Comments

plug and chug what?

Could you perhaps post some sample questions?

I think that plug and chug might be quite reasonable at age 12 and setting up the equations may come in later. But it depends on the details.

-- TracyW - 11 Dec 2005

I've got it scanned & will get some pages up.

You've just brought up a second question, having to do with whether the content is appropriately balanced between the conceptual and the procedural (yes?)

I'd love to get everyone's thoughts on that issue, too. (I really don't know....which is funny, because I thought I was further along in terms of my 'personal philosophy' of math ed....)

At the moment, my question is only about whether it's a good idea to give 11 year olds 'killer tests.'

In other words, if you're going to give tests of procedures, is there something gained by giving very long, demanding tests of procedures?

-- CatherineJohnson - 11 Dec 2005

I'm mystified by the lack scratch paper, myself. I have an accelerated child and a special ed child and neither is give permission to use scratch paper. It is all very weird to me. I can't imagine any math teacher refusing a child a sheet of paper to draw something out or check a calculation. At these younger ages (and especially with strugglers and the easily intimidated) they really need permission and a signal that it's perfectly fine and normal.

Is it an oversight or what?

Maybe they're thinking that they go straight from mental math to calculators. They don't need to do those big, nasty calculations because they all have calculators. I have no idea.

-- SusanS - 11 Dec 2005

Catherine - long, demanding tests of procedures will give a good spread out of marks as those who can work fast and accurately are separated from those who can do one or the other, and those who can do neither. And those who can work the fastest and most accurately get separated out as well.

Whether that is a good thing or not depends on what your goals are.

-- TracyW - 11 Dec 2005

There may be some advantages in learning to concentrate for 45 minutes.

-- TracyW - 11 Dec 2005

I'm mystified by the lack scratch paper, myself. I have an accelerated child and a special ed child and neither is give permission to use scratch paper.

They actually don't allow it?

You've asked??

-- CatherineJohnson - 11 Dec 2005

long, demanding tests of procedures will give a good spread out of marks as those who can work fast and accurately are separated from those who can do one or the other, and those who can do neither.

Interesting......

How does that work, exactly?

I can see where you edit out the kids who can do neither....

From what I see, the tests clearly separate out the natural born Math Brains.

Those kids are amazing.

Like the rest of the kids, they're getting very little practice, and they're aceing the tests.

You can absolutely see the Engelmann stat about gifted kids needing literally half the amount of practice to learn the exact same material.

-- CatherineJohnson - 11 Dec 2005

This tells me that long, tough tests might be a good way to test mastery....

In fact, they might be the best way to test mastery.

I'm thinking about KUMON now.

Offhand, I would say that the KUMON Level Tests are in this category.

I'll take notes on how long the next one is.

I don't think the Level Tests are quite as long as the tests Christopher is taking, but they're quite challenging, and they're timed to the minute.

They have a curve showing you exactly where your performance falls.

If you don't make it into the 'pass' part of the curve, you do more worksheets in that level.

I passed the first one I took (for Level D, fourth grade) and was on the border between 'good' and 'excellent'!

(And I'm pretty good; I'd had LOTS of practice—much more than a real fourth grader, because I'd already done the entire RUSSIAN MATH book.)

-- CatherineJohnson - 11 Dec 2005

They don't need to do those big, nasty calculations because they all have calculators.

They don't have calculators for the test, and they aren't allowed to use mental math!

It's ridiculous!

-- CatherineJohnson - 11 Dec 2005

Tracy

To me it seems intuitively obvious that at some point a student needs to be able to sit down and rip through a VERY tough & long test.....

though I have to say that I'm not sure why this should be true....

Definitely, though, we need tests that show total mastery.

-- CatherineJohnson - 11 Dec 2005

Tracy

It's interesting that you bring this up, because in fact this is exactly what I'm using Christopher's deteriorating chapter test grades to assess: 'strong' mastery.

This morning his dad was wanting to tell me that Christopher was making 'careless errors,' and I wasn't having it.

Yes, he needs scratch paper; there are some handwriting issues here.

