Welcome
That anyone can freely publish anything to be read by anyone, anywhere and at any time is beautiful. To exploit this beauty, I will publish something related to the learning and teaching of mathematics someone in Thailand will find useful and a dialogue will commence.
At least that is the idea.
My name is Jan Einar Nordgreen, I was born in 1952 in Bergen, Norway. I have taught/studied in Norway, Spain, Bahamas and USA.
When I was 21 I made a discovery. “There had been no room for creativity in my math training.” I can still remember, more than 25 years later, the scene where I had my revelation. I was with a few friends discussing our first year at The University of Oslo. We were all from the province and had been thrown into the ‘cement jungle’ of the capital.
At high school we did trigonometry and algebra and so forth. At the University we struggled with calculus and linear algebra. Never did I, or anyone I knew, think or suggest that may be there could be some room for thinking things through on our own. We were being spoon-fed as if that was the only way to eat.
Shouldn’t the teachers have offered us a more varied diet? Shouldn’t our parents have reacted? And what about us, the new generation, why where we silent all these years? The last question is easy to answer. Because we did not know better. Because we did not, aha!, think for ourselves.
Later, I learnt that I had not been alone:
What was lacking in the usual approach, even at its best, was any sense of genuine enquiry, or any stimulus to curiosity, or appeal to the imagination. There was little feeling that one can puzzle out an approach to fresh problems without having to be given detailed instructions.
Aspects of Secondary Education, HSMO 1979
Twenty-five years have passed and I have two kids. How much creativity have they met in their math lessons? You may have guessed the answer, very little. They have not been thrown in at the deep end, developing some fins for swimming. They have not discovered the confidence that comes with solving a problem on your own, as opposed to following a cried out algorithm.
In most classrooms, exposition by the teacher and the consolidation of fundamental skills and routines dominate to the exclusion of virtually everything else.
Zelda Isaacson, Teaching GCSE Mathematics, page 40, Hodder & Stoughton 1987
“You are a parent,” I can hear you saying, “why haven’t you reacted?” Well, I have. I have suggested use of better textbooks, use of enriching software, use of investigations, etc. With no success, which is not surprising. A teacher does not change her ways easily.
I am a teacher. I know what a teacher wants. A teacher wants practical help to come through the next lesson. A teacher needs less inspirational thoughts, less lofty theories, more practical assistance. That is the action part of this site. Wouldn’t it be nice if you could click somewhere and find relevant, rewarding stuff that will brighten up your students’ day, and move them towards a more creative mode? Wouldn’t it be nice to read how other teachers have had their successes, and see if their victories can be replicated? I thought so. So that is one reason for starting this site.
Mathematics teaching at all levels should include opportunities for:
exposition by teacher;
discussion between teacher and pupils and between pupils themselves;
appropriate practical work;
consolidation and practice of fundamental skills and routines;
problem solving, including the application of mathematics to everyday situations;
investigational work.
The Cockcroft Report, §243, 1982
If you want to move from A to B and there is an obstacle in the way, you have a problem. If you know where you are, where you want to go and the tools that are available, you are ready to go. You are at A, in a certain school with all its constraints from the syllabus, the administration, your head of department, your students, etc. But, where do you want to go? Where is your B? And which tools exist that you can use. That is the thoughts part of this site. It’s no use travelling at 100 kilometres per hour, if you are heading in the wrong direction.
An internet site that has impressed me a lot lately is ‘Y? The National Forum On People’s Differences.’ at http://www.yforum.com/index.html. To see the volume of articulated, deeply felt exchanges of views and feeling on important issues, is heart warming. I don’t know if the learning and teaching of mathematics can create a similar dialogue, but it is a mind-boggling thought.
Of course, I have some ulterior motives for this site. Although I have been fortunate to be published in several magazines in more than one country, this medium brings my thoughts further and will last longer. I will empty my drawers for rejected articles, unpublished thoughts, half-baked ideas, etc. Someone who meets these recycled electrons may be able to add a few missing links and create a better understanding.
My secret dream is of course that Mum will be an over-night success and I will have more time to think and ponder. When I was a kid, people said to me ‘You think too much!’ ‘Can one think too much,’ I thought.
Welcome onboard! Let’s go overboard to make this a great place to visit!
PS:
I should not leave you without explaining the title for this site. The way I see things “A is not A” and specifically “Mathematics is not mathematics.” The learning of mathematics has to do with understanding concepts, algorithms and acquiring some problem-solving skills. But, learning mathematics is more than that. It is also about attitudes and feelings like tolerance, self-reliance, trust, courage, perseverance, humour and other things that shape the human character. So when we teach mathematics, we often have ulterior motives, making possible a more complete education of our students. The chapter may be called “Squared roots”, but we have a much fuller agenda.
I hope.
