IrvingtonAndKipp < Kitchen

18 Nov 2005 - 18:37

algebra in the 8th grade: Irvington and KIPP

more of Doug Sundseth's beautiful work (fall 2005):

The KIPP Academy, in the Bronx, is a charter school serving low-income black and Hispanic students, more than 75% of whom are eligible for federal free and reduced lunch program.

Under 2004 HHS Poverty Guidelines, a family of four earning $18,850 or less qualifies for the free and reduced lunch program.

School Matters reports 2004 Irvington median household income at $96,832.

where we stand today

I've pulled this material from an earlier post:

_ _ _ _ _ _ _ _

I've mentioned before that last year (2004-05) our middle school's stated goal was to cut the number of students placed in Phase 4 math, the only course in which students take and master algebra in the 8th grade, (see below) and the only course whose students are on track to take calculus in high school. (AP calculus AB here)

They didn't say how many students they planned to cut, and soon rumors were flying that 25% of the kids would be moved to Phase 3. Ed sent an email to the middle school math chair asking her about the figure; her reply was noncommittal, as I recall.

They were clearly planning to cut more than a handful, because one of the Phase 4 5th grade teachers was telling parents that 30% of the students in his Phase 4 math class 'didn't belong.' That was the word everywhere in the school. Phase 4 math was filled with children who didn't belong. These children weren't gifted or talented in math; they just had pushy parents seeking the high status attached to having a child in Phase 4.

The school planned to correct the situation.

This had us rattled, since Christopher was already in Phase 3 and we were hoping to get him out. If they were planning to cut as many as 25% of the students, what chance did Christopher have?

Right around that time I was present at a meeting in which parents directly asked the principal about his plans to cut students from Phase 4. His response—almost verbatim—was, 'I don't know where these rumors come from.'

How many children did they cut?

35%

Here are my figures on the cuts to Phase 4, based on conversations with school personnel:

school year: 2004-2005
grade 5 class size: 155 students
phase 4 placement: 60 students
number of students moved from phase 4 to phase 3 at end of school year: 21
percent of children cut: 35%

Bear in mind that these 21 are the kids whose parents agreed to the change. I know of at least two kids whose parents said no. I'm guessing there were more, though I could be wrong.

So here you have a highly affluent suburban school district, a district that spends roughly $18,000 a year per pupil, devoting time, energy, and a portion of that $18,000 to decreasing the number of students who master algebra in 8th grade.

what happened?

But here's the interesting development, and this is something parents have no idea also took place.

It's not just that 21 kids moved down.

Another seven kids moved up.

That's 7 kids not including Christopher, who moved to phase 4 in February. Add him to the total, and you've got 8 Phase 3 kids swapping places with 21 Phase 4 kids. If you had to choose just one fact to illustrate the folly of assessing math talent in the third grade, that would be it.

To my knowledge, Irvington has never had 8 kids move from phase 3 to phase 4 in one school year. Never.

I happen to know this because, when I first raised the subject of Christopher changing tracks, I had teachers & guidance counselors saying things like, 'I can only think of one student who's moved up this year.'

Or: 'A student can always move up! It's never too late. We had one phase 3 student who just blossomed this year, all of a sudden.'

Two different people made these statements. One thought he was telling me 'No chance'; the other thought she was telling me, 'There's always a chance!'

But they were saying the same thing.

Question: How many phase 3 math students move to phase 4 in a typical year?

Answer: One.

down to 30%

So here's how things shape up this year, roughly speaking (there are some new kids in the district; I don't know their placements):

155 6th graders, approximately
47 students in Phase 4
30% of '05-06 IMS 6th graders on track to master algebra in 8th grade

Meanwhile the KIPP Academy in the Bronx is reporting as many as 80% of its student body mastering algebra in the 8th grade, and passing the Regents A exam. Per pupil spending: $9,900.

