From The College Board: Reconciling AP Exams With Common Core

I'm very concerned about the information College Board is giving to AASA, the school superintendents association, regarding calculus. "Despite these measures, there are still difficulties in reconciling many AP courses with the Common Core. In particular, AP Calculus is in conflict with the Common Core, Packer said, and it lies outside the sequence of the Common Core because of the fear that it may unnecessarily rush students into advanced math classes for which they are not prepared. The College Board suggests a solution to the problem. of AP Calculus “If you’re worried about AP Calculus and fidelity to the Common Core, we recommend AP Statistics and AP Computer Science,” he told conference attendees. Moreover, the College Board may offer an AP Algebra course (although no plans are definite), which may supplant AP Calculus, particularly in schools rigidly adhering to the Common Core standards." I'm an apcalc and alg2 teacher with a b.s. in classical applied math. The statistics course that I took in college years ago was a calc-based course. Lisa Jones @proudmomom

Nonconscious arithmetic

The modal view in the cognitive and neural sciences holds that consciousness is necessary for abstract, symbolic, and rule-following computations. Hence, semantic processing of multiple-word expressions, and performing of abstract mathematical computations, are widely believed to require consciousness. We report a series of experiments in which we show that multiple-word verbal expressions can be processed outside conscious awareness and that multistep, effortful arithmetic equations can be solved unconsciously. All experiments used Continuous Flash Suppression to render stimuli invisible for relatively long durations (up to 2,000 ms). Where appropriate, unawareness was verified using both objective and subjective measures. The results show that novel word combinations, in the form of expressions that contain semantic violations, become conscious before expressions that do not contain semantic violations, that the more negative a verbal expression is, the more quickly it becomes conscious, and that subliminal arithmetic equations prime their results. These findings call for a significant update of our view of conscious and unconscious processes.

Reading and doing arithmetic nonconsciously Asael Y. Sklara, Nir Levya,1, Ariel Goldsteinb,1, Roi Mandela, Anat Marila,b, and Ran R. Hassina
19614–19619 | PNAS | November 27, 2012 | vol. 109 | no. 48

I'm sure our friend friends the basal ganglia have something to do with this....

Here's the press release.

Yale Open Courses

Yale Open Courses 

Course list

I've started the American Revolution course, which I like tremendously so far.

For some reason, the Yale Open Courses are the first MOOCs I've felt drawn to. I don't know why.

Just noticed they offer for-credit summer courses, too.

Report from the front

The other day I was introduced to a dean at a progressive private school. We chatted, and at some point I asked how the school assesses student learning.

The dean was vague. He mentioned teachers "reflecting" a couple of times, and then said the school is moving more and more to students assessing themselves, which also involves reflecting.

Funny thing: just last week I talked to a friend of mine whose son attends the school. She says the school has rampant grade inflation, and her son has learned nothing but his grades are good. He learns so little at school that he had two full-time tutors all last school year. (This is a very smart kid, by the way. No learning problems, no behavior problems.) When she took him to the SAT tutor she used with an older child in the family, the tutor told her there's no way he can prepare her son to take the SAT Math Subject test.

I told my friend about "Teach Like a Champion" classes: rapid-fire, high-energy events, with cold-calling and choral response, and said we need charter schools for rich kids. Parents should at least have the option of putting their kids in classrooms where kids spend a a lot of time practicing, not just discussing.

My friend is athletic, and she sparked to the idea it instantly. She said her son would love it, and he would remember what's been taught because he would be practicing in class.

Grade inflation and no practice during class-time: that is a recipe for total disengagement in a lot of kids.

Portlander and Anonymous 1 & 2 on Looking it up

Portlander said...

Sheesh. A cynical person would point out that Google is notorious for putting a thumb on their search results. If one has to rely on Google to get facts every time facts are needed, well that's giving Google an enormous amount of power to bias perceptions.

It's not a whole lot different than the mainstream media running pictures of a 12 y.o. Trayvon Martin in a football uniform instead of a 17 y.o. Trayvon Martin smoking a joint and sticking out his middle fingers on Facebook.

So yes, all the facts you need to know Walter Duranty, er... Walter Cronkite, er... The Googleplex will deliver.

Anonymous said...

Not only that; but a person who has a good knowledge base in a field or topic will get much better information out of Google (or any search engine) than an uninformed person will.

Anonymous said...

So if I can look up the translation of an English word into Spanish, that's as a good as being able to speak Spanish?

I think not.

I'm laughing!

Of course, to be fair, Marissa Mayer does not say that looking things up on Google is the path to success.