That anyone can freely publish anything to be read by anyone, anywhere and at any time is beautiful. To exploit this beauty, I will publish something related to the learning and teaching of mathematics someone somewhere may find useful and a dialogue will commence.
At least that is the idea.
My name is Jan Einar Nordgreen, I was born in 1952 in Bergen, Norway. I have taught/studied in Bahamas, Cayman Islands, Norway, Spain, Thailand, and USA.
When I was 21 I made a discovery. “There had been no room for creativity in my math training.” I can still remember, more than 35 years later, the scene where I had my revelation. I was with a few friends discussing our first year at The University of Oslo. We were all from the province and had been thrown into the ‘cement jungle’ of the capital.
At high school we did trigonometry and algebra and so forth. At the University we struggled with calculus and linear algebra. Never did I, or anyone I knew, think or suggest that may be there could be some room for thinking things through on our own. We were being spoon-fed as if that was the only way to eat.
Shouldn’t the teachers have offered us a more varied diet? Shouldn’t our parents have reacted? And what about us, the new generation, why where we silent all these years? The last question is easy to answer. Because we did not know better. Because we did not, aha!, think for ourselves.
Later, I learnt that I had not been alone:
What was lacking in the usual approach, even at its best, was any sense of genuine enquiry, or any stimulus to curiosity, or appeal to the imagination. There was little feeling that one can puzzle out an approach to fresh problems without having to be given detailed instructions.
Aspects of Secondary Education, HSMO 1979
Thirty years have passed and I have two grown-up sons. How much creativity have they met in their math lessons? You may have guessed the answer, very little. They have not been thrown in at the deep end, developing some fins for swimming. They have not discovered the confidence that comes with solving a problem on your own, as opposed to following a cried out algorithm.
In most classrooms, exposition by the teacher and the consolidation of fundamental skills and routines dominate to the exclusion of virtually everything else.
Zelda Isaacson, Teaching GCSE Mathematics, page 40, Hodder & Stoughton 1987
“You are a parent,” I can hear you saying, “why haven’t you reacted?” Well, I have. I have suggested use of better textbooks, use of enriching software, use of investigations, etc. With no success, which is not surprising. A teacher does not change her ways easily.
I am a teacher. I know what a teacher wants. A teacher wants practical help to come through the next lesson. A teacher needs less inspirational thoughts, less lofty theories, more practical assistance. That is the action part of this site. Wouldn’t it be nice if you could click somewhere and find relevant, rewarding stuff that will brighten up your students’ day, and move them towards a more creative mode? Wouldn’t it be nice to read how other teachers have had their successes, and see if their victories can be replicated? I thought so. So that is one reason for starting this site.
Mathematics teaching at all levels should include opportunities for:
- exposition by teacher;
- discussion between teacher and pupils and between pupils themselves;
- appropriate practical work;
- consolidation and practice of fundamental skills and routines;
- problem solving, including the application of mathematics to everyday situations;
- investigational work.
The Cockcroft Report, §243, 1982
If you want to move from A to B and there is an obstacle in the way, you have a problem. If you know where you are, where you want to go and the tools that are available, you are ready to go. You are at A, in a certain school with all its constraints from the syllabus, the administration, your head of department, your students, etc. But, where do you want to go? Where is your B? And which tools exist that you can use. That is the thoughts part of this site. It’s no use travelling at 100 kilometres per hour, if you are heading in the wrong direction.
An internet site that has impressed me a lot lately is ‘Y? The National Forum On People’s Differences.’ at http://www.yforum.com/index.html. To see the volume of articulated, deeply felt exchanges of views and feeling on important issues, is heart warming. I don’t know if the learning and teaching of mathematics can create a similar dialogue, but it is a mind-boggling thought.
Of course, I have some ulterior motives for this site. Although I have been fortunate to be published in several magazines in more than one country, this medium brings my thoughts further and will last longer. I will empty my drawers for rejected articles, unpublished thoughts, half-baked ideas, etc. Someone who meets these recycled electrons may be able to add a few missing links and create a better understanding.
My secret dream is of course that Mumnet will be an over-night success and I will have more time to think and ponder. When I was a kid, people said to me ‘You think too much!’ ‘Can one think too much,’ I thought.
Welcome onboard! Let’s go over board to make this a great place to visit!
One final word. The way I see things “A is not A” and specifically “Mathematics is not mathematics.” The learning of mathematics has to do with understanding concepts, algorithms and acquiring some problem-solving skills. But, learning mathematics is more than that. It is also about attitudes and feelings like tolerance, self-reliance, trust, courage, perseverance, humour and other things that shape the human character. So when we teach mathematics, we often have ulterior motives, making possible a more complete education of our students. The chapter may be called “Squared roots”, but we have a much fuller agenda.
I hope.