Irvington math sequence prior to 2005-2006 this year

Until this year, when revisions in the NY state standards went into effect, the standard Phase 3 math track was the following:

freshman year and 1st semester sophomore year: Math A1, an integrated course combining algebra, geometry, and some trigonometry

second semester sophomore year: students take the Math A Regents Exam in January of sophomore year, then begin Math B, another year and a half long integrated course including algebra, geometry, and trigonometry

junior year, all year: Math B; take Regents B in the spring

senior year, all year: pre-calculus

There is no room for calculus on this track.

fall 2005 accelerated Phase 4 track (incorporating new NY state standards:

8th grade, middle of the school year: finish algebra 1, begin geometry

freshman year, middle of the school year: complete geometry, begin algebra 2

sophomore year, middle of the school year: complete algebra 2 & begin precalculus

junior year, middle of the year: complete precalculus

At this point students have 3 semesters left in which to take advanced math courses.

senior year: AP calculus, either AB or BC

what does the future hold?

Good question.

The tracks have been collapsed for all students younger than Christopher. Mathematically talented kids are being enriched, but they are not being accelerated. update 9-12-2006: The Phase 4 track may not have disappeared; I'm not sure. However, mathematically gifted children are not allowed to accelerate their learning and one family has left the district as a result. Parents have no input. When they complain, they are told their child is being “challenged.”

I spoke yesterday to the mother of a mathematically gifted grade school child. She says no one in the administration has an answer as to whether these children will or will not be able to take AP calculus in high school.

No one knows.

At least, if anyone does know, she hasn't been able to find out.

It looks like we've adopted a slow-moving experimental mathematics curriculum—and ended acceleration—without creating a plan to ensure that students who excel in math are prepared to take calculus in high school.

I can't get a straight answer, either

Meanwhile, the new state standards, mandating algebra for all in 8th grade, have altered the landscape. The state is also returning to the old 3-course sequence of Lower level Algebra, Geometry, Upper level Algebra, taken across 3 years' time.

I was excited to learn that the state was now mandating algebra in the 8th grade, because I thought it meant I wouldn't have to move heaven and earth to get Christopher into Phase 4. Children in high-achieving countries take algebra in 8th grade, so I thought Christopher would be on par with his peers around the world

I was wrong.

Last year, when I asked Lisa Urban, a legendary middle school math teacher who was then department chair, about this she said that, yes, Phase 3 students would, as of this year, study algebra in 8th grade.

But they wouldn't finish studying algebra in the 8th grade.

Freshman year in high school, Phase 3 students would take lower level algebra. They would take geometry sophomore year, and upper level algebra junior year.

The tracks would not change.

That confirmed my conviction that I had to get Christopher into Phase 4.

The only students in Irvington who are even close to being on par with their peers in high-achieving countries are the kids in Phase 4 math.

And now Phase 4 is gone.

if I had it to do over again—

Would I still move to Irvington?

The short answer is yes.

Irvington's math problems are the same as everyone else's math problems, except Irvington kids are doing better. update 9-12-2006: After one year of middle school, a year that included the Assistant Superintendent banning the afterschool math course I taught as a service to the PTSA, I no longer feel this way.

source:School Matters
blue bar: Irvington 4th graders

Moreover, the 'pushy parent' narrative tells you something important: it tells you that Irvington school officials have often been responsive to parents even when they didn't want to be.

The other day I read a letter from a college student who grew up in Rye, a young man who may have been a bit like Christopher when he was younger. He didn't 'place into' accelerated math in the Rye school system, and the school district flatly refused to make an acception. So his parents spent $26,000 a year to send him to The Masters School in Dobbs Ferry, where, I'm told, any student who wants to take a crack at the accelerated math track can do so—and the school will provide the support he needs to succeed.

I spent much of last year expecting to face the same resistance here. Christopher and I were working overtime to bring him up to speed, and I expected our Phase 4 bid to be a battle.

It wasn't. When I spoke to Lisa Urban, she said, and this is close to a direct quotation, 'If a kid wants to do it, and thinks he can do it, and is willing to work hard to do it, I want him or her to have that chance.'

Christopher worked hard to master the material in Phase 3. His school recognized his work, made the move, and supported him through the transition.

The problem with math in Irvington is the problem with math in America. Irvington's doing better than most, and as well as any school in my area.

