Archive for October, 2010

Friday Fun!

I’ve developed a worksheet for graphing linear equations that is somewhat interesting.

Although it doesn’t introduce new concepts, students always have some difficulty with the format –

which is matching.

Also, it is the type of matching where you can’t use the process of elimination as some questions have more than one answer, and some equations satisfy more than one question.


Match each description below with the appropriate letter(s).

Some statements may satisfy more than one of the equations.

Find the equation of a line:

1) Through the point (1, −1)
2) Through the points (5, 2) and (−1, − 4)
3) With a slope of − 3
4) With a slope of 0.5 through the point (5, 6)
5) Through the point (−3, − 6)

A) 3y + x = −21
B) y = x − 3
C) y + 3x = 2
D) 2y = x + 7
E) y = 2x − 3


Find the equation of a line:

1) Through the points (4,−4) and (12,2)
2) Through the point (8,−1)
3) With a slope 1/3 through the point (5,−7)
4) Through the points (1,4) and (−3,1)
5) With a slope of − 2 through the point (5, 5)
6) With a slope of 3/4

A) 4y − 3x = 13
B) y = 0.75x − 7
C) y+7= 1/3(x-5)
D) 2x + y =15


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Benoit Mandelbrot

A Greek among Romans


Benoit Mandelbrot passed away last week in Cambridge, Mass. at the age of 85.

Nassim Nicholas Taleb dedicated his book The Black Swan to Mandelbrot, calling him “a Greek among Romans.”

Mandelbrot is probably the most important mathematician of the last 50 years.  His ideas on using mathematics to describe and understand the world around us have influenced many mathematicians and scientists and led to a new understanding of how to apply mathematical ideas.

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Waiting for Superman

The Media Blitz

So Davis Guggenheim’s new documentary Waiting for Superman is getting a lot of attention these days. The media blitz for the film included multiple articles in New York magazine, multiple reviews and stories in the New York Times and the cover and several stories in Time magazine.

Oprah Winfrey devoted her show of September 20th to the film.  NBC Nightly News featured the movie on its September 22nd broadcast and has an entire website called “Education Nation.”  The Huffington Post website has opened a new section – HuffPost Education, spearheaded by the premiere and reactions to the film.

I haven’t seen the movie and don’t expect to have an opportunity to see it until it’s available through Netflix or Hulu.

That said, I’ve done quite a lot of reading about the issues that the movie addresses and feel that I can competently discuss these issues although I haven’t seen the movie.  There are also a number of reviewers who have seen the movie and I will quote their reviews when necessary.

Gail Collins, in one of the New York Times stories, points out an aspect of the film that other reviews didn’t mention, but which particularly caught my eye.

The public lottery-style pulling balls out of a tub in front of hundreds of anxious parents and children is just mean.

My own particular, narrow wrath was focused on the ritual at the heart of the movie, where parents and kids sit nervously in an auditorium, holding their lottery numbers while somebody pulls out balls and announces the lucky winners of seats in next fall’s charter school class. The lucky families jump up and down and scream with joy while the losing parents and kids cry. In some of the lotteries, there are 20 heartbroken children for every happy one.

Charter schools, please, stop.

She also points out that Davis Guggneheim says that he is not “taking sides” or pushing a particular agenda in the film.

Davis Guggenheim, says he’s not offering an answer:

“It’s not ‘pro’ anything or ‘anti’ anything. It’s really: ‘Why can’t we have enough great schools?’ ”

In The Nation, Dana Goldstein makes a similar point – Guggneheim says that his views on the problems in public education are neutral.  He just wants good public schools.

In the Waiting for Superman companion book, Guggenheim writes about his struggle, as a lifelong liberal, over how to present teachers unions in the film. “Their role in education is not a black-and-white one,” he admits. “I’ve gotten to know union leaders who I think understand that the reforms we need will mean some serious adjustments on the part of their members, and that we need to rethink the rigid systems we’ve gotten locked into since the New Deal era. At the same time, these progressive union leaders can’t get too far ahead of their members. And they understandably don’t want to give aid and comfort to some politicians who are in fact anti-worker and are at least as interested in undermining the power of labor as they are in improving our schools.”

She continues though:

The movie, though, does not attempt any such balancing act. It presents [Washington D.C. schools chancellor Michelle] Rhee as a heroine whose hands are tied by the union…

The film [also] doesn’t acknowledge that Bill Gates, who began his philanthropic career deeply skeptical of teachers unions, has lately embraced them as essential players in the fight for school improvement. His foundation finances a program in Boston called Turnaround Teacher Teams, which works with the district and its teachers union to move cohorts of experienced, highly rated instructors into high-needs schools, while giving them extra training and support.

