Good News for Math Beasts

Good news to report! The Art of Problem Solving has released book 4A from its Beast Academy series and is hard at work at the rest of grade 4 and all of grade 5.

Algebra 1 in the 8th Grade (...or not)

Boston Globe (North) Reading’s New Math Curriculum Runs into Protests The district has adopted a new sequence that leaves more than 80 percent of eighth-graders without a direct path to a high school calculus course. Only 18 percent will be enrolled in algebra 1, compared with 60 percent to 65 percent in previous years, according to Craig Martin, Reading’s assistant superintendent for learning and teaching. [Parents] have expressed concern that the school system’s departure from the traditional math sequence, which required a majority of students to take algebra 1 in eighth grade, may leave little room for a high school calculus class, a requirement at many colleges for acceptance into a science or engineering undergraduate program.

Apparently students who attend Ivy League schools are good memorizers

Yale students seem to have spent so much time memorizing history facts and dates that Professor Joanne Freeman feels compelled to warn students against the Revolutionary War "fact bubble":

Tip number one is don't get lost in the dreaded Revolutionary War fact bubble, which I have to say it makes me think of the first time that I taught this course. I was actually a brand new professor and I had just come to Yale and it was my first course and it was my first lecture in my first course and I'm [sound cuts out] It actually was in Connecticut Hall, which, for those of you who don't know, dates back to the period when this course is talking about and was Nathan Hale's -- essentially his dorm. So there I am. I'm a brand new professor to Yale and I'm teaching a course about the Revolution and it's in a building that dates to the Revolution, so I'm having sort of a "wow" Yale moment as it is, and I'm off, I'm giving my lectures, and I'm really excited. I give about three of them and someone raises their hand after about three lectures and they have a kind of a puzzled expression on their face. I said, "Yes?" And he says, "Excuse me, Professor Freeman. What are we supposed to be memorizing? Where are the facts and dates?" [laughs] So as a new professor my first impulse was: Darn! I forgot the facts and dates. [laughter] I got it wrong. [laughs] But actually, the fact of the matter is, they're not the star of the show. Certainly, dates are not the star of the show. There are dates you're going to have to remember so don't think Easy Street; there's not a date I have to know. There will be some dates, but this isn't a story about dates. It's obviously something a lot more interesting and a lot broader than that. Okay. Avoid fact bubble.

Joanne Freeman "American Revolution" | Lecture 1 Introduction: Freeman's Top Five Tips for Studying the Revolution

Obviously, excessive memorization didn't keep these students out of Yale.

I'm sure there's a reason for that, the reason being that excessive memorization actually helped.

And here is Daniel Willingham:  prior knowledge & working memory in 1 paragraph

"Brief History of Mankind" starts tomorrow (& a MOOC thought)

At Coursera.

I'm loving Joanne Freeman's American Revolution course, though I'm making my way through it only slowly (& doing none of the reading, sad to say).

I had a revelation the other day that watching a videotape of a lecture delivered in a lecture course may actually work for the same reason watching a videotape of a stand-up comedy routine works. The lecture course and the comedy routine are the same form: one person, on stage, talking to a very large group of people who don't know each other.

Freeman's "American Revolution" is a classic lecture-hall survey; she doesn't even use Powerpoints! At one point, early on, she says "So that's what I mainly address for the rest of the lecture, and I'm going to talk about it by focusing on three different points" -- and she holds up three fingers.

The three-finger moment was interesting to me because, at Yale, when a professor says she is going to be focusing on three points, attention is paid. 

From the transcript:

So that's what I mainly address for the rest of the lecture, and I'm going to talk about it by focusing on three different points. Point number one: I'm going to talk a little bit about the distinctive character of the people who migrated to the colonies. [here she reacts to her student audience & starts laughing] It gives you such a sense of power when you're lecturing and you say, "There are three reasons" and the entire rooms goes: "Oh." [laughter] "Three. There are three." So there are three. So number one is the distinctive character of the people who migrated to the colonies. Number two is the distinctive conditions of life in British America, -- and that point I'll talk about for the longest. And then number three is the nature of British colonial administration. And I'll repeat that: the distinctive character of the people who migrated to the colonies, the distinctive conditions of life in British North America, and the nature of British colonial administration."
Lecture 3 The American Revolution: Being a British American | January 19, 2010

Freeman makes a number of references to eager-beaver student behavior throughout her lectures.

