Wednesday, April 29, 2009

Which stories attract readers, and how the press becomes complicit in right-brain teaching fads

As I've noted here, here, here, here, and here, newspaper stories are forever gushing over right-brain classroom practices like group learning; unstructured, child-centered discovery; holistic, interdisciplinary learning; emotional epiphanies; and art and poetry in math and science class.

How come we hardly ever see a story about a teacher that has bucked this trend, planting himself or herself firmly in front of the classroom, chalk in hand, walking students through a series of complex steps towards the solution to a logically challenging problem, and then calling on them to produce the single correct answers to similarly challenging problems on their own?

"I can tell you right away, it just won't fly with editors," a neighbor, who is also a science reporter at one of the city's two major newspapers. "What you're trying to get across is way too complex and subtle a message for most readers."

"What about if we sensationalize it a bit, with an exciting buzzword like 'grade reversal,' and a discussion of how the brightest math buffs are often getting lower grades than other classmates?"

"Only a tiny percentage of readers would be concerned about this issue."

All that may well be true. But the result feels very much like a totalitarian system, in which not just the ideology-makers (the education schools), the policy-makers (the various departments and boards of education), the funders (the education division of the NSF), and the implementers (from the all-powerful textbook companies and education consultants all the way down to the lowly classroom teacher) are complicit, but also the one institution that could expose to the public what all these other parties are up to.

Monday, April 27, 2009

Where right is left and left is right, II

How can a blog page featuring two comparisons of Reform Math problems with Singapore Math problems, two entries about a Comic Book project (still no word on J's latest submission!), and an April 1st entry about local school reform suggest anything about the political leanings of the blogger in question?

My recent exchanges with an educator who defends Reform Math against "Reform Math haters" got me thinking about the politics of "left" and "right." Based largely on my Math Problems of the Week comparison problems, but perhaps also on the Comic Book entries and the April 1st entry, he concluded that it's "ironic" that I call myself "lefty."

Anyone who's followed this blog for any length of time, of course, will know that "lefty" alludes to my left-brain disposition, and that I studiously avoid politics in general here. There should be nothing I've written on this blog that gives any inkling of my views on terrorism, taxation, health insurance, environmental regulation, gay marriage, school prayer, or abortion.

And that's deliberate. People should be able to disagree vehemently on these other issues, and still have a rational debate about education. Indeed, in general, I believe it's best to engage one issue at a time, and focus on the details, where the devil is.

But that doesn't stop those most emotionally invested in particular teaching ideologies from leaping to political conclusions. Could it be that that's an easier way to dismiss the opposition than discussing the actual data?

If you have stories about sweeping assumptions that others have made about your politics based on specific things you've said about education, please share!

Friday, April 24, 2009

Math problems of the week: 5th grade Trailblazers vs. Singapore Math

1. The final fractions problems in the final fractions unit in 5th grade Trailblazers, Math Trailblazers Student Guide Grade 5, p. 399:

Brandon made a cheese pizza. He put pepperoni on 1/2 of the pizza. He put onions on 3/4 of the half with pepperoni. Draw a picture showing the toppings on the pizza.
A. How much of the pizza has pepperoni and onions?
B. How much of the pizza has only cheese?
C. How much of the pizza has only pepperoni, but no onions?

A. Frank's guests ate 2/3 of a cake at his party. How much cake was left over?
B. The next day Frank ate 1/4 of the leftover cake. How much of the whole cake did he eat the day after the party?

2. From the final problems of the 5th grade Singapore Math fractions unit, Primary Mathematics 5A, p. 74.

Larry spent 1/2 of his money on a camera and another 1/8 on a radio. The camera cost $120 more than the radio. How much money did he have at first?

Mrs. Ricci had $480. She used 2/3 of it to buy an electronic fan. She also bought a tea set for $60. How much money did she had left?