In July Gates spoke at the American Federation of Teachers convention in Seattle, saying, “If reforms aren’t shaped by teachers’ knowledge and experience, they’re not going to succeed.”

In the New York Magazine story about Guggneheim’s motivation for making the film, he describes his experience of driving past three public schools on his way to drop off his children at the private school they attend.

What caused him to reconsider taking another run at the topic was the experience of driving his children to school in Venice, California. At 46, Guggenheim is an unrepentant liberal and supporter of the public schools. And yet here he was, passing three of them every day on his way to the private institution that his kids attend…

So, did he go to these schools and see what they were like?

Did he become engaged in the neighborhood he lived in?

Did he work to make the schools better so that he might consider sending his children there?

If he did any of these things, he hasn’t publicized it.

What he has publicized is the movie he made about education in early 21st century America.

Teacher’s Unions and Charter Schools

The most common criticisms of that movie refer to two things in particular:

1)  Teachers’ unions are presented as preventing the reform of our public schools.

2)  Charter schools are presented as success stories.

These two ideas are often thrown together – that is, charter schools are successful because their teachers are not unionized.  Or – the style of education that makes the charter schools successful is being prevented by the teachers’ unions.

Paras Bhayani points out some of the flaws of the movie in his review/commentary at the Huffington Post. Many states either don’t have active teachers’ unions or have very weak union structure.

Wouldn’t it make sense that, if the teachers’ unions were the real problem, then these states and school districts would be the leaders in student achievement?  Actually, heavily unionized Massachusetts turns out to be one of the leaders in student achievement.

…accepting Guggenheim’s logic, we would expect no underperforming schools in states with weak or non-existent unions, like right-to-work North Carolina and Texas. That unionized Massachusetts is the nation’s perennial top-performer might also require some explanation.

Bhayani is no union hack either.  He teaches at a charter school in Chicago and also participated in the Teach for America program (where Michelle Rhee got her start teaching and which is also praised in the film).

So, the idea that doing away with teachers’ unions is a recipe for school success seems to rest on shaky logical ground.

What about the great work being done by charter schools – often in neighborhoods with many low-income families and poorly performing public schools?

Well, as it turns out, charter schools are something of a mixed bag – much like the public schools.

The most authoritative study that I am aware of comes from the Center for Research on Education Outcomes at Stanford University.  Called “Multiple Choice,” the study compares charter and public schools in 16 states.

The study finds that of the approximately 2400 charter schools studied, 46% showed no significant difference in student achievement from the local public schools, 37% were significantly worse than the public schools and only 17% were significantly better than the local public schools.


The issue of public education is a vastly complex subject that is generally not amenable to the narrative style of the modern mainstream media.  Mass media outlets like a story with heroes and villians and, most importantly, a simplistic unambiguous story line.  Unfortunately, real life is stuffed full of ambiguity.

Public education is locally controlled and this can be very positive.  There are many local initiatives that are helping students and parents in public, private, charter and homeschooling situations.

I think that trying to nationalize the debate may leave everyone talking at cross-purposes.  What works for one school may not work for others.

I have worked in a wide variety of educational settings – private tutoring (both independently and as an employee of Huntington Learning Centers), SAT classes, substitute teaching, private school, public school, reservation school,  university and community college.  In each setting the students needed something different from me and I tried to provide what they needed to the best of my abilities.

I think that the curriculum is an important starting point in education.  There is always a lot of talk about “thinking skills” and other “higher level skills,” rather than content.

But the idea of thinking skills always seemed to me to ignore the question of what the students were thinking ABOUT.

Writing, speaking and listening skills are fundamental to learning about and understanding the world around us, as is mathematics.

Finding curriculum that engages the students and teaching it well is a universal recipe for success.  This will mean different things in different schools – and that’s OK.

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I am of the opinion that students need to learn what a calculator is doing in order to use it properly.

Here’s an example – calculating with decimals can be somewhat tedious and there certainly is a point of diminishing returns with regard to the length of problem sets assigned for practicing concepts.

But, if students don’t develop number sense and don’t really understand what a calculator is doing in a situation as simple as adding two decimal numbers, they can get unexpected results and not be sure whether or not they’ve made a mistake.

Suppose someone needs to add 0.547+0.453

Entered into a calculator, the answer is 1

No big deal – IF you understand how adding decimals works.  If you don’t, this answer might be confusing – where did all the other digits go?!

There’s always a balance to be struck between drills and “big picture” ideas and it’s a different balance for different topics and different groups of students.

But, as Professor Wu points out, basic skills vs. conceptual understanding is a bogus dichotomy.

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