kitchen table math, the sequel: 1/22/12 - 1/29/12

Saturday, January 28, 2012

the ridiculous debate over charter schools

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

"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. 

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.”

Thursday, January 26, 2012

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.

Monday, January 23, 2012

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
Nucleus accumbens
Ventral tegmental area
Orbital frontal cortex
Two pathways
Probabilistic learning
Associative learning
Statistical learning
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:


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.

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


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.


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

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

Sunday, January 22, 2012

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?