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Saturday, September 25, 2010
Reflection of the math module
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)
Children trying to solve the puzzle to see the numbers from 1-10( 4year olds)
Geometry
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.
Sunday, September 19, 2010
Chapter-7
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.
Number Concepts
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.
Friday, September 10, 2010
Review of chapter 1 and 2
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.
Math corner
Board game
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.
Math cornerActivity
(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
Board gameCounting, adding,
counting backwards
counting backwards
Pizza game
Counting
Addition game
1. Addition game
(Munch math)
(Munch math)
2. Dice for the game
3. Covering the answer with the counter
4. Who could get all the numbers at first is the winner
Floor game- counting upto 30 in a fun way
Floor game- counting upto 30 in a fun way
Math movie-sorting
Which format should introduce first?
As a teacher, if I am introducing the number34 through concrete (realistic) materials,such as bundles of sticks, I will show them with three bundles of 10 sticks in each bundle and four individual sticks at first. I will encourage them to count, and ask how many tens are there? How many ones are there? Since they can visualise the representations, I will show them that there are three tens and four ones(numbers in tens and ones). Then I will show the place value chart that states that there are 3 tens and 4 ones. Then I will explain to them that three tens is thirty and four ones is four. So it is 30 and 4(expanded notation). So it is together 34(In numerals). Then I will introduce the number word.
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
Tuesday, September 7, 2010
Review of the first lesson(01/09/2010)
Out of the three games that Dr.Yeap introduced, I liked the card games best as it involves the integration of Math and Language. This integration was brought out in a fun and interesting manner. I believe that mathematics has to be taught in a fun and interesting manner such as through games and other activities. As this way, children will remember the various concepts in the long term.Though our group found it challenging at first, to solve the problem, once we understood the strategy behind the game, we were able to arrange the cards from 1-10 as well as from 10-1. When I repeated this activity with my K2 students they were amazed and they said that I was a magician.
The technique of dice game was interesting and unique. Initially, I could not figure out the strategy behind the game. When the teacher explained that the sum of four numbers in one line is fourteen, I realised how easy the problem was. I enjoyed the paper clip game. I tried to win as much as possible by leaving three paperclips to my friend.
The video showed to us was useful. The teacher showed us how he can be a good listener as well as the same time how to facilitate the students' thinking skills to solve a problem.
The whole class was interesting. I understood how learning math can be a fun fill experience.
The technique of dice game was interesting and unique. Initially, I could not figure out the strategy behind the game. When the teacher explained that the sum of four numbers in one line is fourteen, I realised how easy the problem was. I enjoyed the paper clip game. I tried to win as much as possible by leaving three paperclips to my friend.
The video showed to us was useful. The teacher showed us how he can be a good listener as well as the same time how to facilitate the students' thinking skills to solve a problem.
The whole class was interesting. I understood how learning math can be a fun fill experience.
Problem Solving
I think teaching 'through' problem solving is the best approach that allows the students to learn mathematics in the real context. Through this method, students learn mathematics 'through' real contexts, problems, situations, and models. The models allow students to build meaning for the concepts so that they can move to abstract concepts.
We have learnt that problem is defined as any task or activity for which the students have no prescribed rules or methods nor is there a perception by students that there is a specific 'correct' solution method. We also learned that 'problem' must begin where the students are, 'the problamatic aspect of the problem' must be due to the mathematics that the students are to learn and it also requires the justifications and explanations for answers and methods.
Keeping these in mind, our group decided to look for a model that allows the students to build meaning for the concepts so that they can move to the abstract concepts. So we have chosen a sculpture that was in the Art museum which has different shapes on it. Our aim is to introduce a pictograph based on the data collected from the sculpture so that the students can move to abstract concepts. We have focussed only on the different shapes on it. After collecting the data, we decided to create the pictograph as we realised that activities that involve graphing are a good way to connect the children's world with numbers. 'Through' the graph the students are able to analyse and process the data.Through many questions we plan to ask the children, they will be able to solve problems after analysis the graph. Through this activity, I have come to a conclusion that activities involving graphing such as the use of pictographs are a good way for children to learn problem solving skills. 'I strongly believe that teaching should begin with the ideas that children already have, the ideas they will use to create new ones.'
We have learnt that problem is defined as any task or activity for which the students have no prescribed rules or methods nor is there a perception by students that there is a specific 'correct' solution method. We also learned that 'problem' must begin where the students are, 'the problamatic aspect of the problem' must be due to the mathematics that the students are to learn and it also requires the justifications and explanations for answers and methods.
Keeping these in mind, our group decided to look for a model that allows the students to build meaning for the concepts so that they can move to the abstract concepts. So we have chosen a sculpture that was in the Art museum which has different shapes on it. Our aim is to introduce a pictograph based on the data collected from the sculpture so that the students can move to abstract concepts. We have focussed only on the different shapes on it. After collecting the data, we decided to create the pictograph as we realised that activities that involve graphing are a good way to connect the children's world with numbers. 'Through' the graph the students are able to analyse and process the data.Through many questions we plan to ask the children, they will be able to solve problems after analysis the graph. Through this activity, I have come to a conclusion that activities involving graphing such as the use of pictographs are a good way for children to learn problem solving skills. 'I strongly believe that teaching should begin with the ideas that children already have, the ideas they will use to create new ones.'
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| Sculpture |
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