kitchen table math, the sequel: 3/24/13 - 3/31/13

Saturday, March 30, 2013

seeking Tiger Mom

At the WSJ (not sure whether it's behind a pay wall): "To (All) the Colleges That Rejected Me" by Suzy Lee Weiss.
Like me, millions of high-school seniors with sour grapes are asking themselves this week how they failed to get into the colleges of their dreams. It's simple: For years, they—we—were lied to.

Colleges tell you, "Just be yourself." That is great advice, as long as yourself has nine extracurriculars, six leadership positions, three varsity sports, killer SAT scores and two moms. Then by all means, be yourself! If you work at a local pizza shop and are the slowest person on the cross-country team, consider taking your business elsewhere.

What could I have done differently over the past years?


Having a tiger mom helps, too. As the youngest of four daughters, I noticed long ago that my parents gave up on parenting me. It has been great in certain ways: Instead of "Be home by 11," it's "Don't wake us up when you come through the door, we're trying to sleep." But my parents also left me with a dearth of hobbies that make admissions committees salivate. I've never sat down at a piano, never plucked a violin. Karate lasted about a week and the swim team didn't last past the first lap. Why couldn't Amy Chua have adopted me as one of her cubs?
This girl is a fabulous writer!

Friday, March 29, 2013


This paper shows that although the top ten percent of colleges are substantially more selective now than they were 5 decades ago, most colleges are not more selective. Moreover, at least 50 percent of colleges are substantially less selective now than they were then. This paper demonstrates that competition for space--the number of students who wish to attend college growing faster than the number of spaces available--does not explain changing selectivity. The explanation is, instead, that the elasticity of a student's preference for a college with respect to its proximity to his home has fallen substantially over time and there has been a corresponding increase in the elasticity of his preference for a college with respect to its resources and peers. In other words, students used to attend a local college regardless of their abilities and its characteristics. Now, their choices are driven far less by distance and far more by a college's resources and student body. It is the consequent re-sorting of students among colleges that has, at once, caused selectivity to rise in a small number of colleges while simultaneously causing it to fall in other colleges. I show that the integration of the market for college education has had profound implications on the peers whom college students experience, the resources invested in their education, the tuition they pay, and the subsidies they enjoy. An important finding is that, even though tuition has been rising rapidly at the most selective schools, the deal students get there has arguably improved greatly. The result is that the "stakes" associated with admission to these colleges are much higher now than in the past.

The Changing Selectivity of American Colleges Caroline M. Hoxby
NBER Working Paper No. 15446
October 2009
JEL No. H75,I2,J24
Not sure what she means by the 'deal' students get at a selective college.

Will let you know once I've skimmed the study....

Thursday, March 28, 2013

What are standards for? What do they have to do with curriculum?

Q: Why do schools need standards? What are standards for? What do they have to do with curriculum?

A: A set of standards is a *minimum set of requirements* that a product must meet. Let's imagine a house; the building codes are standards. An individual standard says something like "a wall must withstand straight line winds of up to 75 mph" or "studs must be places at least every 24 inches." Standards tell *what* you need to do, but don't tell you how to do it. They are used so that in the event of a serious risk, the whole structure stays standing. The building code for homes applies whether building a tiny townhouse or a 5 bedroom multi-story rambler. They are meant to force people not to cut too many corners. Standards here in math education are similar: they tell you what must be taught to a student, when, year over year. They are still *minimum set of requirements*, the ones that need to apply to every classroom, every school, every student.

A set of building codes aren't plans for a building. They are not a complete design.

A design tells you what *this building* going to look like. It answers the question of what purpose this house serves. It shows you how the floors and rooms fit together, how space is utilized. Architectural plans are a design for a home. They explain what the floor plan is, what the foundation is shaped like, where the plumbing goes, where the electricity goes, how the building will maintain even temperatures, etc. It's a map for everything that needs to be built.  A solid design takes into account the what the end result should be like and plans the structure accordingly. A good design is also relatively easy to build, because it anticipates what elements of the design depend on the other elements.

