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!

Friday, November 28, 2008

Math problems of the week: 2nd grade Everyday Math vs. Singapore Math

A. From the last page of exercises of volume 1 (of 2 volumes) of Everyday Mathematics Student Math Journal, p. 163

4 children share 12 slices of pizza equally. How many slices does each child get? Draw a picture.

Each child gets ____ slices.


5 + 6 + 23 = _____
_____ = 3 + 3 + 12
4 + 3 + 17 = _____
____ = 9 + 2 + 9

Count by 2s.

70, 72, 74, ___, ___, ___, ___, ___, ___,___, ___, ___

B. From the last page of exercises of volume 1 (of 2 volumes) of Singapore Math Primary Mathematics Workbook (2A), p.175

312 boys and 195 girls took part in a swimming test. How many more boys than girls were there?

There were _____ more boys than girls.

There are 292 men, 149 women and 68 children on a train. How many people are there on the the train?

There are _____ people on the train.

Meihua and her sister saved $502 altogether. Meihua saved $348. How much did her sister save?

Her sister saved $______

C. Extra Credit:

Which problem set do you think the University of Chicago Math Department, as opposed to the University of Chicago Math Project, would prefer to see 2nd graders doing half-way through 2nd grade math?

Tuesday, November 25, 2008

Autism Diaries: mind games, part II

When he insisted it was all a dream, I asked J whether it was also all just a dream for Daddy, whom I had called after it had happened so that J could hear me communicate to the other domestic authority figure the consequence of his Friday night behavior--"never, never going to the Chinese restaurant again." J dropped the subject and hasn't revisited it since.

Sort of...

A week later, this past Friday, I appeared unexpectedly in his doorway while he was sprawled on the floor doing something on his computer that he didn't want me to see (either trying to download games for free, or sending emails to people asking to play with their wiis and ceiling fans). He reflexively slammed the door with his foot and unintentionally hit me, hard, in the temple.

He immediately apologized, and, seeing how upset I was, ran down two flights of stairs on his own initiative and brought up an ice pack, which he'd jury-rigged from a sandwich bag around an ice cube, handed it to me, and repeatedly asked me whether I was OK.

Then, suddenly, I could see a thought flit across his eyes.

"Did you lose your memory?" He asked, ever so slightly hopefully.

Sunday, November 23, 2008

Autism Diaries, III: mind games

J. has been addicted to fans since he was 6 months old, but no fans enthrall him more than the ceiling fans at the local Chinese restaurant. I can practically hear them wincing at the other end of the line when I call up to order J's favorite dish, squid with spicy salt, with "please just the squid with nothing else on it--no peppers, no garlic." They most assuredly recognize who the request is coming from, and hope, hope, that that crazy blond boy won't be accompanying his mother into the restaurant when she comes to pick up the order.

Problem is, every time I bring him in he charges past the takeout counter into the dining room, and, if the fans aren't all on fast, climbs onto the first booth to reach across tea cups and torsos to grope at the fan controls. So, naturally, it had been a while since I'd taken him there with me. The last time was about 6 months ago, way back in summer when the fans--whew!--were already on high.

But last week when my husband was away and J had had a good enough week to earn his Friday squid--squid being the one meat he eats, and one he craves it almost as much as fans-on-high--I had no choice but to bring him. He'd matured a lot since summer; surely I could talk him into controlling himself.

The whole way over there, all the rewards for self-restraint and all the penalties for putting fans-on-fast were gone over ad nauseam. Yes, yes, he repeated: he understood. No sooner do we enter the restaurant, than he wrenches his hand out of mine, hurtles his way into the dining room, and throws himself across the booth, nearly knocking the teacups out of the hands of the horrified customers, while I yell "stop" over and over again, tugging back at his jacket until it practically bursts at the seams. It was the loudest, most frenzied scene the two of us had made in years.

"You are never, never, ever, in your entire life, ever going into that restaurant ever again," I repeat, repeatedly, as we head back home. "Never, ever, ever. Do you understand?"

"Yes," he repeated, contritely.

End of story? Three days later, J explains to me that on Thursday night I had fallen into a deep sleep from which I didn't awake until Saturday. He'd had to go to school by himself, come home by himself, and fend for himself for supper. Everything that I might have thought had happened on Friday, he assured me, was nothing more than a dream.

Friday, November 21, 2008

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

A. From "Finding Fractions of a Whole," a 5th grade Investigations (TERC) homework sheet:

1. In a school election, 141 fifth graders voted. One-third voted for Shira and two-thirds voted for Bree.

a. How many votes did Shira get? ____

b. How many votes did Bree get? ____

2. Bob, Liz, and Eli drove from Chicago to Denver. (1,050 miles).
Bob drove 1/10 of the distance.
Liz drove 4/10 of the distance.
Eli drove 1/2 of the istance.
How many miles did each person drive?

