Forecasting the future of “education”, by Eli Horowitz
“Mathematics, take a break, the doggerel has come back !”
Today I start to fill my pail.
Through the next test I will sail.
Common sense must then prevail:
I’ll clear my brain of what’s now stale
To make some space inside the pail.
For competence, the holy grail,
Ensures that I will never fail,
Though moving forward like a snail.
* * * * * * * * * * * * * * * * * * * * *
The whole damn thing’s to no avail.
So one day recently I was bored, and then the following rushed onto the page:
Half of a big pizza is equal to two small pizzas – rewrite this in as precise way as possible.
Is this 3 hours or 1/4 of a pizza?
How many hours equals 1/4 of a pizza?
Apologies to those for whom a clock face is a historical artifact.
How do I know it’s a pizza and not a cake?
Does half a day include half the night?
There are four feet in our yard, mine and my sister’s.
Would you prefer 1/2 of a round pizza or 1/2 of a square pizza?
Are ratios numbers or fractions (or neither) ?
Fractions are parts of the same whole. OK, I’ll have 5 quarters of that pizza (5/4 is a fraction, isn’t it?)
You cut, I choose !
This year fractions are parts of a whole. Next year fractions will be numbers. I guess the other party won the election.
2/3 and 4/6 are equivalent fractions. Equivalent to what ?
The word “fraction” has the same root as “fracture”. So something got broken. I think it was my faith in common sense.
The Common Core test question asked – How long is 3.25 hours. This could be 3 hours and 25 minutes or 3 hours and 15 minutes. I guess it depends on the grade level.
Back to the heavy stuff next time !
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”.
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”.
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.