Tuesday, December 30, 2008

Favorite comments of '08: left-brained epiphanies

Liz Ditz on Left-brained epiphanies:

1984 was a watershed year for me: I acquired an Osborne portable computer (which I named Ozzie). Suddenly, I discovered the satisfactions of quantitative analysis! I did not have to undertake the huge cognitive burden of mathematics my own self -- my faithful friend Ozzie did the calculations, and I could now play with assumptions. I was in an MBA program at the time. I'd read a case study, and have a way of quantifying my sense that "hmmmn, something's wrong here". I had enough math to set up the parameters, and Ozzie's abilities let me play until my intuitions were quantified.
Alison on Are all epiphanies right-brained?
My left-brained-ness would like stories about musicians who are woken up to physics, about preschool teachers who finally understand market economics instead of "feelings", too, but how many left brainers are writing such stories? and who would buy them?
Dawn on Are all epiphanies right-brained?
Hah! I'm been a life-long dreamer who draws and sings and is (or so I thought) as right-brained as the day is long.

Then I started really looking at math while homeschooling my kids and engaging in demanding debates and suddenly I've had a blossoming of rational thought and a found a lot of joy in numbers. It has been wonderful.

Monday, December 29, 2008

Favorite comments of '08: grades

PaulB on Earning high grades in Reform Math III:

Last year I observed a grade 2 Investigations class over the whole year (about once each week). There was this little guy in there who was a pattern Prodigy. He saw patterns in everything and often rearranged the work to suit his pattern fetish. He was something else.

The teacher was always redirecting him, trying to get him to stay on the Investigation's reservation. He'd get all dejected and go away after having his (excellent) observations shot down.

I'm betting he'd be someone that could thrive in another program and get marginal grades in his classroom.I wanted so much to get my hands on him and get him out of there.......
Anonymous on How to ration high grades:
My children's school has the 1-5 grading standards thing going. You can't get higher than a 3 in October, you can't get higher than a 4 in March, and the school won't say what it takes to get a 5.
Catherine Johnson on Why left-brainers depend more than others on high grades:
The whole leadership thing is a nightmare, period.

How many kids are "leaders"?

Our own kid is completely out of the running if that's going to be the criterion -- and he's a verbal/history/humanities type.

His joke with Ed is that when he gets to high school he's going to form a "Leadership Club." (Apparently, founding a club is a BIG WAY a kid can "demonstrate leadership" -- or so the various media reports, etc., say.)

C. is going to found a Leadership Club, and everyone will get to be Leader for one month at a time, on rotation.

I'm sure that will knock them dead in the Ivies.

Sunday, December 28, 2008

Favorite comments of '08: interdisciplinary projects

VickyS on Thoughts on Relevance: How much relevance is relevant?

For 5 years I've been pulling my hair out trying to understand why school is no longer about EXPANDING my kids' horizons. The kids I know long to stretch their intellect and accumulate knowledge. Instead, most school days involve nothing more than navel-gazing. My connections. My family. My neighborhood. My feelings. How utterly boring and uninspiring.
Dawn on Right-brained foreign language assignments: the German tissue box:
And why stop at a tissue box? Imagine the creativity and learning if it were a chip bag or a styrofoam cup or even, oh my, a toilet paper roll!!
KathyIggy on Summer math projects: grade 6:
No summer projects here, thank goodness. I would go crazy as all these "be creative" projects push me over the edge during the year! I had my fill of posters, brochures, advertisements, etc. last year. Social studies for my 6th grader was never ending projects with very little content.
K9Sasha on Math projects and children with autism:
Who is the better artist - someone who's never taken an art class, or someone who knows all about line, space, perspective, color, etc.? Who is the better musician - someone who's never learned to read music, or someone who knows how to change from one key to another, how long to hold each note, when to use melody and when to use dissonance, etc.? While there may be a few people who are naturals, in almost every case the people who understand the fundamentals are able to use that knowledge to be more creative. This c*** about teachers simply telling students to be creative has no basis in the real world.