Check to make sure the total is 1,050 miles.

a. Bob: _____ miles b. Liz: _____ miles c. Eli: _____ miles

3. Carlos and Rick paid $8.75 for a present. Carlos paid 2/5 of the total amount and Rick paid 3/5 of the total.

a. How much did Carlos pay? _____
b. How much did Rick pay? ______

4. A pizza costs $12.00, including tax. Scott paid 1/4 of the total cost. Trung paid 1/3 of the total cost. Pritish paid 1/6. Bill paid the rest. How much did each person pay?

a. Scott: $____ b. Trung: $____ c. Pritish $_____ d. Bill: $____

B. From 5th grade Singapore Math Primary Mathematics 5a, fractions word problems:

1. A tank is 4/5 full of water. If 40 gal more water are needed to fill the tank completely, find the capacity of the tank.

2. There are 1400 students in a school. 1/4 of the students wear eyeglasses. 2/7 of those who wear eyeglasses are boys. How many boys in the school wear eyeglasses?

3. 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?

4. Mrs. Ricci had $580. She used 2/5 of it to buy an electric fan. She also bought a tea set for $60. How much money did she have left?

Extra Credit:

Which problem set involves more "inquiry," "critical thinking," and "argumentation"--all those critical 21st Century Skills we keep hearing about?

Wednesday, November 19, 2008

How to ration high grades, part II

Events in my son's school life since yesterday inspire three additions:

1. Keep all written homework directions sketchy enough that bored kids who don't pay attention won't remember the key details you only give orally.

2. Base tests not on textbooks or other written resources, but only on the notes that students take in class--another way to disfavor bored/distracted kids, who tend not to take notes, as well as disorganized kids, who lose track of their notes, along with the penmanship impaired, whose notes are often minimal and/or impossible even for him/her to decipher.

3. Never, never teach penmanship! That way only certain students (the penmanship "naturals") will end up writing fluently and clearly enough to take good notes and meet today's high standards for neatness.

Tuesday, November 18, 2008

How to ration high grades

...and make sure not too many go to the math buffs and other analytical children that traditional teachers considered "smart."

1. Don't collect homework; leave it up to kids to hand things in. Many smart but disorganized children will lose points to this.

2. Grade via inflexible rubrics that contain at least one "visual" dimension (color, creativity, neatness) that disfavors the artistically impaired. That way, no matter how well a smart, non-artistic kid does on the more academic components, he'll still fall short of a top grade. All the better if you design the entire assignment to strike both smart kids and their parents as inane. That way many of these parents won't bother to make sure their unmotivated children fulfill all the requirements.

3. Don't hand things back until the end of the marking period. This keeps parents from knowing that their kids are losing points for trivial reasons--e.g., for not showing multiple solutions or explaining their answers or using enough colors--and intervening accordingly.

4. Assure kids--and their parents--that the second tier grade that most of them are getting (a.k.a., "B", "3", or "proficient") is a very good grade.

5. Keep the math problems easy and define "exceeding the standard" to include explaining your answers as verbosely as possible, drawing neat, colorful visual representations, and providing multiple "creative" strategies by solving simple problems over and over again. The easier the student finds the math, the less motivated s/he will be to comply, and the more points s/he will lose.

6. Do the same with science, language arts, and foreign language: water down the academic, analytical components, and up the "creative," showy visual requirements.

Sunday, November 16, 2008

6th Grade English Class in the 21st Century: multiple literacies

The part of 6th grade English class that should stump a fluent but grammar and reading comprehension -impaired kid with autism, one would think, would be the reading and writing component.

Somehow, though, my son is getting A's in his reading and writing assignments.

But then there's his "All About Me" shield:

In not wanting to "privilege" the written word, we're shortchanging those with art disabilities.

...And those whose parents aren't motivated to oversee the more questionable assignments.

Thursday, November 13, 2008

Math problems of the week: 4th grade Investigations vs. Singapore Math

1. From the beginning of the 4th grade investigations curriculum

2. From the beginning of 4th grade Singapore Math, Primary Mathematics 4A

The handwriting you see in the Investigations sheet is that of my daughter who, at the age of 5, found it lying around and did a few problems before losing interest.

Wednesday, November 12, 2008

It all goes back to grammar and vocabulary

The more papers I read in cross-cultural pragmatics, the more convinced I am that foreign language classes are overly marginalizing grammar and vocabulary, even in light of their new emphasis on "communicative competence."

I just finished re-reading, for a class I'm about to teach, a 2001 paper by Thom Hudson entitled "Indicators for pragmatic instruction: some quantitative tools." Focusing on speech acts like apologies, requests, and refusals, Hudson notes that intermediate-level ESL students have little trouble figuring out when a particular speech act is called for, or observing the appropriate linguistic conventions in formulating the act in question.

What trips them up, instead, are the more language-intensive aspects of effective apologies, requests, and refusals--e.g., providing appropriate amounts of accompanying explanation. In apologizing for missing a meeting with your boss, or asking a neighbor to lower the volume of his stereo at night, or turning down an invitation for lunch, it turns out, it helps to have a large enough vocabulary and repertoire of syntactic structures to effectively explain why you missed the meeting, or are bothered by the music, or aren't available at lunch time.

However reluctant today's foreign language teachers are to teach the more left-brained nuts and bolts of language content, it turns out that these are key to successfully executing the more social, right-brained aspects of language use.

Monday, November 10, 2008

Another child in trouble for stacking

And this child isn't even one of the kids we're corrupting on the Continental Math League.

