Math guru critical of county's math curriculum

Discussion in 'General Math' started by Dom, Jul 8, 2007.

  1. Dom

    Dom Guest

    http://www.gazette.net/stories/070407/prinsch174932_32360.shtml

    Wednesday, July 4, 2007

    Math guru critical of county's math curriculum

    Board of Eduction member also concerned about math lessons

    by Dennis Carter | Staff Writer

    The question was straightforward: What is 9x8?

    Prince George's school board member Pat Fletcher (Dist. 3) of Landover
    posed the question to a group of middle school students last spring.
    Six of about 25 students could answer the question right away,
    Fletcher said.

    Troubled by the response, Fletcher mentioned the incident at a meeting
    with a longtime University of Maryland math professor and the Prince
    George's school board. Both parties were shocked to hear a math
    coordinator at the meeting say that county students should have a
    "sense" of what 9x8 is, according to a document released at the June
    26 state school board meeting.

    Jerome Dancis, a university math professor for more than 30 years
    until retiring in 2005, and a critic of the state's math curriculum,
    met with county math coordinators and schools officials in April to
    discuss math improvement.

    "A math coordinator said that not all students can memorize the
    multiplication tables, implying that since some cannot, none should be
    required to do it," Dancis wrote in a critical review.

    Dancis did not save his critiques for Prince George's - he criticized
    the state's algebra exam, which allows students to use calculators. He
    said that policy would be a setback for students when they reach
    college.

    "Again, this is a very good strategy if the goal is just to have
    students pass the [state's algebra test]," Dancis wrote. "This is a
    counterproductive strategy if a goal is to have students avoid
    remedial [math courses] when they enter college."

    Using calculators on algebra exams, he said, "allows students'
    arithmetic skills to get rusty" and "covers up students' lack of
    fluency in arithmetic."

    Prince George's saw improvements in Maryland School Assessments (MSA)
    math scores this year. While middle school math scores remain well
    below the state average, the overall math proficiency score shot up to
    60 percent, up 7 percentage points from 2006 and 12 percent from 2005.
    In the 2006 High School Assessments (HSA), which Maryland high school
    seniors will be required to pass by 2009 in order to obtain a diploma,
    46.2 percent of county students passed the exam's algebra portion.
    Forty-two percent of African-American students passed the algebra HSA
    exam in Prince George's. This year's results are expected to be
    released in mid-August.

    Dancis, a Greenbelt resident for more than 30 years, said his concerns
    about the county's math lessons were spurred by his children's time in
    the school system. All three of his children graduated from Prince
    George's schools.

    In his memo released to the state board last month, Dancis said even
    the upper echelon of Prince George's math students would struggle when
    they enter college. Among the county's most advanced math students,
    Dancis wrote, 44 percent took remedial math classes when they enrolled
    in a Maryland college or university in 2004. Dancis found that 53
    percent of advanced African-American math students needed remedial
    college math.

    "The county has a problem," Dancis said in an interview with The
    Gazette. "A massive number of their better graduates need to take
    remedial math in college."

    Fletcher said she expected more students to be able to answer her math
    question because of her experience with multiplication tables as a
    student.

    "I couldn't understand that coming from the old school of times
    tables," she said. "It's something we should improve on."

    E-mail Dennis Carter at .
     
    Dom, Jul 8, 2007
    #1
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  2. That's the rules. Unless a kid is special ed and has exceptions
    documented in an IEP, all kids MUST be held to the same standards.
    One can *encourage* kids to go beyond the minimum, but not require it.

    You know "equal protection under the law". That means that everyone
    gets judged by the same standards, or some will sue ... and win.
    When did the legislature make that a goal?

    "We the people" through our elected representatives have said that the
    primary goal of students is to enable them to pass state standards
    test. All else is secondary, and most is optional. Got a problem
    with this? Then convince "we the people" to want something else.

    Good luck.

    lojbab
     
    Bob LeChevalier, Jul 8, 2007
    #2
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  3. Dom

    Rowley Guest

    I give up - what's the answer..... just kidding = 72 (3x8=24 24x3=72,
    least that's how I did it in my head just now).
    How many of them "knew" the answer and just thought it was a dumb
    question to ask and didn't answer?
    Why was this math professor meeting with the school board?
    My guess is most of the students did and just didn't answer or just
    didn't care enough to actually attempt to solve the problem. Ask the
    same group the same question, but this time tell them that a correct
    answer would get them movie tickets or something - then see how many of
    them could come up with the correct answer.

    I just don't understand why some people can't accept or recognize the
    fact that with some kids you need to provide motivation for them to take
    an active part in education.
    Why? does he seriously think he can fix something and make it work better?

    Have him spend a couple years actually teaching in a regular public school.
    Is memorization the way to go? I never really got into memorizing the
    multiplication tables - and instead just liked to work the problems out
    in my head.
    How many of those twenty-five middle schoolers are going to eventually
    end up going to college? And how many of them that do are going to have
    problems with math?