Friday, December 26, 2008

Favorite comments of '08: Reform Math

Casvelyn on Convincing other parents:

I'm bad at math. I can't do simple arithmatic in my head, and I barely do much better on paper. I have insanely good reading comprehension and writing skills. By all accounts, I should be good at Reform Math and the like. In reality, it's the most confusing thing I ever saw (and this from the 22-year-old who still hasn't mastered parts of 4th grade math). It's so... non-linear is the only word I can really come up with, but it seems to fit. I guess I'm bad with numbers, but I understand the underlying principles of mathematics (and algebra, and trig, and calculus). My beef with Reform Math is that it takes away the principles, and just leaves the numbers, which is the only reason I was even able to complete any math after about halfway-through 4th grade.
Jared M. Stein on Math problems of the week: 3rd grade Investigations (TERC) vs. French math:
I would choose to compose a picture to answer this question. It would be post-pomo collage of photographic images from the civil rights movement and international skirmishes that signifies the struggle of the disenfranchised worker against greedy corporate bigots who stock only boxes of broken crackers in urban marketplaces.
Nancy Bea Miller on Stacking, regrouping, and corrupting the children:
When I showed one of my sons how I had learned addition, i.e. the "stacking" method, he was very impressed. "Wow, that's so cool! That works great! I wonder if my math teacher knows about this?" was his innocent comment.
PaulaV on Everything but the math curriculum:
Sometimes I feel like telling teachers and parents, "Okay, all of you who want reform math, step over here. The ones who want a more traditional curriculum stand over there." To me, it seems reform curriculum is a sinking ship and those of us who are stuck on this boat and what to get off cannot because well, you know, it wouldn't be fair. We should all go down with the ship.
Obi-Wandreas, The Funky Viking on Math problems of the week: 6th grade Connected Math vs. SIngapore Math:
That's one of the biggest problems I have. The kids can't do the problem not because they don't have the mathematical chops but because they can't fscking read!

Granted, that is also an issue, but I'm sick of my kids getting slammed in math for issues that have nothing to do with math.

If the "math" department downtown had any idea how much of this pile of useless flotsam I leave out of my lessons...
Anonymous on Reform Math and nonverbal learning styles:
My county recently adopted Investigations and our school conducted a math night to inform parents of the program. Although I was unable to attend, my husband went and the one comment he heard over and over from parents was how frustrating it was for their kids to have to draw and write in math. Many of the kids know how to add 4 + 7 and do not need to draw a series of apples to figure it out.


Last month, I watched my neighbors's fifth grader walk around from house to house asking those who had cats if he could estimate their length...he was doing a unit in TERC math investigations. How is this going to prepare him for algebra?

Tuesday, December 23, 2008

Autism Diaries V: Hubris (or is it Advent?)

"If I pretend to be God, what happens?"

"Why would anyone believe you?" I reply.

But he's certainly acting like God, at least on the computer.

I left him to his own devices for a little while, and he went to town:

1. Made himself an administrative user;
2. Changed the password on mom's user account and entered as mom;
3. Changed the parental controls so mom can't use the computer when she tries to log on in the morning;
3. Changed mom's email password (via his grandmother's maiden name);
4. Changed the settings on mom's email account so that all mom's incoming and outgoing emails bounce over to his account, leaving no trace on mom's account;
5. Replied to a bunch of emails addressed to mom, in mom's name.
"I don't want Mommy to be on the computer while I'm at school," he partially explained.

Sunday, December 21, 2008

Earning high grades in Reform Math, III

Consider Boy A and Boy B--two 2nd-graders with the same teacher at our local public school, neither of whom is related to me, though I'm friendly with both of their moms, who have shared with me their report card grades.

Both boys try out for Continental Math League, undergoing our 6-page, Singapore Math-derived assessment. Boy A doesn't get past the first half of page 1, answering half the questions wrong. Boy B does about 5 times better, getting one of the top scores among 2nd graders, and subsequently doing extremely well on the Continental Math team, including the many 3rd grade Singapore Math problems we include. He's bright, fast, accurate, and really into the challenge.

On their report cards, which use a 1-4 scale, one of them earns a 4 in math, the highest possible grade, and the other earns a 3. Guess which boy earns which grade?

