And so what? What does it matter? Sure we do need a number of people who can solve such a problem and we probably do have them. To be successful at the university level and beyond takes more things than being able to solve any single math problem. To be a successful society and country take more variety than robots all being able to solve the same problems and nothing else.

Well, while China is teaching their kids math, science and English, the chinese government is over in the US (in Palo Alto!) convincing our schools we need to be teaching our kids Mandarin.

What a clever ploy to distract the best and the brightest in the US and make sure we will never be able to solve problems like this.

I'm sure they're rolling in the isles.

The point is it does matter. If this is the way Chinese universities are expecting their youngest and brightest to be educated then everyone else is going to be left behind. This is how the brightest and best scientists, engineers and researchers are being educated. When it comes to innovations during the next century, these are the ones who are going to do it. Either the best will come from China, or they will be imported here to take the jobs that are college graduates are not ably fitted for. There was once a connotation of mass produced trash associated with the phrase made in China. In the future it could be that this phrase means the most advanced in the world.

If our college students are not being educated to the highest levels, then they are not going to succeed in their chosen fields.

It is also interesting to note that the Chinese value math and science rather than language. It makes the whole MI and FLES debates here look a little pale in comparison. I wonder what PACE would think of this and whether their expertise in math, science and engineering can actually solve these university entrance requirements.

Assessing math skills and talent makes sense for incoming students who will major in disciplines that require that kind of thinking and skill.

For students who plan to major in other areas, it might make sense to assess their spelling. For example, If someone is "rolling in the isles," where would they most likely be?

a. A movie theater in San Jose
b. A beach in northwestern Europe?

English Major: Sorry, I missed the "a".

And does that change the point? Perhaps it reinforces the point?

If one spelling error was that distracting to you that you totally lost the point of the entire post, maybe English is just that important - what kind of 'discplines' don't 'require that kind of thinking and skill' - the ability to communicate.

Did you happen to take any logic or critical thinking classes in between Shakespeare classes?

Though on that topic, I am a little shocked by the number of misspellings that show up online, in the newspapers etc. that do not seem attributable to typographical error. For example, could everyone please learn not to put an apostrophe on "its" to form the possessive? And could everyone also please learn the difference between their/there/they're and affect/effect? These are just a few exmaples of what shows up all the time, including in classroom newsletters written by teachers in PAUSD elementary schools. This convinces me that a whole lot of people are not getting a solid education in English spelling and grammar, here and elsewhere, never mind the advanced math. But we digress.

You jump to conclusions.

So, we know that the kids in some Asian countries beat the pants off our kids in math comparisons. Also that the kids getting into Chinese universities are doing much higher level math.

The relevant question is how do those individuals do after college. Are they creative thinkers? Do they push the boundaries of science and math? The evidence I've seen, anecdotal mostly, is that they do not. The Chinese system drums out those with creative solutions and quashes fun in learning.

Do you want to create a cohort of academic drones, able to complete advanced problems from the textbook but unable to innovate. Or do you want to foster creativity and a love of knowledge?

The Chinese have begun to realize that they are educating lots of people who can do the fundamentals very well but who are not creative, and they are looking to American models to change the way they educate their kids. In some ways, China is decades behind the United States in education.

As for languages, they are pouring money into special immersion-type schools so that their kids will be skilled at both foreign languages and science.

Nellie

You say you only have anecdotal evidence but you make some glaring statements. I see no evidence to suggest that Chinese education is behind the US in education. Time and time again I see US education very low on international comparison lists for science, math, and most other subjects. And as for languages, the money they are pouring into language programs are to teach their students English (so that they will be able to complete globally against those who have not benefitted from their high standards in academics). In other words, they will be able to speak English well and be dominant in science and math. That says a great deal about how they will do after university.

Who says that they aren't creative. I have no doubts that there is creativity there. It sounds to me that you are really trying to make excuses for the poor standards here by saying that we have creativity and that makes up for all the disadvantages.

So who exactly is jumping to conclusions.

