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Serious math

By Katy Murphy
Thursday, August 5th, 2010 at 6:46 pm in Algebra/Math, students.

Over the years, I feel like I’ve come to know you — your political leanings and life experiences, your writing style, sense of humor and average snark level. But what about your math skills?

For example: Can you (or any high school student you know) do this?

Show that there are only finitely many triples (x, y, z) of positive integers satisfying the equation abc = 2009(a + b + c).

Or this?

Let n be an integer greater than 3. Points V1, V2, …, Vn, with no three collinear, lie on a plane. Some of the segments ViVj , with 1 *< i < j < n, are constructed. Points Vi and Vj are neighbors if ViVj is constructed. Initially, chess pieces C1,C2, …,Cn are placed at points V1, V2, …, Vn (not necessarily in that order) with exactly one piece at each point. In a move, one can choose some of the n chess pieces, and simultaneously relocate each of the chosen piece from its current position to one of its neighboring positions such that after the move, exactly one chess piece is at each point and no two chess pieces have exchanged their positions. A set of constructed segments is called harmonic if for any initial positions of the chess pieces, each chess piece Ci(1< i < n) is at the point Vi after a finite number of moves. Determine the minimum number of segments in a harmonic set.

(*Note: This sign (<) should read “less than or equal to,” but I have some keyboard limitations.)

If you couldn’t solve them on the back of your envelope, don’t feel bad. Those questions were from the 2009 China Girls Math Olympiad, where the competitors get a whole hour to solve each of eight such problems. I’m sure I could do it within that generous time frame, especially with a cadre of teen math geniuses doing all the work, but Team USA didn’t pick me this year.

Three teenagers from the Bay Area did make the team — Cynthia Day, a Lynbrook High junior from San Jose, Lynnelle Ye, a Palo Alto High School grad bound for Stanford University, and Jing Jing Li, a recent graduate of Cupertino High from Sunnyvale, who’s going to UC Berkeley.

The team, sponsored by the Mathematical Sciences Research Institute in Berkeley, will compete next week against other brilliant mathematical minds in Shijiazhuang, China. They’re already overseas.

I think they’ll be blogging, too. Here’s a link.

[You can leave a response, or trackback from your own site.]

  • Nextset

    This is real interesting. Now maybe we should eliminate this level of math in OUSD as a requirement, but impose a water safety-swimming test requirement and offer swim lessons to those unable to handle themselves for 20 minutes in the deep end of a pool. Recent events remind us that Otis and Latifah can’t swim – at all.

    At some point you have to sit down and decide just who you are running a school district for. Do you want to have college prep for those relatively few who will go there or do you want instruction that will keep the students from early graves and make it possible for them to assimilate into even the lower middle class world of work?

    By imposing a pointless academic requirements while simultaneously withholding driver’s ed, basic swimming lessons and all the core elements of deportment, you carefully create a 50% plus black/brown drop rate and leave much of the rest unemployable. The college bound kids would have probably made it anyway. Their classes should not be imposed on the lower class youth who are in critical need of survival skills, like how to speak standard english.

    Do we even pretend the urban schools are here to keep the ghetto kids viable in society anymore?

  • AlgebraTeacher

    Oh fun! I’m going to be a new 8th grade algebra teacher in the district this fall, maybe I will give this to my students =P

    This level of math would stump most undergraduates, as it involves some number theory, linear algebra and high level thinking.

    The problem with mathematics teaching in California is the jump from 7th grade math to 8th grade algebra is too large, and the students are not being adequately prepared for algebra. This in turn leaves them farther behind when they enter high school and retake algebra, once again, without the proper background to do so.

    And everyone deserves the preparation to go to college whether they plan to or not. Holding all students to high expectations is the key to this as well as competent teachers who can aid students in success.

  • livegreen

    AlgebraTeacher, How would you ease the transition from 7th Grade to 8th? Bring some of the Algebra in a little earlier?

  • Sue

    Hmmm – I would think the answer to Livegreen’s question would be just the opposite, *don’t* introduce algebra in 8th grade, slow down and make that a year of pre-algebra, then 9th graders would be well-prepared for algebra.

    (And, yes, I know there are a few kids who are capable of handling algebra in the 8th grade – I was one, long,long ago – but my understanding and experience is that the overwhelming majority of kids that age simply aren’t there developmentally. Yet.)

    And Katy, I love the questions, and I wish I had a couple of hours to spend figuring them out. With younger son off to a sleep-away camp today, maybe my week end will be quiet enough for some of that sort of mental “play”.

  • AlgebraTeacher

    Yeah, I don’t think 8th grade algebra is right for everyone. I was advanced in school, so took algebra as an 8th grader, but it was not a requirement (I grew up in the midwest).

    The problem I see is the standards for 8th grade algebra were pulled from 9th grade algebra, but nothing in 6th or 7th grade was adjusted to prepare them for algebra. It’s like a whole year of math is missing for these kids.