3. Extra Credit:
A. Which problem set solicits higher level thinking as opposed to broadcasting the expected strategy?
B. Which problem set should true Constructivist Math Reformers prefer?

Wednesday, April 22, 2009

Smoke detectors, sleep deprivation, and the lost art of Cost-Benefit Analysis

Last night we were awoken, for the second time, by two chirping smoke detectors. Our best guess was that, once again, strong winds had blown pollen into our house, which our smoke detectors then interpreted as smoke particles.

I spent the half hour it took me to get back to sleep thinking about the lost art of the Cost-Benefit Analysis.

Surely a sufficiently extensive, in-depth analysis of the consequences of this latest generation of smoke detectors would have detected their downsides. Higher sensitivity, unless it's accompanied by higher specificity, yields higher false-positives. And false positives mean costs.

As I blinked and yawned my way through traffic this morning, I thought about one of them. How does the likelihood of perishing in a fire from which only an extra-sensitive smoke detector can save you compare with the likelihood of perishing in a traffic accident brought on by smoke detector-inflicted sleep disruption?

Monday, April 20, 2009

The Terra Nova Test: marginalizing the standard algorithms

Children around Philadelphia are currently in the midst of their annual Terra Nova tests. So concerned are some teachers about their students' performance on these national measures of academic achievement that they sent them home with practice tests to take during Spring Break (that week off that, somehow, always immediately precedes the first Sunday after the first full moon after the Vernal Equinox--but that's another story).

This gave me my first close look at what the 2nd Grade Terra Nova tests cover, and I was, of course, particularly struck by the math section.

True to current trends in academics that so favor the visual over the analytical, there turn out to be far fewer problems involving numerical calculation than those involving "geometry". Of the 40 problems in the practice math booklet, just 8 require calculation, while 12 ask students to identify or define particular types of shapes, observe whether pairs or shapes are "similar" or "congruent," say whether a shape is symmetrical, or say what it looks like when flipped, rotated, viewed from a different perspective, or combined with another shape.

Another 7 problems involve charts and graphs.

Then there were the ones that ask students to reflect on best strategies, which presumably aim to measure "higher level thinking", and which also manage to further marginalize calculation. Consider, for example:

Morgan has 29 jelly beans, Paige has 52 jelly beans, Greg has 34 jelly beans and Melissa has 18 jelly beans. Which of the following would be the fastest way to find out how many jelly beans they have altogether?

a. count all the jelly beans
b. add the numbers in your head
c. use a calculator
d. write down the numbers of a piece of paper.
I'm guessing this current generation of Terra Nova math tests is more predictive of future success in graphic design than of future success in mathematics.

Saturday, April 18, 2009

Philadelphia science fair finalists: handicapped by popularity contests?

I couldn't help noticing, in a recent Philadelphia Inquirer article touting the accomplishments of the greater Philadelphia students who participated in the regional Delaware Valley Science Fair, that only one of the 15 winners attends a Philadelphia public school. Most other students hail from Philadelphia's suburbs.

I couldn't help wondering whether this might have something to do with the way the Philadelphia Schools select their finalists. To compete in the Delaware Valley Science Fair, Philadelphia students must first be selected to compete in the Philadelphia-based Carver Science Fair. To accomplish this, I recently learned, they must first be selected by their classmates (after presenting their projects in class). Only those who make it past their peers go on to be judged by actual scientists.

We'll never know how many socially awkward but scientifically gifted Philadelphians are screened out before being fully and fairly assessed on their scientific accomplishments.

In the name of social skills, charisma, and graphic arts, the Philadelphia school system, in yet another way, may be limiting its students' chances to compete scientifically.

Thursday, April 16, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The final 6th grade Connected Math problems involving area and perimeter of circles ("Covering and Surrounding," p.76):

2. The final 6th grade Singapore Math problems involving area and perimeter of circles (Primary Mathematics 6B, "Circles," p. 36-37):

3. Extra Credit:
Given that Connected Math students can use their calculators "whenever you need it," compare the skill sets involved in each problem set. Does the ability to do the first problem set entail the ability to do the second one? Conversely, does the ability to do the second problem set entail the ability to do the first one?

