George, to his teacher:
I have now integrated my preconceived ideas and the enlightenments engendered by yourself, but I still have trouble differentiating between “the limit of” and “the limits of”.
George’s teacher, aside:
I think George would be better off writing a novel. he could call it “The Limits of Continuity”.
This came to me as I was having lunch today:
I borrowed the picture from http://wordsonalimb.com/2014/05/13/self-destruct/comment-page-1/#comment-151
Would it be any better if they were calculators (graphing ones, of course)?
“Mommy, teacher says we all have to get the new eyepad”.
“Why? What’s wrong with the one you’ve got?”.
“She says it’s much better, the screen goes right to the edge, and we can use the Ruler App to measure things”.
Filed under geometry, humor
When is a whole not a whole? (again)
When it’s two wholes (or more) :-
John eats 1/2 of his pizza, Mary eats 3/4 of her pizza. So between them they ate 1/2 + 3/4 of a pizza, or 5/4 of a pizza.
So which whole are we referring to ? John’s pizza ……. No. Mary’s pizza ……. No. Both pizzas …….. No. John’s pizza and Mary’s pizza and both pizzas …….. No.
Conclusion: What we are referring to as “the same whole” is an abstract unit of one pizza, and the fractions are measurements using this unit. Wouldn’t it be a good idea to start off like this, with fractions as measurements, and avoid years of misunderstanding, stress and confusion.
Is this so different from adding whole(adjective!) numbers , as when adding two numbers they have to be counts of the same thing (or whole(!) before it is chopped up).?
Fun arithmetic: 3 apples + 4 bananas = 7 applanas
Desperately fun arithmetic : 1/2 of my money + 1/2 of your money = 1/2 of our money
When is a whole not a whole ?
When it’s a hole.
(which half of the hole shall we fill first, the top half or the bottom half?)
Besides, I thought whole was an adjective.
Filed under fractions, humor
It sure is a number line, and it works perfectly well with the whole or natural numbers.
The question is “How did the number line become straight, with equally spaced numbers, when the ideas of length and measurement have not yet been developed?”. This is the math version of the “what came first, the chicken or the egg?” question.
And, with zero not there no-one can take my last cupcake.
Tom Lehrer on The New Math
I had forgotten all about this one. It’s as to the point now as it was in the sixties.
I’m now going to look for “I hold your hand in mine, dear”
Click the header to see the video
The vision below came to me the other day, and after reading Anthony Cody’s piece I had to put it up
You can find it at http://blogs.edweek.org/teachers/living-in-dialogue/2014/04/the_classroom_of_the_future_st.html
and it contains what before 1984 we would have called a 1984 scenario:
“In this mode of instruction, these devices become the mediator of almost every academic interaction between students and their teacher, and even one another. Students are assigned work on the device, they perform their work on the device, they share work through the device, and they receive feedback via the device. What is more, the means by which learning is measured—the standardized test—will also be via this device.”
So, it is a classroom in the future.
“Now, children, we are going to measure the classroom. How many Ipads long is the room? And how many wide?”