kitchen table math, the sequel: 11/25/12 - 12/2/12

Friday, November 30, 2012

two years is two years

more from Barry's article on the Common Core:
This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them "understand" the conceptual underpinnings.
Once again, knowledge stored in memory is entirely different from knowledge stored on Google.

Biological memory is a biological process that requires a period of time during which new memories are consolidated:
Memory consolidation refers to the idea that neural processes transpiring after the initial registration of information contribute to the permanent storage of memory.
Memory consolidation, retrograde amnesia and the hippocampal complex
Lynn Nadel* and Morris Moscovitcht Cognitive Neuroscience
I don't know how much time the brain requires to consolidate memories, but I recall John Medina suggesting that the figure may be as long as 10 years. (That would jibe nicely with the 10-year rule for development of expertise, wouldn't it?)

The "consolidation lag" between first learning a new skill and really knowing that skill explains why "just-in-time" learning is so crazy. There is no such thing as just-in-time learning. The brain doesn't work that way. No matter how smart you are, if you are 17 and you don't know how to do long division, you can't just have your professor show you how and then start doing it. Knowledge has to be consolidated before you can use it well, and consolidation takes time.

Here is James Milgram on his experience teaching Stanford students who had not been taught long division:
What happens when you take long division out of the curriculum? Unfortunately, from personal and recent experience at Stanford, I can tell you exactly what happens. What I'm referring to here is the experience of my students in a differential equations class in the fall of 1998. The students in that course were the last students at Stanford taught using the Harvard calculus. And I had a very difficult time teaching them the usual content of the differential equations course because they could not handle basic polynomial manipulations. Consequently, it was impossible for us to get to the depth needed in both the subjects of Laplace transforms and eigenvalue methods required and expected by the engineering school.

But what made things worse was that the students knew full well what had happened to them and why, and in a sense they were desperate. They were off schedule in 4th and 3rd years, taking differential equations because they were having severe difficulties in their engineering courses. It was a disaster. Moreover, it was very difficult for them to fill in the gaps in their knowledge. It seems to take a considerable amount of time for the requisite skills to develop. [emphasis added]
Transcript of R. James Milgram
1999 Conference on Standards-Based K-12 Education
There is no just-in-time learning, and you can't catch-up.

For the sake of argument, say it takes two years to consolidate the skill of adding and subtracting double-digit numbers. (I'm guessing it takes more than two, but I don't know.) If a child learns to add and subtract double-digit numbers in second grade, he or she will be proficient in fourth grade.

Delay teaching the algorithms until fourth grade and now you have a cohort of students who won't be proficient in addition and subtraction until 6th grade.

That's the way it works. Two years is two years.

and see:
Eide Neurolearning explains elaborative rehearsal 

by heart

Speaking of knowing things by heart, when did that expression disappear from common usage?

We know it by heart. A lovely metaphor.

These days any and all discussion of remembered knowledge involves obligatory reference(s) to "spitting," "vomiting," and/or "regurgitating."

I swear, if I have to read one more person saying that "spitting back knowledge" isn't "thinking critically," I will do some copious regurgitating of my own.

download this

I just checked out one of the articles Barry quotes and found this:
Paula Tommins asked, “How are we training the teachers and supporting the teachers because they’re going from downloading to coaching.” By “downloading” she meant imparting knowledge, she later said.
Parents question a new method for teaching math
Published: Wednesday, October 31, 2012
Just the other day I was thinking about the download scenes in The Matrix.

Neo would be in mortal danger so he would dial up the home computer and ask the guy they left back on the ship to download How to Fly a Getaway Helicopter into Neo's skull, and in under 5 seconds -- voilĂ . He could fly.

I was thinking those scenes are evidence that everyone's folk theory of learning encompasses the fact that knowledge stored on Google is not the same thing as knowledge stored inside your brain. I mean, the Warchowski siblings could have written the scenes differently, right? (If they'd gone to Teachers College, maybe they would have.) They could have had Keanu Reeves Google "How to Fly a Getaway Helicopter" and then have Google read him the directions really, really fast.