But we're a long way from Singapore.

"If a talent pool were created with the top 10 percent of math students who participated in the fourth grade TIMSS, the U.S. would contribute 9 percent of her students. This is very close to what would be expected if scores were distributed equally among all nations.

Singapore contributes 39% of her students to this pool.

[snip]

If we look at the upper 5 percent, students in the U.S. 95th percentile scored 682, the Singaporean 95th percentile score was 788, Korea’s 727 and Japan’s was 726."

"Some will argue that the average showing of the U.S. in a test such as this is a natural fallout of being democratic—an indication that we educate more of our population than other countries. They argue that if you look at the top students, ours do just as well.

If all the 8th grade students who participated in TIMSS are ranked and a pool is created that represents the top ten percent of students, only 5% of U.S. students are in the math group instead of an expected 10%; but 13% are in the science pool.

In contrast, nearly one in three (32%) Japanese students make the cut in math and 18% are in this top group in science. 45% of Singapore’s students are in the top 10% math group and 32% in the international top 10% science pool."

Hungary has 11% of its students in the math pool and 14% in science.

source:
The American Federation of Teachers looks at TIMSS, PowerPoint presentation

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Wow. Great post. You have gotten to the crux of the matter. By not tracking they are in reality tracking these children right on to the infamous pokey track. There you go. There it is. I would think anyone with a three-digit IQ would be horrified by this.

Do the parents coming up behind you have any idea? I wonder if a meeting with handouts like these would affect any of them.

-- SusanS - 18 Nov 2005

well, we'll see

at this point, I think the answer is 'no,' parents don't know.

We certainly had no idea, when Christopher was placed in Phase 3 in 3rd grade, what it meant for his high school education.

Most parents aren't thinking that far ahead; at least, we sure weren't.

-- CatherineJohnson - 18 Nov 2005

The problem for all of us is the fact that the entire U.S. 'math curve' is way 'off-center.'

It's easy for everyone to believe that 'pushy parents' elbowed their children into the gifted class where they didn't belong, because none of us realizes that the 'gifted track' is in fact the average track everywhere else.

I'm hoping that if people absorb the fact that all of our tracks are behind, the narrative may shift.

Yesterday, when I talked to the mother of the gifted child, she brought up the issue of pushy parents getting their kids into the accelerated class and then 'diluting' it.

I told her to turn that question around, and ask why pushy parents would do that—why would they think they could do it?

The answer is: the accelerated track isn't accelerated. It's work at a level these parents somehow figured out their kids were capable of doing.

I figured it out thanks to Wayne Wickelgren; no idea how other parents figured it out.

But they did, and then they insisted their kids be 'accelerated.'

-- CatherineJohnson - 18 Nov 2005

'There's always a chance!'

Yes; Slim and Fat.

"If you had to choose just one fact to illustrate the folly of assessing math talent in the third grade, that would be it."

I don't know if you've answered this before, but is this a formal assessment, or is it just based on a teacher's recommendation?

"I spoke yesterday to the mother of a mathematically gifted grade school child. She says no one in the administration has an answer to whether these children will or will not be able to take AP calculus in high school. No one knows."

This is incompetence.

"... But they wouldn't finish studying algebra in the 8th grade."

Our public school teaches algebra (concepts) in 8th grade too. The school does basic skills practice too. This is called "balance". Like balanced literacy. Of course, they are doing the balancing.

"Freshman year in high school, Phase 3 students would take lower level algebra. They would take geometry sophomore year, and upper level algebra junior year."

I emailed the chair of the math department at our public high school and asked her for details about their top math track. It consists of Geometry in 9th grade (requiring a rigorous course of algebra in 8th grade), Algebra II in 10th grade, Pre-Calc in 11th grade, and AP Calc in 12th grade. This is fine. I asked her about the math curriculum gap and how prepared the kids are entering high school. She said that they have meetings with middle school math teachers, but they have no control over K-8 curricula. She said that some students take summer courses to improve their readiness. Obviously, there is a problem. However, enough students make the jump to cloud the issue. It could be the curriculum or it could be the students. Nobody asks the question of how many top track kids got outside help.