    I have some ideas to bridge this gap and scaffold the problems to reinforce old material and learn the new, but we shall see where my students are at to begin with.

  • AlgebraTeacher

    Another thing I wanted to add. The kids are developmentally there. The preparation for 8th grade algebra is not. The US ranks 25th (or worse) in the world in math. In grad school, I had colleagues from Romania, Russia, Taiwan and China who all took calculus as sophomores in high school. If people realized how many math jobs were taken by people brought into this country because Americans are just not smart enough for the jobs, maybe we’d wake up.

  • CarolineSF

    Now I’m not saying Katy, but journalists are routinely on thin ice critiquing math education, because journalists are famously incompetent at math. Only two days ago, the San Francisco Examiner had a story claiming that 90% is an increase of 5% from 85%. I would so love to see a math test given to Chronicle columnist Debra J. Saunders, math education critic. Just sayin’.

  • Katy Murphy

    Sadly, Caroline’s observation is all too true. In what grade do we learn how to calculate percent changes? Fifth?

  • CarolineSF

    I had to re-learn how to calculate percentages (assuming I learned it at some point in school) when I became a newspaper copy editor. A rare math-proficient co-worker tutored me. My then-employer, the San Jose Mercury News in its former profitable and powerful incarnation, expected copy editors to recheck reporters’ figures, and good thing, because 4 out of 5 of them, or 90%, were wrong. (Little joke there.) But seriously, the press does have some nerve EVER writing critically about math education in today’s schools.

    I’m exempting Katy on the “innocent until proven guilty” principle.

  • Nextset

    I think higher math is great. Ditto Chemistry.

    Oakland is not Palo Alto. The OUSD population needs to stay out of prison and find work. One of the ways to really screw lower class youth – the dominant block of OUSD students – is to set the school up so you run off these students into the street life.

    That’s why OUSD has a 50%?? drop out rate for black boys. A drop rate that high is program failure.

    Higher education is for those with aptitude and interest in it. It is wrong to try to force this kind of math down the throats of those who make it clear they will not have it. OUSD should have a college prep program, and a good one that can rival SF’s Lowell High. But that programs should be by application or request. Better on it’s own campus.

    Money that the liberal loonies would spend assaulting the lower class with this kind of “education” should be spend on Driver’s Ed, Driver’s Training, Swim lessons, School Nurses, and basic training intended to qualify lower class youth for military, industry or Jr College.

    Trying to force higher concepts into the left half of the Bell Curve at the expense to wiping out the basic education should be a crime. The people doing it know better and they seem to enjoy setting up the Left Side of the Bell Curve for disaster.

    They take sport in taunting the Left Side of the Curve with what they cannot do. They teach that there is something wrong with them if they can’t manage the party line. There is nothing “wrong” with an IQ 80 person. They are what they are and they should be trained to make it in this Brave New World, not made to feel defective because they can’t function in IQ 115 coursework.

  • anon

    Nextset- I’m a parent that would be overjoyed for OUSD to have a good college prep program that would rival SF’s Lowell, and I can think of at least 20 families just in my child’s grade that would sign up immediately if one existed. How do we make it happen?

    I really, really don’t want to move through the tunnel or leave public school for the private school scene, but I also don’t want to hamper my child’s education by placing her in a school where they don’t challenge her, or where she could be surrounded by peers who aren’t as excited and driven to learn as she is. Oakland Tech looks like the closest thing to this right now, but word is that it will be tough to get into the academies soon, if not already. That’s a shame, and I hope OUSD will do something about it- it’s really, really nice to see something working for a change!

  • AlgebraTeacher

    Nextset– Sadly your assumption that Oakland youth are not performing at the levels of their white counterparts in wealthier districts means they are not “smart” enough for that level is depressing. Every student can learn, maybe not the same way you or I learned, but giving up is never the answer. The state has mandated standards that must be taught, regardless of the district. All students can learn these standards and should be taught by qualified amazing teachers.

    Also, most can no longer get a good paying job with just a high school diploma. So Jr. College is at least necessary nowadays. You need at least 2 years of math to get into a Jr. College.

    I suggest you look into the National Educational Standards, precisely what California just adopted last Monday: http://www.corestandards.org/
    From the site: “The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college AND careers.”

  • Jim Mordecai

    Algebra Teacher:

    You don’t need 2 years of math to get into a California Jr. College according to this taken from the net:

    Transfer Admission Requirements
    It is a common practice for students to transfer from one community college to another. Students even transfer to community colleges from four-year colleges and universities.

    No matter what your situation is, the standards are the same for admission to any of California’s 110 community colleges. You will be admitted to the community college of your choice if you meet any of the following conditions:

    You are 18 years of age or older, with or without a high school diploma.
    You are a high school graduate.
    You have the equivalent of a high school diploma.
    If you meet any of the above conditions, then there is a community college program for you.