They didn't do that or anything like that because everyone understands that when it's a matter of life and death you have to know the instructions by heart.

p.s.: 'Downloading' new skills into our brains like characters on The Matrix set to become a reality, say scientists

p.p.s.: how to learn things automatically

more fun with middle school

An Amazon book review:
The reason I gave this book two stars, is because we use this book in our class all of the time. Most of the stories and poems in here are hard to understand and complicated.

I know that you are supposed to use your mind, and there is no right or wrong answer, but you can not use your mind if you dont know what is going on. I keep getting zero's on my daybook assignments, because all I can put in the margins or the pages to write what you think, is that I can't write anything because it was hard to understand, so I get zero's for not understanding, and that to me isnt fair! So, I think that if to this book you tell your opinion, I think that if your opinion is that you didnt understand it, than that should still be counted as "no right or wrong answer".

Amazon review of Daybook of Critical Reading And Writing (Grade 6)
The fabulous thing here is that this student is attempting a fairly sophisticated argument. It's an argument of the jailhouse lawyer type, of course, but still. He or she is onto something. S/he just needs better writing skills to pull it off.

Unfortunately, better writing skills aren't in the offing, I predict. Daily zeros on daybook assignments are a proven time-waster even the Writing the Essay people don't go in for.

p.s: Someone needs to tell this student about the Postmodernism Generator.

p.p.s.: I was going to title this post "Why we fight" but I thought that would be over the top.

explain yourself - Barry on the Common Core

Barry writes:
A few weeks ago, I wrote an article for describing some of the problems with how math is currently being taught. Specifically, some math programs strive to teach students to think like "little mathematicians" before giving them the analytic tools they need to actually solve problems.

Some of us had hoped the situation would improve this school year, as 45 states and the District Columbia adopted the new Common Core Standards. But here are two discouraging emails I received recently. The first was from a parent:
They implemented Common Core this year in our school system in Tennessee. I have a third grader who loved math and got A's in math until this year, where he struggles to get a C. He struggles with "explaining" how he got his answer after using "mental math." In fact, I had no idea how to explain it! It's math 2+2=4. I can't explain it, it just is.
The second email came from a teacher in another state:
I am teaching the traditional algorithm this year to my third graders, but was told next year with Common Core I will not be allowed to. They should use mental math, and other strategies, to add. Crazy! I am so outraged that I have decided my child is NOT going to public schools until Common Core falls flat.
This may sound wildly off topic, but the struggle a third grader has "explaining" why two plus two equals four strikes me as being of a piece with the struggle basic writers have trouble writing a conclusion, especially a conclusion in a 5-paragraph essay, a highly compressed form that leaves you no room to "ask a rhetorical question" or "suggest future lines of inquiry" or "close with a quotation that captures your view" and the like.

With the 5-paragraph essay, when you get to paragraph 5 you've said everything you were going to say (if you're lucky), but the teacher wants you to say something more.

But what?

One thing I always liked about William J. Kerrigan's X-1-2-3 approach is the fact that he didn't bother with introductions and conclusions. The introduction was 1 sentence - Sentence X - and the conclusion was 1 sentence, too. Kerrigan called the final sentence the "rounding off" sentence, as I recall. Really, that's all anyone should do in a very short paper; otherwise your introduction & conclusion - 2 paragraphs out of 5 - take up 40% of the essay.

I've had to abandon Kerrigan's one-sentence policy, though, since I'm pretty sure other instructors don't look kindly upon one-sentence introductions and conclusions, not that I've asked.

So my students, like the 3rd grader trying to explain 2+2, solve the problem they've been set and then struggle to say something else about the something they've just said.

Writing the Essay at Urban Dictionary

I think someone's going to be getting a Writing the Essay mug for Christmas.

the boss compositionists