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"The Math Myth and Other STEM Delusions"

  1. Feb 29, 2016 #1

    Andy Resnick

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    Last edited: Mar 1, 2016
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  3. Feb 29, 2016 #2
    Hacker brings up the issue that has been or is being debated still. In our hurry to increase the number of scientists and engineer back in the sixties our educational system left behind the majority of citizens who only need the fundamentals of numeracy. Hacker has contriubted to the NY time in the past with this article "Is Algebra Necessary"

    In an article by Don Byrd, he discusses one of the early articles on the problems of teaching math by Paul Lockhart "A Mathematician's Lament " musing in part on what if we taught music like we teach math. It would be unthinkable.

    Bryd singles out two problems, over use of abstraction i.e., use of symbols, and poor environment for student engagement i.e. not creating an environment that stimulates students curiosity and interest.


    Keith Devlin further https://www.maa.org/external_archive/devlin/devlin_03_08.html [Broken] using it as a springboard for his https://www.maa.org/external_archive/devlin/devlin_07_11.html [Broken] , adapting Lockart's use of the proper teaching of music as a paradigm for math.

    So when will educators get the message that we cannot all be mathematicians?
     
    Last edited by a moderator: May 7, 2017
  4. Mar 1, 2016 #3

    Astronuc

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    I had an interest in math and science, and I found algebra, geometry, trigonometry, analytical geometry and calculus fairly easy. However, the majority of students in high school weren't particularly interested in those subjects. In high school, I expected to go to university and do math and physics, which is pretty much what I did, but then migrated to nuclear engineering, which is more or less applied nuclear physics. So for me, STEM was absolutely necessary.

    There were programs for kids who could only manage basic math, like consumer mathematics and some simple algebra.

    If numeracy is a problem, perhaps there are problems with the way math is taught and/or a lack of support at home.
     
  5. Mar 1, 2016 #4
    Did you have a support system in regards to math?
     
  6. Mar 1, 2016 #5

    Astronuc

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    My parents gave me a lot of encouragement, but more in terms of getting me into summer programs (during summers between 7, 8, 9, 10 grades) at a local university, which did have math and science courses, an the summer program got me access to the university library. My parents bought an encyclopedia, which had a lot of natural history and historical information, which included articles on topics in chemistry, physics, and other subjects, including biographies of mathematicians, scientists and political figures. My parents bought my brother and me a chemistry set, and my folks bought me one of those 100-in-1 electronic kits.

    Besides the university library, my dad took me to the city public library and another university library, but also to a technical book store where I was able to buy textbooks on analytical geometry and calculus, basically so I could teach myself some calculus. I did a lot of self study, and by grade 11, I was beyond my parents in mathematics.

    The second high school I attended had a really good program in math. My 11th grade (algebra, trigonometry, analytical geometry) teacher worked closely with my 12th grade (calculus) teacher, and they worked closely with the chemistry teacher who had an MS in chemistry. The three of them prepared major works (MW)/honors and AP courses for 30 to 40 students, who were planning to go to the top universities in the country. We had numerous students going to Harvard, Yale, Princeton, MIT, Caltech, Stanford, Cornell, . . . , but some stayed in state and went to UT or TAMU.
     
  7. Mar 2, 2016 #6

    Andy Resnick

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    I think there's increased interest in reviving this type of program, in Ohio they are calling it 'financial literacy'. I envision the content in this type of program to be more than just arithmetic and algebra drills, but also include some statistics. In crude terms, the idea is to teach rational consumerism.
     
  8. Mar 2, 2016 #7
    Those programs have its merits but I feel there is some danger involved.
    The big problem is students that are not interested in maths in the least.
    Some classes will consist of students so uninterested it will be next to impossible to captivate and motivate students to do well.

    A lot of those students will remain uninterested whatever efforts we do, helping them understand the maths necessary to allow people to spend rationally or do some quick calculations like finding the amount of carpet needed.

    A final remark is the fact that all students seem to benefit from at least a few stronger students in the group (stronger as in faster, more inquisitive and more enthousiast). Unfortunately I only found a reference in a dutch book.

    tl;dr
    Introducing such a program needs a lot of consideration in advance.
     