She seemed hesitant to criticize. She said that the biggest transition problems are the study skills, amount of homework, and attention to mathematical details. She said that they emphasize precision rather than "close enough". That is telling. I told her that I can also see a gap in content and skills and I wanted to get a list of textbooks/syllabi of the high school math courses so I could judge for myself.

-- SteveH - 18 Nov 2005

I don't know if you've answered this before, but is this a formal assessment, or is it just based on a teacher's recommendation?

Good question!

This is one of the problems.

The news that your child has been tracked into Phase 3 simply arrives in the mail, in a letter telling you what teacher your child has been assigned, when you'll hear about school supplies, etc.

As far as I know, parents aren't filled in on the process.

I don't think the process is a secret, but unless you ask, no one tells you.

However, I'm fairly certain that some form of testing occurs. I always assumed the TONYSS scores were part of it.

-- CatherineJohnson - 18 Nov 2005

YES!

That is the track.

No one knows a thing about this track unless he or she does what you did, and pursues an answer.

I finally got the low down on the math tracks by debriefing a high school freshman.

Again, it's not a secret.

But no one goes out of his way to fill parents in.

-- CatherineJohnson - 18 Nov 2005

She said that they have meetings with middle school math teachers, but they have no control over K-8 curricula. She said that some students take summer courses to improve their readiness. Obviously, there is a problem. However, enough students make the jump to cloud the issue. It could be the curriculum or it could be the students. Nobody asks the question of how many top track kids got outside help.

unbelievable

-- CatherineJohnson - 18 Nov 2005

well....I should add that the TRAILBLAZERS decision was made before the current Superintendent & Assistant Superintendent got here, and that the word is that Lisa Urban, the Legendary Middle School Math Teacher (she's probably one of the main reasons Irvington kids end up doing so well in math, assuming they are doing well in math in h.s.....) was railroaded into the TRAILBLAZERS selection.

The two superintendents are working on fully articulating curricula across grades & classrooms, and have instituted exit exams, so everyone will know what's inside kids' heads at the end of each year.

I don't really have a 'read' on the superintendent, but if I had to bet, I'd say Ralph Napolitano wouldn't be a fuzzy math guy. He has 3 kids who took a gazillion AP courses (& he's appropriately skeptical of AP courses as presently constituted); he knows the score.

-- CatherineJohnson - 18 Nov 2005

She said that the biggest transition problems are the study skills, amount of homework, and attention to mathematical details. She said that they emphasize precision rather than "close enough". That is telling.

yup

that tells you everything you need to know

-- CatherineJohnson - 18 Nov 2005

The thing is, in our school the math gap is going to 'hit' in 6th grade, unless they just get rid of the Phase 4 class Christopher is taking.

I don't see any way a child coming out of 5th grade Trailblazers is going to be able to take Prentice Hall Pre-Algebra.

-- CatherineJohnson - 18 Nov 2005

Gulp! Median household income for Irvington for 2005 is $152,009. (click, click, click) Oh. Westchester. Okay.

Compare to these demographics for Houston: median household income of $60,637.

Oh cool, here are the expenditures. Including operating, capital, and all other expenditures, it's only up to $8200 per student. Wow, my eyes just popped out of my head. Irvington's total is $30K per student.

At $18K vs $7K, you ought to expect a lot more, especially since you don't have to contend with this.

-- KtmGuest - 19 Nov 2005

But we have a Kipp Academy too, which manages to achieve outstanding results, while drawing from the same demographic pool.

-- KtmGuest - 19 Nov 2005

Those math tracks are sending up red flags for me. The "phase 4" track is more than doubly-accelerated: The Math B Regents is intended to be given to "normal" (non-accelerated) students at the end of 11th grade.

But then they slow down in 9th, 10th, and 11th grade -- they get the kids 2.5 years ahead and then put them in a holding pattern so that they end up 1.5 years ahead by the middle of 11th grade and then only 1 year ahead by the end of 12th grade.

