SingaporePlacementTest < Kitchen

06 Jul 2006 - 16:39

Singapore again

So this morning I took half of what is supposed to be a 30-minute placement test given to a student who has finished New Elementary Mathematics Textbook D.

I think it took me 2 hours.

To do half.

I was thinking that was OK, because New Elementary Mathematics Textbook D is a 9th grade text.

It's not.

It's a 7th grade text.

In Singapore, I'm still in 7th grade.

I'm halfway through Saxon Algebra 1, I scored 80% correct on the ALEKS algebra 1 assessment, and I thought the placement test (pdf file) for Thomas Jefferson High School of Science and Technology, reportedly the best math and science high school in the country, was a breeze.

That translates to 7th grade in Singapore.

juku city

Thomas Jefferson, you may recall, is the public school that's so competitive and respected that colleges all over the country are recruiting its graduates and giving them 4-year scholarships. Parents move to Fairfax County so they're in the district, then send their kids to Kaplan & KUMON to prepare them for the test. People call the area "Juku City."

I passed that test.

Easily.

Not the logic part. I passed the mathematics part. Questions 1-120, p 36-56. I may not have missed a single answer, and all the items were easy.

Then it takes me two hours to do 11 questions on an 8th grade placement test in Singapore. And those were just the algebra problems; I didn't even bother with the 9 items on geometry. (I didn't understand some of the terms, which may be different in the U.S., and I haven't practiced geometry enough to remember various other terms I knew a couple of months ago.)

arrgh

I need a personal organizer

So I'm looking at these 11 items, asking myself why exactly they should consume 2 hours of my life.

They're not hard.

I conclude that I'm having a major problem organizing my work.

I write things down, then lose track of what they refer to, then go back to the beginning and try to figure out what part of the problem I was doing, then I run out of paper so I'm flipping back and forth trying to find the figures I wrote on the preceding page.....it's pathetic. If I had to take Ms. K's math class, the school would have to institute corporal punishment to deal with my level of math-paper chaos. Twenty points off wouldn't even begin to cover it.

The other problem is that I don't have enough insight into these problems yet to take shortcuts & trust that my shortcuts will work, so I'm writing out every step and then some, which makes everything worse.

I don't know what happened to me on item 9:

A man bought 450 books for $1,350. He sold half of them at a profit of 20%, 150 of them at a profit of 10%, and the rest at a loss of 4%. What was his gain percent, to the nearest percent?

I just could not do this problem.

I came up with one wrong answer after another, and the answer I finally settled on was wrong.

It's not a hard problem.

When I checked the answer key, and found out my answer was wrong, it took me about 5 minutes to do it right.

Looking at the problem now, I think my difficulties may have had almost nothing to do with actual math.

I think the obstacle was working memory, organization, and eyesight. Can't remember if I've mentioned this: I can't wear my glasses to do close work any more. My glasses are bifocals, so in theory I'm wearing reading glasses, but....I can't wear them. They strain my eyes. (My optometrist, Mel Kaplan, says it's not the glasses, it's me. He also says that progressive lenses are horribly stressful.)

I don't need glasses to read, but, otoh, I do need strong light to see by, and dark ink on the page. High contrast. Otherwise everything starts to look kind of gray. So naturally I opted to take the test in dim light using a pencil with soft, thick lead. That's because I have no common sense-y.

I've decided not to panic

I don't think this is quite as bad as I thought.

Saxon Algebra 1, which is algebra integrated with geometry, is supposed to be a 9th grade book, but I'm going to have Christopher using the book at the beginning of 8th. Singapore puts me midway through 7th grade; Saxon puts me midway through 8th.

I'm further behind when you take geometry into account, but not by much.

I do have a question about problem solving and word problems in Saxon. In 70 lessons, I've done almost no word problems. Algebra 1/2 focuses on word problems, and I skipped that book. If the next 50 lessons don't contain a lot of word problems, I'll do the problems in my other books: Dolciani (Dolciani Teacher Edition), Jacobs (Jacobs Teacher's Edition), Johnson.

maybe I'll panic just a little

So....what does this tell us about our best versus their best?