  9. Mar 2, 2016 #8

    Astronuc

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    There was/is a similar program in the high school my son attended. I think it was termed 'consumer math' or something like that.
     
  10. Mar 2, 2016 #9
    My primary and secondary education ( '47 - '59) of course was exactly this scenario. I think it did spur especially the average student (me at the time) to exert more effort. In my schools and at this time I suppose most where graded on a straight scale. You know what you had to do to get an A. You knew who the good students were. So yes I think there is a benefit for a heterogeneous group. Did it affect all students in the same way I cannot say. Did it to paraphrase Goethe -make a man better because you took him as he should be not as he is?

    A common critique of the type of class is that the less able students hold up the class and bore the more able students. But this criticism begs the question "Is the course overly sensitive to the needs of the less able students"? Could the course especially an elementary one be structured so as to remain significantly challenging to the able students without demoralizing the less able. Certainly at some point one must create separate pathway according to ability and/or interests. That brings up the question of when should this occur.
     
  11. Mar 2, 2016 #10
    I am unsure what is taught currently here in New Jersey, for instance, but 'financial education' would be an extremely valuable lesson for most....issues such as compound interest when saving, economic growth and GDP, stocks, bonds, borrowing costs of credit cards, incorporating businesses to limit liability, wills, unemployment insurance, Roth versus traditional IRA's, defined contribution versus defined benefit plans, leasing versus buying, financial security, retirement saving, health savings plans, life,disability and liability insurance, effects of government debt and deficits and borrowing, strong versus weak currency, diversification of investments, risk/reward, etc.
     
  12. Mar 2, 2016 #11
    Yes, consumer math or financial math is useful to the more mathematically inclined too. Certainly not from the mechanics of the math but certainly from the context that are relevant to applications. Sometimes one has to pull facts out the the provided statistics or numbers i.e., do some math, to get a handle on their significance.
     
  13. Mar 3, 2016 #12

    Astronuc

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    Mine was in the 60's.

    Reflecting on the earliest years, my first and second grade classrooms had cuisenaire rods.
    https://en.wikipedia.org/wiki/Cuisenaire_rods

    They were very practical with respect to learning the relationship of numbers, e.g., 5 x 2 (or 2+2+2+2+2) = 2 x 5 (or 5+5) = 10. One could understand addition and subtraction. I don't know if is sank into my classmates as readily.

    In second and third grade, I had a classmate with whom I competed. On rainy days, when we had indoor recess, he and I used to write numbers (1, 2, 3, . . . .) on a personal chalk board to see who could achieve the highest number during the recess period. He always got to higher numbers. It was also good way to start to see relationships between numbers, e.g., multiples of 2, 3, 4, 5, . . . I think we just naturally discovered patterns. I don't think our other classmates were invested in such activities. By the time I got to number lines, counting and natural numbers, reals numbers and so on, I had a pretty easy time with understanding numbers, i.e., arithmetic was pretty easy, whereas many classmates struggled at various levels.
     
  14. Mar 3, 2016 #13
    There seems to be some connection between having some visual representation of numbers and learning their relationships.. What about the Abacus as a teaching aid?
     
  15. Mar 3, 2016 #14

    Andy Resnick

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    One of the 'new' ideas is called 'competency-based instruction'. In this model, students progress at their own pace, determined by passing exams. This is fairly easy to implement on computer-based instruction (math, spelling, etc). My dystopian view is that it helps train students to be mindless cubicle-dwellers, interacting only with computer programs.
     
  16. Mar 3, 2016 #15

    bcrowell

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    [A moderator deleted almost all of this post, so that what remained was not an accurate indication of my thoughts. Therefore I've deleted the small amount of remaining content.]
     
    Last edited: Mar 5, 2016
  17. Mar 4, 2016 #16

    billy_joule

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    Well hopefully there's some middle ground as the traditional one size fits all approach has been clearly failing. I find the modern classroom to be much less cube-farm-like, there's a lot more active participation, collaboration and group work while still being assessed individually, back in my day it was sit down shut up and do your sums! And everyone took the same tests. My 'day' was the 90's - 00's so pretty recent, I'm comparing changes in the school I attended that my daughter now attends.