But the point still stands: how does one become good at looking things up?

To a very large degree, you become good at looking things up by acquiring knowledge of the field you're looking things up in. I go back to my struggles with the basal ganglia. Today I'm better able to 'look things up' productively because I've developed a sense of the field, of who the major researchers are, and, to a lesser degree, what the differences of opinion are amongst them.

When Marissa Mayer says "It's not what you know, it's what you can find out," she is misformulating reality. You have to know something to find things out.

Beyond that, how often is it actually true that you have to acquire new knowledge/information in order to do your job?

I don't know the answer to that question, but as far as I can tell a great deal of work depends upon doing what you know how to do: applying the knowledge you possess to the situation at hand.

Marissa Mayer is misinformed

2010: HOW IS THE INTERNET CHANGING THE WAY YOU THINK?

Marissa Mayer: It's not what you know, it's what you can find out. The Internet has put at the forefront resourcefulness and critical-thinking and relegated memorization of rote facts to mental exercise or enjoyment. Because of the abundance of information and this new emphasis on resourcefulness, the Internet creates a sense that anything is knowable or findable — as long as you can construct the right search, find the right tool, or connect to the right people. The Internet empowers better decision-making and a more efficient use of time.

---

Thoughts:

1. There was an "abundance of information" available before the internet, too, yet somehow nobody thought that the presence of a World Book Encyclopedia in your house meant you didn't have to know anything.
   
2. Interesting that Mayer sees "memorization of rote facts" as something you might do as a form of "mental exercise" or for "enjoyment." She's right! Learning stuff is fun! Thinking, on the other hand, is not fun. Not for the most part. 
3. Better decision-making and more efficient use of time...I have no way of guessing whether either of those things is true (I'm skeptical of the first claim), but the internet is beyond fantastic for writers. Ed is writing his textbook now, and he can't believe how easy it is to find the sources and information he needs. As a historian working with primary documents, he hadn't really joined the JSTOR revolution. Now he has, and he's amazed.
4. Speaking of JSTOR, the general public needs access, too. 

Former Reddit co-owner founder arrested for excessive JSTOR downloads

Prior knowledge gets around working memory limits

[I]t’s well known that extensive background knowledge allows one to circumvent the limitation of working memory. To take an obvious example, if I ask you to hold six letters in mind for one minute, it will be much easier to do with B-R-A-K-E-S than with X-P-W-M-Q-R. Although both are a string of six letters, the first forms a word, so you can treat it like a single unit. It’s like holding one thing in working memory, not six. Naturally, this saving of space in working memory only works if you know the word “brakes.” The same phenomenon is observed in many other domains. The chess expert looking at a board does not see 16 white pieces—she sees several clusters of pieces, each cluster defined by the relationship of the pieces to one another and to opposing pieces. Whether it’s chess pieces or letters in a word, the compacting of many things into one thing in working memory is based on prior knowledge.
Have Technology and Multitasking Rewired How Students Learn? by Daniel T. Willingham

Jeopardy

I hope some of you are watching Jeopardy.

Ben, the contestant who has won at least 5 days in a row, I think, looks very familiar.

Here he is.

This is funny:

With great intentions, he bought two “very thick books filled with lists of facts, and promised myself I’d read through them every night,” he says. “That lasted exactly one night. I can’t memorize facts very well. I spent a lot of time adding and subtracting large numbers with pen and paper, because I didn’t want to mess up the final wager, especially being a math major.”

VB6

C. has lost 10 pounds on Mark Bittman's VB6 diet!

VB6 ("Vegan before 6") is an amazingly user friendly diet: it's the first diet I've ever tried that uses eating things you like to positively-reinforce not eating things you like without causing the whole diet to crash and burn. I've spent years trying to make the Premack principle work for weight loss, and I think Bittman has actually done it.

The funny thing is, back when I briefly became a hard-core vegan (I've been a 'part-time' vegan since then), I started out by doing exactly what Bittman did: I stuck to a vegan diet during the day, then ate a regular dinner with the family.

But I saw my own 'VB6' as a way station to full-time veganism; it never occurred to me that you could actually lose weight on that regimen.

Turns out I was wrong.

Here's an excerpt:

Six years ago, the man I most trusted with my health said to me, “You should probably become a vegan.”

Not exactly the words I’d wanted to hear, and certainly not what I was expecting. But I’d asked Sid Baker, my doctor of thirty years, what he recommended, given that he’d just told me that at age 57, I had developed the pre-diabetic, pre-heart-disease symptoms typical of a middle-aged man who’d spent his life eating without discipline.