Rather, it was his mother who showed him "how I learned to solve this kind of problem." And he found her way more efficient than the "splitting" that his teacher prefers. But then his teacher caught him stacking, and advised him that when you split instead of stack it's much easier to explain your answer (key to getting full credit).

Meanwhile, at Continental Math League practice today, I reminded kids that they can solve the multi-digit calculations using any method they want. The first few times they opted for stacking, I asked why.

"It's much faster," said one. "With splitting you have to keep splitting and splitting, and then you lose track of what you're doing and forget what's going on."

Saturday, November 8, 2008

Convincing other parents

Allison's post yesterday at kitchentablemath on how difficult it is to convince fellow parents of Reform Math's shortcomings coincides with my receipt of our school's latest Home and School Association report.

According to this report, 89% of the 70+ parents who attended the school math consultant's parent presentation rated it "helpful" to "extremely helpful." This, despite the fact that she made an evidence-free argument against having children solve problems by "stacking" (arranging numbers vertically and using the standard algorithms), asserted that we should be teaching our children the multiplication tables at home because teachers don't have time to in school, and spent about half of her presentation soliciting our multiple strategies for multiplying 85 by 4 and dividing 120 by 3, thus demonstrating how it is that time is used up in the classroom.

Like Allison, I feel that no one takes me seriously when I carry on about the dire effects of Reform Math.

No one, that is, except my friends. But these people, for all the concerns they've been expressing, appear to have been written off by the HSA as "friends of lefty."

Here, for what it's worth, is the latest from one of these friends, the parent of a 1st grade mental math whizz:

Just as we expected, J has been struggling with the “show your work” portion of his math homework. He got an “incomplete” one week for failing to illustrate how he added 2 and 2, or some such thing. This week, on a “3 + 5” problem, he had a solution: he drew a stick figure with a thought bubble, put “3 + 5” in it, and labeled it “me”!

Thursday, November 6, 2008

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

1. This week's 2nd grade Investigations homework:

2. From a similar point in the 2nd grade Singapore Math workbook (Primary Mathematics 2A):

Doubles vs. multiples. (Apologies for the poor resolution; I'm still learning how to scan).

Wednesday, November 5, 2008

Today's computer programming: whither recursion?

Over the last few weeks I've been trying, and thus far failing, to acquire some basic programming software for my autistic son that I can run on a computer at home. BASIC? FORTRAN? Even C?

The more time I spend on this, the more I wonder how many people still have opportunities to learn the programming fundamentals that to me seem not just essential, but fun: recursion, nested loops, flow charts, logic.

Back when I was in high school, students could write basic programs directly onto their primitive home computers. What about today's high school students? How many of them are nesting loops or creating self-calling functions--as opposed to writing html tags, cutting and pasting from someone else's code, or "programming" games using high-level programs like Director?

In the course of these musings, I came across a recent blog by a Penn graduate that questions whether even college-level courses are now teaching such fundamentals as pointers and recursion.

The more today's programming limits itself to "cut and paste" and high-level parameter setting, the more we lose the kinds of flexibility and creativity crucial for novel software applications--whether for entertainment, research, or education.

All the more reason for me to track down a programming package for my autistic son, who may one day find his most promising niche in what may already be a dying vocation! Any pointers?

Monday, November 3, 2008

Friday, October 31, 2008

Alternatives to stacking, II

I've received, both here and at kitchentablemath, a number of interesting non-stacking strategies for computing 825 - 267 that I had never thought of before. This made me wonder about just how far one can get without stacking. What happens when we add a few more digits?

For example, how about--using numbers randomly generated by my software program--885.66 minus 746.85?

My new question: Is there a way to subtract 746.85 from 885.66 that

1. Isn't massively facilitated by stacking one number on top of the other;
2. Only uses methods that grade school children can discover on their own;

3. Doesn't place excessive demands on short-term memory?
If so, please share it here!

Thursday, October 30, 2008

Math problems of the week: 3rd grade Investigations (TERC) vs. French math

1. From 3rd grade TERC Investigations, "Things that Come in Groups," p. 89:

There are 26 crackers in a box. Each cracker can be split into 2 equal pieces. How many pieces will there be?

Show how you solved this problem. You can use numbers, words, or pictures.


2. From Professeur Phifix, a web resource for French curriculum materials, "Multiplication and Division" problems for CE2 (3rd grade), translated from the French:

August has invited 4 friends over for his birthday. His mother bought him 3 cookie boxes each containing 25 cookies. After playing soccer, the children come to eat and celebrate August's 10th birthday.

Calculate the number of cookies that each child will eat.


3. Extra Credit:

Using words, numbers, or pictures, explain why the Investigations problem, but not the French problem, stipulates that students must explain their answers.

Tuesday, October 28, 2008

Continental Math League Update:

Enthusiasm from students and parents; skepticism from teachers.

Specifically, about "stacking."  (Today's word for how we used to add, subtract, and multiply numbers by placing one number on top of the other.)

Kids love it.  And not just the ones on our team.  As Nancy Bea Miller writes:
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.
Yes, she does, and she doesn't like it.  At least if she resembles the teacher who approached me after math practice yesterday and recounted the dismay she felt when she caught one of her students stacking numbers, thus abandoning the more "meaningful" and "faster" way he used to solve problems.