Tuesday, April 14, 2009

One more enlightened exchange

...with an individual who does not wish to be called "a defender of Reform Math," and who is, most emphatically, neither a relative, nor an associate, of E. Paul Goldenberg (the latter being a much-respected friend of a friend of mine).


1. Any choice among curricula should include comparisons of specific problem sets.
2. The problem set comparisons on my blog that you find so unfair compare Reform Math to Singapore Math.
3. You yourself have said that you don't possess Singapore Math materials, and that you currently do not have "an adequate opinion to comment" on Singapore Math.
4. I have taught children of all ages all levels of Singapore Math for the last four years, problem set by problem set.
5. For a forthcoming book I've spent years analyzing specific Reform Math problems from a variety of curricula and at a variety of grade levels.
6. I've invited you to adduce what you consider to be fairer problem set comparisons than those I offer on my blog... and am still waiting for a reply.
7. Yet I'm apparently the one who is "deeply prejudiced and uninterested in learning a thing that [I] don't already know is Absolute Truth".

Mr. Goldenberg:

Funny. We have two anonymous people (the blogger and one of the his sychophants), slapping each other on the back while neither has the guts to post anything under his own name. If "Lefty" was so interested in a responsible exchange of ideas, he'd post under his real name. I don't waste time with cowards. Offer a real name and a reliable e-mail address (e.g., not web-based and untraceable) so that you are accountable for what you write, and I'll worry about what you have to say.

Let's recall that you came to MY blog and started in about Singapore Math on an item that was NOT about that. You then returned to "scare" me about your public posting of our exchange (and maybe you need to read a bit more of my blog before labeling me a defender of "Reform Math"; not to mention that I am one person, not multiple people, so your claim of exchanging with "defenders" is as phony as your pseudonym).

I guarantee I've written more words criticizing specific reform books than you have written criticizing any aspect whatsoever of Singapore Math. True believers NEVER find flaws in those books, though I've met with Singaporean mathematics educators who do, oddly enough. That's because they don't have religious blinders on. Too bad the same can't be said for you, "Lefty."

You may just want to get the other side of your brain engaged, because the one you claim to favor isn't doing such a wonderful job. And that book you're promising on "selected" reform math problems? That should be one interesting example of selectivity.
Note at what great length Mr. Goldenberg is willing to carry on about how religious and non-lefty I and my "sycophants" must be, but can't "waste time" addressing a single one of my specific points--until (or so he suggests) such time as I supply my actual name and email address.

I've dropped enough clues by now that anyone who really wants to can figure out who I am (including email address, professional activities, and Facebook friends) in about 5 minutes; at the moment I'm enjoying being gender neutral to those who don't choose to spend the time. It's been an interesting experience seeing what assumptions people tend to make about my gender, (not to mention my politics and religiosity). But because of my book, which isn't published anonymously, I will be coming out of the closet soon.

Monday, April 13, 2009

Enlightened exchanges with Reform Math defenders

Recently I came across a blog by a math educator named Michael Paul Goldenberg who expresses a degree of skepticism about some of the criticisms of Reform Math. The purpose of his blog, he has written, is

to provide direct replies to entries on other blogs where the blogger invites feedback but refuses to post negative responses, critical comments, uncomfortable questions, etc., of ANY kind, regardless of how polite they may be. What do such people fear, I wonder?
I posted a query on his blog, which led Mr. Goldenberg to post a comment on my blog, which led me to post a comment on his blog, which led him to post a comment on my blog. Our back and forth, I believe, says much about the heights of intellectual honesty, ethical consistency, and mutual respect to which the Math Wars have soared. Here's the conversation, unedited, in its entirety:
Lefty: [commenting on this post]

How do you feel about the content and pedagogy of Singapore Math?