But you can't read through his test and see a kid who's mastered the material. Not even close (his dad wasn't saying so, either).

Those tests are highly informative in that sense.

When you put the pedal to the metal, he hasn't got hold of these concepts.

If you give him 5 minutes he can simplify an expression that contains decimals & variables.

Give him 45 minutes to do a zillion of them, he's in trouble.

That's not mastery.

-- CatherineJohnson - 11 Dec 2005

Naturally, we're going to harrass the principal about this.

The class average on the last test was 85; the average for the morning class was 74.

That's not working. (We think Christopher's class average is being pulled up by the two or three kids who get 96s and above. There are only 16 kids in the class, something like that.)

We're going to say that if they've got whole classes of kids getting 85s and below, which they do, these kids haven't got a lock on the material.

He'll undoubtedly tell us the course is for TAG kids and we'll undoubtedly bat that one away.

Teach to mastery.

Formative assessment.

Everybody learns the content, and everybody learns to mastery.

This ain't brain surgery.

It's pre-algebra.

-- CatherineJohnson - 11 Dec 2005

We have a whole new scheme for test practice around here; it's cool.

Which reminds me, we have more practicing to do....

-- CatherineJohnson - 11 Dec 2005

Umm, yes, it's the gifted kids who get things and get them fast.

At high school I was friends with the girl who was second to the dux. She once said to me she preferred physics to chemistry as for physics tests she could derive everything from first principles, while for chemistry she actually had to memorise stuff and study for the exam. And these exams we were sitting were reasonably long.

I'm not sure whether everyone should be able to work that fast though. Perhaps on pure plug-and-chug tests, but I think that there was a difference in how fast my friend could take in information and figure out how to set up a problem which was partly in her genes or nutrition or whatever it is that creates intelligence. So on tests that involve problems which aren't immediately obvious how to solve (e.g. word problems rather than "What is 16 x 12.78?") I'm not sure that every student should be able to sit down and rip through a very tough and long test.

-- TracyW - 12 Dec 2005

So on tests that involve problems which aren't immediately obvious how to solve (e.g. word problems rather than "What is 16 x 12.78?") I'm not sure that every student should be able to sit down and rip through a very tough and long test.

Offhand, my feeling is that those tests should be different.....

The whole testing issue is fascinating; I need to start reading Number 2 Pencil.

-- CatherineJohnson - 12 Dec 2005

Tracy, what does 'second to the dux' mean?

(but hey... I do know what 'rattle yer dags' means).

-- CarolynJohnston - 12 Dec 2005

"...long, demanding tests of procedures will give a good spread out of marks as those who can work fast and accurately are separated from those who can do one or the other, and those who can do neither. And those who can work the fastest and most accurately get separated out as well."

True but not the whole story. Has the teacher done her job well or not? Absent a teacher, I assume Gauss would still ace the tests, but...

Not so?

-- VerghisKoshi - 12 Dec 2005

The dux is top of the school academically. My friend's title was actually something like "proxima accessit to the dux" but I can't remember how to spell the first two words. (They're Latin.) The title was only handed out at the end of 7th form (final year of high school), but we could tell by the end of 3rd form (first year of high school) who both would be.

I think it is something like the American idea of graduating summa cum lauda?

Yep, I definitely did not learn Latin to mastery at school.

-- TracyW - 12 Dec 2005

Verghis - at school even in those classes where the teacher was particularly bad there was still generally the same spread of marks with the same students at the top and the bottom.

The gifted kids can just pick up stuff faster and from less information. Plus quite often gifted kids spend their non-school life seeking some intellectual excitement so they learn more of the world around them and so have a greater understanding of how whatever is being presented fits in.

-- TracyW - 12 Dec 2005

I think the American analogs are valedictorian and salutatorian for the highest ranking and second-highest ranking students (respectively).

-- DougSundseth - 12 Dec 2005

"Verghis - at school even in those classes where the teacher was particularly bad there was still generally the same spread of marks with the same students at the top and the bottom."

Quite, but wouldn't they all have learned more with a good teacher? More concretely, wouldn't even the gifted kids learn more with a good teacher than without?