My co-coach and I tried to explain that the Continental Math League numbers are big enough, and random enough, that Reform Math's methods aren't faster and more meaningful, but inefficient and confusing. It's one thing to add 48 and 39 by reasoning that:
48 is 2 less than 50, and 39 is 1 less than 40, so add 40 and 50 and get 90 and then count backwards by 3 and get 87."
But take one of the problems we did at Continental Math League yesterday: 825 - 267. Restricting myself to the kinds of calculation that these second and third graders are able/expected to do in their heads, here's the most efficient non-stacking method I can come up with:  
The closest friendly number to 825 is 800, and the closest friendly number to 267 is 250.  825 is 25 more than 800.  250 is 10 more than 260, and another 7 gets you 267.  10 plus 7 is 17.  So 267 is 17 more than 250.  So subtract 250 from 800. Well, 800 minus 200 is 600, minus 50 more is 550.  Then subtract 17 from 25 by counting up from 17.  Seventeen plus 3 more is 20 plus 5 more is 25.  3 plus 5 equals 8.  Add 8 to 550* to get 558."
*By this point in the problem, how many people remember what they should be doing with this 8?

Anyone with a more efficient non-stacking method for subtracting 267 from 825 (no calculators allowed!) is invited to share it here.

Monday, October 27, 2008

Internet problems

Hope to be back tomorrow!

Thursday, October 23, 2008

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

1. From Mathland Daily Tune-Ups Grade 5, second-to-last problem set:

*There are 4 cups in 1 quart. How may cups are there in 6 quarts?
*There are 2 pints in 1 quart. How many pints are there in 4 quarts?
*There are 4 quarts in 1 gallon. How many quarts are there in 4 gallons?
*If there are 4 quarts in a gallon, and you have only 2 quarts, how many gallons is it?

2. From Grade 5 Singapore Math, Primary Mathematics 5B, end of "Measures and Volume" unit:

A rectangular container measuring 12 in. by 10 in. by 11 in. is completely filled with water. After 240 in.3 of water are taken out from the tank, what is the height of the water level in the container?

[picture of container with its measurements shown]

Extra Credit:

1. Estimate the percentage of Singaporean 1st graders who can do the Mathland set.

2. Estimate the percentage of American 5th grade teachers who can do the Singapore problem.

Tuesday, October 21, 2008

An alarming report card on Investigations Math

Pat's teacher is 27 years older than Pat. Pat is 9. How old is Pat's teacher?
Pat's teacher is _______ years old.
This was one of the easiest problems on the assessment I gave the 2nd and 3rd graders who were trying out for the new after-school math team.

Answers among these mathematically inclined students varied alarmingly widely. The most common wrong answer was 27, but there were others.

Many students who got this problem wrong were able to do harder, multi-digit calculations later on in the assessment--harder calculations than what our school's Investigations curriculum offers them. From this, I can't help inferring that they're somehow finding extra-curricular opportunities to calculate.

And whatever, or whoever, the outside influence might be seems to be doing a better job than Investigations does.

For word problems--not hard calculations--are the pride and joy of the Investigations curriculum. 

And even if some of the wrong answers resulted from sloppy reading or poor reading comprehension, Investigations, which cares so much about language arts, should surely have addressed this by now.

Instead: after two or three years of this curriculum even many of the more mathematically inclined of the 2nd and 3rd graders of the highly educated parents that predominate at our school are unable to do a simple word problem involving 27, 9, and a comparison of two different ages.

Sunday, October 19, 2008

Stacking, regrouping, and corrupting the children

At this fall's first "parent education workshop," our school's math consultant told us that we shouldn't show our children how to add numbers by "stacking" them one on top of another. Children don't understand how stacking and regrouping work, and would be better off devising their own solutions.

The many skeptics in this record-sized crowd were given no opportunity to ask questions. A few new converts, though, had chances to confess to being "stackers," and their humble admissions suggested hope that the sins of the fathers won't be visited upon their children.

Not if I can help it. This coming week, during our second math team practice, my co-coach and I will be showing the most mathematically inclined and advanced quartile of the second and third grade classes how to stack and regroup. Not only that, but we'll be picking this forbidden mathematical fruit from a particularly controversial Tree of Knowledge.

Our kids seem eager to be corrupted. The first problem set we sent home, plucked straight off this tree, was--if parent reports are accurate--devoured with reckless glee, as these 8 and 9-year-olds threw off the mathematical abstinence the higher powers in education have foisted on them.

Thursday, October 16, 2008

Math problems of the week: grade 3 Trailblazers vs. Singapore Math

1. From 3rd grade Math Trailblazers, end of the fractions unit:

Look for fractions at home and in your neighborhood.  You might look in the newspaper (especially in the ads) or in magazines, in cookbooks, in the mail, or on signs.  Try to find at least six fractions.

Write about each fraction you find.  Tell what the whole is, and try to draw a picture that shows the whole and the fractions.