The kids who compete to get into Thomas Jefferson are our top math students.

Our top kids have to go to cram school & Kaplan to pass the entrance exam for Thomas Jefferson in 8th grade.

I'm thinking that in Singapore an average graduate of 6th grade wouldn't have any trouble with it.

That gives me an idea.

Why don't I take the 6th grade test?

Why don't I take the 6th grade test with the reading lamp TURNED ON this time?

Bonne idee.

[pause]

Well, I can't say the 6th grade test was a lot easier, though I did pass (89% correct), and I did all the geometry problems but one.

There's no way the kids in Ms. K's class could pass this test. The 2 to 4 mathematically gifted kids in her two classes might pass, though I wouldn't bet on it. Nobody else.

If I were placing myself in a Singapore Math text, I think I'd start at the beginning of New Elementary Mathematics Textbook 1. Grade 7. [update: maybe not. Following KUMON's & Engelmann's injunction to start before your level, I should place myself in 6A. sigh. Sometimes it seems like I'll never make it to calculus.]

Which I just so happen to have sitting here on my bookshelf. My neighbor bought it a year ago, then never used it. I'm going to take a look.

I'm thinking I should probably also skim through Primary Mathematics 6A & 6B and see if there are Units I ought to do.

Table of Contents

Singapore Math placement tests
ALEKS assessment

-- CatherineJohnson - 06 Jul 2006

Back to main page.

Comments

After entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.
Please consider registering as a regular user.
Look here for syntax help.

currentdolciani currentjacobs

-- CatherineJohnson - 06 Jul 2006

Doesn't that make you nuts? I find it grossly unfair that the mathhead people not only have the math genes, but they tend to remember the shortcuts. I think it should be the other way around.

While working with math kid on math (something I avoid like the plague) I had him do a perimeter problem with a half circle just to make sure he remembered stuff. The radius of the half circle was 6. So I see his little scribble of 6 x 3.14 and I think, "Aha, I got him." I make my grand pronouncement that the diameter was 12 and that he made a mistake, of course thinking that you take the diameter, multiply by 3.14, and then divide by two. Well, he just looks at his poor ole' math phobe mom and says that he divided it already. Of course, it took me a second to realize what he was saying.

I would have probably done those problems my whole life without noticing that I could have just taken the radius and multiplied it.

However, math kid forgot how to divide fractions. He inverted both fractions and multiplied. He also had no memory of why you would do that. Math phobe mom actually had something to teach the little bugger, albeit reminding herself that he was, after all, finished with dividing fractions by the third grade and starting pre-algebra in the fourth.

Still, it's good to be queen for a second.

-- SusanS - 06 Jul 2006

I find it grossly unfair that the mathhead people not only have the math genes, but they tend to remember the shortcuts. I think it should be the other way around.

I love it!

-- CatherineJohnson - 06 Jul 2006

I have done SO MUCH DRILL, not to mention SO MUCH FACTORING, that I divide the diameter by 2 first.

I'm going to have to do lots of percent/fraction/ratio word problems.

Those are the problems where I can't tell whether a 10% profit on the full amount you paid for 60 TVs is the same thing as a 20% profit on 30 of those TVs.

I had to spend some time showing myself that it was.

Now I'm embarrassed.

-- CatherineJohnson - 06 Jul 2006

I have done SO MUCH DRILL, not to mention SO MUCH FACTORING, that I divide the diameter by 2 first.

Okay, well then I am truly pathetic.

Those are the problems where I can't tell whether a 10% profit on the full amount you paid for 60 TVs is the same thing as a 20% profit on 30 of those TVs.

See, that's what mathheads sit around and think about for fun. And then they keep it to themselves cause they like to see the regular folk suffer. (I'll talk about them since none of them have wandered over here yet.)

-- SusanS - 06 Jul 2006

well then I am truly pathetic

yeah, well, you didn't see your way clear to doing 200 KUMON worksheets in Levels D, E, F, & G

that's the problem

nor did you do 2000 factoring problems in Russian Math

-- CatherineJohnson - 06 Jul 2006

I'll talk about them since none of them have wandered over here yet.

you want to see a sterling example of utterly opaque mathheadery?