I don't think point-spreads tell the whole story.

-- VerghisKoshi - 12 Dec 2005

Tracy,

I think you meant "proxime accessit", as in "'(he or she) came nearest'; n. competitor next to prize-winner."

-- VerghisKoshi - 12 Dec 2005

Thanks Verghis. Proxime accessit sounds right.

Yep, I agree the gifted kids would have learnt more with a good teacher.

However I was studying in a system which still had strong overtones that the point was to pick the smartest kids and never worry what they'd actually studied.

-- TracyW - 12 Dec 2005

Understood; I think we're in agreement.

But it's almost 1 a.m. here in California, cold-ish on a winter's night, and I'm off to bed. I think it's high summer in NZ, about 5 p.m., correct? Warm-ish?

G'night!

-- VerghisKoshi - 12 Dec 2005

Verghis - at school even in those classes where the teacher was particularly bad there was still generally the same spread of marks with the same students at the top and the bottom.

This is my experience.

When we first talked to Christopher's Phase 3 teacher about moving him to Phase 4 she said every class—every class—had 3 'groups.'

The 3 groups were:

• the kids who got everything immediately & needed no reteaching (Christopher was at the top of this group)

• the kids in the middle who needed more time & teaching

• the kids at the bottom who needed reteaching for pretty much everything

She also said that the Phase 4 classes had the exact 3 groups; this was what caused her to realize Christopher could be moved up. If he was at the top of Phase 3, he could be in the middle of Phase 4 (of course, now he's dropped to the bottom.....absent good teaching you're in trouble).

She hadn't thought about bell curves, but when we pointed out to her that she was talking about a normal distribution, she realized that's what everyone had in every class.

-- CatherineJohnson - 12 Dec 2005

The gifted kids can just pick up stuff faster and from less information.

Absolutely.

I've mentioned this before: my neighbor, who has a Masters in math & has taught & tutored math for probably 20 to 30 years, told me that the gifted students 'seem to breathe the books in.'

That's how it looks from the outside; they're breathing the books.

-- CatherineJohnson - 12 Dec 2005

Needless to say, Christopher is not going to be breathing in any math books, and nor am I.

-- CatherineJohnson - 12 Dec 2005

However I was studying in a system which still had strong overtones that the point was to pick the smartest kids and never worry what they'd actually studied.

At this point, I'd say that's the foundational philosophy of our middle school, whether they recognize this consciously or not.

It is a 'sorting machine.'

-- CatherineJohnson - 12 Dec 2005

What would the gifted kids learn with good teaching?

It's an interesting question.

In Russia—I have GOT to post that article—mathematicians meet with mathematically gifted youngsters at night, in their homes. It's an informal mentoring process that is well-established.

-- CatherineJohnson - 12 Dec 2005

I should start a pool on how soon into our meeting with the principal he brings up 'apples and oranges' or moving Christopher to the slow track.

-- CatherineJohnson - 12 Dec 2005

While you're lobbying for scratch paper (which I think it is ridiculous to withhold), you might consider having that scratch paper be GRAPH paper. My teaches Saxon pre-algebra and algebra and always has her students with poor handwriting use it. It helps them line up columns and keep better track of their work. Once they find the solution, they circle the answer, "box" all the work for that question, and label the left-hand corner with the question number so that it can be found easily later.

-- AndyJoy - 12 Dec 2005

My guess is that:

(1) The teacher assumes that the kids know how to use scratch paper, because she comes from an era when long division was taught, and everyone used scratch paper,

and either

(2a) The kids haven't asked about scratch paper, because they've never been introduced to the concept and don't know it can be done,

or

(2b) The kids haven't asked about scratch paper, because although they've been introduced to the concept (in another grade or at home), the teacher hasn't mentioned it, so they assume that it's not allowed.

My desk is FULL of scribbled-on pieces of scratch paper.

Graph paper is a great idea, but don't get the kind with the teensy squares. The kids will probably do best with larger squares, especially the ones with horrible handwriting.

Finally, a note about regionalisms. In some places, "scratch paper" is called "scrap paper"; in fact, I think I grew up calling it "scrap paper" (Southeastern US). This quiz is all over the Internet.