    Just how serious is this "problem"? How many students entering college
    this year are having to take an remedial math class? 100%, somewhere
    between 100% and 50%? or less than 50%? It would be nice to see some
    actual numbers and not just base any action on the advice of one
    concerned retiree.
    Despite the fact that public schools constantly tell their students,
    "You need to go to college...." - it is not really mandatory that they
    do (go to college). The goal of the state standardize testing is to see
    what students have learned in public school - not to be a college
    entrance exam.

    What about these hs student's Advanced Placement test scores - what were
    those like? How many of these students took the AP test? Just curious.

    Why is such a bad thing that some students might have to take some
    remedial class their first year of college. Is it a stigma thing where
    the other college students are making fun of these students?
    But the students like using them instead of doing the work long hand.
    Wonder why he waited till after the kids graduated to complain.
    Less than 50% in one group and just slightly above for AA students -
    where did he dig up these statistics? How many of the students coming in
    from other school districts needed to take the remedial math classes? Or
    the out-of-state students?

    And am I reading this right - these are all "the county's most advanced
    math students"? someone is saying that 50% of the most advanced math
    students in the country are having to take remedial classes.

    Again, I'm wondering how many of these kids that are needing these
    remedial math classes took and passed the Advanced Placement test. I
    know we had a lot of students taking these tests here this year (more so
    than any previous year - or so I heard) and we're just a rural school
    district.

    http://www.collegeboard.com/student/testing/ap/subjects.html
    Their better graduates..... yeah, I say there is a problem.
    And when exactly was that? 40+ years ago. Times change, people's
    perspective change. I seriously doubt that Ms. Fletcher really remembers
    what it was like to be a kid at that age and asked a question like she
    asked. My guess is she might have been one of the few that threw her
    hand up and answered - but the rest of her peers would have stayed
    silent too.
    The results would be the same.

    Martin
     
    Rowley, Jul 9, 2007
    #3
  4. It would also be nice to know how they define "remedial math". In the
    old days when most kids took *no more than* 1st year algebra, math
    expectations in college were probably somewhat lower than they are
    now. Comparing a first year college math textbook from 1940 with one
    from the present would undoubtedly be an eye opener.
    I suspect that the definition of "remedial classes" is politically
    convenient.

    A math professor might even consider someone who passed AP calculus
    but who has to retake calculus in college as taking "remedial
    classes".

    More realistically, a kid who has taken a precalculus class in high
    school, but who then has to take some preparatory class before taking
    calculus is a mite bit different from a kid who has to take the
    non-credit "bonehead math" that would allow him to take a college
    level algebra class.

    Back in the day, of course, they didn't use math placement tests in
    most schools. If a kid had passed algebra in high school, he was
    presumed to not need algebra in college. The only placement test I
    took on entering college was in foreign language, and that was
    optional.

    lojbab
     
    Bob LeChevalier, Jul 9, 2007
    #4
  5. The question itself also reveals ignorance on the part of the poser.

    The question should not be: "What is 9x8?".

    A *properly posed* mathematical question would ask:

    If the domain is the real numbers, what real number [or integer]
    *equals* 9x8?

    Valid answers to the original question might include

    "9x8 is an integer"
    "9x8 is the product of two integers"
    "9x8 is a real number".
    "2, if the domain is Z/7Z"
    etc.

    If the poser, hearing one of these latter responses, then says "Yes,
    but
    which number?", one might say "that was not the question asked".
    One needs *specificity*, and this was lacking in the original
    question.
    Part of posing a problem should be stating the DOMAIN in which the
    problem arises.

    Yes, I am being pedantic. But part of learning mathematics needs to
    include learning how to pose unambiguous questions. Half of solving a
    problem in math is posing the right question. Math is a language in
    which
    it is possible to state *precisely* what is intended. But this aspect
    of
    math is hardly ever taught in our schools because the teachers
    themselves
    only have a "hand waving" understanding of what they are doing.
     
    Pubkeybreaker, Jul 9, 2007
    #5

  6. Yes!! But a major part of the problem with today's education is that
    they
    *SHOULD* care. The fact that they don't can be blamed mostly on
    parents.
    (although lousy teachers contribute as well)

    Parents should be responsible for motivating in their children the
    idea that
    education is important, and that much of their success in life (or
    lack thereof)
    will derive from their education. But too many parents are failing in
    this duty.
     
    Pubkeybreaker, Jul 9, 2007
    #6
  7. Dom

    Rowley Guest

    They should also do a lot of things - but they (most) don't.
    I think that our society in general contributes to this attitude. Heck,
    if it wasn't for the fact that someone is giving me a paycheck (which I
    need) - there are days when I would probably stay home instead of going
    to work.
    Keep in mind that there are parents who "success" (working a steady job
    at Wal-mart) in life doesn't come from needing all that great of an
    education.