He’d laid out the depressing facts for me: “Your blood numbers have always been fine but now they’re not. You weigh 40 pounds more than you should. You’re complaining of sleep apnea. You’re talking about knee surgery, which is a direct result of your being overweight. Your cholesterol, which has always been normal up until now, isn’t. Same with your blood sugar; it’s moved into the danger zone.”

A more conventional doc would’ve simply put me on a drug like Lipitor, and maybe a low-fat diet. But Lipitor, one of the statin drugs that lowers cholesterol, is a permanent drug: Once you start taking it, you don’t stop. I didn’t like the idea of that.

Furthermore, its effectiveness in healthy people has never been established, and it’s also been implicated in memory loss and other cognitive complications; I didn’t like the idea of any of that, either. And at this point, low-fat and lowcarbohydrate diets have essentially been discredited: They might help you lose weight, but they’re not effective for maintaining that loss in the long term, and they may even wreak havoc on your system.

But becoming a vegan? A person who eats no animal products at all? Calling that a radical change to my lifestyle was more than a bit of an understatement. Yet it was clear that something had to be done. I asked Sid, “Is a compromise possible? Any other ideas?”

“You’re a smart guy,” he said. “Figure something out.”

The answer, to me, was this: I’d become a part-time vegan. And for me, this part-time veganism would follow these simple rules: From the time I woke up in the morning until 6 in the evening, I’d eat a superstrict vegan diet, with no animal products at all.

In fact, I decided to go even beyond that: Until 6 p.m., I’d also forgo hyper-processed food, like white bread, white rice, white pasta, of course all junk food, and alcohol.

At 6 p.m., I’d become a free man, allowing myself to eat whatever I wanted, usually—but not always—in moderation. Some nights, this meant a steak dinner; some nights, it was a blow-out meal at a good restaurant; other nights, dinner was a tunafish sandwich followed by some cookies. It ran, and runs, the gamut.

Whatever happened at dinner, though, the next morning I turned not to bacon and eggs or a bowl of Trix but to oatmeal or fruit or vegetables. For lunch, rice and beans or a salad—or both. Throughout the day I snacked on nuts and more fruit.

I called the diet “vegan before six,” or VB6. And it worked.

A month later, I weighed myself; I’d lost 15 pounds. A month after that, I went to the lab for blood work: Both my cholesterol and my blood sugar levels were down, well into the normal range (my cholesterol had gone from 240 to 180). My apnea was gone; in fact, for the first time in probably thirty years, I was sleeping through the night, not even snoring. Within four months, I’d lost more than 35 pounds and was below 180—less than I’d weighed in thirty years. And the funny thing was, the way I ate in the daytime began to change the way I ate at night.

An excerpt from Mark Bittman’s “VB6″

AND SEE:
I Answer Frequently Asked Questions about VB6
Help for the afflicted
Application of the Premack principle to the behavioral control of extremely inactive schizrophrenics

Why students have to memorize things - revised

I've been trying to get this post right, and it's getting closer.

I'm sensing an uptick in anti-knowledge sentiment, so I need a rebuttal.

What do children want?

Fabulous post from a substitute teacher in Great Britain

Knowledge and memory posts

6/24/2006: Mastery learning and IQ (warning: broken links; page can't be edited)

10/25/2006: On not teaching to mastery (warning: broken links; page can't be edited)

4/26/2007 How to build a fast learner

4/26/2007: Extremely fast learning

6/10/2007: On Intelligence (Jeff Hawkins)

9/9/2010: The rule of 20

1/23/2012: Why students have to memorize things

3/30/2012: Look it up

8/13/2012: Jeff Hawkins: intelligence is memory, memory is intelligence

6/18/2013: Deeper shmeeper

7/2/2013: Why students need to memorize, Common Core edition

President Obama has a really bad idea

President Obama recently visited a school that "relies 100 percent on project-based learning." Not just visited, lauded.

Sigh.

Apparently the White House is launching a "High School Redesign" initiative, which appears to be supported by the National Governors Association and the National Association of State Boards of Education:

Today's global economy requires new approaches to teaching and learning in America's high schools to foster problem solving and analysis, to support creativity and collaboration, and to connect student learning directly to the real world. Students learn best when they are engaged in complex projects and tasks aligned with their interests and when they work with others through practical examples and case studies that engage them in rigorous academics and in the application of knowledge.
Fact Sheet: Redesigning America's High Schools

Manor New Technology High School, a 100% project-based school, is cited as one of five Promising Examples of Redesigned High Schools.