-- KtmGuest - 12 Dec 2005

Hi Andy!

you might consider having that scratch paper be GRAPH paper

no kidding

This is the difference between middle school & elementary school.

Last year I made up my own 'quadrille' paper for Christopher to use; the squares were a bit bigger than the squares on commercial paper.

I gave copies to the teachers—just left them in their mailboxes so they could see it—and they all contacted me and asked permission to Xerox it & use it for the rest of their students!

Now that is 'partnering' with a parent.

I'd left the paper just to show it to them......and they jumped on it.

-- CatherineJohnson - 12 Dec 2005

(1) The teacher assumes that the kids know how to use scratch paper, because she comes from an era when long division was taught, and everyone used scratch paper,

and either

(2a) The kids haven't asked about scratch paper, because they've never been introduced to the concept and don't know it can be done,

or

(2b) The kids haven't asked about scratch paper, because although they've been introduced to the concept (in another grade or at home), the teacher hasn't mentioned it, so they assume that it's not allowed.

I'm assuming the kids just haven't asked.

But otoh, I sent an email last week asking the teacher if he could use it, and she hasn't responded.

She's not quick with email, so she may not have seen it.

-- CatherineJohnson - 12 Dec 2005

Finally, a note about regionalisms. In some places, "scratch paper" is called "scrap paper"; in fact, I think I grew up calling it "scrap paper"

oh, that's funny!

what do you call pop?

I'm guessing you might have used the word 'soda' once in awhile?

And what do you call a 'semi'???

-- CatherineJohnson - 12 Dec 2005

I love that poll!

Thanks!

-- CatherineJohnson - 12 Dec 2005

American schools are not already using graph paper for maths?

At school in NZ even at the start of primary school we had books with graphed pages. And of course in high school it made drawing graphs much easier.

Anyway, Verghi, when I was posting last night it was about 9 pm local time and muggy and raining. When I was on the East Coast of the USA I had it worked out that NZ was 1 day later but 6 hours earlier (so if it was 8 pm on Monday in Boston it was 2 pm on Tuesday in NZ). That was in a Boston wintertime and NZ daylight savings.

As for warmth, I'm in Wellington where the climate has its own plans and generally spring is about the worst season. It's gotten warmer but it's drizzly and there was a cold wind last night. On the other hand, Wellington has the best approaches of any city I have ever seen.

-- TracyW - 12 Dec 2005

At school in NZ even at the start of primary school we had books with graphed pages. And of course in high school it made drawing graphs much easier.

That's one of those Weird American No Common Sense-y things.

(Weird American No Common Sense-y things—hey! I just coined a phrase!)

The first time I went to Europe and saw stacks and stacks of composition books with graph paper, I was stunned.

-- CatherineJohnson - 12 Dec 2005

what do you call pop?

I have to assume you're talking about "coke", as in the following exchange:

Texan 1: Wood yew lock sumpin ta drank?

Texan 2: Shore, gimme a coke.

Texan 1: Whut flaver?

Texan 2: Hows about a Big Red?

Texan 1: Here ya go!

Either that, or you're asking about my dad. ;-)

But... although I am in Texas now, where your "pop" is my "coke", I grew up in Virginia, where your "pop" was still not called "pop". Maybe I can't think what they were called when I was growing up because we didn't have many in the house, they weren't in the schools, and we didn't go out to eat much. I think we just called them by their brand names, e.g. "Fresca" (which was in the house) or "Sprite".

On one overseas trip, I was surprised to see the term "lemonade" used for "pop"/"soda"/"coke".

-- KtmGuest - 12 Dec 2005

We called it "coke" over in the Southeast, too, yessirree. The first time I heard "pop" was from a Yankee.

That's one of those Weird American No Common Sense-y things.

That goes for writing paper, also. They seem to have this new-fangled idea that really young children just learning to write should do it on big blank sheets of paper with no lines whatsoever. Sort of an invented upper and lower case handwriting experiment, I guess.