Hint: the school uses the Investigations (TERC) curriculum.

Yes, indeed: the same teacher gives a 2nd grader who is thriving in 3rd grade Singapore Math a lower grade than a 2nd grader who was stumped by the 2nd grade Singapore Math in our math assessment.

Is some sort of hidden agenda at work here?

Friday, December 19, 2008

Math problem of the week: 5th grade Investigations vs. Singapore Math

1. From the end of the 5th grade Investigations (TERC) unit on fractions and percentages ("Name that Portion"):

Rudy ate 25% of a pizza. Eli ate 50% of a different pizza. Is it possible that Rudy ate more pizza than Eli? Why do you think this?


2. From the end of the 5th grade Singapore Math unit on percentages ("Percentage"):

There are 55 apples in a box. 40% of them are red apples and the rest are green apples. How many green apples are there in the box?


3. Extra Credit:

(a) Estimate the proportion of 5th grade math buffs who will give satisfactory answers (sufficient verbosity; no sarcasm allowed) to the Investigations problem.

(b) Of the 5th grade Reform Math students who provide satisfactory answers to the Investigations problem, estimate the proportion that can provide satisfactory answers to the Singapore Math problem.

(c) From your answers to (a) and (b), estimate the correlation between success with Investigations and success with mathematics.

Wednesday, December 17, 2008

Teaching with withitness

Malcolm Gladwell's article in this past week's New Yorker about how to identify the best classroom teachers risks being misinterpreted as one more reason to de-emphasize book smarts.

Gladwell's focus: a project led by Bob Pianta, the dean of the University of Virginia’s Curry School of Education, which involves videotaping teachers in classrooms and analyzing their interactions with students. From these videotapes Gladwell concludes, along with Pianta et al, that the most successful teachers exhibit a high level of awareness of what's going on in the classroom and communicate this awareness to their students. "It stands to reason," he writes, "that to be a great teacher you have to have withitness."

Taking this a step further, Gladewell argues that this withitness trumps academic preparedness:

Educational-reform efforts typically start with a push for higher standards for teachers—that is, for the academic and cognitive requirements for entering the profession to be as stiff as possible. But after you’ve watched Pianta’s tapes, and seen how complex the elements of effective teaching are, this emphasis on book smarts suddenly seems peculiar.
Confounding Gladwell's conclusions is his conflation of cognitive and academic preparedness with teacher certification credentials:
A group of researchers—Thomas J. Kane, an economist at Harvard’s school of education; Douglas Staiger, an economist at Dartmouth; and Robert Gordon, a policy analyst at the Center for American Progress—have investigated whether it helps to have a teacher who has earned a teaching certification or a master’s degree. Both are expensive, time-consuming credentials that almost every district expects teachers to acquire; neither makes a difference in the classroom. Test scores, graduate degrees, and certifications—as much as they appear related to teaching prowess—turn out to be about as useful in predicting success as having a quarterback throw footballs into a bunch of garbage cans.
In actual practice, the inanity of much of the certification requirements, disproportionately turning off the smarter applicants, means that certification and masters degrees in education predict weaker-than-average cognitive and academic credentials. In other words Kane et al's conclusions, above, are no surprise whatsoever.

Also, while it's true that cognitive and academic credentials don't guarantee a knack for teaching, a teacher's intellectual or academic weaknesses, however pedagogically gifted s/he might be, places serious limits on what s/he can teach students--limits rivaling those of an under-challenging curriculum.

If your goal is to master upper-level mathematics, who would you choose as your teacher: Robin Williams, or a member of the Princeton math department, however dry and out of it s/he might be?

Monday, December 15, 2008

Please visit an actual classroom before you make recommendations, IV

Here we go again.

From a front page article in the Health & Science section of today's Philadelphia Inquirer:

Temptation to learn
With science scores sagging, schools seek to make the subject more appealing. At Temple, one answer is wine.

At many schools, there is a long tradition of watered-down science courses - heavy on memorization and low on true understanding - for students who seek merely to fulfill a graduation requirement. Physics for Poets, say, or Rocks for Jocks.
Not Professor Levis' Chemistry of Wine class at Temple University:
Levis and his colleague David Dalton want their charges to grasp the why and how of science - to ask their own critical questions and devise a way to find answers.