-- CatherineJohnson - 06 Jul 2006

I'll talk about them since none of them have wandered over here yet.

you want to see a sterling example of utterly opaque mathheadery?

read the first paragraph

-- CatherineJohnson - 06 Jul 2006

you want to see a sterling example of utterly opaque mathheadery?

Oh my. I think that's what it sounded like in my last high school math class. Or so it seemed.

-- SusanS - 07 Jul 2006

See, that's what mathheads sit around and think about for fun. And then they keep it to themselves cause they like to see the regular folk suffer. (I'll talk about them since none of them have wandered over here yet.)

Ahem. :-)

We keep it to ourselves because we have learned empirically that non-mathheads find mathheads' ideas of fun to be some combination of boring, peculiar, and frightening.

Whereas mathheads have to figure this out empirically (and some never do), non-mathheads know this instinctively.

There is speculation that a lot of geeky engineer types (mathheads) are Aspies. Go figure.

-- GoogleMaster - 07 Jul 2006

Okay, I just followed the link. What's funny about it? /scratches head

-- GoogleMaster - 07 Jul 2006

Embarrassed that I actually read that last night. I want to share this bit that just tickled me:

No, no, no, no, no. The thing that's wrong with education today is that so many people (not just kids) just wants the shortcutting, life-applicable, "give me the bullet" answer without taking the time to really think about anything. Do you truly believe that in the thousands of years of brilliant, creative thinking about math, that no one noticed that .999... seems at first to be less than 1? The sun seems to be revolving around the earth, but we don't question the astronomers. Matter seems to be infinitely divisible, but we don't question atomic physicists. Consuming sugar seems to be the right thing to do when I feel that my blood-sugar level is low, but I didn't question my doctor when he (correctly) explained that this would (counterintuitively) just perpetuate the low-blood-sugar cycle. We trust professional chefs to make our restaurant food taste good, airline mechanics to fix our planes, architects to design our skyscrapers. All of these people have spent years and years studying their fields and they hold lifetimes of research and intuition in their heads. But mathematicians are just too dorky and clueless to understand a basic (although slightly counterintuitive) fact about representing numbers in our base 10 notation system? Give me a break.

I'm not claiming to be right on everything, just this fact about math. And I'm not claiming to be the greatest teacher in the world. But I'm not what's wrong with our education system. Your non-appreciation for rigorous math, and the centuries of thought that went into it is what's wrong with our education system. Sticking your fingers in your ears and going La-La-La-La-I-Won't-Listen-To-Math-Geeks-La-La is what's wrong with our education system. Show some humility. Polymathematics

I hope to count myself in the group of non-math-geeks with tons of humility and appreciation for those others of you.

-- LynnGuelzow - 07 Jul 2006

"Sticking your fingers in your ears and going La-La-La-La-I-Won't-Listen-To-Math-Geeks-La-La is what's wrong with our education system. Show some humility."

That's hilarious! While I am certainly no math geek, I do appreciate them. Perhaps we could start a list:

You may be a math geek if . . . you would rather calculate pi than eat it.

We could also start a list for the math education obsessed folks like those of us here at KTM. For example:

You may be math obsessed if . . . you have ever started a conversation about math education with your hair stylist.

-- KarenA - 07 Jul 2006

Here's another one for the list:

You may be math obsessed if because of your constant harangues about the failure to teach math fundamentals . . . your family now considers "math" a four-letter word and instructs you to hereafter refer to it as the "m" word.

-- KarenA - 07 Jul 2006

... if you seek out obsolete and antique math texts in the "used and rare" bookstores

... if you do math problems in your head to conquer insomnia

... if that wakes you up rather than putting you to sleep

-- GoogleMaster - 07 Jul 2006

...if you are incapable of taking the word 'perpetual' figuratively

-- TracyW - 07 Jul 2006

A mathhead girlfriend of mine actually told me how she used to fall asleep staring at her clock and making up number games as a child. For hours. She was positively giddy when she told me the details.

-- SusanS - 07 Jul 2006

... if, while watching people playing poker, you continually calculate "expectation value".