Why spend 2 years on pre-calculus? Especially since a bright kid who has done well in Math B could go directly to calculus without a "precalculus" course. (The kid might be a bit weak on conic sections and some of the art of factoring polynomials, but Math B is a pretty good preparation for calculus.)

What are those phase 4 kids doing in 9th, 10th, and 11th grade? Why would kids who are good enough to end up 2.5 years ahead by 9th grade then end up needing 1.5 years to complete a 1 year calculus course? It's a mystery!

-- RudbeckiaHirta - 19 Nov 2005

... as does Wesley Elementary the DI school that serves one of the poorest areas (94% econ disadvantaged)of Houston.

-- KDeRosa - 19 Nov 2005

Oh wow, fabulous link to the schoolmatters.com site.

My hometown school fares relatively well in math (especially in 4th grade).

-- RudbeckiaHirta - 19 Nov 2005

hey way to go Niskayuna

-- CatherineJohnson - 19 Nov 2005

yeah, the KIPP folks are putting everyone to shame

although my neighbor clicked on the link, and spotted the 18-hour school day plus Saturdays & summers and said, 'I hope that's not what we're advocating'

-- CatherineJohnson - 19 Nov 2005

lol

-- CatherineJohnson - 19 Nov 2005

beats me

things seem to evolve around here....under pressure from the various STAKEHOLDERS (Carolyn had a hilarious line about Irvington parents I'm going to have to put in a post—I love it! We're not exactly an easy-going lot.)

The idea is to end up with 1 1/2 years to take calculus BC....but you only need 1 year, right?

I should add that I may have this down wrong.

The 'normal' track I got directly from a student who had been on it, and I took careful notes, having her repeat herself when I got behind, etc.

I got the accelerated track at the Big Math Meeting, and I had to write fast, listen, suppress panic, etc.

On the other hand....I was listening closely.

I do know that they start algebra in the middle of 7th grade, because my neighbor's son is starting algebra in the middle of 7th grade this year.

AND they take the first regents exam at the end of 8th.

-- CatherineJohnson - 19 Nov 2005

hmmm

I wonder if that can possibly be right....

However, if it's off, it's off by one semester only. (I'm wonder if they actually finish Math A in the middle of 8th grade.)

-- CatherineJohnson - 19 Nov 2005

ok, here's what's missing

the presentation got wonky at that point, because NY state is changing things back to algebra 1, geometry, algebra 2

I've left out sophomore geometry.

-- CatherineJohnson - 19 Nov 2005

R H

Thanks for pointing that out.

Yes, the schedule above is the new schedule Christopher & the 2 grades above him will follow. (After those 3 grades go through the Trailblazers kids will be coming in.)

I think that, under the previous standards, the fast-track kids finished 'Math A,' the integrated course you took....hmm

I have a memory that they finished it at the end of 8th grade. (This I learned over a year ago in a conversation with Lisa Urban.)

Actually, yes.

That makes sense.

The Phase 4 kids are supposed to be 1 1/2 years ahead of everyone else.

Apparently there's also an in-between track, but I don't know how it works.

-- CatherineJohnson - 19 Nov 2005

I can see pros and cons of having 1.5 years for calculus.

In a school district that has a large fraction of its students planning on taking calculus in high school (um, like, um, not yours), some of those students might fare better with 1.5 years to learn the material. Downside: the most capable students should have no trouble learning 1 year of material in 1.5 years -- but they might get bored.

In a schol district with carefully filtered, tracked, and groomed students (like yours, like Niskayuna's top-top track*), having 1.5 years after finishing pre-calc would allow the opportunity to teach a three-semester calculus class. (Almost unheard of.) My BC calc class split the difference: when we finished the material required by the AP exam (the Diff Eq chapter), my teacher went on to teach us almost a semester's worth of Diff Eq of the plug-and-chug variety (none of the existence/uniqueness stuff).

When I was at Niskayuna, there was NO TRACKING in 6th or 7th grade. EVERY 7th-grader was in the SAME math.*** The eighth graders were split up: about 3/4 of them took 8th grade math and about 1/4 took 9th grade math.

