dysteachia, part 2

A popular textbook on special education (Rosenberg, et. al, 2008), notes that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given explicit instruction.
Mathematics Education: Outwitted by Stupidity Barry Garelick

So the sequence is:

a. Collaborative group inquiry with spiraling
b. Huge increase in children diagnosed w/learning disabilities
c. Provision of explicit instruction (w/o spiraling?) to children diagnosed w/learning disabilities
d. Followed by 50% of learning disabilities resolving

Back on my home planet, we didn't bother with Steps A, B, and D.

dysteachia

In a well-publicized paper that addressed why some students were not learning to read, Reid Lyon (2001) concluded that children from disadvantaged backgrounds where early childhood education was not available failed to read because they did not receive effective instruction in the early grades. Many of these children then required special education services to make up for this early failure in reading instruction, which were by and large instruction in phonics as the means of decoding. Some of these students had no specific learning disability other than lack of access to effective instruction. These findings are significant because a similar dynamic is at play in math education: the effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.
Mathematics Education: Being Outwitted by Stupidity by Barry Garelick

The effective treatment for many students who would otherwise be labeled learning disabled is also the effective preventative measure.

and see Galen Alessi's classic: Diagnosis Diagnosed

habit, part 1

I keep mentioning my Eternal Basal Ganglia project...the one that never, ever gets done. (It's close! I swear!)

One of the issues I've been struggling with is the question of how people develop good habits as opposed to bad habits. More to the point, how would one go about developing a good habit on purpose?

Which, of course, raises the question of what, exactly, a habit is.

Answering that question has turned out to be more difficult than I expected. We all know a habit when we see one, and we all have numerous habits of our own, some of which we're trying to "break." But when you try to reverse-engineer the concept, it gets slippery.

I think Piers Steel's terrific book, The Procrastination Equation: How to Stop Putting Things Off and Start Getting Things Done, has helped me finally make the jump from "What is a habit?" to "What would I need to do if I wanted to create a habit on purpose?"

More later.

technologeeeeee!

Six-year-old Maria shows how to learn Spanish on a mobile phone to German Chancellor Angela Merkel, right, and then-Spanish Prime Minister Jose Luis Rodriguez Zapatero, left, at a technology fair in Hanover, Germany, in 2010.—Focke Strangmann/AP-File
Europe Seen Leading the Way in Hand-Held ComputingBy Ian Quillen | Education Week

Quick! Somebody get that little girl a node chair.

global shmobal

Still trying to persuade my district to adopt college readiness as a goal.

A couple of years ago, when our then-superintendent was writing her second Strategic Plan, I lobbied the administration to include the words "college preparation" on the Plan. No dice.

Our high school's publicly stated philosophy: "It's better to be happy than to get into a selective college." When I say "publicly stated," I mean publicly stated: the high school principal says these words publicly. It's more important to be happy than to get into a selective college. Last spring, one of the two candidates for school board - the candidate we did not support - quoted the h.s. principal at the candidates' forum. The candidate said he'd spoken to the principal of the high school, and the principal had told him it's more important for students to be happy than to get into a good college "no matter how much parents obsess over it."

He won in a landslide.

Westchester school districts aren't too interested in college readiness, and there's no pressure on them to change.

The Procrastination Equation

the equation:

Motivation = E x V/I x D

E = Expectancy: your level of confidence (but not over-confidence) you'll actually get whatever you're trying to do done
V = Value: how much you value getting whatever you're trying to do done
I = Impulsiveness: (no explanation required)
D = Delay: length of time before you realize the reward/goal/etc. - people "irrationally find present costs more salient than future costs"

The book is fantastic. Briliant. Amazing.

More anon.

The Procrastination Equation.

The Procrastination Equation at Science Daily.