Parent,

Yes, as I said, if you look narrowly (standardized test scores up to college), the U.S. is behind. I'm asking you to consider what those tests measure and to look beyond those scores.

One way to think about this is to consider how many international prizes in math and physics go to China, for instance. Not many. Very few, when you consider how many kids come out of Chinese universities every year.

That is why educators in China are worried and looking to the U.S. as they consider changing how they teach their kids. They are coming to realize that the measure of success in science and math is not a standardized high-school test. It would do us all a lot of good to recognize the same thing and stop bleating about test scores.

It may be that some people in China think of learning English purely in terms of getting ahead academically, as you approvingly suggest. The rest of us see a panoply of benefits to studying foreign languages.

You admire the Chinese system, but do you know how it works? Are you ready for 60 kids in a class with one teacher? No recess? Killer science tests at 17 that determine your access to higher education for life? Etc.? I suspect you admire the test scores but don't know at what cost they come.

Actually, I have no idea as you apparently do at how it works. I do know that the results seem to show that it works. As for larger classes, no recess, I had larger classes and less recess than my kids and I was in no mollcoddled. I also had very difficult tests at age 15 and 17 (as well as less meaningful but equally difficult tests at other ages). If I did not pass then I had to wait a year and could re-do them.

I do admire what I see from outside the US and I can imagine that the students work very hard to get there. They probably spend more hours per day and more weeks per year at school without all the odd days off for teacher development and local holidays. They probably do get their heads round problems from many different angles without all the field trips, the movies, the group projects and busy homework that abound in our schools.

As for the international prizes that US students appear to be winning, I imagine that you must know more than I on the subject because I know very little. However, when I see prizes being won by students here, it is usually those whose parents were educated elsewhere who seem to be winning them and who make sure that their kids spend time studying outside school in an effort to succeed.

Web Link

Why is everyone so freaked out about this problem? Given that we've got kids who are doing two years of college math in our high schools, I don't think a geometric proof is beyond them. Even one in three dimensions.

As others have pointed out, you don't need all future college students to solve these kind of problems. What you want is to find the kids who find these kind of problems *fun*. Because those are the kids who will push the envelope and innovate.

Of course, the particular problem doesn't involve creative problem-solving; you just have to remember the appropriate postulates.

Yes, U.S. education could be better. It's sloppy. However, unlike many, many other countries, we don't educate just the best and the brightest. We give lots of second chances and make allowances for kids who have talent, but might not be ready for gung-ho studying at 14.

It's not about how early you can do it, but how far you can go. We don't kick kids off the academic track when they do badly on a test at 11 or 14.

In other words, if it's so bad here, how come foreign students keeping coming to our universities? Oh, maybe it's something about all those American universities in the top 10. But, hey, China's got one school in the top 20.

In this area, at least, the big dragon's got a way to go. That little problem the Chinese government has had with freedom of thought has kind of gotten in the way over the years.

Here is a point to ponder:
Go to any (I really mean any) tier 1 University. Go to its Graduate School of Engineering and look at the demographics.
It will shock you.
In yester years these students would be eager to stay back in US after they graduate. Not anymore.

There is a reason our Work Visas are filled every year, ( now the quota is filled before the budget year even begins) with immigrants who have graduated from universities in math/science/tech fields. We desperately need these employees, and can't find enough USA citizens to do the type of educated work these guys bring in.

One day we will realize this, and push our own math/science more. It will happen again when we are shocked by our complacency, like it did when we weren't the first in space.

In the meantime, as usual it is the immigrants who come here who understand the value of hard work and education, and so their kids, SURPRISE!! go onto Universities in a much higher percentage than others.

I applaud them, and am grateful to the immigrants who are strengthening us, and reminding us to push ourselves a little bit more. I hope we keep absorbing the good of this influence into our whole society. I am not too worried about most of us absorbing TOO much.

There is some talk in these communities that they might be pushing their kids TOO hard ( and, I would agree it needs to lighten up some!), but the attitude is one of adjustment of balance, not abandonment.