Such efforts to boost scientific literacy are afoot elsewhere. The University of California at Berkeley, for example, offers a rigorous course called "Physics for Future Presidents," in which students must demonstrate their mastery of concepts by writing essays.

But education experts say the push needs to start well before college. Last week, it was announced that the performance of American students on the most recent international science test had declined. And researchers have found many students do not retain what they've learned, says Sarah Miller, codirector of the Wisconsin Program for Scientific Teaching, at the University of Wisconsin in Madison.

Some fault could lie with the instruction, she says - particularly in cases when science is presented "as this known quantity of information that must be memorized, which is the antithesis of the scientific endeavor."


Lectures are part of the course, too, but they are not of the traditional stand-behind-the-podium variety.

In one recent class, Levis bounded up the stairs of the auditorium to illustrate how red wine gets its color. He was pretending to be a molecule of a pigment called malvidin, which jumps to a higher energy level (a higher "stair") when struck by light.

The molecule absorbs some of the light, from the blue-green end of the spectrum, whereas the color red passes through. So that's the only color we see.

Levis, a serious wine buff who makes wine in his garage, carried a ball of tinfoil in his hands as he leapt up the stairs. The ball represented a unit of light called a photon, which is emitted when the molecule goes back to a lower energy level. So when Levis jumped back down to a lower stair, he "emitted" the ball, tossing it at student Paige Gilbert. She was unfazed.
Nor am I. Indeed, is any of us fazed by this breathless reporting of old hat?

More to the point: has either Inquirer reporter Tom Avril, or scientific teaching expert Sarah Miller, visited an actual k-12 science classroom recently?

Yes, the science is watered down. But it's watered down not because classes are "heavy on memorization," or because they don't ask students to write essays, or draw pictures, or reflect on "how" and "why." (Cf: here, here, here, here, here, here, and here).

Rather, science is watered down, and our test scores are down, because, in their zeal to have students to write essays, log journal entries, and draw pictures about science, and to entertain them rather than to educate them, science classes no longer teach students the basic facts they need as a foundation for true scientific understanding.

Thursday, December 11, 2008

Math problems of the week: 2nd grade Investigations vs. Singpore Math

1. ~One third of the way through our school's 2nd grade Investigations curriculum:

2. ~One third of the way through 2nd Grade Singapore Math:

Wednesday, December 10, 2008

Everything but the math curriculum, II

An article in yesterday's Philadelphia Inquirer profiles one of the few schools in the Delaware Valley to use Singapore Math: the five-year-old Folk Arts-Cultural Treasures Charter School (FACTS) in Philadelphia's Chinatown, whose math scores have risen impressively:

In 2006, 27 percent of fifth graders passed the state math test; this year, as seventh graders, 67 percent passed.
For a reaction, the article turns to Janine Remillard, a professor of math education at University of Pennsylvania, who cautions against giving too much credit to the Singapore Math curriculum:
Remillard... said that while Singapore math may be responsible for the improved test scores at FACTS, other curricula - such as Everyday Math, used in many districts around the country, including Philadelphia - have also shown promise when taught well.

"A curriculum provides a way of representing the mathematics, but it is only one piece of the puzzle," Remillard said. "How the teacher uses that curriculum is really, really critical."

How true. Good teachers trump nearly everything. Including--though I challenge you to find a math education professor who will admit this--the most "traditional", "drill-and-kill" of math programs.

But the one thing a good teacher can't trump--unless s/he simply tosses most of it out the window--is a curriculum that places too low a ceiling on conceptual challenge.

And that is why Singapore math trumps Everyday Math--and Investigations, and Trailblazers, and Mathland, and Connected Math, and the rest of the lot.

Monday, December 8, 2008

Thoughts on Relevance: How much relevance is relevant?

to learning, that is?

Today's educators tell us that students learn best from material that relates to their personal lives. But has anyone bothered to ask students how they feel?

If anyone had asked me how I felt when I was a student, I would have replied that quite often I prefer the exotic and abstract to the personally relevant.

