CPA Approach
This approach was highlighted & largely emphasized over the whole week. It is important that teachers first teach from using concrete, to pictorial, then to abstract concepts.
On a personal note, I have observed some of these pitfalls to commercial resources & easy access to the Internet in my own teachings & some of my fellow teachers'.
A previous example that I've used before was when I showed a child a cartoon picture of a cow & he told me that it was a cow. So I asked him, how many legs does the cow has? He looked at the picture and told me that the cow has 2 legs. I remembered I was about to correct him until I realised that it was because the picture that I showed him was only a side view of a cow. And it was not even a picture of a real cow.
As I recalled this conversation between the child & I, it set me thinking about how we need to teach using the CPA approach. As much as possible, teachers need to make children's learning as real as possible. I would not want another child to tell me a cow has 2 legs or if I show another toy cow figurine & says that the other cow has 4 legs. And then it becomes confusing because then many cows have many different number of legs!
Theory of Variability
The choice of materials used for teaching makes a difference when we teach young children. Similarly to the CPA approach, we should know when to include variables that are different for the children's level of understanding. This is so that we do not confuse them when teaching various concepts.
Lesson Planning
Dr. Yeap led us to questions to think about when planning lessons for our students . I particularly like the question:
"What do I want the students to learn?"
Because many a time, teachers are more concerned about what they want to teach, rather than what they want children to learn. When that happens, the focal point becomes the lesson, not the children.
Another key part to lesson planning is also ensuring that there is a space for every different learner to learn. This does not just make a teacher more effective in her teaching but also playing a significant role in the building blocks of the children's learning journey.
Friday, 5 April 2013
Find the pattern. Solve the mystery.
1. Joining the dots.
As we worked on using a familiar lesson of the "Geo-Board", it was challenging to work around forming only a 4-dot polygon & expanding our minds to create many different types of polygons. I felt that because we are often confined to the familiar & commonly taught shapes, it took a while to get started. I think this is what Dr. Yeap wants to share with us; how do we challenge the young minds to think out of the box & be creative about the way they learn.
As we moved on to understanding the area of the polygons, the learning was brought to another level when we began shifting around to find out which polygon has the same area or how many times the same area of another polygon. Just like the lessons learnt over the last few days, there are different ways of explaining & justifying how each solution was derived. Again, I am convinced that we should always look into the process of thinking & finding a solution, rather than insisting that the children get the solution through the same method.
Note to self: Ask more thought-provoking questions to stimulate learning. Path the way to the concept, not provide the solution.
2. Patterns & Algebra
As we worked on using a familiar lesson of the "Geo-Board", it was challenging to work around forming only a 4-dot polygon & expanding our minds to create many different types of polygons. I felt that because we are often confined to the familiar & commonly taught shapes, it took a while to get started. I think this is what Dr. Yeap wants to share with us; how do we challenge the young minds to think out of the box & be creative about the way they learn.
As we moved on to understanding the area of the polygons, the learning was brought to another level when we began shifting around to find out which polygon has the same area or how many times the same area of another polygon. Just like the lessons learnt over the last few days, there are different ways of explaining & justifying how each solution was derived. Again, I am convinced that we should always look into the process of thinking & finding a solution, rather than insisting that the children get the solution through the same method.
Note to self: Ask more thought-provoking questions to stimulate learning. Path the way to the concept, not provide the solution.
2. Patterns & Algebra
I enjoyed this activity today. As we moved along to find the different possible ways of ensuring numbers in the boxes for both directions add up equally, Dr. Yeap drew the example to the use of algebra in this problem.
What I really like was how we were motivated to solve the "mystery" on our own, without being "bugged" or "told" exactly how/ what to do. It was more like we wanted to keep finding out & working out for more solutions to the same problem. This made me appreciate mathematics better now. And because it was intrinsic to think & learn, I definitely enjoyed the process a lot more.
I believe this is what the new MOE model of "Teach less, Learn more" is all about. Then if that is so, it is crucial to begin this whole model right in the young lives we work with. Then they will not learn the way most of their teachers were taught when they went to school, but rather a whole new idea of learning mathematics in this era.
Thursday, 4 April 2013
One Problem. Different Solutions.
As we learn to help children construct their knowledge, we need to provide the exposure for children to different types of ways of concepts. This example was shown through addition, just as a part-whole & before-after. This is so that children can be provided the opportunities to stimulate their ideas & thinking skills.