... if you look at the price of E85 gas and use the energy density of ethanol to calculate E85's relative cost efficiency. (It's a bad deal, at least around here.)

-- DougSundseth - 07 Jul 2006

I'm not sure where this link belongs, but seemed appropriate in this thread. Johns Hopkins held a summit in the spring of 2006 on Thinking Big: Accelerating the K-12 Math and Science Curriculum. The papers from the summit are quite short, but encouraging. Here's one snip:

"In an increasingly quantitative, technological, and science-driven world, it is advantageous for both individuals and American society to have our students learn as much mathematics and science as possible in K-12.

In this light, a good Pre-K to 12 mathematics and science curriculum would: A) Teach students at or near their capacity to learn with the assistance of a (skilled)teacher

B) Be coherent, non-repetitive, and cover essential topics

By this standard, the current K-12 Mathematics and Science curriculum in the United States is an underachiever."

And then there is this:

"Thus, from the first day of school in the U.S., we have a de facto national curriculum that significantly underestimates the mathematical and scientific capabilities of the populace. The elementary- and middle-grade mathematics curricula students experience in school tend to be repetitive; continually touching on many topics without requiring mastery of a sequenced set of the foundational skills needed for success in high school mathematics or without deeply developing students’ problem-solving abilities (Lemke 2004, Ginsburg et al 2006)."

I hadn't seen this summit posted on KTM, but there's a lot of good stuff in these papers.

-- LynnGuelzow - 08 Jul 2006

I know!

I love that passage!

OK, the list is started....

-- CatherineJohnson - 08 Jul 2006

what I really want to know is does .999 really equal 1???????

-- CatherineJohnson - 08 Jul 2006

Lynn thanks!

I taught writing for Johns Hopkins CTY, and they were HUGE on acceleration. At the time I didn't realize there was another school of thought (enrichment).

It was acceleration all the way.

I taught my freshman rhetoric course to middle schoolers.

-- CatherineJohnson - 08 Jul 2006

I have to say, though....I'm kind of intrigued by the fact that Singapore doesn't teach calculus to high schoolers.

Their curriculum ends up being quite repetitious (in a good way), I think, based in what I saw in the TOCs of New Elementary Mathematics.

The impression I got, just from those TOCs, is that their goal is to teach algebra to everyone, and to teach it incredibly well - to produce high school graduates for whom algebra is second nature.

I like that.

(They do teach trig....but that almost seems to flow from the huge attention they pay to geometry from the get-go.)

I have the sense they don't teach proofs, but don't trust me on that.

-- CatherineJohnson - 08 Jul 2006

The answer is yes -- .9999. . . . is equal to 1.

The proof is at Polymathematics

I really like this totally cool proof:

"Let's look at some reasons why it's true. Then we'll look at some reasons why it's not false, which is something different entirely. The standard algebra proof (which, if you modify it a little, works to convert any repeating decimal into a fraction) runs something like this. Let x = .9999999..., and then multiply both sides by 10, so you get 10x = 9.9999999... because multiplying by 10 just moves the decimal point to the right. Then stack those two equations and subtract them (this is a legal move because you're subtracting the same quantity from the left side, where it's called x, as from the right, where it's called .9999999..., but they're the same because they're equal. We said so, remember?):

10x = 9.99999999.....
- x = .999999999......
_________________________
 9x = 9

Surely if 9x = 9, then x = 1. But since x also equals .9999999... we get that .9999999... = 1. The algebra is impeccable."

-- LynnGuelzow - 08 Jul 2006

wow

I'm going to have to mull

I know this technique....I retaught it to myself just last week.

But it never occurred to me that it's a proof that .999... = 1!

-- CatherineJohnson - 10 Jul 2006

WebLogForm
Title:	Singapore again
TopicType:	WebLog
SubjectArea:	CompareAndContrastPosts, SaxonMath, SingaporeMath
LogDate:	200607061238

Navigate KTM

Kitchen Table Math

KTM User Pages

Service Groups

Parent Groups

Personal Pages

Blogs

Special lists

Help

Singapore again

Comments