What Philadelphia 5th graders should know how to do

I recently came into possession of one the Philadelphia School District Parent Teacher Brochures, which breaks down the goals that each Philadelphia School District student should be able to meet by the end of each grade level.  Since I'm homeschooling my 5th grade daughter, I was particularly interested in the goals for fifth grade. And I was shocked, shocked, to find myself more baffled than enlightened after reading through these goals.

The language arts goals are all about process, purposes, and genres, with a developmentally inappropriate assignment thrown in in the form of a research project:

•Continue to build a reading, writing and speaking vocabulary
•Read to learn new information
•Read a wide range of stories, books and magazines for enjoyment
•Understand a problem or conflict in stories or books and talk or write about an appropriate solution
•Make connections between stories and texts that they have read and the world around them
•Tell and/ or write a summary that gives the main idea of what they read and the most important details or events
•Complete a research project including a written report
•Write stories with several paragraphs
•Write poems, plays, and reports

Not a word about specific reading skills (vocabulary level, sentence complexity, making deductions and bridging inferences within the context of the text) or writing skills (grammar and punctuation, sentence construction, paragraph construction).

As for the math goals, most are vague ("compute" and "find the relationships"), easy (locating numbers on a number line; comparing numbers; sorting shapes), and emphasize verbal explanations over mathematical performance. Four out of the 13 goals are about data and probability. Here the developmentally inappropriate goal (especially given what isn't covered here) involves algebra:

• Compute and find the relationships using whole numbers, fractions, and decimals
• Locate positive and negative numbers on a number line (integers)
• Explain to you what prime numbers, factors, multiples and compositie numbers mean
• Compare numbers (equal to, greater than, and less than)
• Collect, organize, display, and analyze data in a variety of ways
• Find mean (average), median (middle number), mode (most frequent) and range (difference between largest and smallest) of data
• Predict or determine all possible combinations and outcomes, such as, "How many outfits can be created with six shirts and eight pants?"
• Calculate the chance of a simple event happening
• Use a variety of methods to solve for unknown quantities in simple one-step algebra equations (solve for x)
• Sort polygons according to their properties and angles, such as triangles, rhombi, and parallelograms
• Define and compare perimeter (distance around) and area (amount covered inside) of shapes
• Understand properties of a circle
• Explain how they solved a math problem in their own words.

Not a word about which computation skills the child should develop, what sorts of numbers, fractions, and decimals the child should be able to do computations on (perhaps only the "friendly" fractions and decimals), and what level of computational fluency the child should have. Not a word about multiplication tables, long division, repeating decimals, ratios and percents, and multi-step word problems.

Turning to science, only one substantive topic is mentioned (solar energy) and goals pertaining to it remain vague ("build an understanding;" "recognize"). Most the goals pertain to process rather than achievement, many of them involving developmentally inappropriate activities that wrongly assume that children can function as little scientists:

• Develop skills that will emphasize the five senses while doing science
• Use prior knowledge when making observations
• Make predictions and hypotheses based on observations
• Design investigations with a control and one or two variables
• Gather, organize and display data independently
• Build an understanding of how solar energy is transferred
• Recognize that the sun is the main source of energy for people and they use it in various ways
• Design and conduct experiments with variables. Students should be able to explain cause and effect
• Study the relationship in an ecosystem that shows the relationship of an organism to its environment
• Conduct hands-on investigations to discover and understand their world
• Record observations in science notebooks

It would seem that, "goals" aside, the Philadelphia Schools are avoiding any commitment to help your 5th grader increase his or her vocabulary, reading level, sentence construction skills, or computational fluency with "unfriendly" numbers; or learn any scientific content other than a few vague propositions about solar energy.

(Cross-posted at Out In Left Field).

Merit Aid for Parents

Catherine has kindly offered me the keys to make the occasional post here at KTM. My kids are too young to have issues with math education yet, so I will probably stick to posts about college admissions, which has been a big topic lately. I thought I'd start with a primer on merit aid.