From the President's speech:

• at Manor a history teacher might get together with a math teacher and develop a project about the impact of castles on world history and the engineering behind building castles
• or a group of students might be in charge of putting together a multimedia presentation about the moral dilemmas in literature as applied to WWII
• folks who use mathematical equations to build musical instruments
• tests on bungee jumping with rubber bands and weights
• robots that were being built
• all kinds of great stuff
• there's a lot of hands-on learning here
• part of what makes this place special is that there's all this integration, various subjects and actual projects, and young people doing and not just sitting there listening
• I could not be prouder of what's happening here at Manor

AND SEE:
Help Desk: Project-Based Learning
High School Redesign Gets Presidential Lift
Smartbrief on How to Make Project-Based Learning Work
Tips for Transitioning to Project-Based Learning
Manor New Technology High School

The founder, chairman, and CEO of Netflix has a really bad idea
Larry Summers has a really bad idea
David Brooks has a really bad idea
David Brooks has a really bad idea, part 2
All is forgiven.

The good news

The good news....

A recent report shows that although project-based learning is a growing trend in education, only about 1% of schools nationwide use the practice on a regular, committed basis.

How to make project-based learning work

One percent!

One percent is not a growing trend for a teaching method that dates back at least one hundred years. At least, I hope not.

There's bad news, too. (President Obama has a really bad idea.)

Willingham on interdisciplinary work

. . . Gee retells (via Jonah Lehrer) the story of a building at MIT that housed professors from a wide variety of disciplines, with a concomitant flowering of intellectual cross-fertilization. Gee quotes (with approval, I guess) Lehrer: “The lesson of Building 20 is that when the composition of the group is right—enough people with different perspectives running into one another in unpredictable ways—the group dynamic will take care of itself.”

As an academic who has been doing interdisciplinary work for 20 years, I would counter: “Like hell it does.”

Virtually every school of education is housed in a building with people trained in different disciplines, and interdisciplinary work remain rare. For reasons I won’t get into here (and much to the despair of university administrators) interdisciplinary work is hard.

Book Review: Theory and Practice
7/1/2013

Why students need to memorize, Common Core edition

"...anything that occupies your working memory reduces your ability to think."
- Daniel Kahneman | Thinking Fast and Slow

The only way to clear space in working memory is to store knowledge in long-term memory.

AND SEE:
Why students have to memorize things
#whystudentsneedtomemorize

"Wasting time in school"

Have just this moment stumbled upon a UK education blog: Wasting Time in School."

Check out this post.

Brilliant.

This reminds me of that business idea we all had a while back, doing school projects for beleaguered parents.

Thought experiment: since the parents are already doing the projects & everyone knows it....wouldn't a School Project Business be legit in a way a term-paper business is not?

I think it might.

Gone fishing (and did NCLB work?)

In Princeton, NJ, waiting for our room to be ready.

While I wait I'm looking at NAEP scores, and wondering.

Are we seeing evidence that No Child Left Behind worked?

• Compared to the first assessment in 1971 for reading and in 1973 for mathematics, scores were higher in 2012 for 9- and 13-year-olds and not significantly different for 17-year-olds.
• In both reading and mathematics at all three ages, Black students made larger gains from the early 1970s than White students.
• Hispanic students made larger gains from the 1970s than White students in reading at all three ages and in mathematics at ages 13 and 17.
• Female students have consistently outscored male students in reading at all three ages, but the gender gap narrowed from 1971 to 2012 at age 9.
• At ages 9 and 13, the scores of male and female students were not significantly different in mathematics, but the gender gap in mathematics for 17-year-olds narrowed in comparison to 1973.

About NAEP
NAEP Summary

the "triple dissociation" and slow and fast readers

re: We can see just 7 or 8 letters at a time

The NYU reading-speed study, which has come up a couple of times on ktm, found a "triple dissociation" amongst three contributors to reading speed:

• Decoding by phonics (62% of reading speed)
• Whole-word recognition (16% of reading speed)
• Word-prediction via knowledge of grammar and context (22%)

"Triple dissociation":

Surprisingly, the effects of the knockouts on reading rate reveal a triple dissociation. Each reading process always contributes the same number of words per minute, regardless of whether the other processes are operating.

I've just this moment realized the implications of the triple dissociation they found:

1. If students don't know phonics, they can never read quickly enough to do college-level reading,  which requires at least 200 wpm. 
2. Students who don't know the grammar of written English well, will be significantly slower readers than students who do. ("Know" in the procedural sense of being able instantly to comprehend grammatical structures such as appositives and relative clauses and anaphora and the like.)
3. Until you have substantial background knowledge in a subject, you will be a slow(ish) reader in that content area. 