I will have to pester my dad (consultant for NYS) to find out more about the newest change in NYS curriculum

*Niskayuna's top-top-track takes BC calc in 12th grade (about 25 students, typically over 90% score 4 or 5 on the AP exam), the next track down takes AB calc in 12th grade (about 45 students). Graduating class usually is close to 300 students.

**When I took Calc III, I felt betrayed: Why weren't they teaching this to us all along? In our pre-calc class we had learned all the 3D geometry and matrix manipulations necessary for Calc III.

***It kind of sucked -- at least the way they were doing it.

-- RudbeckiaHirta - 19 Nov 2005

In a school district that has a large fraction of its students planning on taking calculus in high school (um, like, um, not yours)

lol

-- CatherineJohnson - 19 Nov 2005

Niskayuna's top-top-track takes BC calc in 12th grade (about 25 students, typically over 90% score 4 or 5 on the AP exam), the next track down takes AB calc in 12th grade (about 45 students). Graduating class usually is close to 300 students

That is amazing. (Although I should add that I don't know the percentage of Irvington kids taking BC calculus; it may be high. Everyone says the high school is fantastic. I have no reason to think it isn't, but the sheer logic of time means brainy kids have to show up at high school having mastered algebra.)

Do you want to write a 'guest post' about your school & how they did what they did?

-- CatherineJohnson - 19 Nov 2005

I'll be very interested to hear what your dad has to say.

From where I sit, the big question is: what does algebra in 8th grade actually mean?

It seems to mean 'exposure to concepts,' as I think Steve may have put it, not mastery.

Interesting that no one was tracked at all until 8th grade.

I've just learned that Briarcliff has what I think is a fabulous system.

They're using one of the constructivist curricula, but they pre-test & post-test each unit. Any child who tests out of the unit moves on.

That wouldn't be the right way to do it with a text like Singapore; you'd have to have fluid ability grouping, because there's no fluff in the books.

Still, the concept of fluid ability grouping strikes me as perfect both pedagogically politically.

-- CatherineJohnson - 19 Nov 2005

The tracking issue is WAY more complicated than I've said so far -- it's been editted for brevity and to stay on point.

My school tracked for math starting in 2nd grade. I think that in 2nd through 4th grade there were four math groups (two teachers per grade, each teacher had two groups) and in 5th grade there were two math groups (one per teacher). My impression is that a few kids switched math groups each year, around the fringes of each group.

Then in middle school EVERYONE was de-tracked for 6th and 7th grade. Then they re-tracked in 8th grade.

My memories of my school math experiences are too hazy to write a guest post on the details of what we actually did in math class -- especially in the early years.

Mostly, though, I'm guessing that their successes result from the right mix of parents and peers: Niskayuna is home to the Knolls Atomic Power Lab and GE's Research and Development Lab, and it is near a lot of colleges/universities and other employers of high-achievers. (Almost 30% of the over-25 population of Niskayuna has at least a masters degree.) You'd probably see similar numbers coming out of Shenendehowa (next district to the north). I know that my primary motivation in math class was that I wanted to get better grades than Jeff and Jonah (I rarely did, but I often came close).

-- RudbeckiaHirta - 19 Nov 2005

oh!

I see.

Why did they de-track for the first two middle school grades?

-- CatherineJohnson - 19 Nov 2005

I know that my primary motivation in math class was that I wanted to get better grades than Jeff and Jonah (I rarely did, but I often came close).

Yup.

Peer power.

Works every time.

Works in the other direction, too.

-- CatherineJohnson - 19 Nov 2005

Irvington parents are a brainy lot, but there aren't many tech types. We have doctors, lawyers, & Wall Street.

The Wall Street guys are math-savvy, but aren't heard from too often.

Another issue with the demographics is that because families are affluent there are lots of stay-at-home mothers. These moms tend to dominate the conversation, if only because they can get to meetings, and because they don't take anything lying down. They're vocal. (A good quality in my view.)

There were two dads at the Coffee with Principal Fried, one of them being my husband. And he was there because I made him go.

Moms also dominate the extensive fundraising we do, as well as, IMO, the grant-making process. Their focus tends to be on extra funding for the arts, and art-related subjects.