Merit aid is probably the least well-understood piece of financial aid. The entire way that colleges figure out what you will pay is purposely vague anyway. It is based on a sense that a college that costs a lot is perceived to have a high value, while lowering tuition makes a school seem like it is lower in quality. I’m not kidding here – a few years ago, a consultant recommended that to raise our enrollment, we raise our price by 10K per year and raise average financial aid per student by 9.5K. They figured that would actually attract more students by making us look high quality and generous with aid.

The cost of college is adjustable – an institution won’t tell you the real cost until after you have been accepted and they see your FAFSA (which is basically the information on your tax return – imagine if a car dealer asked for that information before you started negotiating!) Most schools have a discount rate, which is the ratio of the real cost to the sticker price, but the published discount rate isn’t meaningful. Instead, the discount rate is different for every student.

So what should a parent understand about this process? First, the largest non-need based scholarships are grouped together as merit aid. You never apply for merit aid specifically. Instead, you are considered for merit aid as part of the admissions process. For the most part, privates give more merit aid as part of so-called enrollment management, though as Catherine noticed, state schools are also starting to compete with merit aid, especially for out of state applicants. Enrollment management is the process of getting a class of students with the desired statistics (grades/scores) that can pay the bills. So a student who is in the bottom 25% of the admitted students will be asked to pay full fare (or full fare minus any federal or other need-based financial aid, but that’s another topic). The admissions and financial aid folks know this person is probably excited to be admitted at all, so will make it work. Another student in the top 10%, on the other hand, has other options and is likely to get a better package with some kind of scholarship.

To some extent, every college wants the same students, but some schools give more merit aid than others. The Ivies and the top liberal arts colleges, which admit ~10% of their applicants, don’t give much merit aid. They don’t have to – even their top 25% applicants are excited to get the admissions letter and they can fill a strong class without discounting tuition.

There is a book out there that discusses all this in more detail, called The Financial Aid Handbook: Getting the education you want for a price you can afford.

If you go to the Amazon link and search inside the book for merit aid, you can get the main points. The Amazon site also lets you look at their list of sixty schools that give a significant amount of merit aid. You will notice that the 75% verbal/math SAT score for most of these schools is 1300-1400. So a student with 650+ SATs and solid grades can potentially score some good deals, although not at schools anyone has necessarily heard of! Also, the 25%/75% SAT numbers are public (although as the CMC scandal shows they may not be totally accurate.) You can see an example here, and find many others at collegeapps.about.com

The final thing parents and students should know is that, within a tier of institutions, you can bargain with financial aid. If Oberlin gives you a better package than Macalester, it is worth seeing if Macalester will match or beat it. However, Yale will not be impressed by an offer from Oberlin, but would try to match or beat an offer from Harvard or Princeton.

Google shmoogle

In the Times:

Silicon Valley may be booming again, but times are still tough for the 200 out-of-work professionals who crowd into Sunnyvale’s City Hall every Thursday morning.

Most of them hold advanced degrees in engineering and have more than a decade of experience in the technology sector. They fill all of the seats in the City Council chamber and spill out into the aisles.

They are members of Pro Match, a government-financed support group and “interactive career resource center” for educated older workers who have suddenly, and usually involuntarily, found themselves on the job market. Most have been out of work for months.

[snip]

While Web-based companies like Facebook and Google are scouring the world for new talent to hire, older technology workers often find that their skills are no longer valued.

[snip]

Hiring managers at the Bay Area’s fastest-growing technology companies were blunt. Seth Williams, a director of staffing at Google, said his firm was looking for candidates who are “passionate” and “truly have a desire to change the world.”

Brendan Browne, who heads hiring at the professional networking site LinkedIn, said his firm wanted every new hire to be entrepreneurial. Mr. Browne said that approximately 25 percent of LinkedIn’s new hires came from the company’s recruitment efforts at colleges and universities.

Lori Goler, the head of human resources and recruiting efforts at Facebook, said her company was looking for the “college student who built a company on the side, or an iPhone app over the weekend.” The company also hires more-experienced workers, if “they are results-focused and can deliver again.”