If more U.S. schools were to use Singapore Math instead of Everyday Math, Trailblazers, or Investigations, do you believe that would lead to an improvement, or a further decline, in U.S. math education?

My blog ( gives regular comparison problems between Singapore Math, French Math, and Reform Math.

Micheal Paul Goldenberg: [commenting on this post]

Ah, Lefty, I see what you're about. Do you seriously propose that you've offered a balanced sampling of the two curricula? Why not just state outright that you are choosing to trash CMP? Not that your tactics are at all subtle.

Love those extra credit problems, too. Lovely propagandizing. Just nothing to do with what this debate is really about. I'd hoped for better when you left your link on my blog, but all I see thus far is predictable, dull, and utterly useless.

I'm sure your fans, however, are VERY impressed. Too bad those of us who actually have seen all the CMP materials know that you are stacking the deck, loading the dice, and, like most anti-reform ideologues I've met, trying to rig the game entirely to favor your own prejudices.

Lefty: [attempting to comment on this post, but "moderated out"]

Given that you find my blog, in your words, "predictable, dull, and utterly useless," I can't expect you to return and read my reply to your post there. So I'll copy my reply here, and see if you publish it. (The language of your comment, btw, suggests why you've chosen to moderate comments on your blog.)

Here is my reply:

The devil, I like to say, is in the details. Please cite some specific 6th Grade Everyday Math percents problems that pose a (mathematically) conceptual challenge similar to (or greater than!) the 6th grade Singapore Math problem cited [on the post you commented on]! I, myself, have been unable to find anything like the conceptual challenge offered by Singapore Math within the corresponding grade levels of today's Reform Math. But I am OPEN, yes, OPEN, to being proved wrong! Please do so, with specific examples.

Let me add that I know many, many kids who say they are under-challenged in their Everyday Math and Investigations Math classrooms, and who go on to say that they love Singapore Math once their parents start using it at home. In our "debate", as you call it, let's not ignore these many, very real children, at least some of whom I suspect are telling the truth.

Michael Paul Goldenberg: [commenting on this post]

Oh, Lefty, you're so clever. More snide cracks about calculators and EM users! How very witty.

I would love to "play" your silly games, but my time is very short just now. You should have come onto my blog a few weeks ago when I had a lot more time for this kind of thing. For now, let me simply point out that your "dare" (you were, in essence, "daring" me to allow your last post on my blog) was a sure-fire way to ensure I would not let it through. Schoolyard tactics are not any more appealing to me now than they were when I was actually a schoolboy.

Further, I don't think my blog is the place to discuss what obviously is YOUR agenda: after all, you've got your audience here. If I decided to post some similarly loaded comparisons of SM, EM, and INVESTIGATIONS, your comments would be welcome. But that wouldn't be the way I would do things. I don't play the rigged games of others, nor do I rig games in my own favor.

Clearly, you dislike progressive ideas in mathematics education (or at least some of the books that emerged from the early waves of the reform movement of the last two decades). Of course, that's your prerogative, though if you wanted to do SM proud, you shouldn't be so arch about its "competitors." I very much doubt that ANYONE in Singapore thinks about the national curriculum there with the same sort of snide chauvinism that its American supporters evidence when they try to bash specific US programs with it. The Singaporean mathematics educators with whom I've met (wonder which ones you've met with, Lefty) were modest, reasonable people who seemed to have a great deal of respect for US mathematics education (but not blindly so). It's odd that the Mathematically Correct and NYC-HOLD folks who drool over Singapore Math don't seem to be able to countenance the SLIGHTEST criticism of it. That strikes me as fanatical, almost religious. On the other hand, I've openly critiqued things about many progressive textbook series, not for political or ideological purposes, but in order to suggest ways to improve matters. That's one major difference between me and the right wing anti-reform bashers I've had to deal with these past 17 years or so of the Math Wars.

