2005-05-07
Computation, a note for teachers
With my daughter I was reading one of those books that teach children how to count and add numbers. She’s always interested in numbers and very often picks books with numbers in it. In this book there was a picture of two flowers, one with 4 leafs and one with 3 leafs. The question was, how many leafs have these two flowers? The answer: “One flower is missing a leaf!” Another picture shows 3 smiling bears and 2 sad bears. The answer: “The two bears should smile. Why are they sad?” Without the book she would immediately give the right answer when you ask her to add 4 and 3. The problem is that many books add to much distracting details. Adding detail is not the way to simplify computation. Simplification is the way. It remembers me of a fragment of the book ‘Mr God, this is Anna.’ Anna is also having computation lessons at school. Her teacher asks her, “if you’ve got 4 sweets in one hand and 5 in the other, how many sweets do you have?” “I’ve got none,” replies Anna. “And your question is not fair. It’s mean to say I’ve got sweets when I’ve none.”
Computation is not easy to learn. It is very abstract. It doesn’t help to write stories and add details that move away from the abstraction. For me, mathematics became more difficult when new methods were introduced that wrapped the questions in little stories. In general it took me one minute to cross out the details and 2 seconds to answer the mathematical question.
There is another thing that most books do not teach children. It is one of the fundaments of mathematics. I was very pleased when my daughter started discovered it herself some time ago. She started counting with 0. Her reasoning was simple. Before you’ve got one thing (apple, finger, balloon or whatever you’re counting) you’ve got zero. So you start without anything, thus zero, and then comes one. I’ve never found it in one of her books. I don’t know if somebody else told her, but I was surprised. This week I was even more surprised. “Daddy, 0 + 0 = 0,” she said with a special look in her eyes. She noticed that there was something special with this computation. I complimented her for this discovery. I did not explain her how essential this computation is for mathematics. I’m also not going to explain it here. I just state that there is a need for the identity operation in mathematics.
Mister God, this is Anna.
Just a little note about the book I mentioned above. It is written in 1974 and I would characterise it as a romantic tale that illustrates many mystical insights. It’s romantic in the sense of the noble savage. In this book it is the pure child Anna who has unbelievable mystical insights. I still have the intention to make an analysis of all the mystical insights and philosophical ideas that presented in this book. There is a section on mirrors and reflections…
I like the Introduction by Vernon Sproxton, especially where it comes to the Truth question.
Some reviews at amazon.com
Computation is not easy to learn. It is very abstract. It doesn’t help to write stories and add details that move away from the abstraction. For me, mathematics became more difficult when new methods were introduced that wrapped the questions in little stories. In general it took me one minute to cross out the details and 2 seconds to answer the mathematical question.
There is another thing that most books do not teach children. It is one of the fundaments of mathematics. I was very pleased when my daughter started discovered it herself some time ago. She started counting with 0. Her reasoning was simple. Before you’ve got one thing (apple, finger, balloon or whatever you’re counting) you’ve got zero. So you start without anything, thus zero, and then comes one. I’ve never found it in one of her books. I don’t know if somebody else told her, but I was surprised. This week I was even more surprised. “Daddy, 0 + 0 = 0,” she said with a special look in her eyes. She noticed that there was something special with this computation. I complimented her for this discovery. I did not explain her how essential this computation is for mathematics. I’m also not going to explain it here. I just state that there is a need for the identity operation in mathematics.
Mister God, this is Anna.
Just a little note about the book I mentioned above. It is written in 1974 and I would characterise it as a romantic tale that illustrates many mystical insights. It’s romantic in the sense of the noble savage. In this book it is the pure child Anna who has unbelievable mystical insights. I still have the intention to make an analysis of all the mystical insights and philosophical ideas that presented in this book. There is a section on mirrors and reflections…
I like the Introduction by Vernon Sproxton, especially where it comes to the Truth question.
Some reviews at amazon.com
# posted by Sander @ 23:22 
