patrick.net

marcus says

About the trig,

And here's how I do it:

1. Plot cos(x) and sin(x)

2. Add a shift: cos(x) +a

3. Add an amplitude: Acos(x)

4. Now put 2 and 3 together.

5. Add a phase shift: cos(x+b)

6. Now put 4 and 5 together.

7. Add a frequency multiplier: cos(fx)

8. Now put everything.

9. Practice on your own: 10-20 examples with various combinations of a, A, b and f

10. Now complicate things even further, e.g. add an absolute value, or a sum of a trig function and a linear function, or make the argument non-linear.

It is points 10. and (to a leaser extend) 9. where you want the students confused, stuck for long time thinking and discovering. Not at points 1, 2, 3,..

marcus says

You get what you pay for.

Except for American public education.

FP says

The CPM approach is intrinsicly faulty.

This is your opinion. But if you can't acknowledge the positives that the the CPM method provides, then you aren't being honest. I get it, it's not the way you think it should be done. And you may even be right, that the best methods are in between what CPM does and the traditional approach. But if you can't acknowledge tohe good aspects of it, then I can't respect your opinion as anything more than emotion.

FP says

It just allows them to hide their laziness behind CPM.

Actually when first doing it, it's very hard to let go of being a control freak and letting the kids loose to explore and put things together on their own. I have difficulty with it becasue of how long it takes, and when I teach it, I combine with traditional and can't use their lessons all the time. Truth is I haven't taught CPM much, and I haven't done it well. But I find it WAY more difficult than traditional, so your laziness point doesn't hold up. Teachers find teachingthe CPM way VERY difficult.

The main thing you don't get is that the teachers do feel accountable, so it's very hard to let go with those collaborative student driven lessons. You really have know idea what drives the typical teacher.

I wish we would replace Geometry and Trig with Logic, which would be far more useful for most people (and society generally).

The best thing to do would be to Reform English spelling, so we save months of time wasted. Even phonics can only do so much: Through, Bough, Though, Tough, Cough. Clue, Blue, Due, Rue but Clew, Blew, Dew. Glue and True, yet Threw and Pew. And settle the French vs. Dutch spelling for profit (more letters=more lines=more profit) from the time of the English Civil War.

The Spanish did it by saying "Starting on X date, any petitions, filings, etc. to the Royal Court must use the new spelling or it will be rejected."

It's funny people flip out over the milisecond it takes to double tap the spacebar, but are opposed to reforming the spelling which would slash months of learning, and probably weeks off lifetime of writing.

CBOEtrader says

Why are you still sending your kid there? Put him on khan academy and curate his path at home.

What choice do I have? It's a top rated public school :) I didn't expect this based on our middle school experience.

Khan academy is good for explaining things but not for a complete education.

So I am going the home path way - math, physics and programming. I have ordered some soviet books from Mir publishing, some in English, some I'm translating. I'm also translating my old textbooks from midddle and high school (we had physics from 6th grade).

FP says

marcus says

If so, then it's a bad teacher. Small sample size though, and you're generalizing conclusions about what, all American Math teachers and CPM from this ?

I have talked with many people and students. All the teachers in the school are like this. It is not a case of a single bad techer. The CPM approach is intrinsicly faulty. Furthermore, there are no criteria or controls for evaluating how the teachers apply this method. It just allows them to hide their laziness behind CPM.

Slow clap bro. W your dedication your son will certainly outpace his classmates. Test him against his Russian cousins and report back how the foreign students match up.

Sorry in the sun and quoted wrong post above

marcus says

FP says

The CPM approach is intrinsicly faulty.

This is your opinion.

Not only my opinion.

1. It is the documented opinion of hundreds of educators - school and university. It is also the opinion of every single of my colleagues that I have discussed the matter with. These are theoretical physicists with degrees from Stanford, Berkeley, Princeton, MIT, Cornell, UIUC, Harvard and so on.

2. There is empirical evidence showing that CPM is inferior to the "traditional" approach.

3. There is no reliable, statistically significant evidence that CPM is better.

BTW, I never said there are no good aspect of CPM.

CBOEtrader says

It is not uncommon for an entire US PHD physics department to have 100% foreign educated grad students. These are the affluent who have the money to attain a superficial credential.

Physics, Medicine, Engineering are the prime value added careers that formed the best and most sustainable businesses in the US. The US started outsourcing, and the foreigners kept increasing their STEMM.

The US is exactly where we designed our self to be.

CBOEtrader says

Test him against his Russian cousins

I'm not Russian... neither Ukrainian, nor Belorussian.

CBOEtrader says

bob2356 says

Quants are graduate level people usually PHD's.

You consistently assume you know more than you know. This will always lead you to poor conclusions.

Quants is a broad term. This conversation was regarding entry level quantitative developers. Most of these people have the equivalent of undergrad or masters programs. On eastern Europe I am told they often recruit from tech trade schools.

Then you should have been more specific. My conclusion is drawn from the fact that common usage for the term quants, of which my cousin is a very good quant with a double Phd, is for a quantum analyst. Which is a phd position.

Maybe you could fill us in on what company is doing this recruiting and what eastern european schools they are recruiting from and let us draw specific conclusions based on actual facts rather than a broad based pontification on the state of US education based on a vague someone said something about something that may mean something to someone.

FP says

bob2356 says

So where are all the eastern european countries that are doing better at math and science? Estonia, which is northern europe and has a population less than San Jose, is the only one that scores higher in both subjects.

This type of rankings are not very telling for several reasons. I'll explain later when I have time.