In math education, this design is the curriculum. The curriculum is the plan for each year of math education, starting with a foundation, then the walls, the plumbing, the electrical, the floors, the roof, the interior. Like a good design for a building, a good curriculum is easy to implement, anticipating not just the end product, but how to ease the building of the elements as they are put in place.

A design is necessary for a home, but we don't live in an architectural drawing. The home must still be built So there are builders. Clearly the builders need to know the standards, and build according to them, so the structure is safe. But they build according to the standards while the build up the plan, starting with the foundation, and then moving on through the structure. They complete the plan.

Teachers are the builders. They are building the house of mathematics that students will live in. Some teachers are like builders who just doing the efficient thing, putting the pieces up in order. Others are like exquisite craftsmen. The most experienced teachers are like the most experienced builders who are able to look at the plans and figure out what won't quite work in this context, and where changes should be made. They know how long the job will take, and where the hard parts are before they start. They make very few mistakes, and correct them before they cause more problems. A great math teacher is building above and beyond the minimum standards where and when she can; she is on the lookout for the pitfalls in the curriculum, ready to point them out and rework them; she is improving her own skills, employing new innovations, and producing beautiful results.

Bad standards mean the structure is unsafe. Unfortunately, this isn't always visible to the eye. The owner may not find this out until a minor tremor comes and the whole house collapses. Likewise, a bad plan means the house is not a comfortable or useful place to live, or worse, could be dangerous. If the house was designed incorrectly, then the second story may not be able to hold up the third story, and it could collapse. A truly terrible design usually can't be rebuilt, but needs to be torn down. And a bad builder means things go wrong and break in your home, and again, if bad enough, the errors could mean that the house collapses. 

Likewise, in math education, bad standards means the whole structure of math that a student is building up is faulty, and sooner or later, it is going to collapse. But good standards aren't the same as a good design. Students themselves don't need to learn the standards, any more than a homeowner needs to know the building code. Schools need to have a design, a curriculum, for their teachers, the builders to work from. A bad design won't support another story being built on top, year after year after year. And a bad builder on a floor means nothing can be built on top of it until a great builder comes in and rips out the bad work and rebuilds.

Every part of the process matters. Good standards, good curriculum, good teachers.

Cross-posted at

Tuesday, March 26, 2013

MOOCs, the doomsday scenario

More from the Times on MOOCs:
That the acronym MOOCs rhymes with “nukes” seems apt. Massive open online courses, or MOOCs — led by two profit-making start-ups, Coursera and Udacity, founded by entrepreneurial Stanford professors — are a new disruptive force in education.


The MOOC skeptics have a variety of qualms, but especially about what is lost in the retreat of face-to-face teaching — a point eloquently made by Andrew Delbanco, a professor of American studies at Columbia University, in an article in the current New Republic, “MOOCs of Hazard.”

Michael A. Cusumano, a professor at the Sloan School of Management at M.I.T., raises a different issue in an essay published this week: the economics of MOOCs and the implications.

His article appears in Communications of the ACM, the monthly magazine of the Association for Computing Machinery, and he had circulated a version of it earlier to his M.I.T. colleagues. After reading it, L. Rafael Rief, M.I.T.’s president, asked Mr. Cusumano to serve on a task force on the “residential university” of the future, including online initiatives.

“My fear is that we’re plunging forward with these massively free online education resources and we’re not thinking much about the economics,” Mr. Cusumano said in an interview.

The MOOC champions, Mr. Cusumano said, are well-intentioned people who “think it’s a social good to distribute education for free.”

But Mr. Cusumano questions that assumption. “Free is actually very elitist,” he said. The long-term future of university education along the MOOC path, he said, could be a “few large, well-off survivors” and a wasteland of casualties.

Mr. Cusumano’s concerns grow out of his study of the software and media industries in the face of price pressure from free, open-source software and digital distribution over the Internet. Two-thirds of the public companies in the software industry disappeared between 1998 and 2006, as companies failed or were acquired. In the media world, Mr. Cusumano contends that newspaper and magazine companies — including The New York Times Company — made a strategic mistake by giving away their publications free on the Web....