The only constituency math ed has is parents of GATE kids.

otoh, I'm hearing stories of parents loathing TRAILBLAZERS, which is certainly nothing anyone ever heard back when we were using SRA Math. (And SRA isn't an especially good series.)

We'll see how things develop.

-- CatherineJohnson - 19 Nov 2005

This will seem like déja vu: the reason that they detracked in 6th and 7th grade was because there was no district-wide unified plan at the time. The elementary schools had one vision (based on ability grouping), and the middle schools operated based on heterogeneously grouped "teams."

I have no idea what they do there now -- but I'm sure that it's trendy.

-- RudbeckiaHirta - 19 Nov 2005

Yeah

Sounds familiar

Although this is possibly the major issue the new superintendents are working on

-- CatherineJohnson - 20 Nov 2005

This post is a classic.

-- CarolynJohnston - 20 Nov 2005

We certainly had no idea, when Christopher was placed in Phase 3 in 3rd grade, what it meant for his high school education.

What's amazing is the complete absence of any thought to the flowing-down of requirements. College educations have requirements that should flow down to high school; high schools have requirements that should flow down to middle schools and below.

If industry did their planning this way, we'd be living in caves eating roast rat for dinner.

-- CarolynJohnston - 20 Nov 2005

What does pre-calculus involve?

(In NZ we just took maths, until the final year of school when you could take "maths with calculus" and/or "maths with statistics". But by then I'd been doing calculus and statistics in maths class for years).

-- TracyW - 20 Nov 2005

Pre-calculus comes in two flavors.

The more appropriately named one focuses on firming up the algebra skills necessary to be successful in calculus: improving skills at graphing by hand (with transformations), more practice working with piecewise functions and functions like absolute value, a lot of work with trigonometry, working with conic sections other than just parabolas. Sometimes it will also include parametric equations, polar coordinates, and complex numbers.

The less appropriately named one is, in some sense, a superset of the former. This latter version of precalculus is often taught to the stronger students. They don't have as many gaps to be filled in, so more time can be spent on other topics -- usually (but not always) topics that can be understood by a high school student but that are sometimes not formally taught in college classes. Matrix arithmetic and Cramer's rule, DeMoivre^?'s Theorem, proof by induction, etc.

-- RudbeckiaHirta - 20 Nov 2005

How interesting. In NZ, if my memory is right, we didn't learn things like conic sections, polar coordinates and complex numbers until after we'd learnt some basic calculus.

And from memory we were first introduced to algebra in fourth form (about 14 years old) and then to calculus next year in fifth form (about 15 years old). So not much time spent firming up algebra.

I wonder how the different countries came up with quite different sequences for teaching maths.

-- TracyW - 20 Nov 2005

If the USA is contributing 9% of its population to the top 10%, and Singpore is contributing 39% to the top 10%, then some other countries are presumably contributing considerably less than 10%.

I wonder who they are.

-- TracyW - 21 Nov 2005

And from memory we were first introduced to algebra in fourth form (about 14 years old) and then to calculus next year in fifth form (about 15 years old). So not much time spent firming up algebra.

wow

I wonder how the different countries came up with quite different sequences for teaching maths.

me, too

.....you're reminding me I have to get the great Hypomanic Comparison New Zealand - U.S. data posted

fabulous stuff

-- CatherineJohnson - 21 Nov 2005

If the USA is contributing 9% of its population to the top 10%, and Singpore is contributing 39% to the top 10%, then some other countries are presumably contributing considerably less than 10%.

At some point I read some comparison or other saying the U.S. ranked with Kuwait. (Probably apocryphal, but that's what I was thinking for awhile.)

I told our principal, Don Kuhn, and he said, 'Yeah, and they've got oil.'

His wife is a high school math teacher, so he's seen it all.

-- CatherineJohnson - 21 Nov 2005

WebLogForm
Title:	algebra in the 8th grade: Irvington and KIPP
TopicType:	WebLog
SubjectArea:	IrvingtonMath
LogDate:	200511181337

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algebra in the 8th grade: Irvington and KIPP

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