    Jim Mordecai

  • Nextset

    Anon & Algebra Teacher: It’s just great that there are college prep classes for those with the ability and desire for them. That’s not so many people in Oakland unified. Most of OUSD’s constituients cannot use those classes – ie most of the black boys for example. They need basic and vocational ed. If their needs were attended to your drop rate in that large demographic would not be 50% and higher.

    My point is that it is more important to provide basic needs for all than to merely have some college prep and turn the majority of the black students into the prisons and welfare rolls. Thus I believe OUSD should fund basic swimming (water safe requirement)/driver’s ed/school nurses, etc at the expense of a broader college prep program.

    I just don’t get they joy in having a few college students, while producing a mass of unemployables who are not water safe and have no driver’s license in CA.

    Not that I don’t value the few OUSD students who go directly to Stanford or Ivy League. They are just not worth what OUSD does to the majority of it’s students.

    It’s my opinion and mainly rhetoric. Perhaps OUSD’s left side of the Bell Curve are too far gone for basic training? Maybe we should openly short them for the benefit of the 4 year degree wanna-bes.

    Brave New World.

  • Nextset

    While we are on the subject of teaching math: Here’s an MSNBC article about changing puberty rates that claims that currently in the USA 23% of the 7 year old black girls have started puberty up from 15% in the 1997 study vs 10% and 5% of the white 7 year old girls in the same studies.

    The Black students have issues which greatly affect classroom performance – physical differences. We need to remember this when we are jacking up the high school graduation requirements and repeating all the nonsense about how everybody should be going to college.

    People are different. OUSD and the other urban school districts are here to do well by their students, not to drive them out of school at 9th grade.

    Brave New World. – and it’s a new thing that these onset of puberty ages are dropping.

  • Nextset
  • AlgebraTeacher

    Now this was exactly what I was saying. Every student is different for many different ways, but the state has mandated a set of standards everyone must learn, regardless of sex, race, ethnicity, whatever. HOW we teach those standards may be different for different districts and schools, but all students should learn what is necessary to be successful in life after high school. A high school education is a right in this country, not a privilege; this is what sets us apart in from many other countries.

    Telling students in OUSD they are incapable of learning such material is just setting them up for failure!

  • http://educationreport CJA

    Jees, you sure do know a lot for being new* Algebrateacher, I would put $$$ that you are TFA.

  • AlgebraTeacher

    No, I’m not TFA. I have been studying math for quite awhile, and have seen what happens when students don’t get the proper math background. I’m new to secondary education, but have been teaching at the college level for awhile.

  • Nextset

    Telling students the truth about themselves is not setting them up for failure. It’s the beginning of making the best of what you have to work with.

    If a student tests out to have no aptitude for higher math they should be shown the results, and informed when the test is being offered again. Everyone is good at something. The schools should be assisting the students in learning where their skill lie. Part of doing that is flunking them out when they turn in failing work in a class that doesn’t suit them.

    A good school will not pass a flunking student or cover up failure. People learn from failure and they need to learn fast. Either change behavior (study/get help) or change classes.

  • Katy Murphy

    In case you were wondering, one of the U.S. teams won second place in the tournament (out of 48 teams)! From the news release:

    U.S. GIRLS TEAMS SCORE GOLD, SILVER AND BRONZE MEDALS AT CHINA GIRLS MATH OLYMPIAD Second place overall for team of American high school girls at international math competition

    BERKELEY, California – The Mathematical Sciences Research Institute (MSRI) announced today that one of the two U.S. teams that competed this week at the 9th annual China Girls Mathematical Olympiad (CGMO) has placed second, behind a team from China, in the overall standings among 48 teams of girls from about ten countries throughout the world. Of the eight high school girls on the two U.S. teams, seven students won top honors–five gold medals, one silver medal and one bronze medal–and one student earned an honorable mention at the international competition held in Shijiazhuang, the capital of Hebei Provence, China.

    Gold medals were awarded to Shiyu (Jing-Jing) Li from Sunnyvale, CA, a graduate of Cupertino High School, who will enter the University of California, Berkeley this fall; Jae Eui Shin, a senior at Phillips Andover Academy in Massachusetts; Elizabeth Synge from Lexington, MA, a senior at Boston University Academy; Lynnelle Ye, who recently graduated from Palo Alto High School and will attend Stanford University; and Shijie Joy Zheng from Bellevue, Washington, a senior at Phillips Exeter Academy in New Hampshire. A silver medal was won by Cynthia Day from San Jose, CA, a junior at Lynbrook High School; a bronze medal was awarded to Adisa Kruayatidee from Stevenson Ranch, CA, who is a senior at Phillips Exeter Academy; and an honorable mention acknowledged Andi Wang from Stoneham, MA, a recent graduate of Choate Rosemary Hall in Connecticut, who will attend MIT this fall. The team that ranked second overall consisted of Jae Eui Shin, Elizabeth Synge, Lynnelle Ye, and Shijie Joy Zheng.