Honestly, I've never thought or perceive addition or subtraction in this way. It made me ponder over such concepts & reflect upon how I have been teaching addition to my students & even when I'm helping my younger cousins in their school work. Mathematics is no more about doing the right method nor getting the right answer. It is about working out the problem to your understanding & justifying your answers. I am beginning to appreciate that there can be many methods in solving the same problem. Teachers need to teach in a less rigid & more creative way to make mathematical concepts meaningful :)
One other learning for tonight is to use of fractions in our daily lives & routines. Sometimes children do not see fractions as fractions.
A question I'm seeking in my teachings is "How do I introduce the concept of fractions to the children I teach?"
Fractions seem complicated to me & sometimes I find it challenging to explain fractions to children. But after yesterday's & tonight's lessons, it's like a renewed perspective to look at the denominator as a noun & not something that is variable, unlike the numerator. I am now better able to explain fractions & have a clearer picture what NOT to say or which word to avoid using when teaching mathematical concepts. It is less confusing when we understand that numerators are actually whole numbers when doing fractions.
When teaching becomes less rigid, there are less no boundaries to children's learning. And we should never limit the learning of these young developing minds. Let's adopt the "one problem, different solutions" as much as possible :)
When teaching becomes less rigid, there are less no boundaries to children's learning. And we should never limit the learning of these young developing minds. Let's adopt the "one problem, different solutions" as much as possible :)
Wednesday, 3 April 2013
Jerome Bruner. Three Modes of Learning.
Jerome Bruner proposed three modes of representation:
* Enactive representation (action-based)
* Iconic representation (image-based)
* Symbolic representation (language-based)
(taken from http://www.simplypsychology.org/)
* Iconic representation (image-based)
* Symbolic representation (language-based)
(taken from http://www.simplypsychology.org/)
This was the key learning for me tonight. Although it was funny how each time Dr. Yeap brought out a question, he would say, "How do we solve this problem? What can we do? Ask Jerome Bruner!" Indeed it is through meaningful concrete learning through actions that will first help to build the knowledge of the children we work with.
Some of the children I work with do not have sufficient exposure to concrete learning and experiences such that they may fall behind in some areas. Drawing an analogy to what Dr. Yeap shared about the skills required for learning, some of these children fall back on their physical muscular development and eye-hand coordination. These skills include using the scissors, tearing, bilateral hand movements, visual perception and a few others. There is a need for children to learn experientially. These skills are crucial and fundamental. We should encourage more outdoor play and daily adaptive skills in these young lives so that they are provided with opportunities for a good start. I made a mental note to teach starting from choosing the appropriate concrete activities.
The other takeaway I have tonight is the teaching of fractions. Even though I do not need to teach fractions in the syllabus, it can still be applicable and appropriate for children to pick up some prior knowledge. An equation I learnt tonight can be put simply into this:
It is good for preschool teachers to know the primary school syllabus. But it does not mean for us to teach the syllabus. It simply means preschool teachers should teach to PREPARE children for the syllabus.
So we do not just need to know our kindergarten syllabus, but also the primary school syllabus as well. It takes more proactive learning and doing on our part if we want the best for our students. this:
It is good for preschool teachers to know the primary school syllabus. But it does not mean for us to teach the syllabus. It simply means preschool teachers should teach to PREPARE children for the syllabus.
So we do not just need to know our kindergarten syllabus, but also the primary school syllabus as well. It takes more proactive learning and doing on our part if we want the best for our students.
It is little wonder why the preschool curriculum talks so much about learning through PLAY.
Because with kids,
WORK IS PLAY & PLAY IS WORK! :)
Because with kids,
WORK IS PLAY & PLAY IS WORK! :)
Tuesday, 2 April 2013
The Use of Language
Today's lesson covered largely on the use of language and whole numbers. The use of language drew me to much thinking and learning tonight. I used to struggle a lot with problem sums, or story sums in primary school days. I often thought to myself if it's the teachers' way of tricking us into scoring less for our math tests or examinations. But as Dr. Yeap explained and elaborated more about the use of language and how it is incorporated into mathematical thinking, I realized that it is indeed not as easy as it seems.
In primary schools, some children have difficulties adjusting because so much language is incorporated into the learning. And when children have language difficulties, they struggle with mathematics too. Today I learnt about the importance of using the right terms and words to create an addition story.
Story 1:
John has 6 marbles. Johnny has 8 marbles. How many marbles do they have altogether?
Story 2:
Mary bought 6 marbles. May bought 8 marbles. How many marbles did they buy altogether?
Some personal questions that I pondered over and pointers I considered:
* Do "has" and "buy" come with any prior knowledge or assumptions?
* Is there a a difference in meaning if I use either word?
