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

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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.

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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.

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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?

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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




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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):


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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