2. From the 3rd grade Singapore Primary Mathematics (3B) end of fractions unit:

Polly has 12 ribbons.  1/3 of the ribbons are red.  The rest are yellow.
(a) What fraction of her ribbons are yellow?
(b) How many ribbons are yellow?

Extra credit:

What fraction of each assignment involves math?

Monday, October 13, 2008

Everything but the math curriculum

In the last week, I've seen two articles expressing concern about the nation's school children:  one about boys, and the other about girls. Both leave out one of the biggest underlying factors, namely, the grade school math curriculum.

First there's an article in Teacher Magazine about Peg Tyre's new book, The Trouble with Boys, which, quoting Teacher Magazine, "details the problems boys are facing in school and argues for a new, boy-focused “gender revolution.” As far as the curriculum's role in all this goes, Tyre faults it for being too narrow and test-focused.

Then there's an article in the New York Times about a forthcoming article in the Notices of the American Mathematical Society about how few American-born girls are competing in top math competitions like the Math Olympiad and the Putnam Math Competition. This article makes no mention of our country's new Reform Math, instead blaming the numbers on anti-nerd biases that especially ostracize female math students.

Once again, people are happy to blame everything but the math curriculum. But the boys I know who are languishing in school are doing so because of Reform Math's dumbed down math and emphasis on language arts.  

This may also explain the disproportionately small numbers of American girls--which is accompanied, though outnumbered, by a disproportionately small number of American boys--performing well in the top math competitions. Perhaps, outside of school, gender stereotypes still have people identifying and encouraging boy math buffs more than their female counterparts.  

And, as America's math classrooms dumb themselves down under the Reform Revolution, what happens outside of school--including ongoing sexist assumptions about math ability--wields an ever greater influence over who does well in math.

Thursday, October 9, 2008

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

1. From one month into the 2nd grade Investigations curriculum, Coins, Coupons, and Combinations, "What Will You Need" worksheet:

1. Complete each sentence.

1. If I have 4, I will need ____ to make 10.
2. If I have 6, I will need ____ to make 10.
3. If I have 3, I will need ____ to make 10.
4. If I have 7, I will need ____ to make 10.
5. If I have 2, I will need ____ to make 10.
6. If I have 8, I will need ____ to make 10.
7. If I have 1, I will need ____ to make 10.
8. If I have 9, I will need ____ to make 10.
9. If I have 5, I will need ____ to make 10.
10. If I have 0, I will need ____ to make 10.

2. From one month into the 2nd grade Singapore Math curriculum: Primary Mathematics 2a, p. 40:

1. Add:

   648         436    700
+ 201 + 231 + 135

   540    625    213
+ 249 + 173 + 153

   107    445    657
+ 381 + 124 + 330

3. Extra Credit:

A generation from now, which country will be most able to extricate itself from a financial crisis?

Tuesday, October 7, 2008

Latin redux: A response to Constructivist language teaching?

Today's New York Times reports on the rising numbers of students enrolling in Latin classes.  

The resurgence of a language once rejected as outdated and irrelevant is reflected across the country as Latin is embraced by a new generation of students like Xavier who seek to increase SAT scores or stand out from their friends, or simply harbor a fascination for the ancient language after reading Harry Potter’s Latin-based chanting spells.
Coming at a time when increasing numbers of French, Spanish, and German classes are adapting Constructivist teaching methods (implicit learning through group conversations, skits, and interdisciplinary projects), the surge of Latin enrollment may have yet another partial cause.

Latin, after all, doesn't lend itself as naturally as living languages do to group conversations about high school social dynamics, or student-made travel guides and restaurant menus, or the marginalization of grammatical structure. And, while there's perhaps nothing preventing a Latin teacher from having students "decorate a tissue box with Latin vocabulary words," such assignments may not appeal to the kind of person who chooses to teach Latin in the first place.

For students and teachers who care about foreign language grammar, and who prefer explicit instruction to skits and crafts, Latin is the perfect antidote to current practices.

Sunday, October 5, 2008

So you want to do a science experiment? Knock yourself out!

But wouldn't you rather write a personal reflection about science instead?

Every week J. has to do 15 points worth of science homework.  A "response sheet" gets you 5 points (this week's:  a "note to Josh" about your ideas about stream tables); a personal reflection about a science article earns you 7 points.  

But if you really want to do science, you can do the science experiment.  This week's involves the following:
Set up a scene with about 2 inches (5 cm) of sand or soil in the box.
Build and/or add one type of barrier, in the middle of the box.

Turn on the fan and let it run for five to ten minutes, depending upon the action you observe.

Photograph the changes in your soil or sand. Be sure to notice what happens both in front of and behind the barrier.

Repeat with several different barriers in the wind path. 
Building barriers; acquiring sand and soil; pouring it into boxes; blowing it; taking pictures; repeat?  Hmm... maybe we should do the personal reflection instead.

Except that we saw how J's teachers feel about his personal reflections....

Friday, October 3, 2008

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

1. From the end of the first unit of 6th grade Connected Mathematic Prime Time

A group of students designs card displays for football games. They use 100 square cards for each display. Each card contains part of a picture of a message. At the game, 100 volunteers hold up the cards to form a complete picture. The students have found that the pictures are most effective if the volunteers sit in a rectangular arrangement. What seating arrangements are possible? Which would you choose? Why?