In English/Language Arts, this meant fantasy, science fiction, and historical fiction.

In social studies, faraway times and places.

In science, cosmology and the intricacies of cell life and natural selection.

And in math, base 8, formal proofs (what made 9th grade Geometry so refreshing), and polar coordinates.

Often, the further removed from family, community, peers, current events, and "all about me," the better.

My favorite teachers weren't those who showed how everything related back to daily life and current events, but those who knew how to guide us to the most exotic nuggets and help to make them crystal clear.

They made things personally relevant in the best sense: not by making us relate them back to ourselves, but by helping us care enough about them, and understand them deeply enough, that we made them a part of ourselves.

Isn't the best teacher, after all, one who helps our minds expand to embrace new material, rather than one who limits new material to what he/she thinks our current minds can personally relate to?

Friday, December 5, 2008

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

1. From the Connected Math unit "Data About Us," Investigation 5: "What Do We Mean by Mean?"

A store carries nine different brands of granola bars. What are possible prices for each of the nine brands of granola bars if the mean price is $1.33? Explain how you determined the values for each of the nine brands. You may use pictures to help you.

2. From "Review 1" in 6th Grade Singapore Math, Primary Mathematics 6A.

The average price of three mugs is $4. One of the mugs costs $p and another mug coasts $3. Express the price of the third mug in terms of p in the simplest form.

3. Extra Credit

There are two sixth grade math problems. One involves the open-ended pricing of nine granola bars, complete with optional pictures; another involves using the formula for averages to calculate an algebraic expression. Estimate the average level of difficulty of the two problems, and then determine which one is more likely to contribute to the Lake Wobegon effect.

Wednesday, December 3, 2008

Autism Diaries IV: life skills

My son enjoys Set:

And he recently noticed that our Set deck was missing exactly one of its 81 cards. Since he's autistic, it's no surprise that he deduced, in no time, exactly which combination of shape, color, number, and filling this card had.

Much more surprising was that he succeeded, all by himself, in getting the Set company to send him a replacement.

First he tracked down their website and found a contact person. Then he sent them the following email message:
Subject: Lost card

I have lost a set card. It is 2 purple unshaded, unstriped ovals. Please get me new one. My address is [exact address, properly formatted, complete with zip.]
After receiving back the following reply:
Dear Mr. [],

Please send us a self-addressed stamped envelope with a note stating which card you've lost and we'll be happy to mail it to you with 24-48 hours of receiving your mail.
He tracked down an envelope, put his address and a stamp on it (expressing great enthusiasm for the concept of a self-addressed, stamped envelope), and inserted it into another envelop along with the following message:
He received the card in the mail a few days later.

Monday, December 1, 2008

Overseas colleges: a more promising option for left-brainers?

What options exist for the hyper-focused student who lacks the well-rounded portfolio of extra-curriculars and leadership roles considered so important by America's elite colleges? Overseas universities, with their greater interest in academic credentials and narrower academic training, may represent a better fit. Consider an article in today's New York Times about St. Andrews University in Scotland:

For American students, a university like St. Andrews offers international experience and prestige, at a cost well below the tuition at a top private university in the United States.

Scottish universities have a different approach from American institutions to education. Students apply to the department they wish to study in and specialize from the beginning, with no requirement that they take courses in many different fields, as is generally the case in the United States.

The Scottish admissions process is straightforward, mostly a matter of meeting numeric benchmarks. While requirements vary among departments, St. Andrews generally wants SATs of 1950 (out of a possible 2400) and a 3.3 grade point average.

Applicants write no essays on their most-admired public figure, or what they learned from their summer travels, or, as Dresser put it, "those hilarious American college-admissions essays on 'If you were going to sing a song in a talent show, what would you sing and why?'"

Students need not present themselves as the well-rounded package of perfection, as many feel they must to impress American admissions officers.

"The fluff is irrelevant," said Rebecca Gaukroger, a recruiter for the University of Edinburgh. "It's built into the UK system that students will have strengths and weaknesses, and if a student wants to study chemistry, we don't need to know if they're good at history."
The fluff is irrelevant. How refreshing!