OhlonePar,
The Universities of US are educating non-Americans. Does that surprise you.
Americans kids are not going far enough as you want them to....

I think it is interesting that with all the posts on this thread, there isn't one that says that they know of a senior who can do either of these problems.

I ask the math teachers, what do you think, can our seniors do these problems?

I ask the students themselves, those who I know read these posts, can you do these problems?

I have asked both my freshman college student and my freshman high schooler. The college student says yes on the second and is looking at the first to try it. My algebra/geometry student says he thinks he could do the first but hasn't spent any time trying, but the second in trigonometry and he hasn't a clue how to do trig yet as that is taught completely separately although there is a chapter in his text book about it and his STAR tests this week included some trig. and "no one knew how to do them".

Please can someone who knows really tell us if our students can do these problems.

As a high-school senior 25+ years ago in PA schools, I could have answered both these questions. I think I had my trig class as a junior. The 2nd question is quite straight forward.

Why do you think so many foreigners are coming here for their college educations? Even if they are going back to their countries after completing their educations due to the increased opportunities, they are still coming here in droves. We must be doing something right.

Also, I think this country has more opportunities for kids of every ability, and those who are "late bloomers" - no need to pass some difficult, one-shot only entrance exam to attend college. which is the case in some countries.

Why is it important that the average person can solve these problems? Although we need to produce world class scientists and engineers, I think we are trying to teach higher level math to too many kids who will never use it, will never enjoy it and will never be particularly good at it. Why are we spending time trying to hammer Algebra and Geometry into kids who should really be learning how to balance a check book or invest in the stock market or just budget for the grocery store. The majority of us need real world math, not proofs.

There are people who are naturally good at math (and some who are naturally good at swimming, baseball, writing, empathizing). Not that hard work is not equally important in all these areas, but we need to admit that students are capable of being great students in every subject, they will be naturally better at some. We need to stop making them feel like failures if math is not their thing - and find ways to keep it interesting along the way. Remember, we all grow up to be specialists.

Crescent Park PA Mom

I agree that looking at the whole child is good in respect to any one individual child. I think the bigger picture is important however. Yes, many children will not grow up to need the math they learn in school. But, the country does need mathematicians generally and if we are not finding them here in Palo Alto in our schools, then where are they going to be found? Certainly abroad so it appears.

If we do not strive to teach our children to the highest, then we will achieve second best. Yes, there are many who won't want to get there, but how do we know if we don't try. Many people regret that they didn't learn more at school to help their future careers.

You can learn how to invest in the stock market, balance a check book and budget for family groceries as well as get a great fundamental knowlege of advanced math in school. What you also get are options for the future.

There's an interesting column written by Thomas Friedman in today's PA Daily, entitled "Will the next Einstein come from China?

Paly Parent - I agree you can learn to balance your checkbook etc. and get fundamental knowledge of advance math. My concern is that we are not teaching enough fundamental knowledge of regular math.

By high school, you have a good idea of your strengths and weakness. Not that you shouldn't work to improve, but what if your "thing" is writing or art or video making and you spend 4-5 hours a week working on math homework instead of pursuing your passion. How much energy should you put into learning something you will never need vs. things that will benefit you your whole life. This is not about teaching to a whole child, its about teaching kids what we think they need to learn (often merely for a test) instead of what they truly need to learn.

Chances are the next Einstien could very well come from China or India. But he will be the next Einstien after he immigrates to US.

Einstien was not born and educated in US.

Ooops.. sorry. the above post is not by Lorraine - my bad using cut/paste.

Author is 'any person'

I think I will re-phrase my question as it sounds that I am not making myself clear.

I know that not all Paly or Gunn seniors are math orientated and are able, or desire, to answer these questions. What I would like to know is if there are classes, either at AP level, college level, or regular level that teach the material that answers these problems and at what levels they are being taught?