2. From the end of the first unit of 6th grade Singapore Math Primary Mathematics 6A

Simplify the following expressions:

12 + 8h – 6h =

9a + 1 -3a =

7 + 4k – 2 – 2k =

15x + 8 – 10x -3 =

Extra Credit

Estimate the ratio of linguistic complexity to mathematical complexity in each problem.

To quote Connected Math, which would you choose, and why?

Thursday, October 2, 2008

Autistic personal connections don't pass muster

Besides the narcissism of the "All About Me" unit, we have the narcissism of the "personal connections" paragraph that students are supposed to write after each night's reading.

Again, only neurotypical connections count.  My son's "personal connections" (about Harry Potter, Chamber of Secrets) earned him a D:
I never drink polyjuice potion before. I never do magic before. I liked that chapter because Harry and Ron realized that Draco Malfoy is not the heir of Slytherin.
His teacher's comment:  "Maybe J should find a book that he can make connections with to make the reflection section more meaningful."

Lurking within this neurotypical self-love, it seems to me, is a kind of subtle hatred of autism.

Tuesday, September 30, 2008

Autistic Time Lines

My autistic son's sixth grade English teacher is insisting that he redo the "First Five Years of My Life Timeline" he created for this month's "All about Me" unit.

The problem?  The events he included:
November, 1999:  I thought the porch fan switch was broken.
June, 2001: I realized that Mommy was only pretending the switch was broken so I wouldn't keep turning it on and off.
September, 2001:  Porch fan switch actually broke.
May, 2002:  Porch fan switch fixed.
I tried to tell her that J did this assignment in good faith, and that these really were among his most memorable milestones. 

"The assignment doesn't meet expectations," she insisted.  

One of the ironies here is in the premise behind such narcissistic units as "All about Me:"

Students learn best when relating things to their personal interests.

Apparently only the personal interests of neurotypical children count, and what is supposed to be an alluring tie-in for most students becomes a major obstacle for those with autism.

Sunday, September 28, 2008

Autism Diaries, II: a universe far, far away

Step one:  Set up a gmail account in your babysitter's name.

Step two:  From that account, email her the following message:
You & I have a same first name, same middle name, and same last name. My life is same as yours. I babysit "J" [His name] like you. I look like you. I babysit different "J". I live in different universe which is quadrillion light years away from you. I have a special computer internet which radio ways are quadrillion light years per second.
The least plausible claim in this email message is that there's anyone anywhere else in the universe like "J".

Friday, September 26, 2008

Math problem of the week: 4th grade Trailblazers vs. Singapore Math

1. From 2/3 of the way through the grade 4 Math Trailblazers workbook, p. 144:

A. When Shannon and her family arrived at the park on Saturday, Shanon counted 3 children on each of the following: the slide, the swings the monkey bars, and the merry-go-round. How many children were at the park when Shannon arrived?

B. If there were 8 more children than adults at the park, how many adults were at the park?


Shannon treated her little sister and her mother to a treat. At a nearby stand she bought two cans of juice at 65c each and three popsicles at 85c each. She gave the vendor $5.00. How much change will Shannon receive?


2. From 2/3 of the way through the grade 4 Singapore workbooks, Primary Mathematics 4b, p. 120

A computer costs $2290.  An oven costs 1/5 the cost of the computer.  How much more does the computer cost than the oven?

A basket, together with 6 cans of mushrooms, weighs 3.05 lb.  Each can of mushrooms weighs .43 lb. Find the weight of the basket when it is empty.


OILF's Assessment

In the first Trailblazers problem, the italic each gives away the multiplication operation, and the problem is split into two parts so you know to multiply first, then add--unlike the Singapore problems, where you have to figure out which operations to use, and in what order.

Both Trailblazers problems stick to friendly numbers:  2, 3, 4, 5, 8, 65 and 85.  Their Singaporean counterparts, meanwhile, use a four digit number, a fraction, and two unfriendly decimals.

Playgrounds and refreshments vs. major appliances.

Tuesday, September 23, 2008

Eliminating the SAT: disadvantaging the left-brainers

A commission convened by some of the country’s most influential college admissions officials is recommending that colleges and universities move away from their reliance on SAT and ACT scores and shift toward admissions exams more closely tied to the high school curriculum and achievement.
So reports yesterday's New York Times.

The commission, convened by the National Association for College Admission Counseling, cites three concerns.  In the words of study leader William R. Fitzsimmons,  the dean of admissions and financial aid at Harvard University:

(1) "test scores appear to calcify differences based on class, race/ethnicity and parental educational attainment."

(3) "the contrast between opportunities and fancy suburbs and some of the high schools that aren’t so fancy"

(3) "academic research that suggests that test preparation and coaching results in an increase of 20 to 30 points on the SAT"

As a result of such concerns, the Times writes:
A growing number of colleges and universities, like Bates College in Maine, Lawrence University in Wisconsin, Wake Forest University in North Carolina and Smith College in Massachusetts, have made the SAT and ACT optional. And the report concludes that more institutions could make admissions decisions without requiring the SAT and ACT.
More than 280 four-year colleges do not require standardized test scores for admission, according to the study.
According to Mr. Fitzsimmons, Harvard may be next.