I used to ask for big lined paper for my LD son because I thought it was really obvious that somebody needed to give him something to anchor his letters to. They always agreed, but then some pre-packaged test or quiz would be used and all the answers were to be just written on white space. Not even a little line for them to write their answers. Of course, his were completely illegible and all different sizes due to his disability.

By the time my other son came along I noticed the same thing. They don't spend even a fraction of the time on handwriting that they did with us, so I just assumed they'd give him a fighting chance by providing lines for them to figure it all out with. No such luck.

I have mentioned this to every teacher I speak to and they just give me a blank stare or a nod, and nothing changes. God-awful illegible handwriting does not concern them in the early grades. It must be because it's "natural" and they will have time to correct all of this later. This is the only motivation behind this that I can think of.

Of course, in another year they need to be capable of writing a 4-6 paragraph narrative essay for the state tests.

-- SusanS - 12 Dec 2005

coke???!!!

you call it coke???!!!

-- CatherineJohnson - 12 Dec 2005

Well, sure, if it's COKE you call it COKE

If it's pop, you call it pop

anyone knows that

-- CatherineJohnson - 12 Dec 2005

They seem to have this new-fangled idea that really young children just learning to write should do it on big blank sheets of paper with no lines whatsoever. Sort of an invented upper and lower case handwriting experiment, I guess.

just shoot me now

-- CatherineJohnson - 12 Dec 2005

They always agreed, but then some pre-packaged test or quiz would be used and all the answers were to be just written on white space.

yup

I'll get Christopher's test pages posted at some point

-- CatherineJohnson - 12 Dec 2005

Not in the south. Like KTMGuest said, then we call it by its brand name.

We put salted peanuts in coke, too. (bottles) That wasn't on the test. Although PEE-can was.

-- SusanS - 12 Dec 2005

I have mentioned this to every teacher I speak to and they just give me a blank stare or a nod, and nothing changes. God-awful illegible handwriting does not concern them in the early grades. It must be because it's "natural" and they will have time to correct all of this later. This is the only motivation behind this that I can think of.

Of course, in another year they need to be capable of writing a 4-6 paragraph narrative essay for the state tests.

shoot me twice

-- CatherineJohnson - 12 Dec 2005

Pop is yore daddy.

-- SusanS - 12 Dec 2005

We put salted peanuts in coke, too.

that's just wrong

-- CatherineJohnson - 12 Dec 2005

I guess that means you won't be stopping by any boiled peanut stands either.

-- SusanS - 12 Dec 2005

She probably won't be eating any battered, deep-fried Oreos at the state fair, either.

-- KtmGuest - 12 Dec 2005

check

and

check

-- CatherineJohnson - 13 Dec 2005

I am from Illinois

where we eat sensible foods

by which I mean foods that have been boiled

-- CatherineJohnson - 13 Dec 2005

I suppose if you had to you could boil your deep-fried Snickers bar (preferred to deep-fried Oreos by [random number] out of 10 people in a blind test). I mean, who'd stop you?

Oh, and the correct term is "soda pop".

-- DougSundseth - 13 Dec 2005

in the great state of Illinois, we do not boil Snickers bars

we boil broccoli, cauliflower, and green beans

-- CatherineJohnson - 13 Dec 2005

occasionally, we boil carrots

-- CatherineJohnson - 13 Dec 2005

also, I for one do not eat Snickers bars

I eat 3 Musketeers

-- CatherineJohnson - 13 Dec 2005

also Milky Way

-- CatherineJohnson - 13 Dec 2005

There is nothing fundamental stopping you from deep-frying either a Milky Way or a Three Musketeers. Also, I was not advocating boiling deep-fryed Snickers bars, merely supporting you in your apparent desire to cook anything you wish like bad English food.

I'm all about freedom of choice.

I mean it's not like you were suggesting a banana and mayonnaise sandwich or a peanut butter and pickle sandwich or something.

Those are just wrong.