* What implications do I have when I use "has" or when I use "bought"
The use of language really made me ponder because there is so much weight in the use of words when we teach young children. This links up to the second key learning I took back tonight. It is to rethink the practices and conventions used in teaching kindergarteners. Sometimes children pick up conventions from other platforms such as peers, adults and learning programs. It is definitely crucial for us, as early childhood educators to ensure that children pick up the right conventions and we need to first make sure we know the appropriate conventions used in our syllabus so that we can model for the children we teach.
In primary schools, some children have difficulties adjusting because so much language is incorporated into the learning. And when children have language difficulties, they struggle with mathematics too. Today I learnt about the importance of using the right terms and words to create an addition story.
Story 1:
John has 6 marbles. Johnny has 8 marbles. How many marbles do they have altogether?
Story 2:
Mary bought 6 marbles. May bought 8 marbles. How many marbles did they buy altogether?
Some personal questions that I pondered over and pointers I considered:
* Do "has" and "buy" come with any prior knowledge or assumptions?
* Is there a a difference in meaning if I use either word?
* What implications do I have when I use "has" or when I use "bought"
The use of language really made me ponder because there is so much weight in the use of words when we teach young children. This links up to the second key learning I took back tonight. It is to rethink the practices and conventions used in teaching kindergarteners. Sometimes children pick up conventions from other platforms such as peers, adults and learning programs. It is definitely crucial for us, as early childhood educators to ensure that children pick up the right conventions and we need to first make sure we know the appropriate conventions used in our syllabus so that we can model for the children we teach.
Monday, 1 April 2013
Concrete is where the ground is
WOW. I would definitely enjoy mathematics again after attending the first lesson tonight. Although it was rather overwhelming with some of the mathematical terms, it was interesting to rack our heads in search for patterns & formulas.
Dr. Yeap brought out a teaching concept when teaching children new ideas. This intrigued me as it became more obvious to me as I thought about the way I teach.
To teach ideas and concepts in this order:
1. Model
2. Scaffold
3. Provide
4. Explanation
Like many teachers, I often just stick to using modeling and scaffolding. In the regular classroom that I was taught in, I was never provided with much explanation in the use of certain ideas and concepts. Which I subconsciously did not see the need to explain much to the students that I teach. As I thought about it, I think I would like to give it a try to work on a little bit of explanation when teaching mathematical concept and link it with some form of daily usage so that my students can learn meaningfully too.
With this, Dr. Yeap also brought out Bruner's Theory of teaching using concrete materials, to visuals and then to more abstract ones. He demonstrated and gave us concrete materials such as cards to solve problems.
Personally, I find it a struggle to keep using concrete materials. This is because it is always easier to prepare visuals such as searching online, printing and laminating. Whereas if I were to have more concrete materials, I would require plenty of storage space and need to know where exactly to source for such concrete materials. At times, concrete learning may also cost more. However, I definitely agree that concrete learning must take place especially in young children's learning. Only after the children grasp the ideas, teachers should then move on to more abstract teaching.
As we move on to tackle more head-racking problems in the next few days, I am making it a point to create opportunities for more experiential learning with concrete materials so that my students can learn meaningfully :)
Dr. Yeap brought out a teaching concept when teaching children new ideas. This intrigued me as it became more obvious to me as I thought about the way I teach.
To teach ideas and concepts in this order:
1. Model
2. Scaffold
3. Provide
4. Explanation
Like many teachers, I often just stick to using modeling and scaffolding. In the regular classroom that I was taught in, I was never provided with much explanation in the use of certain ideas and concepts. Which I subconsciously did not see the need to explain much to the students that I teach. As I thought about it, I think I would like to give it a try to work on a little bit of explanation when teaching mathematical concept and link it with some form of daily usage so that my students can learn meaningfully too.
With this, Dr. Yeap also brought out Bruner's Theory of teaching using concrete materials, to visuals and then to more abstract ones. He demonstrated and gave us concrete materials such as cards to solve problems.
Personally, I find it a struggle to keep using concrete materials. This is because it is always easier to prepare visuals such as searching online, printing and laminating. Whereas if I were to have more concrete materials, I would require plenty of storage space and need to know where exactly to source for such concrete materials. At times, concrete learning may also cost more. However, I definitely agree that concrete learning must take place especially in young children's learning. Only after the children grasp the ideas, teachers should then move on to more abstract teaching.
As we move on to tackle more head-racking problems in the next few days, I am making it a point to create opportunities for more experiential learning with concrete materials so that my students can learn meaningfully :)
Build the ground, lay the foundation.
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