Regardless of age, Ms. Goler said, “We ask: Are they going to get to do what they love to do for fun at work?”

Some observers say much of this language is just code for age discrimination. They point to the case of Brian Reid, a 52-year-old manager who was fired by Google in 2004 — nine days before the company announced plans to go public — after his supervisors, including the company’s vice president for engineering operations, allegedly called him a poor “cultural fit,” an “old guy” and a “fuddy-duddy” with ideas “too old to matter.”

Mr. Reid sued Google for age discrimination and said that his unvested stock options would have been worth at least $45 million if he had stayed there.

Google denied the charges and asked that the suit be dismissed, calling such remarks “stray comments.” But the California Supreme Court ruled that the claims, if true, would constitute discrimination. The case was resolved out of court “to the mutual satisfaction of all parties,” said Lori Ochaltree, Mr. Reid’s lawyer, who declined to say how much the settlement was.

A Google spokesman declined to comment on the case or the amount of the settlement.

In an interview, Norman S. Matloff, a professor at the University of California, Davis, who has studied hiring patterns in the technology sector, said workers over 35 regularly face discrimination by technology companies.

Kris Stadelman, director of NOVA, the local work force investment board, which released a survey of human resource directors at 251 Bay Area technology companies last July, said that in her experience, candidates began to be screened out once they reached 40.

“Especially in social media, cloud computing and mobile apps, if you’re over 40 you’re perceived to be over the hill,” Ms. Stadelman said.

Old Techies Never Die; They Just Can’t Get Hired as an Industry Moves OnBy AARON GLANTZ

I've never liked Google.

Now I don't like LinkedIn or Facebook, either.

Hmmph.

Aloha from the Help Desk

In my email queue this week:

Did you forget your Connect username or password? Please visit the link http://connect.edu/ and click on “Forgot your password” to look up your username and password.

Have you been locked out of your Connect Account because of too many failed login attempts? Please contact the Help Desk at xxx-xxx-xxxx or helpdesk@edu to unlock your account.

Have you forgotten your Outlook Email Password or need to reset it? Please visit http://www.edu/pass

More evidence that Something Happened in 1985, bouncing me and mine off our home planet and onto the planet we're on now, the one where Salman Khan is the man you summon to help you spice up your presentations and the Usability Profession never got invented.

'If the price of something rises a lot, people look for substitutes'

With regards to colleges, consumers typically have believed that there are no good substitutes ...

Things are changing, but it's debatable how quickly change willl occur.  The search for alternatives is leading to other entities offering credentials for much less than the $30,000-$60,000 per year that colleges charge.  New agreements between Burck Smith’s StraighterLine, the Education Testing Service (ETS), and the Council on Aid to Education (CAE) to offer online competency tests have just been announced.

Students can tell employers, “I did very well on the CLA and iSkills test, strong predictors of future positive work performance,” and, implicitly “you can hire me for less than you pay college graduates who score less well on these tests.”

More at Cost of College

Related:
M.I.T. adds credentialing to its online course program
Higher education is a prisoner’s dilemma

Stop me if you've heard this one

In Waterloo, Iowa, Investigations in Number, Data and Space, is being used and getting rave reviews, according to this article.


Here's a quote taken right from the article. Stop me if you've heard it before:

"Administrators describe the curriculum, published by Pearson Education, as providing rich, problem-based, student-centered lessons that foster inquiry and develop critical thinking skills. They believe the result of developing those skills will be increasing student achievement."

the ridiculous debate over charter schools

http://www.ajc.com/news/fulton-school-board-denies-1266177.html

A Georgia school board denies a charter renewal request by an award-winning charter school in a 7-0 unanimous decision.

http://www.washingtonpost.com/local/education/fairfax-teacher-proposes-charter-school/2012/01/18/gIQAHTsS9P_story.html

"Virginia law gives local school boards authority to approve or deny a charter proposal. Charter advocates say the system creates a difficult hurdle because local boards are often loath to help create direct competition." 