    I don't think anything I learnt though high school and university math made me a more well informed voter (bar a small amount of statistics).
    What did hurt my political viewpoint was not taking a single humanities or social science class since I was 14 (as is fairly normal for engineers in my country). Taking only math & science classes gave very little insight into how the 'real' world works.
     
  18. Mar 4, 2016 #17
    Do you have kids? Kid make bad choices and not wanting an education is one of them. You can't dump them on the street where they will make many more bad choices. There is a reason that education is compulsory and its not to just to babysit them. You want as many functional and educated adults as possible. All cultures have rites of passage to prepare kids for adulthood and in civilized society schooling is one of them.

     
    Last edited by a moderator: Mar 4, 2016
  19. Mar 4, 2016 #18

    Astronuc

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    That would be taking it to the extreme.
    Yes, children, young adults, and even some adults, make bad choices. However, the sooner someone reaches an individual, the sooner hopefully the individual will learn to make better choices.

    I think it is necessary to make arithmetic/mathematics, science, humanities relevant, and it seems for many, it is not.

    Perhaps I was fortunate, because I knew, probably from first grade, that my education was relevant, and that I could some day be one of those adults who practiced math and science. I have encountered so many in the past, and I encounter so many as a professional, who struggle in this world.
     
  20. Mar 5, 2016 #19

    Fervent Freyja

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    I imagine that the No Child Left Behind Act of 2001 has had much to do with many issues of this sort. I was around 12 when this was implemented into the school system, standards were lowered in order to meet progress reporting but there was no longer much support for children that loved to learn. They become an additional "problem" for the teachers and were suddenly pulled from accelerated/gifted programs.
     
  21. Mar 5, 2016 #20
    On the one hand, I agree that not every student needs or wants to be a mathematician. On the other hand, students often don't know what they want or need at this age and a lot will opt for "consumer math" as an easier path through school just because they get indoctrinated into thinking math is "hard" or "geeky". The proposal to reduce the math taught strikes me as elitist. I'd rather see math instruction that makes the problems relevant -- why do you need algebraic skills? Because there are practical applications in adapting recipes when you're cooking (or brewing), hunting, fixing your car, hiking in the woods, etc.
    The big problem I see isn't that schools teach math, it's the way some of them teach it. Most of the problems I've seen circulating as "Common Core" are just asinine (of course, the problems sets people object to are the ones most likely to be circulated) and I have to wonder about the practical experience of the people who generated them. I know I am more "math-friendly" than most as a working engineer but I have also worked with teenage boys for nearly 30 years and have always endeavored to make any skills I teach both relevant and interesting. I haven't seen how my nephews are taught but some of the homework problems I've looked at are just abominable.
     
  22. Mar 5, 2016 #21
    We had the perfect system when I was at school. General math for every day life, advanced math...for obvious and ordinary math for students that didn't care or had trouble.

    Seniors earned credit points for tutoring juniors.

    Every kid could achieve at one or more of these classes. Students could freely go up or down across the three subjects.

    Teachers were happy students were happy and parents were happy.

    Education academics destroyed this proven system for their ideologies by assuming all children can be scientists and engineers.
     
  23. Mar 5, 2016 #22

    bcrowell

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    Since my #15 was phrased in a way that seems to have bothered a moderator, I'll try again in less colorful language.

    There is a broad consensus in the US that education is a public good. I'm using "public good" in the nontechnical sense: that education is widely believed to help society in general. There are several completely different ways in which education can be a public good:

    (1) Education increases wealth, and this effect is not just limited to the individual who gets the education. Wealth produces more wealth, and that wealth ripples outward through society so that we all become richer.

    (2) Education may enhance social mobility (although I think it's actually very poor at doing that in practice in the US today). Social mobility is arguably a public good because our society is constructed in such a way that it gets its stability by giving lots of people economic hope (so they don't become revolutionaries), rather than getting its stability by having a rigid class system.