I'd love to know how that 22% is distributed between grammar and background knowledge. The researchers did not test to see how grammar and background knowledge

Source:
Parts, Wholes, and Context in Reading: A Triple Dissociation by Denis G. Pelli mail, Katharine A. Tillman

We can see just 7 or 8 letters at a time

I've always wondered about this:

Let us consider the behaviour in which you are currently engaged – namely, reading these words. What exactly is your brain is doing right now? What kind of behaviour is reading and what must the brain do in order to achieve it?

[snip]

Reading, when reduced to the rather prosaic level of motor actions, depends on the brain’s ability to orchestrate a series of eye movements. Now, as you read these words, your brain is commanding your eyes to make small but very rapid (about 500° per second) left-to-right movements called saccades (right-to-left or up-and-down for some other written languages). You are not consciously aware of it, but these rapid movements are frequently interrupted by brief periods when the eyes are fixed in position. Watch someone reading and you will see exactly what I mean. You’ll notice that the eyes do not sweep smoothly along the line of text, rather they dart from one fixation to another. It is only during the fixations, when the eyes dwell for about a fifth of a second, that the brain is able to examine the text in detail. Reading is not possible during the darting saccadic movements because the eyes are moving too quickly across the page. You are not aware of the blur and confusion during a saccade because fortunately there is a brain mechanism that suppresses vision and protects you from visual overload.

Reading is only possible between saccades, not only because the eyes are then stationary but also because gaze is centred on the retina’s fovea. The fovea is the only part of the retina specialized for high acuity vision (see Chapter 5), but it scrutinizes a very small area of our visual world. As a literal rule of thumb, foveal vision is restricted approximately to the area of your vision covered by your thumbnail held at arm’s length. It is a small window of clear vision within which you are able to decipher just 7 or 8 letters of normal print size at a time. The task for the brain is to generate a precise series of motor commands to the eye muscles which ensure that at the end of each saccade your high acuity vision is fixed on that part of the text you need to see most clearly next. As your eyes approach the end of a line, the brain generates a carriage return. Of course the return saccade must be to the left, of the correct magnitude and associated with a slight downward shift in gaze in order to bring the first word on the next line onto the fovea.

I have considered only the simple case of the brain directing eye movements alone, as if nothing else affects gaze direction. But of course the relative positions of the eye and page are affected continuously by head, body, and book motion. Thus the brain must continually monitor and anticipate factors affecting the future position of your eyes relative to the text. The fact that you can effortlessly read on a moving train while eating a sandwich is evidence that your brain can solve this problem quite easily. Importantly, it is done automatically and on an unconscious level without you having to think through every step. If you had to consciously think about the mechanical process of reading, you would be illiterate!

Our lack of conscious awareness of underlying brain processes can also be illustrated by reflecting on the subjective experience that the comprehension of written material represents. While reading we are not conscious of the fragmented nature of comprehension imposed by underlying move—stop—move—stop activity of the eyes I’ve just described or by the fact that only 7 or 8 letters can be deciphered at each stop. On the contrary, our strong subjective impression is that comprehension of the text flows uninterrupted and moreover that we can read several words or even whole sentences ‘at a glance’. That this is not the case can be illustrated by reading a sentence containing a word that has more than one meaning and pronunciation. For example, the word tear has two very different meanings and pronunciations in English – tear the noun of crying and tear the verb of ripping apart. Clearly such word ambiguity complicates the brain’s task of providing you with an uninterrupted comprehension. If for instance the word tear occurred at the beginning of a sentence its meaning might remain ambiguous until the subject of the sentence appears later. Because you cannot read the whole sentence at a glance your brain may be left with no option but to choose one of the alternative meanings (or sounds, if you are reading aloud) of a word and hope for the best.

While we cannot read whole sentences at a glance, the brain does recognize each word as a whole. What is quite surprising however is that the order of the letters is not particularly important (good news for poor spellers). That is why you will be able to read the following passage without consciously having to decode it.

I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdgnieg. It deosn’t mttaer in waht oredr the ltteers in a wrod aer, the olny iprmoatnt tihng is taht eth frist dan lsat ltteer be in the rghit pclae. The rset cna be a taotl mses and yuo can still raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?

The Brain: A Very Short Introduction by Michael O'Shea

The NYU study of reading speed (found that reading happens at 3 levels:

• Decoding (phonics): 62% of reading speed
• Whole word: 16% of reading speed
• "Sentence or story context": 22% of reading speed

And see:
How many words can readers predict?