Some comments on the Washington Post's facebook:

That's CRAP!!! That wouldn't be fair to the kids who are not high-performance....

Charter Schools STEAL educational advantages from the students left behind. Disgusting! Public schools should not allow a caste system for students...

Sounds like reinventing the wheel. Why not FIX the schools that need it instead


How curious, because most charter schools I know have admission by lottery. Of course, higher-achieving students might be more wont to apply to a charter school, causing a statistical bias. Is the argument against charter schools really, "they'll draw the brighter students away?" Because of course the brighter lower-income students who can't afford private school should be FORCED to stay imprisoned, and cooped-up.

College Goal Sunday helps students obtain financial aid

College Goal Sunday is a program dedicated to assisting students and families in accessing financial aid for college.  Events are held nationwide where students can go to:

• Get free on-site professional assistance filling out the FAFSA (Free Application for Federal Student Aid) form.
• Talk to financial aid professionals about financial aid resources and how to apply.
• Get information regarding state-wide student services, admission requirements, and more!

Check out their website to find a location near you.  Act quickly because you must pre-register and some sites are very popular.  I will be at the New Rochelle College Goal Sunday on February 12, but it has filled up and is no longer accepting registrations.  Yonkers is nearby and still has open slots.

ALSO:  Don't wait too long to request financial aid

(Cross-posted at Cost of College)

afterschooling circa 1910

YOUNG Thomas Jones came home from school with sad and solemn air;
He did not kiss his mother’s cheek nor pull his sister’s hair;
He hungered not for apples, and he spoke in dismal tones;
‘T was very clear misfortune drear had happened Thomas Jones.

“My precious child,” his mother cried, “what, what is troubling you?
You ‘re hurt–you ‘re ill–you ‘ve failed in school! Oh, tell us what to do!”
Then Thomas Jones made answer in a dull, despairing way:
“I ‘ve got to write an essay on ‘The Indian To-day.’”

His tallest sister ran to him, compassion in her eye;
His smallest sister pitied him–nor knew the reason why;
And all that happy family forsook its work and play
To hunt up information on “The Indian To-day.”

They read of Hiawatha and of sad Ramona’s woe–
You found encyclopedias where’er they chanced to go.
They bought a set of Cooper, and they searched it through and through,
While Thomas Jones sat mournfully and told them what to do.

For three whole days the library was like a moving-van.
“Is Mr. Jones,” each caller asked, “a literary man?”
And day by day more pitiful became young Thomas’ plight,
Because, alas! the more he read, the more he could not write.

“Write what you know,” his mother begged (she stirred not from his side).
“I do not know one single thing!”that wretched child replied.
“Oh, help me, won’t you ? Don’t you care?” Then when assistance came,
“Don’t tell me–don’t! It is n’t fair!”he pleaded just the same.

The night before the fateful day was quite the worst of all.
Black care upon the house of Jones descended like a pall.
All pleasure paled, all comfort failed, and laughter seemed a sin;
For “Oh, to-morrow,” Thomas wailed, “it must be handed in!”

When, lo! the voice of Great-aunt Jones came sternly through the door:
“I cannot stand this state of things one single minute more!
The training of a fractious child is plainly not my mission;
But–Thomas Jones, go straight upstairs and write that composition!”

And Thomas Jones went straight upstairs, and sat him down alone,
And–though I grant a stranger thing was surely never known–
In two short hours he returned serenely to display
Six neatly written pages on “The Indian To-day”!

His teacher read them to the class, and smiled a well-pleased smile;
She praised the simple language and the calmly flowing style;
“For while,” she said, “he does not rise to any lofty height,
‘T is wonderful how easily young Thomas Jones can write.”

I need a maiden aunt.

poem posted by historian Zachary M. Shreg at his terrific site 

Katharine Beals in the Times

Wonderful letter:

Excluding the higher functioning [autistic] children [from the autism diagnosis] means that schools will have to do more to make regular classrooms hospitable to them without the early intervention based accommodations mandated by the Individuals With Disabilities Education Act. 

