Isn't there one right answer to "how many ways can we achieve the sum of 23"?
Isn't the answer: "There are an infinite number of ways to achieve the sum of 23"?
Another thing: would this question be asked, in this way, in combinatorics? (In the time I've spent trying to learn combinatorics, I haven't encountered a question with more than one right answer. Nor did I encounter a question with an answer of infinity.)
(And how is this question "topical"?)
I am watching in amazement as Common Core rolls across the land.
It's as if every constructivist in the country has suddenly been handed a lifetime prescription for anabolic steroids.
All those years of No Child Left Behind and Adequate Yearly Progress must have created a massive pent-up desire in the breasts of America's educators to conduct mini-lessons and ask math questions with no right answer.
Here's a weird thought to ponder: across the land, future teachers are being taught that direct instruction is bad, that they should be the guide on the side, that the discover method is the best way to educate...but exactly HOW are they being taught this? Does a guide on the side help them to discover the enduring understanding that this is the best way to teach? I bet not. I bet they are being directly instructed not to directly instruct. Hmm...
ReplyDeleteThe reason this came to mind is that I was remembering a curriculum writing workshop in which I was instructed (and it felt direct to me) that if a question has a single correct answer then it is not an essential question.
What has happened is that the understanding-by-design crowd has claimed the term "essential question" as their own special buzzword. I guess the common core crowd is using it too.
"How many ways can we achieve the sum of 23"?"
ReplyDelete"Isn't the answer: "There are an infinite number of ways to achieve the sum of 23"?"
No, the answer is that you don't want these people, with their own "way" of education, teaching your children. That should be left up to parental choice.
Of course, the irony is that education students are encouraged to discover that discovery is the only way. Sometimes it's done using direct instruction. They want you to discover their one solution. Apparently there is only one solution to education.
They also like to take over definitions, like understanding and critical thinking. They redefine math, but you have no choice in the "way" your child is taught. Best practices means best to them. Few educators want to go to a cocktail party and talk about the importance of drill and skill for understanding. They want to define their own argot so that they sound erudite. I call it brain research misdirection. Meanwhile, they lower expectations and put the onus of success entirely on the student and parents.
Blah, blah, woof, woof.
You can't argue with them if they get to make the definitions. It's hard for parents to have a discussion at that level. It's not nice. It's their turf. If you take away discovery learning, they have nothing left.
Shall we make a list of all of the ways that teachers and schools keep parents in their place? The anecdotes of really bad parents are used to control all parents. I called them preemptive parental strikes. Then there was this:
"Yes, your son has a lot of superficial knowledge."
We got that in first grade, along with a lecture on having first graders find their "voice". Phonics and spelling are just not as important.
You can't let them control the definitions and the debate questions. You also can't win if what you want is fundamentally different from the only thing they learned in school. When my son was in first grade, I sent a message to some school committee members and told them that they need to hand out Hirsch's Core Knowledge Series: "What your first (second, ..) grader needs to know" and tell parents that this is NOT the education their child will get.
"Isn't the answer: 'There are an infinite number of ways to achieve the sum of 23'?"
ReplyDeleteIt depends on the set of numbers allowed in the answer. For natural and whole numbers, there is a finite number of ways to add two numbers together to get 23.
I've seen this sort fo problem before (in a Russian early grade textbook, I think...) where the question didn't make a lot of sense if the kids knew about rational numbers.
-Mark Roulo
@Mark
ReplyDeleteAnd negatives.
none; "the sum of 23"
ReplyDeleteis not an achievement,