Wednesday, September 29, 2010
Geometry
When we were doing the activity on geometry, I was confuse and feeling lost. I could not understand how the answers were derived so I started to ask my classmate who was sitting next to me. When she explained to me and draw out the figure then I start to visualise what people could visualised. After the lesson, I felt that it is important for children to have the visualization ability to 'see things hidden' in a picture.
The textbook mentioned that "Spatial sense includes the ability to mentally visualize objects and spatial relationships-to turn things around in your mind." (Walle, Karp & Bay-Williams, 2009, p.400). Therefore, it is important to provide children with ample opportunity to explore with shape and spatial relationship so that children can develop spatial sense over time.
Pierce Van Hiele Theory has five levels that describes how we think and what types of geometric ideas we think about. The levels are as follows:
1. Level 0 - Visualization
2. Level 1 - Analysis
3. Level 2 - Informal Deduction
4. Level 3 - Deduction
5. Level 5 - Rigor
During lecture in class, it was mentioned that most of the children are between level 0. However, there are children who are at level 1 too. Based on Piaget, constructivism theory, knowledge will be constructed when the learner himself connects it with his experience. The learner need to reflect on the information learnt and communicate it by collaborating. At the end of the lesson, I had a better understanding on the rules and guidelines of geometry and the relationship. I was able to make connection with what I have learnt in primary school as well.
The four content goals for geometry are shapes and properties, transformation, location and visualization. I found visualization a challenging task if there is insufficient spatial sense.
References
Van de Walle, J. (2009). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman
The textbook mentioned that "Spatial sense includes the ability to mentally visualize objects and spatial relationships-to turn things around in your mind." (Walle, Karp & Bay-Williams, 2009, p.400). Therefore, it is important to provide children with ample opportunity to explore with shape and spatial relationship so that children can develop spatial sense over time.
Pierce Van Hiele Theory has five levels that describes how we think and what types of geometric ideas we think about. The levels are as follows:
1. Level 0 - Visualization
2. Level 1 - Analysis
3. Level 2 - Informal Deduction
4. Level 3 - Deduction
5. Level 5 - Rigor
During lecture in class, it was mentioned that most of the children are between level 0. However, there are children who are at level 1 too. Based on Piaget, constructivism theory, knowledge will be constructed when the learner himself connects it with his experience. The learner need to reflect on the information learnt and communicate it by collaborating. At the end of the lesson, I had a better understanding on the rules and guidelines of geometry and the relationship. I was able to make connection with what I have learnt in primary school as well.
The four content goals for geometry are shapes and properties, transformation, location and visualization. I found visualization a challenging task if there is insufficient spatial sense.
References
Van de Walle, J. (2009). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman
Reflect on Practice - Number Sense
Number sense develops gradually as children are given the opportunity to explore numbers, visualizing them in a different contexts and relating them in different ways.
As mentioned in the textbook, "children come to school with many ideas about number. These ideas should be built upon as we work with children and help them develop new relationships." (Walle, Karp & Bay-Williams, 2009, p.125).
Teachers are encouraged to use the following recommendations to enhance children's learning in mathematics:
Common practice that are already in preschool are as follows:
Reference
Van de Walle, J. (2009). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman
As mentioned in the textbook, "children come to school with many ideas about number. These ideas should be built upon as we work with children and help them develop new relationships." (Walle, Karp & Bay-Williams, 2009, p.125).
Teachers are encouraged to use the following recommendations to enhance children's learning in mathematics:
- Enhance children's natural interest in mathematics and their disposition to use it to make sense o their physical and social worlds
- Build on children's experience and knowledge
- Base mathematics curriculum and teaching practices on children's cognitive, linguistics, physical, and social-emotional development
- Use curriculum and practices to strengthen children's problem solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas
- Ensure curriculum is coherent ans compatible with known relationships and sequences of important of mathematical ideas
- Provide for children's deep and sustained interaction with key mathematical keys
- Integrate mathematics with other activities and mathematics with activities
- Provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest
- Introduce mathematical concepts, methods, and language, through a range of appropriate experiences and teaching strategies
- Support children's learning by thoughtfully and continually assessing all children's mathematical knowledge, skills, and strategies
Common practice that are already in preschool are as follows:
- Relationships of more, less, and same
- Early counting
- Numeral writing and recognition
- Counting on and counting back
- Estimation and measurement
- Data collection and analysis
- Doubles and near doubles
- Anchoring numbers to 5 and 10
Reference
Van de Walle, J. (2009). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman
Final Reflection
Before the start of the course, I was wondering what will be taught in this module. I have some fear and reservations about attending this module as mathematics was my weakest subject. Although I do not hate or detest mathematics but I do not have the confident that I can do well in this module.
However, I really enjoyed the lectures and I have fun too. I had never imagined that mathematics can be taught in such fun, creative and interactive manner. I wish that I could be given the opportunity to learn mathematics in such fun, creative and interesting manner during my childhood education.
