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I have learned that math is an ''excellent learning vehicle for the development and improvement of a person's intellectual competence in logical reasoning, spatial visualisation, analysis and abstract thoughts." I also realised that learning math will give an experience of joy and excitement. I found the different theories taught by Dr. Yeap about Van Hiele's level of thought and Jerome Bruner's representation theories very insightful . Now I can assess my student's level of thought as it is in the level 0 (visualisation), level 1(analysis) etc. Though I am introducing a new concept to my students through concrete materials first( enactive representation) , followed by the pictorial(iconic representation), lastly by abstract (symbolic representation), I did not realise that I have been following the Jerome Bruner's theory until Dr. Yeap explained this. Another idea that I got from this module is that " Knowledge can be learned by learners itself. Information can be procured from others. If you get information and experience together, learners will get knowledge." Now I also want to create an environment in such a way that my students also want to get information and experience together.

When we did the problem solving through environment I realised that incidental learning can take place via environment based task.This module changed my mind set regarding the methods to teach math to young children. Through different activities, games, E-games and links (that have different math activities in it) that the lecturer gave us will definitely help me to provide different interesting activies in my class.

My students are learning the distance concept in a fun way (using non standard measurement) can be seen in the picture.

When we did the problem solving through environment I realised that incidental learning can take place via environment based task.This module changed my mind set regarding the methods to teach math to young children. Through different activities, games, E-games and links (that have different math activities in it) that the lecturer gave us will definitely help me to provide different interesting activies in my class.

My students are learning the distance concept in a fun way (using non standard measurement) can be seen in the picture.

A child is measuring the distance of the aeroplane that she has been launched.(6 year olds)

The class about area, angles and shapes was very interesting. After the quiz when Dr.Yeap started to challenge us to tell our strategy, I thought there was only one way to solve the problem. But when different students came with different solutions, surprised me. This made me realise that as an early childhood educator, I have to give opportunity to my students to think widely and to find their own solutions. Creating different shapes with tangrams was interesting as I usually asks my students to create different shapes with it. But when I started to create square with all the seven pieces took some time to solve it.When the lecturer asked to find the total angle of a pentagon, I use the three triangle method as shown in the figure.

When different students come up with different solutions such as a triangle and rectangle, triangle and trapezium, or with six triangles I realised that all of us are unique and we think differently as same as our own students do in our class.

When different students come up with different solutions such as a triangle and rectangle, triangle and trapezium, or with six triangles I realised that all of us are unique and we think differently as same as our own students do in our class.

Before I started reading, I think that computer is the only technology I will choose. But when I had read through the book, the technology that I liked is the calculator. The chapter is an eye opener for me. As a preschool teacher I seldom use calculators. I think calculators are for secondary students who have to do differentiation, integration, graphings etc. Now I understand that calculator is much more than a device for calculation. It can be used to develop concepts and enhance problem solving and drills, improve attitudes and motivation. The book also states that "count by ones" on the calculator can reinforce students, oral counting, identification of patterns, and can even be used by one child to count thier classmates as they enter into the class room. One quote that caught my eyes was, ' Research results reveal that students who frequently use calculator have better attitudes towardsthe subject of mathematics" (Ellington,2003). So in the future I will also use calculators to reinforce the number concepts to my students.

The activity which I like from the link is Creating, Describing and Analyzing Patterns to recognize relationship and make predictions. Through this E-game children will make patterns,describe the patterns and finally they can extend the patterns. This activity will enhance their critical thinking. I am using this activity with concreate materials as well as soft ware. Our centre is using I- Pal soft ware for children. This programme has theme base math activities in which children can do different math concepts including patterns. They are enjoying doing that.

The activity which I like from the link is Creating, Describing and Analyzing Patterns to recognize relationship and make predictions. Through this E-game children will make patterns,describe the patterns and finally they can extend the patterns. This activity will enhance their critical thinking. I am using this activity with concreate materials as well as soft ware. Our centre is using I- Pal soft ware for children. This programme has theme base math activities in which children can do different math concepts including patterns. They are enjoying doing that.

After I looked through the activities I realised that the activities 8.3 (Fill the chutes) and 8.4 (Find and press) have not been conducted in my class. When I read the activity about "fill the chute" I thought it was a good activity that I can include in my curriculum for four year old children. I usually play board games with children using die, which is similar to 'Snake and ladder' game. Though I am using computer, and old telephones to play 'Find and press game', I did not use calculater to allow the children to do the same game. I think it will get children's attention and definetly in the future I will use this strategy.

The activity 8.6 (Counting on with counters) is a common activity in my class. I usually give different counters to four year olds to count and asks them to give me a particular number of counters.( Less than 10). I will do it as a game. I gave some counters to five children at the same time. Then I will tell a number loudly, they will count and take that number of counters. Whoever gives me the correct number of counters is the winner.

Another activity which is common in my class is activity 8.2 (Find the same amount). I will give two sets of identical cards to two children. When a child show a particular number of cards other child has to show the same number of cards in which number as well as the pictures are shown.