The report's recommendations:

1. Institutions should "consider dropping admission test requirements unless they can prove that the benefits of such tests outweigh the negatives."

2. "what is needed is a new achievement test, pitched to a broad group of students, that would predict college grades as well as or better than available tests."

Such an achievement test, the report claims, would (quoting the Times quoting the report):
“encourage high schools to broaden and improve curricula,” and would also send a message to students to focus on their high school course material instead of on test preparation courses.
OILF's concerns:

Re the new achievement test:

1. The original point of the SATs was to open up college admissions to students who didn't come from fancy schools and who were thereby disadvantaged in subject-area college admissions tests.  Why would replacing the SATs with a new achievement test make things any more equitable?  To the extent that the proposed new test encourages the weaker high schools "to broaden and improve curricula," such changes take years, if not decades, to put into place, let alone to trickle down to actual students.

2. The influence may just as likely go in the other direction, with the power brokers in the education establishment, rather than reforming the schools, retrofitting the new achievement test--with all the predictable results.  E.g.: assessing students not on doing hard math and science, but on how well they communicate about math and science.

Re assigning greater weight to grades: 

1. As I've argued here, here, here, here, here, here, here, here, and here the latest pedagogical priorities have made it harder and harder for even--and sometimes especially--the smartest left-brainers to earn good grades.

2. For such students, the SAT is increasingly the one recourse for distinguishing themselves academically and, therefore, for gaining admission to selective colleges.

Sunday, September 21, 2008

Right-brained foreign language assignments: the German tissue box

When I learned, this weekend, that my nephew had to decorate a tissue box for German class, I was curious whether this was the brainchild of his particular teacher, or a general trend in German language instruction.

I googled "tissue box" "German," and found three links touting my nephew's assignment:

Note, especially, the grading rubric, with its ratings for creativity and craftsmanship.

I find myself brimming over with questions as I peruse these sites; perhaps the most burning one of all is this:

When will this contagious meme (to use Richard Dawkins' term), this sticky idea (to use Malcolm Gladwell's term), this creative, crafty pedagogical epiphany, catch on in other Germanic language classrooms--like Swedish and Dutch?

Who knows, it might even liven up French, Russian, and Chinese.

Thursday, September 18, 2008

Math problem of the week: 2nd grade Investigations vs. Singapore Math

1. From the beginning of the grade 2 Investigations curriculum (Counting, Coins, and Combinations, Family Letter about Benchmarks/Goals):

7 + 3 = 5 + 1 = 5 + 2 =
6 + 4 = 6 + 1 = 2 + 8 =
5 + 5 = 1 + 9 = 2 + 7 =

2. From the beginning of the grade 2 Singapore Math curriculum (Primary Mathematics 2B, p. 13)

1 more than 76 is
1 less than 76 is
10 more than 72 is
10 less than 76 is

2 more than 76 is
2 more than 76 is
20 more than 76 is
20 less than 76 is

2 more than 38 is
10 more than 63 is
20 more than 80 is
2 less than 75 is
10 less than 86 is
20 less than 94 is

Extra Credit: 

Which problems does your 7-year-old find most challenging?  Most interesting?

Wednesday, September 17, 2008

Please visit an actual classroom before you make recommendations, III

This time the recommendations come from Natalie Angier, a science reporter with the New York Times.

In this week's Science Section, she reports on two studies showing connections between two cognitive number mechanisms:

1. The approximate number system: in Angier's words, "an ancient and intuitive sense that we are born with and that we share with many other animals."

2. The abstract, symbolic system that allows us to "manipulate representations of numbers" and make precise calculations.

One study shows that a person's facility with the approximate system is connected to his/her facility with the symbolic system. The other shows that, in Angier's words:

[P]reschool children are remarkably good at approximating the impact of adding to or subtracting from large groups of items but are poor at translating the approximate into the specific.
All this, Angier reports, has "potentially broad implications for math education:"
Taken together, the new research suggests that math teachers might do well to emphasize the power of the ballpark figure, to focus less on arithmetic precision and more on general reckoning.
Huh? Less on symbolic and more on approximate? This is a non-sequitor, unless we know that the causality flows from approximate to symbolic.

But as Angier quotes one of the researchers (Lisa Feigenson of Johns Hopkins) as saying, “We can’t draw causal arrows one way or another" between "your evolutionarily endowed sense of approximation" and "how good you are at formal math.”

And, as Angier herself writes: "The researchers caution that they have no idea yet how the two number systems interact," and that it's currently an "open question[] ...how malleable our inborn number sense may be, whether it can be improved with training, and whether those improvements would pay off in a greater appetite and aptitude for math."

So how does Angier leap to the conclusion that schools should be stressing approximate number sense over symbolic numerical reasoning?

It seems that our science reporter has managed to:

1. avoid visiting actual classrooms, where she would see how much symbolic math has been jettisoned the sake of "number sense," and by how much overall levels of math achievement have therefore declined.

2. fall under the influence of the reigning ed school orthodoxy, which is as enamored of intuition as it is contemptuous of abstract reasoning.