Ironic, then, that you call yourself "Lefty." Everything about you and your blog suggests quite a different political and social viewpoint. Again, your prerogative, of course. But it is ironic.

When you have something new to say, something I've not heard from the more well-established reform haters, do visit my blog again. Especially visit if you're interested in intellectual discourse rather than winning rigged contests. I'm too old for that sort of nonsense.
Lefty (informing Mr. Goldenberg of this post):

I fully understand why you would choose not to post a comment that quotes you calling another blog "predictable, dull, and utterly useless." However, fyi, I've posted our exchange on my blog, for all to see: [url]

It amuses me, btw, that you would attempt to infer my political leanings from a single page of my blog that featured two entries about a comic book assignment, one about an after school math club, and two Singapore Math-comparison math problems. Is that really what this debate is all about?

Michael Paul Goldenberg (no relation to E. Paul Goldenberg):

Lefty, I'm here to amuse you. It's my main purpose in life. And to provide you with fodder for your blog. Should you prove to be worth more of my attention, I might return the compliment here, but you seem a lightweight based on what I've seen of you thus far. I hope your many fans enjoy your continued straw-man "battles" between Singapore Math and the least mathematical problems you can find in EVERYDAY MATH and/or INVESTIGATIONS. You didn't invent this trick: the Mathematically Correct and HOLD folks were WAY ahead of you on this front.

I don't believe I called your entire blog predictable, dull, and utterly useless," though it wouldn't shock me to discover that the rest of it is no better than what I saw when I went to where you pointed me in your previous comment on a previous thread here. As is typical of anti-reformers, you think you can take potshots at reform authors and texts with impunity, but when someone calls you on what you're doing, suddenly you become very aware of "offensiveness" and profess yourselves to be above such "dirty" tactics. Those of us who've been in this fight for close to two decades now find the irony of such nonsense highly rich.

As for "debate," your blog post that I looked at wasn't a debate. It was your "clever" mocking of texts you dislike. You're free to do so, of course, but the snide nature of what you wrote was obvious. You shouldn't be ashamed to admit it. Stop posing as some sort of fair-minded, objective person, because anyone with more brains than a hammer could see after 60 seconds on your blog that you are deeply prejudiced and uninterested in learning a thing that you don't already know is Absolute Truth.
This exchange reminds me of an earlier one I had with a doctor who treats autism with ear tubes.

Saturday, April 11, 2009

The comic book project, revised

He's preserved the pictures, but changed the text (inspired, in part, by one of his favorite movies):

We'll see how tomatoes instead of bombs goes over on Monday.

Thursday, April 9, 2009

Math problems of the week: 3rd grade Everyday Math vs. Singapore Math

1. From the final money problem (the second to last problem overall) in the 3rd grade Everyday Mathematics Workbook (Student Math Journal, Volume 2), p. 317.

I bought a beach ball for $1.49 and a sand toy for $3.96. How much change will I get from a $10 bill?

$ ___

2. From the final money problem (the final problem overall) in the 3rd grade Singapore Math Workbook (Primary Mathematics 3B), p. 184.

Lauren received an allowance of $6.00 last week. She spent 3 quarters on candy and $3.60 on a book.
(a) What fraction of a dollar did she spend on candy?
(b) How much money did she have left?

3. Extra Credit:

The list price of the 3rd grade Everyday Mathematics Workbook (Student Math Journal, Volume 2) is $9.15 and the list price of the 3rd grade Everyday Mathematics Workbook Answer Book (Journal Answer Teacher Book, Volume 2) is $19.65. The list price of the 3rd grade Singapore Math Workbook (Primary Mathematics 3B) is $11.50 and there is no corresponding teacher answer book.
(a) Compute the total cost of the two workbooks, and of the two workbooks plus the Everyday Math answer book. What fraction of these two totals is the cost of the Singapore Math workbook? (If you are an Everyday Math user, you may use your calculator to solve this problem).
(b) Dicuss the need for answer books in the two curricula.