The activity 8.6 (Counting on with counters) is a common activity in my class. I usually give different counters to four year olds to count and asks them to give me a particular number of counters.( Less than 10). I will do it as a game. I gave some counters to five children at the same time. Then I will tell a number loudly, they will count and take that number of counters. Whoever gives me the correct number of counters is the winner.

Another activity which is common in my class is activity 8.2 (Find the same amount). I will give two sets of identical cards to two children. When a child show a particular number of cards other child has to show the same number of cards in which number as well as the pictures are shown.

The main points that stuck in my mind after I had read the first chapter were the three out of six different principles and standards for school mathematics. They are 'teaching', 'learning' and 'technology' principles. I strongly agree with the authors that effective mathematics teaching requires understanding what students know and need to learn. Then as a teacher I can challenge and support them to learn it well. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

Another point that stuck in mind after I have read the chapter is about the five process standards such as 'problem solving', reasoning and proof', 'communication', 'connections', and 'representation'. All these five aspects are important for educators.

For example:

Problem solving standard builds new mathematical knowledge

Reasoning and proof standard develop and evaluate mathematical arguments and proofs

Communication standards organize and consolidate student's mathematical thinking through communication

Connection standards recognize and use connections among mathematicall ideas

Representation standards create and use representations to organize, record and communicate mathematical

ideas.

My first math teacher was my father. He taught me about the cocept of counting, adding, subtracting, sorting and measuring with concrete meterials. The interest to learn mathematics started from those days and I still enjoying doing it. So I believe that as early childhood educators, we have a high influence on young children and so we have to teach mathematics in a fun way so that their interests will be kindled. I also believe that including technologies will help most of the children to develop interest towards learning. One of the example I posted in the site shows how 4year olds are learning sorting using a movie. I shoot this movie with the help of some older children and four year old children. All the children were excited and most of them were able to sort according to three attributes at the same time after I introduce the concept of sorting through this movie.

I agree with the authors about the importance of creating an environment for young children to learn which is mentioned in the chapter two. I also created an interesting environment by occupying my math corner with different math activities that children can do the problems in a fun way. I will also make sure that I will change the activities every two weeks. My math corner and some of the activities in the corner are posted in the site.

I believe in the constructivist theory in which it states that integrated networks are both the product of constructing knowledge and the tools with which additional new knowledge can be constructed. I also agreed with the authors about building new knowledge from prior knowledge. So I will try to provide opprtunities for my students to talk about mathematics, build in opportunities for reflective thought, encourage multiple approaches, treat errors as opportunities for learning, and scaffold a new content.

Another point that stuck in mind after I have read the chapter is about the five process standards such as 'problem solving', reasoning and proof', 'communication', 'connections', and 'representation'. All these five aspects are important for educators.

For example:

Problem solving standard builds new mathematical knowledge

Reasoning and proof standard develop and evaluate mathematical arguments and proofs

Communication standards organize and consolidate student's mathematical thinking through communication

Connection standards recognize and use connections among mathematicall ideas

Representation standards create and use representations to organize, record and communicate mathematical

ideas.

My first math teacher was my father. He taught me about the cocept of counting, adding, subtracting, sorting and measuring with concrete meterials. The interest to learn mathematics started from those days and I still enjoying doing it. So I believe that as early childhood educators, we have a high influence on young children and so we have to teach mathematics in a fun way so that their interests will be kindled. I also believe that including technologies will help most of the children to develop interest towards learning. One of the example I posted in the site shows how 4year olds are learning sorting using a movie. I shoot this movie with the help of some older children and four year old children. All the children were excited and most of them were able to sort according to three attributes at the same time after I introduce the concept of sorting through this movie.

I agree with the authors about the importance of creating an environment for young children to learn which is mentioned in the chapter two. I also created an interesting environment by occupying my math corner with different math activities that children can do the problems in a fun way. I will also make sure that I will change the activities every two weeks. My math corner and some of the activities in the corner are posted in the site.

I believe in the constructivist theory in which it states that integrated networks are both the product of constructing knowledge and the tools with which additional new knowledge can be constructed. I also agreed with the authors about building new knowledge from prior knowledge. So I will try to provide opprtunities for my students to talk about mathematics, build in opportunities for reflective thought, encourage multiple approaches, treat errors as opportunities for learning, and scaffold a new content.

Activity

(Fill in the missing

numbers)

(Fill in the missing

numbers)

Activities in the Math corner

Weighing balance

Pizza- introducing

fraction

Addition games,

Patterning

Pizza game-counting& board games

Pizza- introducing

fraction

Addition games,

Patterning

Pizza game-counting& board games

Counting, adding,

counting backwards

counting backwards

Pizza game

Counting

Addition game

2. Dice for the game

3. Covering the answer with the counter

As a teacher, if I am introducing the number34

Hence my steps will be:

1. 3tens and 4 ones - the numbers in tens and ones

2. 3tens and 4 ones in chart - using place value

3. 30 and 4 - expanded notation

4. 34 - numerals

5. thirty-four - number words

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