily and to persevere can be unnerving. Initially I found this to be quite a challenge as my first instinct would be to prompt the correct answer to the children. I have had to hold back, give the children time to reflect and think through. I would then step in by asking questions, to help children make connections with what they know-drawing from their earlier experiences. When I encourage children to make predictions, the children are involved in a higher level of thinking.

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