Tuesday, April 7, 2009

The comic book project, II: the problem with boys

He colored, he captioned, he concocted an original plot. But, given panels such as these, below, J's teacher has asked us, ever so politely, to have him redo his 6th grade English comic book assignment:

Having watched parts of the PBS documentary Raising Cain, I strongly suspect that the creative output displayed here is a function not of autism, but of maleness.

If so, it illustrates yet another way in which open-ended projects, combined with implicit expectations of niceness, shortchange boys in particular.

Particularly those who lack the social motivation to please their teachers.

Sunday, April 5, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

I. From the end of the percents unit in 6th grade Connected Math, Bits and Pieces II:

As you work on these ACE [Applications/Connections/Extensions] problems, use your calculator when you need it.

1. Find three examples of advertisements, news reports, or other information in which percents are used. Store windows, newspapers, magazines, radio, and television are good places to look. Write down each example, or cut it out and tape it to your paper. For each example, describe how percents are use and what they mean.

2. Faaiz and Tat Ming go to a restaurant for dinner. Their meals total $13.75.

a. The local sales tax is 5%. How much tax will be added to the bill?

b. They want to leave a 15% tip based on the bill and the tax combined. How much should they leave? Explain.

c. If Faaiz decides decides he should pay $2.75 more than Tat Ming because he ordered the most expensive dinner, how much should each pay? Explain.

II. From the end of the 6th grade Singapore Math unit on percentages, Primary Mathematics 6A, p. 62:

1. 20% of Menon's books are comic books. If Menon has 52 comic books, how many books does he have altogether?

2. Sulin's savings is 75% of Meifen's savings. If Sulin saves $300, how much does Meifen save?

III. Extra Credit

1. Predict which Connected Math problem Connected Math students will need calculators to solve.

2. Predict whether Connected Math students will be able to solve the two Singapore Math problems with help from calculators.

Friday, April 3, 2009

This one's no joke: the comic book project

I thought I should follow my last post with this one. For the problem of the week, tune back in this weekend!

This week's 6th grade English (now known as "literacy") assignment:

The Comic Book Project


1. Original artwork and/or computer graphics
2. Your comic-book characters must have original names.
3. Your comic book must have an original plot.
4. Minimum, five pages long.
5. If you handwrite, the final copy must be in ink.
6. Each page must have at least four to six pictures, with captions included with each picture. You may decide how large each panel should be, but make all panels the same size! Each panel needs at least one or more of the following:
A. scene or a setting
B. dialog or script
C. sound effects
D.captions or word balloons.
7. Your comic book must be in color.
8. Your comic book must have an original cover.
9. Your comic book must be rated for general audience reading!
10. The class will have a "Comic Book Read-Around Day" on the due date to read one another's books.
For J, self-interest, not comic book creativity, is the best motivator.

"Do you want to get a good job?" I asked him.


"To get a good job, you need to get into a good high school. To get into a good high school, you need to have mostly A's. To get an A on this project, you need to follow all the directions."

Most of our city's high schools are terrible; only 40% of city students get into magnet high schools; for admission, grades matter tremendously.

From coloring and captioning to getting a good job: for now, the absurdity escapes J.

Wednesday, April 1, 2009

Local school reinstates local control and evidence-based education

Classes using evidence-based teaching methods like Direct Instruction and Singapore Math will now be offered.

Parents will be allowed to choose whether their children enroll in these classes, or in ones that use the more traditional, child-centered, Constructivist protocols, like Investigations.

Mathematicians and scientists from the partnership university will be allowed into the school to give workshops to teachers and curriculum developers.

Children will be asked whether they prefer to work independently rather than in groups, and their wishes will be respected.

Children will be asked whether they prefer to approach material by making personal connections, or whether they prefer exotic new material that has nothing to do with them.

Children will be allowed to work at their own levels and at their own rates.

Children will be graded based on what they learn at school from teachers and textbooks.