-- DougSundseth - 13 Dec 2005

There is nothing fundamental stopping you from deep-frying either a Milky Way or a Three Musketeers.

yes

there is

a person cannot deep-fry a Milky Way or a Three Musketeers bar, under pain of death

remember that

-- CatherineJohnson - 13 Dec 2005

your apparent desire to cook anything you wish like bad English food

I don't desire to cook anything I wish like bad English food

I have a duty to cook anything I wish like bad English food

it's my job

-- CatherineJohnson - 13 Dec 2005

Well, alright then. Can't argue with that.

Though now you've got me wanting a deep-fried Milky Way.

-- DougSundseth - 13 Dec 2005

you only think you want a deep-fried Milky Way

-- CatherineJohnson - 13 Dec 2005

you don't really want a deep-fried Milky Way

-- CatherineJohnson - 13 Dec 2005

you want a regular Milky Way, or, better, a regular Three Musketeers

-- CatherineJohnson - 13 Dec 2005

I had a Butterfinger instead. Not deep-fried, more's the pity, but I made up for that by eating a frosted cinnamon roll.

Understanding the concept of field-expedients is important.

-- DougSundseth - 13 Dec 2005

what?

-- CatherineJohnson - 13 Dec 2005

No deep-fried candy bars available, so I ate a candy bar and a donut. My mom always assured me that they'd just mix up in my stomach anyway.

Field-expedient deep-fried candy bar.

8-)

-- DougSundseth - 13 Dec 2005

Field expedient: Military jargon: something that will do the job in the absence of the actual tool normally required.

E.g., Rock: field-expedient hammer.

-- DougSundseth - 13 Dec 2005

Or:

After-schooling: field-expedient competent teacher.

-- DougSundseth - 13 Dec 2005

oh my god

this is a New Thing Under The Sun

A whole new term people who eat junk they shouldn't because they didn't have the other junk they really wanted to eat on hand can use to describe their behavior.

Actually, it's better than that: there isn't any term for this behavior!

There are people all over America, right this minute, breaking their diets eating junk they don't actually want to eat, BECAUSE they already psychologically broke their diet, AND THEN DIDN'T HAVE THE JUNK THEY PSYCHOLOGICALLY BROKE THEIR DIET FOR IN THE HOUSE.

So then they have to find some other junk to break their diet with.

I've done this.

Field-expedient......CHEERIOS & SKIM MILK AT BEDTIME!

BECAUSE THE BROWNIES I THOUGHT WE STILL HAD IN THE REFRIGERATOR ARE GONE!

-- CatherineJohnson - 13 Dec 2005

I love it!

-- CatherineJohnson - 13 Dec 2005

I'm reasonably slim, btw.

Just so you know.

-- CatherineJohnson - 13 Dec 2005

I did some field-expedient eating YESTERDAY.

I was feeling seriously stressed over Christopher, and I decided to do some emotional eating.

Of course, then there was no decent emotional food in the house.

I wanted.....hmm. What was it. oh! I wanted some Pillsbury chocolate chip cookie dough, which Martine had bought a couple of days before.

It was all gone!

There was nothing else I wanted to eat, but as I had consciously decided to do emotional eating, and I wanted to do emotional eating, I had to find something.

So I went downstairs and got a bag of snack-sized Lay's potato chips that Ed for god-only-knows-what-reason continues to buy at Costco.

-- CatherineJohnson - 13 Dec 2005

"I'm reasonably slim, btw."

Perhaps I should have mentioned the Diet Mt. Dew? Heck, it was even a 24-ounce bottle, so that balances off the Butterfinger and donut.

Just think what I could have eaten if it had been a 2-liter bottle!

8-)

-- DougSundseth - 14 Dec 2005

oh please don't mention liters & ounces

otoh, I can now sling the Unit Multipliers like nobody's business

thanks to Saxon Math

which reminds me, MY BOOK ORDER IS STILL WAITING

-- CatherineJohnson - 14 Dec 2005

Three Musketeers has that whipped stuff in the middle. I just can't countenance that whipped stuff.

Milky Way though is pretty good.

Though still inferior to Nestle's Crunch.

-- CarolynJohnston - 14 Dec 2005

Nestle's Crunch is acceptable, I agree

but nothing beats the whipped stuff

-- CatherineJohnson - 14 Dec 2005