Passage from McGuffey's Sixth Reader

I'd been wanting to post a passage from McGuffey's Sixth Eclectic Reader Revised Edition (1879) for ages now, but it seemed too long for a blog.

Now that I've discovered Blogger's Page feature, I've added a Page called "What people used to be able to read."

Bad-news scores

My district's first set of Common Core scores. (Sample test questions.)

I read a funny letter in the Times today from the mother of a child in third grade:

[snip] I am a journalist and editor, and I found the writing on my third grader’s sample language arts test so dense (and dull!) that even I sometimes had trouble reaching correct answers. Likewise, sample questions for the third-grade math test, which are intended to measure greater complexity in thinking, looked to me like basic word problems with lots of superfluous words.

Naturally that second observation forced me to drop everything (or, more accurately, further delay beginning everything) and check the 3rd-grade math questions.

I found this:

Two groups of students from Douglas Elementary School were walking to the library when it began to rain. The 7 students in Mr. Stem’s group shared the 3 large umbrellas they had with Ms. Thorn’s group of 11 students. If the same number of students were under each umbrella, how many students were under each umbrella?

You may use the space below to draw a picture of the problem.

Mom's got a point.

Goodreads!

I saw a bunch of you 'friended' me (or whatever it is one does on Goodreads) -- fantastic!

What fun!

Leader shmeader

Debbie S. sent me this link to a Times story on Berkeley's holistic approach to reading applications --- amazing!

....Another reader thinks the student is “good” but we have so many of “these kids.” She doesn’t see any leadership beyond the student’s own projects.

Listening to these conversations, I had to wonder exactly how elite institutions define leadership.

Confessions of an Application Reader
Lifting the Veil on the Holistic Process at the University of California, Berkeley
By RUTH STARKMAN
Published: August 1, 2013

Remind me to tell you my story about the time the Dartmouth admissions officer came to Irvington.

Actually, why don't I go ahead and tell the leadership part of the story now.

During his talk the Dartmouth guy mentioned "leadership" so many times that finally a parent in the audience raised his hand and said, "What if your child isn't a leader?"

The admissions officer said, and I am close to quoting: "There are many ways to be a leader. Being a good follower is being a leader."

Perplex this!

I'm thick in the middle of things, but in my travels today I came across this passage (two seconds ago, actually) and I had to post.

Dan Meyer, 31, is in the process of becoming a celebrity math teacher (hey, it’s a small group). Much of his rapid trajectory upward can be explained by his message, which involves a digital curriculum that will (he says) instantly engage and perplex kids and thus resolve all classroom management issues (more on this later), a message tailor-made to appeal to both techies, since it implicitly attacks all teachers, and progressive educators, since it is inherently constructivist.

Dan Meyer and the Gatekeepers
educationrealist

He had me at "instantly engage and perplex kids and thus resolve all classroom management issues."

In the cabin

I'm loving the anonymous "Insider" (aka "Stakeholder") quotes in the report from Whiteboard Advisors.

My favorite, re: President Obama's proposed tobacco tax to fund preschool:

"Houses the idea safely in the ‘this will never be agreed to’ cabin."

We need that cabin in my district.

On when ESEA reauthorization will take place:

"Never. It’s now a moth in amber–preserved in perpetuity. They ought to send it to the national archives and put it under glass."

"At this point, there is zero leadership on this at ED, and zero interest on the Hill."

On PARCC and SBAC: right track or wrong track?

"As many predicted, this is turning out to be one of the greatest boondoggles of all time."

"It is the beginning of the end for both. States are going to start running for the door. To many reasons to get out. The Administration ultimately spends ~$350 million for something states didn’t want and the market took care of."

"Smarter Balanced is headed in the wrong direction educationally; PARCC is headed in the right direction but is afflicted with grievous problems of organization, management and delivery."

“The Common Core is having a PR problem, very generally.”

“They were artificial constructs that didn’t have any actual support behind them other than a way to spend money. It would have made more sense to give the money to states and encourage them to build their own consortia so that they actually wanted to participate and be part of it.”

