The problem with the blind procedures is that it relies *heavily* on memory which in turn only functions when you have a cool calm environment which for most isn't achieved in the high pressure distracting and socially charged environment of public schools, meaning the stress of math class creates of opposite environment for the memorization necessary to do well. For me math was really intuitive and I would arrive at the right answer by just mulling it over in my head. This served me well through elementary and middle school until I hit algebra. I continued to arrive at the right answer but the problem was I didn't know how I got the answers, and without doing all the massive hundred step procedures on the paper you didn't get credit for your work, resulting in bad grades and discouragement, which in turn resulted in stress and pressure and eventually cascaded into me tuning math class out completely when we got into Algebra. It's a shame because I had some natural talent at looking at the problem and turning it around in my mind until the answer presented itself. The viciousness of my teachers (including insisting I was cheating etc.) Turned me off math (specifically anything overly fourmulaic) for life. I still enjoy the beauty of math, but I never finished my degree (majored in psychology, minored in anthropology and philosophy) because I still have to take 2 math courses to complete it and the very thought makes me panic. It's incredible the damage that modern teaching in public schools can do to a person. I homeschool my children (as we don't have a Waldorf School nearby) and I infuse much of their education with a Waldorf approach to the best of my understanding from reading and study on the topic. They are still young, but I look forward to teaching them mathematics with a firm grounding in the history of math and the context in which they might use it, as well as an appreciation for the raw beauty of math, geometric form and logic (which I very much enjoy).
Looking at how the pie-pieces align, one can see how half the circumference ends up and the other half down. Now in the 3rd example where v r cutting simply infinitely small strips the size of a line, and then align them, i cannot visualize half the circumference going up and the other down. One end of the strips are at the edge of the cicle and all the other ends connect/overlap at the center. Hence the length of the rectangle isn't half, rather full 2PiR. Can someone help me visualize this correctly please.
Seriously? That"s advanced education? Come on....as if teachers at public schools just pull crap out of their asses and that's that. No explanation, no diriving to set formulas, no problem solving, no excercises - you know, no sign of doing any actual teaching ....idk about the US, but here in Europe, that's what teachers are supposed to do.
6:35 Nice demonstration. And it is very important kids get to see what is a demonstration. Great teacher.
The impressive thing is the guy in the audience still remembered where and when he learned this this way.
The problem with the blind procedures is that it relies *heavily* on memory which in turn only functions when you have a cool calm environment which for most isn't achieved in the high pressure distracting and socially charged environment of public schools, meaning the stress of math class creates of opposite environment for the memorization necessary to do well.
For me math was really intuitive and I would arrive at the right answer by just mulling it over in my head. This served me well through elementary and middle school until I hit algebra. I continued to arrive at the right answer but the problem was I didn't know how I got the answers, and without doing all the massive hundred step procedures on the paper you didn't get credit for your work, resulting in bad grades and discouragement, which in turn resulted in stress and pressure and eventually cascaded into me tuning math class out completely when we got into Algebra. It's a shame because I had some natural talent at looking at the problem and turning it around in my mind until the answer presented itself. The viciousness of my teachers (including insisting I was cheating etc.) Turned me off math (specifically anything overly fourmulaic) for life. I still enjoy the beauty of math, but I never finished my degree (majored in psychology, minored in anthropology and philosophy) because I still have to take 2 math courses to complete it and the very thought makes me panic. It's incredible the damage that modern teaching in public schools can do to a person.
I homeschool my children (as we don't have a Waldorf School nearby) and I infuse much of their education with a Waldorf approach to the best of my understanding from reading and study on the topic. They are still young, but I look forward to teaching them mathematics with a firm grounding in the history of math and the context in which they might use it, as well as an appreciation for the raw beauty of math, geometric form and logic (which I very much enjoy).
Great teacher, thank you.
:çu.whao
Mr. York. , can you explain why the circumference of the circle is 8 times pi? Unfortunately for me that is just another memorized formula.
This is so genius. I don't quite understand it but it is clearly genius.
Looking at how the pie-pieces align, one can see how half the circumference ends up and the other half down.
Now in the 3rd example where v r cutting simply infinitely small strips the size of a line, and then align them, i cannot visualize half the circumference going up and the other down. One end of the strips are at the edge of the cicle and all the other ends connect/overlap at the center. Hence the length of the rectangle isn't half, rather full 2PiR. Can someone help me visualize this correctly please.
So a square is just the sum of 2 circles?
Confusing. Why the five lines out of the first quartered circle?
It's not 5 lines...try to see it in terms of pies...there are 4 pies in the circle and he laid down 4 pies side by side one facing up and next down...
archimedes-method-for-computing-areas-and-volumes-introduction
Also why 2pir and not 2rpi for the circumference in your last drawing or does it matter?
Mathematics go in alphabetical order, ultimately it doesn't matter because multiplication is commutative
Seriously? That"s advanced education? Come on....as if teachers at public schools just pull crap out of their asses and that's that. No explanation, no diriving to set formulas, no problem solving, no excercises - you know, no sign of doing any actual teaching ....idk about the US, but here in Europe, that's what teachers are supposed to do.