I know that we do have many students who love to do math and science, who spend hours enjoying the challenge of mathematical puzzles. These are the students I would expect to be able to do these problems. These are the ones who I expect would go on to college to study math and science. These are the students I expect to go on to be engineers, tech whizz kids, and the innovaters of the next generation. My question is, are they being prepared for this type of future in our schools?

As a supplement, it would be interesting to know what percentage of our students are able to do this.

I am sorry that I keep going on about this, but I do really want to know. I keep hearing of jobs going to those educated outside the US and also that our colleges are filling up with overseas students coming here to do a masters degree and then go into industry here. From my own experience, I see employers finding it difficult to get US born employees in these tech fields and have to worry about getting visas and the like for their employees. I think that this is getting to be a big problem here in silicon valley and one of the reasons why we have so many immigrants here from Asia and other places. They are getting the jobs that we are not educating our kids for. Look around all the power lunch places in downtown Mountain View for a start. You will find it hard to find a homegrown American accent - and that often goes for the wait staff too.

This is my rationale for asking these questions.

Paly Parent - Why don't you ask Suzanne Antik in the Paly Math Department?

Interesting video about the topic "Do schools today kill creativity?"

Web Link

Palo Alto Mom,

I have forwarded these puzzles to both my kids' math teachers, but as yet have had no reply.

Ask the people who qualified who the USAMO, it looks awfully like some of the questions they answered. And personally as a student at Gunn, if I found that sort of stuff interesting and not just "work," it would be pretty simple to just take some time and solve it. It's a simple proof that might have been a very evil challenge problem that Mr. Herreshoff is so fond of giving (sophomore year geometry btw).

Gee, U.S. universities educating foreigners--no, not a surprise. Again, it supports my point that we have top universities, which, in fact, draw students from everywhere.

Engineering is a ESL enclave, in part because a) it doesn't require the levels of English required in other areas and b) it's not as attractive a field as it once was--in part because of outsourcing overseas.

As for the problem--do most of you not see that it's not that difficult a problem? I'm not a math type and I could see what was needed. As Student confirmed it's high-school geometry--that's freshman year for those on the AP track, sophomore for those on the traditional.

It's really a question of breaking it down. I suspect you don't get problems like that on American standardized tests because writing out proofs does take time--both to do and to check.

OhlonePar,

You comment that "Engineering is an ESL enclave " is very disappointing.

Gee ...
today "engineering is an ESL enclave",
tomorrow it will be "Medicine",
a day after tomorrow it will be "Accounting"
and later ...

Gosh.. We import most of our stuff anyways... we really dont need educated population of our own. Have you checked the trade deficit lately ?? Time to buy begging bowls for our future generation... change that... for our current generation.

a)

I could not prove BD ^ A₁C since
these are skewed lines. However I can prove BD ^
plane A₁CC₁

Since planes AA₁C₁C and ABCD are perpendicular and BD
is perpendicular to AC which lies on the plane AA₁C₁C
then BD is ^ to AA₁C₁C

b)

Angles between the planes A₁BD and BC₁D works out to be:

180 - tan^-1Ö 3/3 - tan^-1 Ö3

c)

AD and BC₁ are non intersecting lines (skewed) and hence cannot determine the
angle between them.

 

Educated in Third-World

I purposely wrote b) as above instead of 90 degrees to show my work.

ESL,

Medicine requires interaction with patients and can't be outsourced overseas, so different set of pressures than there are on engineering. Accounting needs to be in compliance with the laws of a particular country, so some outsourcing is possible, but there's not a compelling reason to do it.

I suppose I sound a little jaded because I heard this panic 20 and 30 years ago. Americans, native-born and acquired, are flexible and it's why we have a relatively flexible education system. Remember when Silicon Valley was doomed because we'd lost the chip wars? Instead we ended up with the Internet. Culturally, we're open to changes. Some changes have been awful, but the dynamic is a formidable one.

Why is everyone freaking out about this problem? I went to Paly and had the skills to solve this problem as a sophomore, and I'm sure practically everyone else in my class did too. I was in the highest math lane, but I'm not primarily a math and science person. Palo Alto schools are good - chill out, everyone.