Pray tell I'm always willing to learn. It's the rankings that are used. Good or bad, it's what is out there. The rankings show more about income inequality and national wealth than anything about teaching. Also the weighting of subjects matters a lot. Finland students scores higher on number properties than US students but lower in algebra which carries a much lower weighting in TMISS for example. Stanford did a big study on this I read a few years ago, but I'm not seeing it online to link to.

Translated Grade 4 (may not be equiv. to our Grade Four) Soviet Textbook.
ftp://math.stanford.edu/pub/papers/milgram/russian-grade-4-problems.pdf

Huge focus on the why and when to use Math, rather than "Just use the fucking formula" system I was taught.

FP says

2. There is empirical evidence showing that CPM is inferior to the "traditional" approach.

Could you share some of your best sources for this please ?

I get it that People that came up with traditional find it annoying. I did too. And still do with parts of it.

So what is it you think they are trying to accomplish with it ?

@FP

You made me go down the Rabbit Hole... lots of Russian Math Classics here

http://www.cbspd.com/website/index.php/sciences/mathematics-and-statistics.html

marcus says

FP says

It is points 10. and (to a leaser extend) 9. where you want the students confused, stuck for long time thinking and discovering. Not at points 1, 2, 3,..

True. But it was in an Algebra one class. Many don't even see the simplest right triangle trig until geometry. So is it so wrong to be exploring ? They will see more in trigonometry geometry, Algebra 2 and Precalc or trig.

What I was talking about in a paragraph above was graphing something like sin(3x + pi). Intentionally no altered amplitude or vertical shift.

Method one: it's sin(3(x+pi/3)) so the period is 2pi/3, and the horizontal shift is pi/3 to the left.

Method two: solve 3x + pi = 0, and 3x + pi = 2pi to get a starting point and end point for one full sin wave and graph the rest from there. Fool proof. Both methods assume an understanding of the function sin(x) .

Graduate in the US with a STEM degree as a US citizen, and the most likely outcome is that your application to STEM-related jobs that you actually want will be ignored. A few years later, even if industry does start hiring again, they'll write you off because you weren't able to find a job sooner.

Its a real vicious cycle. Lots of great US citizen talent is destroyed this way.

marcus says

I could not delete this comment. Invalid nonce.

Thanks for telling me. Will look into it.

From my experience as a teacher, the biggest threat to education in the sciences is the removal of all desktops in the science lab and replacing them with chromebooks.

marcus says

Could you share some of your best sources for this please ?

Here - in no particular order and apologies is some of the links are not working any more; it has been awhile since I was reading them
(I have more sources, but they are scattered over emails that I've exchanged):

http://bonniewren.com/2005/cpm-math-vs-traditional-math.htm/comment-page-1
http://www.mathematicallycorrect.com/study1.htm
http://www.csun.edu/~vcmth00m/riley.html
https://patch.com/connecticut/fairfield/letter-data-shows-pilot-math-program-is-detrimental-t551c25d6ec
http://www.mathematicallycorrect.com/polycmp.htm
http://www.mathematicallycorrect.com/cpmwb.htm
http://www.mathematicallycorrect.com/programs.htm
http://fairfieldmathadvocates.com/one-size-does-not-fit-all/
https://medium.com/@TP.Political/cpm-math-controversial-in-westerville-oh-9f8eb975cc40

Lashkar_i_Trumpi says

You made me go down the Rabbit Hole... lots of Russian Math Classics here

http://www.cbspd.com/website/index.php/sciences/mathematics-and-statistics.html

@Lashkar_i_Trumpi,

Thanks. I didn't know this site. Looks good. Only wished they were showing the contents + a few sample pages.

I you read Russian, check this out:
http://www.mccme.ru/

StrictReason says

Are we really that bad in Math? If so, how come we are doing so well in International Mathematics Olympiad?

International Math Olympiads have very little to do with math education in general. Believe me, I have been there.

It is all about training a few motivated students. A large part of this training is classifying the type of problems that appear at the competitions and learning/memorizing approaches to solve them.

We can save STEM. We just need more videos like this:

www.youtube.com/embed/46h-LfNWPn8

www.youtube.com/embed/Wllc5gSc-N8

If you don't like having bisexual orgies, you are backwards barbarian.

^^ I'd really like to see the conversation wherein a producer agreed to this idiocy.

I couldn't imagine a better parody of the insanity within today's regressive left.

I've always felt our culture works against us. Math & science are strongly associated with being a nerd, which has negative connotations tied to it. Some people have enough self confidence to be proud & exclaim that they're a nerd, but most people feel it's a label they don't want attached to themselves, and so they avoid any behaviors that might lead to someone calling them one - and that means avoiding math, science, and sometimes just plain using your head.

How many times have you heard someone on TV disclaim themselves before doing a tiny bit of math? Like: "Hang tight folks, we're gonna get a little nerdy for a moment - $4 a day times 5 days a week times 52 weeks per year times 10 years = $10,400".

It's sad that someone ballpark-estimating how much they spend on Starbucks feels the need to disclaim themselves before they do some extremely basic math. Children pick up on these cues, and it affects them.

CBOEtrader says

^^ I'd really like to see the conversation wherein a producer agreed to this idiocy.

I couldn't imagine a better parody of the insanity within today's regressive left.

The thing is 90% of the people cringe, including liberals. So it's self correcting. We're not going to follow Canada's bill c-16.

goat says

I've always felt our culture works against us. Math & science are strongly associated with being a nerd

You have a point. But in public schools with enough academic diversity, that is with a high enough population of academically strong college bound students, many of the most respected cool kids are nerds. So you don't have that phenomenon.

But in low income and "inner city" areas, where too many kids are behind grade level, and long since not buying in to education as the best way out of poverty (parents not buying it either - in part because they are uneducated and think it's harder than it is (psychologically more complicated than that)), they don't have a critical mass of higher performing kids setting an example for the others.