Limits

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”.

Math takes a vacation. Hello real world.

This came to me as I was having lunch today:

 

 

 

 

 

 

 

Electronic pacifiers

I borrowed the picture from http://wordsonalimb.com/2014/05/13/self-destruct/comment-page-1/#comment-151

Thankyou, Lora

Would it be any better if they were calculators (graphing ones, of course)?

In the future (tomorrow?)

“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”.

Fractions are parts of the same whole, part 3

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

 

Fractions are parts of the same whole, part 2

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.

Number lines, or lines with numbers on them

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 Classroom of the Future (next year?)

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?”

On a lighter note, or a lower plane