    And you also have examples of people who are HUGE successes despite the
    fact that they don't have an education. It's not too hard for students
    to see that what baseball player for instance earns and what a teacher
    earns is very dissimilar, even though the teacher probably has a better
    education than the ball player.

    Martin
     
    Rowley, Jul 9, 2007
    #7

  8. YES!!! But the number of such examples is TINY compared to the vast
    majority of people who are uneducated. What we have is yet another
    example
    of innumeracy: drawing a false conclusion (i.e. I can probably make
    big bucks
    even though I lack an education) based on a small sample. The truth
    is that
    the "probability" here is very small. Most people lack the education
    to realize this!

    The result is that people base their expectations on wishful
    thinking. Curing them
    of wishful thinking also requires... you guessed
    it!............... education.
     
    Pubkeybreaker, Jul 9, 2007
    #8
  9. Dom

    Rowley Guest

    Yes - most educated and mature people do realize this - problem is, kids
    don't tend to fit that description. Doesn't matter to them (kids) that
    the number is extremely small - most of them feel that if it could
    happen to just one person then there is a chance that it could happen to
    me. Now that I think about it, the same is pretty much true for the
    people that play the lottery. I could be that 1 in a 55,000,000+ person
    to get that one wining ticket...... and of course there sometimes is
    that one person.
    Hmm, I think it takes more than just education - I think it also takes
    some experience - some hitting the proverbial brick wall a few times.

    Martin
     
    Rowley, Jul 9, 2007
    #9
  10. Why? Because some oddball professor was visiting and asking a
    question? What's in it for them? (That being the question that we've
    taught the younger generation is solely important - by example.)
    That isn't the issue. The issue is showing interest enough in a silly
    question asked by a strange adult in order to offer to answer it.

    A teacher will ask a question in class about just-covered material.
    No one raises their hand. Is it because they don't know the answer,
    or is it because they don't value education? No, it is because there
    is no virtue with peers in raising your hand and volunteering. They
    risk being wrong and looking stupid, and they risk getting thought of
    as a kiss-up if they are right.

    lojbab
     
    Bob LeChevalier, Jul 10, 2007
    #10
  11. Dom

    Barb Knox Guest

    "Properly posing" an unambiguous question is even trickier than you
    think. Consider "What integer equals 9x8?"

    Some legal but unwanted answers are:
    "Three score and twelve"
    "Eight zero base nine"
    "LXXII"

    Tightening the question to "What base-ten integer equals 9x8?" still
    allows the unwanted:
    "Zwei und Siebsig"

    We certainly do not want to have to say something as cumbersome as "What
    base-ten integer, expressed as a sequence of digits without leading
    zeroes, equals 9x8? (And even this relies on the implicit convention
    that the sequence is "big endian".)

    Which as shown above is very tricky. A lot of what passes for explicit
    non-ambiguity actually relies on implicit conventions, such as what the
    "simplest form" is.
    --
    ---------------------------
    | BBB b \ Barbara at LivingHistory stop co stop uk
    | B B aa rrr b |
    | BBB a a r bbb | Quidquid latine dictum sit,
    | B B a a r b b | altum viditur.
    | BBB aa a r bbb |
    -----------------------------
     
    Barb Knox, Jul 12, 2007
    #11
  12. Dom

    ghughes Guest

    A high school boy with whom I was speaking just this week knew the
    value of 72; unfortunately, I had just asked him for the product of 7
    times 8. I say: VIVA THE OLD MULTIPLICATION TABLE!!

    Regards,

    Grover Hughes retired engineer, Sandia National Laboratories
     
    ghughes, Jul 12, 2007
    #12
  13. Dom

    toto Guest

    I wonder what the *average* baseball player makes compared to the
    *average* teacher though. Most baseball players are not in the major
    leagues. My understanding is that minor league players make
    somewhere around $14,000 per year with some kind of meal allowance
    added to that. They might make a bit more after they complete their
    first season, but it isn't likely to be anywhere near the major league
    salaries.

    There are a total of 30 (?) major league teams. Lets say each team
    has a total of 40 players (there are less actually, I think). That
    means there are a total 1200 major league players who make those big
    salaries. How many teachers are there in the US? There are many,
    many more than 1200 teachers. In fact, there were over 1200 teachers
    in my town of 80,000 people.

    I know, kids won't do this analysis, but you would think that their
    parents might.

    --
    Dorothy

    There is no sound, no cry in all the world
    that can be heard unless someone listens ..

    The Outer Limits
     
    toto, Jul 14, 2007
    #13
  14. Dom

    Rowley Guest

    The point I was trying to make - is that there are examples out there -
    and students don't tend to focus on the fact that there is a small ratio
    of these kind of "successes" compared to the mundane ones.

    Parents are what they are.

    Martin
     
    Rowley, Jul 14, 2007
    #14
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