On Randi Weingarten's proposed moratorium on high-stakes testing:

“Over the last 60 days, the entire CCSS architecture has gotten wobbly. Anything is possible now. Opponents smell blood in the water.”

“The centrist, compromise position will become ‘delayed.’ Those who support it will go out of their way to show they are not ditching accountability.”

And Arne Duncan, unbeloved:

“Arne Duncan has blinders on and thinks that he is the nation’s superintendent, chief school board, and principal for every school. He doesn’t understand or accept criticism, and doesn’t see how poorly this is going. States will freak out when they see the assessments and their cut scores and will do everything and anything to back away from this land mine as quickly as possible.”

I wonder what nuggets I'll find in the report from April 2013.

Yet another reason for instructional grouping

Abstract

Two studies tested the effect of humor, embedded in learning materials, on task interest. College student participants (NStudy 1 = 359, NStudy 2 = 172) learned a new math technique with the presence or absence of humor in the learning program and/or test instructions. Individual interest in math was measured initially and also tested as a factor. The results showed that the effect of humor in the learning program depended on individual interest in math. Humor raised task interest for those with low individual interest in math but slightly lowered task interest for those with high individual interest in math....

The effect of humorous instructional materials on interest in a math task
Kristina L. Matarazzo • Amanda M. Durik • Molly L. Delaney | Motiv Emot (2010) 34:293–305

"Growing headwinds for Common Core"

I haven't been following the progress of PARCC....and I hadn't realized how central the idea of common assessments were to the Common Core undertaking, although I should have.

Looks like things aren't going well on that front:

Yesterday, PARCC released the cost of its tests—and right on cue, another state, Georgia, dropped out of the testing consortia. This is a disaster.

At this point, I won’t be surprised if we end up with 20 or more different testing systems in 2014–15. So much for commonness, so much for comparability. Rigor and alignment with tough standards are likely the next to fall.

That's how the consortia crumble
Andy Smarick / July 23, 2013

Here is Truth in American Education on Whiteboard Advisors Insider Results on Common Core.

And here is T.H.E. Journal Magazine on Remaining PARCC States Affirm Commitment, Get on Track for Field Testing By Dian Schaffhauser 07/30/13

The "Insider" brief is fun: Tracking Measures, Growing Headwinds for Common Core, and Prospects for Administration Policy Proposals May 2013.

This reminds me David Steiner's observation, which I've heard him make twice...which was that, at least in his view, the point of Common Core was to get around the fact the Constitution leaves education up to the states. That's why Common Core produced standards instead of curricula, Steiner said: the U.S. federal government cannot constitutionally impose a central curriculum on the states.

So the idea was to impose a central set of standards instead.

I guess common assessments adopted willingly by individual states were another means of circumventing that obstacle. (They would pretty much have to be if the goal is to circumvent the constitution.)

The whole undertaking now seems crazy to me.

Get around state prerogatives?

By creating a complicated and expensive common assessment states have to buy?

[pause]

Maybe this is crazy; I haven't thought it through.

If you really want common assessments - if you actually want to make common assessments happen as opposed to almost make them happen and then have states pull out of the consortium - pass a law requiring every student in the country to take one of the already-existing standardized tests when he or she leaves school.

SAT, ACT, SAT Subject Matter tests, Accuplacer....pick one, pass a law requiring 18-year olds to take it (is that constitutional? I don't know), and fund it.

Then you have a nationally standardized comparison of all students in the United States.

Andy Smarick's other post is worth reading, too: The Complicated Economics of Testing in the Era of Common Core Standards


The Role of the Federal Government in Public Education in the United States

Enduring links from childhood Math and reading

Abstract

Understanding the determinants of socioeconomic status (SES) is an important economic and social goal. Several major influences on SES are known, yet much of the variance in SES remains unexplained. In a large, population-representative sample from the United Kingdom, we tested the effects of mathematics and reading achievement at age 7 on attained SES by age 42. Mathematics and reading ability both had substantial positive associations with adult SES, above and beyond the effects of SES at birth, and with other important factors, such as intelligence. Achievement in mathematics and reading was also significantly associated with intelligence scores, academic motivation, and duration of education. These findings suggest effects of improved early mathematics and reading on SES attainment across the life span.