For now, I really want to make a different in children's learning in mathematics. I hope to assist children to lay the proper foundations in mathematics before they transits to primary school and give them the right attitude towards learning mathematics.
There are two theories that I have learnt during lectures that have left a great impact and impression on me. The first one is Polya's Model - Let's Solve it which involves the following process:
However, I really enjoyed the lectures and I have fun too. I had never imagined that mathematics can be taught in such fun, creative and interactive manner. I wish that I could be given the opportunity to learn mathematics in such fun, creative and interesting manner during my childhood education.
For now, I really want to make a different in children's learning in mathematics. I hope to assist children to lay the proper foundations in mathematics before they transits to primary school and give them the right attitude towards learning mathematics.
There are two theories that I have learnt during lectures that have left a great impact and impression on me. The first one is Polya's Model - Let's Solve it which involves the following process:
- Understanding the problem
- Devising a plan
- Carrying out the plan
- Looking back
- Concrete materials
- Pictorial
- Abstract
Sequencing Learning Task for Place Value
According to Jerome Bruner's theory children learnt best through CPA approach. The CPA approach is as follows:
1) C-Concrete materials
2) P- Pictorial
3) A- Abstract
Therefore, I would sequence the place value task as follows:
1) Place Value Chart
The place value chart should be the next step to be introduced or shown to children after the introduction of 3 tens 4 ones done through concrete materials. By doing so, children will be able to understand the place value of 3 tens 4 ones better as they have been introduced to it earlier through concrete materials.
2) Tens and ones notation
Children have seen from the place value chart that 3 is in the tens position and 4 in the ones position from the earlier introduction. Therefore, introducing the tens and ones notation now will further enhance their understanding in place value.
3) Numbers in numerals
Now we can introduce the numbers in numerals to children as they can see that 30 + 4 means 34.
4) Expanded notation
At this stage, children will have a better understanding that 34 is make up of 3 tens 4 ones. So now is a good time to reinforce children's learning and check their understanding on the concept of the place value.
5) Numbers in words
The numbers in words should be introduced to the children at the last stage after they have understand the concept of numerals.
1) C-Concrete materials
2) P- Pictorial
3) A- Abstract
Therefore, I would sequence the place value task as follows:
1) Place Value Chart
The place value chart should be the next step to be introduced or shown to children after the introduction of 3 tens 4 ones done through concrete materials. By doing so, children will be able to understand the place value of 3 tens 4 ones better as they have been introduced to it earlier through concrete materials.
2) Tens and ones notation
Children have seen from the place value chart that 3 is in the tens position and 4 in the ones position from the earlier introduction. Therefore, introducing the tens and ones notation now will further enhance their understanding in place value.
3) Numbers in numerals
Now we can introduce the numbers in numerals to children as they can see that 30 + 4 means 34.
4) Expanded notation
At this stage, children will have a better understanding that 34 is make up of 3 tens 4 ones. So now is a good time to reinforce children's learning and check their understanding on the concept of the place value.
5) Numbers in words
The numbers in words should be introduced to the children at the last stage after they have understand the concept of numerals.
Problem Solving - Environment Based Task
As mentioned in the textbook, children are learning mathematics by doing mathematics (Walle, Karp & Bay-Williams, 2009, p.33). The teaching must begin with the prior knowledge that children already have so that they can create new knowledge as they build on their existing knowledge. When children are given a problem to solve, as teachers we should encourage them to put on their 'thinking cap' and use their ideas to solve the problem. Personally, I feel that teachers can and should use the THINK framework as this framework supports and fosters the metacognition of children.
When we were out looking and observing the environment, we already had in mind to teach addition skills. When we saw the numbers from the different building, bus-stop, signage and a stretch of metal gate make up of squares, we decided to use the tic-tac-toe idea to introduce and teach addition skills with number bond concept.
We had fun as we tried out the game ourselves. We were trying to outwit one another to be the winner. As we were playing the game ourselves, we were also exploring the possibility of teaching subtraction skills. However, I think we can use this game to teach divison and multiplication skills for the lower primary students.
In fact, using George Polya's four step problem solving process to help and guide children to solve their problem will improve children's ability to solve problems.
The four step problem solving process is as follows:
1. Understanding the problem
2. Devising a plan
3. Carrying out the plan
4. Looking back
When we were out looking and observing the environment, we already had in mind to teach addition skills. When we saw the numbers from the different building, bus-stop, signage and a stretch of metal gate make up of squares, we decided to use the tic-tac-toe idea to introduce and teach addition skills with number bond concept.
We had fun as we tried out the game ourselves. We were trying to outwit one another to be the winner. As we were playing the game ourselves, we were also exploring the possibility of teaching subtraction skills. However, I think we can use this game to teach divison and multiplication skills for the lower primary students.
After going through the lectures, I believed and supports that teaching mathematics should be done in a fun, creative, interesting and interactive way that starts from where the children are. At the same time, teaching children to use problem solving strategies like guess and check and look for a pattern to solve the problem is also important.
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