In particular, teachers will have to stop requiring children to work in groups, share personal reflections and do organizationally demanding interdisciplinary projects — all of which are challenging for the sort of child who, rightly or wrongly, has sometimes received a diagnosis of mild autism/Asperger. 

The new American Reform Math is also problematic for this population, since it waters down the actual math and teaches it less systematically. 

KATHARINE BEALS
Philadelphia, Jan. 23, 2012 

The writer is a lecturer at the University of Pennsylvania Graduate School of Education and the author of “Raising a Left-Brain Child in a Right-Brain World.”

Common Core PARCC Test?

Our state is part of a 24 state group that will use the Partnership for Assessment of Readiness for College and Career (PARCC) tests that are (will be) tied to the Common Core Standards (CCSS). There was a big article about it in our local newspaper. It is a step up from NCLB, but it's still "one size fits all". Schools will still be able to get away with using curricula like Everyday Math.

The claim that:

"Students who will know if they are on track to graduate ready for college and careers"

is more true than for our old NCLB test, but it says little about being ready for STEM careers. You can meet CCSS standards and still have career doors close.

The interesting thing I see is that it's a 24 state group working on a common test. It seems that we are moving towards a national curriculum and test. This should provide better data to compare states and towns. Our state will have to compete with others. The way it is now, our NCLB tests can only be compared with two other states using the same test. However, they have to (once again) restart the collection of longitudinal data.

I haven't seen sample tests, so I might change my mind.

Why students have to memorize things

re: Larry Summers' claim that "in a world where the entire Library of Congress will soon be accessible on a mobile device..., factual mastery will become less and less important":

Larry Summers is wrong.

Factual mastery has not and will not become less important, for the simple reason that it is not possible to think about something stored on Google.

While you are thinking about something, that something has to be lodged inside working memory, not Google.

Biology does not work the way Larry Summers thinks it works.

Working memory

If I ask you to multiply 36 by 3 inside your head, working memory is what you use to do it.

Working memory (WM) does three things:

1. Holds the problem -- "multiply 36 by 3" -- in consciousness 
2. Retrieves the relevant knowledge from long-term memory (the times tables, in this case)
3. Performs the calculation

Boiling it down, working memory is:

1. a form of storage
2. a search engine 
3. a "computer" or thinker

"Critical thinking" is accomplished by working memory.

3 to 5

The fact that we can think only about things stored inside working memory leads directly to the need for "factual mastery."

Factual mastery—knowledge stored inside long-term memory—is essential because although long-term memory is vast, working memory is tiny:

...cognitive tasks can be completed only with sufficient ability to hold information as it is processed. The ability to repeat information [you have just heard or read] depends on task [difficulty]... but can be distinguished from a more constant, underlying mechanism: a central memory store limited to 3 to 5 meaningful items in young adults.

The Magical Mystery Four: How Is Working Memory Capacity Limited, and Why? by Nelson Cowan

Working memory can hold three to five items at once. That's it. That's the limit.

Three to five.

I hit this limit all the time trying to write about new topics. The basal ganglia, for instance. For well over a year, I have been endlessly working and re-working a project on the basal ganglia, a subject I knew essentially nothing about going in. Where the basal ganglia were concerned, my long-term memory was a blank slate.

The upshot: I was not able to write about the basal ganglia until I actually learned about the basal ganglia: learned as in committed the material to memory. It didn't matter how many times I looked up basal ganglia on the internet. I looked up the basal ganglia on the internet a lot, as a matter of fact; then I forgot whatever it was I had looked up while I was looking up something else to do with the basal ganglia, after which I'd have to go back and re-look up the first thing all over again.

Try it if you don't believe me.