3. take, on faith, the bizarre claims by one of the researchers about the parlor games played by mathematicians:
“When mathematicians and physicists are left alone in a room, one of the games they’ll play is called a Fermi problem, in which they try to figure out the approximate answer to an arbitrary problem,” said Rebecca Saxe, a cognitive neuroscientist at the Massachusetts Institute of Technology who is married to a physicist. “They’ll ask, how many piano tuners are there in Chicago, or what contribution to the ocean’s temperature do fish make, and they’ll try to come up with a plausible answer.”
Not the mathematicians I know!

Why doesn't anyone ask them about what they think of what's going on in today's actual classrooms?

Sunday, September 14, 2008

Reform Science and the fate of the science experiment

"It's not as if I have the kids go in and do a science experiment, and then go in the next day and do another experiment, and so on.." my son's 6th grade science teacher told me.

Rather, he assured, today's science classes focus on more important things, like communicating scientific ideas through presentations and posters.

The science experiment is now an optional home venture: the fourth and final option on the weekly homework sheet, listed after (1) the calculator-facilitated metric conversion worksheet, (2) the calculator-facilitated area & volume worksheet, and (3) the communications assignment (pick a science article, summarize it, and write a personal reflection of what you thought about it).

And the experiment's instructions are so imprecise that it's not clear what you're actually supposed to be doing or testing out.

The question:

Does the amount of salt in water affect the amount of freshwater produced?

In one trivial sense, the answer is yes. Any significant amount of salt reduces the amount of freshwater down to zero, because when you add enough salt to freshwater it's no longer fresh.

In another trivial sense, the answer is no: adding substance B to substance A doesn't subtract from substance A.

Whatever. Maybe the directions will somehow illuminate matters:
Mix salt and water to make salt water.
Do the proportions matter? A sprinkling of salt? A whole ladel full?
Add about 2 inches of the water to a pot.
But remember the area and volume sheet! Inches are linear! What on earth is "2 inches of water"?
Put an empty glass in the bowl.
Just "put?" Centered? On its side? Upside down?
Seal plastic wrap over the top, weigh it down with a rock (centered above the bowl?)... Now you've made a solar still.
Oh, OK. Let's re-position the cup accordingly.

But what if no one at home knows what a solar still is already?
Repeat with fresh water.
"Two inches" of water?

In a pot the same size as the first? Actually, it's a good thing this is left unspecified: we don't have two equal pots. (Do most people?)

Do two inches of fresh water get you the same amount of H2O as two inches of salt water? Is this what we're trying to find out? Or is starting out with the same amount of H2O a prerequesite for answering a different question about what happens to the water later on?
Put the stills outside in the sun. Leave it [sic] alone for a few hours, or even a whole day. When you're ready, measure the water.
In inches?

And doesn't how long we leave them out affect the answer we get?

Assuming we even know what the question is...

Yes, I see now that communicating scientific ideas is very important. Perhaps we'll go with Option 3 next time.

Thursday, September 11, 2008

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

1. The first assignment in Connected Mathematics Prime Time: Factors and Multiples

My Special Number

Many people have a number they find interesting. Choose a whole number between 10 and 100 that you especially like.

In your journal
*record your number
*explain why you chose that number
*list three or four mathematical things about your number
*list three or four connections you can make between your number and your world

As you work through the investigations in Prime Time, you will learn lots of things about numbers. Think about how these new ideas apply to your special number, and add any new information about your number to your journal. You may want to designate one or two "special number" pages in your journal, where you can record this information. At the end of the unit, your teacher will ask you to find an interesting way to report to the class about your special number.

2. The first assignment in Singapore Mathematics Primary Mathematics 6A

A watermelon weighs m kg and a pineapple weights 2 kg.
(a) Express the total weight of the fruits in terms of m.

(b) if m = 4, find the total weight of the fruits.

(c) if m = 6, find the total weight of the fruits.


Apparently I'm in the minority: I don't have a favorite number. But I do have preferences within mathematics, and generally prefer algebra to number journaling.

If you have favorite numbers, or other mathematical preferences, please share them.

Tuesday, September 9, 2008

Using your analytical left brain to get out of Jury Duty

Usually a Ph.D. does it, but sometimes our city's courts are so desperate, or a particular panel of jurors too educated, for lawyers to peremptorily dismiss all those with advanced degrees. This was driven home to me several years ago when I served on my first jury.

A fascinating experience, particularly for me as a linguist.

But this time around, it was urgent that I get out, as I've just started teaching a graduate class for which there's no one who can substitute. While this doesn't constitute a "serious hardship," it was, in the end, this class that helped disqualify me. Among other things, I'm teaching conversational analysis--which includes, among other things, reading between the lines.

Things looked grim during the voir dire.  I had a low number--10 out of 40--and a half dozen others had already been dismissed.  But as soon as the judge asked me what I did as a linguist, my spirits soared.

Leaving out the other, more legally innocuous hats I wear, I replied, "I do pragmatics, which means I analyze conversations."

The judge looked bemused, and said, "You mean, you can tell me what I'm really thinking?"

"Exactly," I replied.

It took less than 5 seconds for them to dismiss me.