Enduring Links From Childhood Mathematics and Reading Achievement to Adult Socioeconomic Status
Stuart J. Ritchie and Timothy C. Bates | Psychological Science 24(7) 1301–1308 2013

I've been reading many abstracts of late.

Andrew in August

For all of Andrew's^* life, until my mother died in January 2011, we went to Illinois every August. First to Springfield, then to Chicago. Always, without fail.

August is upon us again, and Andrew has been lobbying for his trip to Illinois for days now: lobbying Ed and me and, when that goes nowhere, searching for Chicago and "grandma's house" on Google.

Today his teacher^* sent home this list of sentences Andrew wrote on the computer at school:

I go to Staybridge on August 16th.
I go on the airplane.
First I go to camp.
Then I go to Staybridge.
I will see grandma in Staybridge.
Grandma's house is in Staybridge.
Staybridge is in Chicago.
I love Grandma.
Mommy and Daddy are going with me.
I have to pack my bags.

I have no idea how to handle this.

^* For passersby, Andrew is 19 years old and has autism. The references to Staybridge are to the Staybridge Inn in Springfield, our home away from home. 

Color me not surprised

In sum, we propose that adults never fully outgrow the cognitive and perceptual biases that are so striking in infants and preschoolers. That is a humbling thought, much as it was humbling to discover that humans are not the center of the universe or as rational and ‘‘in control’’ as once thought. However, if clarity can come from investigating extreme cases, then perhaps studying children, who show these biases more blatantly than adults, might be a rich source of insight and future hypotheses about adult cognition.

Not Quite as Grown-Up as We Like to Think: Parallels Between Cognition in Childhood and Adulthood
Adele Diamond and Natasha Kirkham | Psychological Science Volume 16—Number  4 | p 291-297.

I'm just waiting for the day they find out crows are smarter than people.

A lot smarter.

Gutting Out the Grammar

Lately, I have been thinking more about SteveH's experience of an elementary teacher dismissing his young son's knowledge of geography as "mere facts" because I have steered my family's educational boat even more towards the classical model over the last year or so.  (We have even started Classical Conversations one day a week, the model of which would horrify the type of folks who say "drill and kill.")

Because, well, *OF COURSE* his son only had superficial knowledge, mere facts.  He was an elementary student.  That's what they do, those little collectors of knowledge.  Those sponges.  They absorb facts.  And if you don't provide them with useful ones, they will happily populate their brains with the name and basic biographical information of every character in the Star Wars Extended Universe.  (They may even do that, anyway.  Mine sure have.)

Here's what I don't understand about the folks who think it is so horrible to load up a child's brain with "mere facts" -- do they really, *really* think it never has to be done?  Do they not mind that the fact-can just get kicked down the road to either high school or college, when you can no longer progress without the domain knowledge but your brain is no longer developmentally eager to be constantly memorizing and chanting inane things?

Then I was thinking of Catherine.  And basal ganglia.

Well, I did no actual thinking about basal ganglia, to be sure, because I don't know the first thing about it.

Of course, there's the rub -- what is the "first thing" about basal ganglia?

As Catherine wrote much about when she started plunging into her studies, you have to learn the lingo.  You have to absorb the "mere facts" -- the grammar -- of any new field.  Why wait to do it until you have to simultaneously struggle with the logic and rhetoric (to use the classical model's terminology)?

The whole thing just makes me angry.

I can't tell you how many moms I have met who tell me a similar story: They "hated" math.  They feared having to teach it to their kids.  Then after going through Singapore (or even Saxon, for that matter) in the elementary levels, it all clicked and they realized they *liked* math and were good at it.

My pet theory is that if you look at math from the grammar --> logic ---> rhetoric model point of view, grammar has been gutted out of the picture in many schools for some time and it is fashionable to try to jump straight into logic (if not rhetoric) right away.  And now we have these moms who are *finally* getting their grammar stage math competence, and suddenly the logic / rhetoric stage math is no longer frightening (and, in fact, fun and fascinating) because they finally have the foundational underpinnings to understand it.

Maybe?