Here are some terms related to the basal ganglia:

Dorsal striatum
Ventral striatum
Putamen
Nucleus accumbens
Ventral tegmental area
Orbital frontal cortex
Dopamine
Two pathways
OCD
Addiction
Habit
Impulsive
Compulsive
Intuition
Probabilistic learning
Associative learning
Statistical learning
Serotonin
Orbitofrontal cortex
Cortico-striatal circuit

Now supposing I handed you a laptop and asked you to look up each term on Wikipedia, then write a coherent, reasoned 5-paragraph essay on the basal ganglia: what it is and what it does. Just a quick summary organized into 5 coherent paragraphs.

You couldn't do it.

You couldn't do it because every time you wrote about the ventral striatum, the dorsal striatum, and the orbitofrontal cortex, you would forget the VTA and the putamen—and you would forget the VTA and the putamen because your working memory will hold only 3 to 5 things at once. Something has to go.

That's what happened to me when I took the SAT with a calculator I didn't know how to use. Each time I swapped the steps for using the calculator into working memory, my brain swapped the information for the problem I was doing back out of working memory. Then, when I tried to cram the information for the problem back into working memory, the calculator steps got squeezed out again.

I could remember the problem, or I could remember the calculator, but I couldn't remember both at the same time. Too much information, literally.

My calculator fiasco illustrates the reason you need to practice until you learn content and skills to the point of 'automaticity.' (Automaticity is another basal ganglia term, by the way. The basal ganglia are the part of the brain that underpins automaticity.) Once you've learned something so well you don't have to think about it, you free up space in working memory to hold other things.

Thus if you know the times tables "by heart," you don't need to pull "3x6=18" into working memory. Working memory can locate "3x6=18" inside long-term memory and use it without displacing "36x3."

Knowledge stored inside the brain is different from knowledge stored outside the brain

Experts always possess factual mastery of their fields. Always.

The reason experts always possess factual mastery of their fields is that knowledge stored in long-term memory is different from knowledge stored on Google.

Knowledge stored in long-term memory is (or becomes) biologically connected, or "chunked." Thus to an expert on the basal ganglia, ten facts about the basal ganglia are just one or two big facts about the basal ganglia.

Chunking is the magic, because working memory doesn't care about chunk size. Working memory can hold 3 to 5 small and simple items or 3 to 5 large and complex items. Either will do. Chunking gets around the limits on working memory.

Dan Willingham's demonstration of working memory

For a demonstration of the chunking principle, read the list below, then look away and try to remember what you've read:

CN

NFB

ICB

SCI

ANC

AA

How many letters did you recall?

To find out how many letters you would have recalled via prior chunking inside long-term memory, see Daniel Willingham's explanation in "How Knowledge Helps" (American Educator | Spring 2006).

(The answer is all of them.)

You can't Google knowledge chunks

Knowledge chunks can be created only inside the brain, via learning. You can't Google someone else's complex knowledge chunks and swap them into your own working memory. It doesn't work that way. Your own brain has to do the work of chunking, and your brain does that work through the process of learning, bit by bit and step by step.

Which means that the process of storing content in long-term memory is not a simple matter of "memorizing facts" so you can "regurgitate" them later.

Over time, memorization creates the complex knowledge chunks that allow knowledgeable people to engage in complex thought.

Experts think better than novices because experts have factual mastery

To a gratifying degree, I can now think about nearly all 19 items on the basal ganglia list at the same time. I'm still struggling with "putamen" and "ventral tegmental area," but the other 17 are stored in memory: my memory, not Google's. So, for me, those 17 items are no longer 17 separate items, but closer to 2 or 3. When I think about 1 item on the list, I'm thinking about the others.

I reached this point by committing these terms and concepts to memory. As the terms entered my long-term memory, they became biologically connected and chunked. Now that I can think about them at the same time, which means I can write about them, too.

What makes experts expert, to a large degree, is factual mastery of their fields. Factual mastery allows experts to think deeply and well because the content they are thinking about has been biologically connected and chunked inside their brains, and there is no obvious limit to the amount of chunked content working memory can manage so long as knowledge has been chunked into no more than 3 to 5 separate entities.