Give-away pricing in education, Mr. Cusumano warns, may well be a comparable misstep. The damage would occur, he writes in the article, “if increasing numbers of universities and colleges joined the free online education movement and set a new threshold price for the industry — zero — which becomes commonly accepted and difficult to undo.”

Beware of the High Cost of ‘Free’ Online Courses
New York Times | MARCH 25, 2013, 5:04 PM
"Massive open online courses, or MOOCs — led by two profit-making start-ups, Coursera and Udacity, founded by entrepreneurial Stanford professors — are a new disruptive force in education."


We have disruption now?

As far as I can tell, "creative disruption" is occurring when a new business is actually winning. MOOCs aren't a business, and they aren't winning, not at the moment.

And I don't recall distance learning being a disrupter back in the 1990s.

As far as I can tell, the only reason we're even talking about MOOCs is that we are 5 years into a depressed economy, and "free" is sounding like an awfully good idea right about now.

But as for disruption....I fear that the kind of disruption people seem to have in mind when they use the word already happened in the 1990s, and MOOCs are the least of it. Lots more administrators, lots fewer full-time professors, and now MOOCs. Swap in videos of Harvard professors, swap out the adjuncts. More for me!

I suppose you could characterize the bureaucratization of colleges and universities as creative disruption that benefits the administrators, but that's not what Clayton Christensen had in mind when he developed the concept.

"Mr. Cusumano’s concerns grow out of his study of the software and media industries in the face of price pressure from free, open-source software and digital distribution over the Internet....Give-away pricing in education, Mr. Cusumano warns, may well be a comparable misstep."

Right, but.

People like music and news; people listen to music and read news instead of getting down to work.

College courses, on the other hand, are work. A college course is the activity you listen to music and read news to avoid. MOOCs are going to be hard to give away, not easy.

For most of the MOOC discussions I come across, executive function is the Great Unsaid. That, and the fact that Free is not a business model.

Monday, March 25, 2013

80 mph

My brother showed me this video --- can't remember if we've ever posted it here.

What I love about it is that the girlfriend actually comes up with a guesstimate that's pretty close to correct, which reminded me of something I once read about the difference between really good math students versus the "works hard" variety.

To wit: the really good students devise elegant and efficient solutions and proofs. The 'works hard' students go on wild goose chases.

Works-hard students do get to the answer or the proof eventually, but the process isn't pretty. (Speaking as a person who has spent a lot of time teaching herself math, I relate.)

The process may not be pretty, but it can be funny.

Another thing: this exchange is a brilliant example of "inflexible knowledge" in action. The young woman isn't transferring the meaning of "per hour" to a different phrasing of the same situation.

Speaking of inflexible knowledge, in Atlantic City this weekend we had a semi-galling episode of Failure to Transfer. My father-in-law has been deaf for years, and Ed and I -- and Andrew -- have had iPads for at least two. We use Andrew's iPad to communicate with him via typing (Andrew types, too). Yet it had never occurred to us that we could do the same for Ed's dad.

Two years to make the connection!

Immediately after I'd had the blinding revelation that iPads work for old people with hearing loss as well as young people with autism, we began plotting and scheming how to get an iPad for Ed's dad (would he use it?? Which one should we get?? The big one?? The little one that would take up less space on a dinner table?? Etc.)

It took me a good 5 minutes to figure out that Ed's dad does not need an iPad. He can talk.

We had a chuckle over that & then an hour or so later Ed raised the subject again.

We have spent a LOT of years living with people who can't talk.

"How I Used Math to Beat a Traffic Ticket"

At RealClearScience

Very fun.

Gone fishing, plague edition

Sorry to be AWOL - we flew to Chicago, where I contracted an epic case of stomach flu (still recovering), then drove down to Atlantic City this weekend for bar mitzvah -----

Today I'm trying to figure out if I'm on Spring Break. You'd think I'd know these things. (I'm tutoring in the Bronx this semester & don't know whether the Learning Center stays open during break.)

Back in a bit.