Naturals and strivers

To understand how talent and achievement are perceived, three experiments compared the assessments of “naturals” and “strivers." Professional musicians learned about two pianists, equal in achievement but who varied in the source of achievement: the “natural” with early evidence of high innate ability, versus the “striver” with early evidence of high motivation and perseverance (Experiment 1). Although musicians reported the strong belief that strivers will achieve over naturals, their preferences and beliefs showed the reverse pattern: they judged the natural performer to be more talented, more likely to succeed, and more hirable than the striver. In Experiment 2, this “naturalness bias” was observed again in experts but not in nonexperts, and replicated in a between-subjects design in Experiment 3. Together, these experiments show a bias favoring naturals over strivers even when the achievement is equal, and a dissociation between stated beliefs about achievement and actual choices in expert decision-makers.

Naturals and strivers: Preferences and beliefs about sources of achievement
Chia-Jung Tsay, Mahzarin R. Banaji Journal of Experimental Social Psychology 47 (2011) 460–465

I wonder why this is?

Why would experts hold the bias (while believing they hold the opposite bias) while nonexperts don't?

Is this likely to be specific to the music world? (I have no idea.)

"The virtues of opaque prose"

ABSTRACT

Instructors tell their students to write clearly. This prescription meshes with our intuition, wins confirmation in scores of books on writing, and finds empirical confirmation in research on perceptual fluency: People like content that is easy to process. Nevertheless, in some circumstances people expect content to be difficult, and ease might be interpreted as a lack of quality. We investigate this possibility by asking people to judge the quality of written text which varies in fluency (through the manipulation of font and facial feedback). Across three studies, disfluent content was judged to be of higher quality when it was thought to come from a source focused on conveying information than one designed to maximize enjoyment.

The virtues of opaque prose: How lay beliefs about fluency influence perceptions of quality Jeff Galak, Leif D. Nelson Journal of Experimental Social Psychology 47 (2011) 250–253

I'm trying to decide whether Galak and Nelson's prose is opaque enough to make me believe them...

Goodreads

Is anyone else on Goodreads?

I joined a couple of months ago & am still getting the hang of it.

I'd love to get book recommendations from all of you---

I think you can find me here.

Fort Hood

I stayed for a day and a half of presentations and ended up missing a fabulous talk by a retired British.... Colonel, I think.

He talked about the French army and confirmed everything Ed had said previously on the subject of France being a warring nation, which I hadn't known. If I get to it, I'll post a couple of Ed's slides listing all the wars the French have fought over the centuries. There are many.

[pause]

Forget Ed's slides. Check this out.

France may also be the longest continuously existing state, btw. Another thing I didn't know.

Ed says Glen told the soldiers that they have to think of the French military as the Marines; they are that good.

He also made a point that had never occurred to Ed or me although it's obvious once you hear it: armies need to fight wars. Meaning: the only way to stay in practice is to fight real wars. War exercises aren't enough.

The French army fights real wars. Glen showed videos of the Mali operation, and the take-away was essentially that the French army is brilliant. French soldiers were doing 9000-mile sorties and making them look like a field trip to the recycling plant.

He also showed photos (videos?) of the German army, which is choc-a-bloc with expensive weaponry and aircraft, but whose soldiers haven't fought in a real battle since --- WWII? His opinion is that if something happens in Europe, only two countries will be prepared to fight: England and France.

In terms of defense, the issue is Russia, which has been sending probes into the airspace over the Baltic States (I now know what the Baltic states are, so time well spent...) and over Sweden. Apparently Russia is too intimidated by Finland to poke its nose into Finnish air space.

Russia also stages showy war exercises to practice an invasion of the Baltic states. The Russian army is doing one now, I think -- now, or not long from now. Military analysts assume Russia would like to take back the Baltic states because they have warm-water ports, which don't freeze in winter. Russia is too weak to attempt that now, but, on the other hand, Putin may not know that. He may be surrounded by people telling him the country is a mighty power; there is no way to know.

At dinner Glen told Ed that his first experience as a soldier was in Northern Ireland. In a situation like that, he said, you have to pay as much attention to the men under your command as you do to the situation you're trying to control because the men you lead are 18- and 19-years old and terrified. One of his soldiers came within a hair's breadth of shooting a civilian because the man was walking down the street carrying an umbrella in the rain.