Factual mastery is required for complex thought.

Which brings me back to Larry Summers.

If our schools are going to ask students to 'think' about material they haven't learned, students are going to be thinking about 3 to 5 small, not-well-elaborated items at a time. Period. Their thinking will be superficial, and the conclusions they reach will be superficial, too.

Which is exactly what we see in Larry Summers' op-ed about education, a field in which he is neither expert nor learned.

AND SEE: 
Superior Memory of Experts and Long-Term Working Memory (LTWM)
Extremely fast learning & extended working memory
The Number and Quality of Representations in Working Memory by Weiwei Zhang and Steven J. Luck
How Knowledge Helps by Daniel T. Willingham American Educator Spring 2006
#whystudentsneedtomemorize

Larry Summers has a really bad idea

In today's Times, Larry Summers weighs in on the question of what college students ought to learn in college.

Larry's answer: not too much, because the entire Library of Congress will soon be accessible on a mobile device with search procedures that are vastly better than any card catalog!

Larry bases his novel and highly original thesis (to wit: "factual mastery will become less and less important") on "what we now understand about how people learn."

(Does Harvard have node chairs, I wonder? Sounds like no.)

OK, I'm going to go look up calculus on the internet. I've always been interested in calculus, so now that I've received a mobile device for Christmas, I'm going to look it up. Then I'm going to collaborate with some friends who also looked up calculus on the internet to figure out what to do about the 21st century global world meltdown.

I'm going to do this because I've noticed that economists use calculus in their collaborative group papers.

[pause]

There is a reason why students must commit content to memory as opposed to looking it up on a mobile device with search procedures that are vastly better than any card catalog.

That reason has to do with working memory.

More anon.

What You (Really) Need to Know by Lawrence A. Summers

update: Why students have to memorize things
and see: Extremely fast learning & extended working memory

AND SEE:
The founder, chair, and CEO of Netflix has a really bad idea
Larry Summers has a really bad idea
Wash U professor on Reed Hastings' really bad idea
Barry Eichengreen has a really bad idea
President Obama has a really bad idea

David Brooks has a really bad idea
David Brooks has a really bad idea, part 2
David Brooks has a really good idea

The Daily has a really bad idea

Algebra for Parents

My employer, the School of Education and Human Services at Oakland University, is currently considering (at my urging) offering one or more online courses for parents of secondary school-aged children.  Our target audience is homeschooling parents, but others are welcome as well.  We plan to offer, as our pilot offering, "Algebra for Parents".  If that is successful, we would look into expanding to a larger menu of courses.

The main idea behind these classes would be to help parents shore up their content knowledge, with a secondary focus on the pedagogy of home-based education.  These would be not-for-credit courses run through our professional development program; we are framing this as "Professional Development for Homeschool Teachers".

I know that Ed Schools are not very popular on this blog, and PD in math ed has a pretty poor reputation for being superficial and light on content (often, unfortunately, completely deserved).  And I know first-hand that many homeschoolers are skeptical about getting entangled with institutions.  But I have pretty high hopes for this venture.  For one thing, I'll be teaching the course, and I have complete creative control over what gets done.  For another thing, I myself am the parent of five home-educated & unschooled children, all of whom learn quite differently, so you can count on an atmosphere that is open to a wide range of approaches.

All the details of format and pricing are still being worked out, but right now I am thinking that the class will run in six-week sessions.  Each week we will meet once for a single two-hour, real-time webinar (ugh, hate that word), with the rest of the week filled out with individual work and forum discussion.   Figure total involvement at anywhere from 2-6 hours per week, depending on how much you want to engage with the work.

Catherine has given me permission to announce the class here for the purposes of gauging interest.  So please let me know (either in comments, or in private email):  Would you be interested in taking (and paying for) a class like this?  Does the format and focus sound right for you, or are there other things we should consider?