Tuesday, September 28, 2010
Monday, September 27, 2010
Reflection
During the first lesson, I learned that "Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence in logical reasoning, spatial visualisation, analysis and abstract thought."
That statement seemed very vague then.
Now, I have a better understanding of what the statement means.
Throughout the 24 hours of lesson, some old friends of Dr. Yeap and their theories were introduced to the class:
Often, teachers teach the way they were taught, by memorizing formulas and equations. Even though I am aware that children learn best through concrete representation and I do use manipulatives during math lessons, I do not know that it is also important to bring variations into the picture.
By going through the environmental task, dice trick, geometry solving, sudoku with cubes (to name a few), I finally understood what perceptual variability and mathematical variability is all about, and how I can bring it into my classroom. Who would have thought that dice can be used to play magic tricks and teach addition? Or that a theorem can be obtained by observing the pattern and relation between the dots that a shape is drawn on and dots that are found in the shape? Or incidental learning can take place anywhere, everywhere?
I remember there was a question on solving fractions ( ¾ ÷ ½ ) where I changed the '÷' into a '×' and '½' into '2'. I do not know the logic behind when being asked and is unable to explain the word problem. It was like a 'rule' that was installedyears back and I have never question it since. Now that it was brought up, I was thinking, "Oh yah, why huh?" And everything became clearer and easy to understand after concrete materials were used to explain the problem.
That statement seemed very vague then.
Now, I have a better understanding of what the statement means.
Throughout the 24 hours of lesson, some old friends of Dr. Yeap and their theories were introduced to the class:
- George Polya's Model (Understand, Plan, Execute, Reflect)
- Newman's theory for difficulties in word problem solving (Read, Comprehend, Know strategies, Transform, Procedures, Interpret answers)
- Jerome Bruner's Concrete-Pictorial-Abstract approach
- Z. Dienes's theory on the principle of Variability
- Richard Skemp's theory on Instrumental understanding, Relational understanding, and Conventional understanding
- George Pick's theorem
- etc
Often, teachers teach the way they were taught, by memorizing formulas and equations. Even though I am aware that children learn best through concrete representation and I do use manipulatives during math lessons, I do not know that it is also important to bring variations into the picture.
By going through the environmental task, dice trick, geometry solving, sudoku with cubes (to name a few), I finally understood what perceptual variability and mathematical variability is all about, and how I can bring it into my classroom. Who would have thought that dice can be used to play magic tricks and teach addition? Or that a theorem can be obtained by observing the pattern and relation between the dots that a shape is drawn on and dots that are found in the shape? Or incidental learning can take place anywhere, everywhere?
I remember there was a question on solving fractions ( ¾ ÷ ½ ) where I changed the '÷' into a '×' and '½' into '2'. I do not know the logic behind when being asked and is unable to explain the word problem. It was like a 'rule' that was installedyears back and I have never question it since. Now that it was brought up, I was thinking, "Oh yah, why huh?" And everything became clearer and easy to understand after concrete materials were used to explain the problem.
"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya
"But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer." -- Tom Lehrer
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