    (3) Democracy without education is destined to fail. In #15 I gave an example that I'm sure any American right now can guess, but there are plenty of other examples in other times and places. For example, Egypt is a failed democracy, and Egypt also ranks very low in the quality of its educational system.

    Andrew Hacker's opinion piece cites poor numeracy in the US, and says that "We should be doing better," but he doesn't explicitly say why he thinks it's important that we do better. Should we do better because of compassion for individuals? Because numeracy is a public good? The only hint is that the study he cites was done by the Organization for Economic Cooperation and Development. This suggests that he thinks numeracy is a public good, and that the reason is #1 above.

    The trouble here is that if we don't think about his unexamined assumptions, we may be led to the wrong conclusions. He advocates teaching "an undergraduate class I call Numeracy 101, for which the only prerequisite is middle school arithmetic." He claims positive results. Are these positive results a public good? I suspect not. If we consider the three reasons above why education is a public good, I suspect that in each case, his plan would be the opposite of a public good -- a "public ill."

    Education increases wealth. Math education certainly increases your wealth if you're an engineering major. But what evidence is there that the much narrower goal of numeracy would increase people's wealth? It seems unlikely to me. A huge chunk of the US population is innumerate, and they're not all unemployed.

    Education may enhance social mobility. I haven't seen any evidence that numeracy enhances social mobility. Hacker is educating non-STEM majors. Is there really a difference in social mobility between numerate people who have a degree in history from Queens College and innumerate people who have the same degree from the same school? That would be very surprising.

    Democracy without education is destined to fail. A country like Egypt might not have become a failed democracy if there had been better education. Italy might not have brought Mussolini to power if more Italians had been educated. (I would take up the case of my own country at the present time, but discussion of that seems to be prohibited.) But what evidence is there that more numerate Egyptians or Italians would have preserved their democracies? It seems much more likely to me that there is something about the experience of college that immunizes people against authoritarianism. US college students meet people who are Muslims. They meet people who are immigrants. They discuss a wide range of topics, and their professors require them to carry out that discussion using facts and logic. There are multicultural education requirements, history requirements, and so on. It seems far more likely to me that these general features of the college experience are what provide the social good -- not anything as specific as numeracy.

    People might say, but what's wrong with promoting numeracy? It's clearly desirable.

    I think the opposite may be true. Numeracy education may be a public ill. Hacker doesn't propose supplementing math education with additional courses to promote numeracy. He proposes replacing challenging coursework in high school and college with a second, easier track in which the sole goal is numeracy. The problem with this is that it's likely to work against the public-good goals of wealth and social mobility. For example, if you go to an inner-city school, the only math AP course may be AP Numeracy. They won't offer AP Statistics (which Hacker depicts as if it's some kind of cruel and unusual punishment).

    This appears to be exactly what Hacker is proposing: a return to what was known in the 60s as "tracking." The trouble is that tracking can very easily contribute to educational inequality. The brown kids get put in Math for Daily Life, while the white kids take calculus. This is why tracking lost favor in the 70s. There's probably an argument to be made for more tracking, but you can't just ignore its potential to cause inequality.
     
    Last edited: Mar 5, 2016
  24. Mar 5, 2016 #23
    May I challenge your assertions, paraphrased, that education increases wealth and democracy.

    As brutal as it sounds an uneducated slave work force has historically supported more wealth; refer any historical regime eg British empire.

    I would argue the Asian tigers have increased wealth initially by having a work force with no rights or education to be exploited by western democracies.

    Just saying.
     
  25. Mar 5, 2016 #24

    bcrowell

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    About education and wealth, you could conceivably be right, although I don't think it's that easy to extract lessons from history. There are too many uncontrolled variables. For example, there have been various debates about US history and whether the slave-labor system in the antebellum South was actually economically better than free labor would have been. These debates are always going to be inconclusive, because we can't do a controlled experiment and compare with a system that was identical except for the labor system. (The North had a completely different type of economy.) The debate is also going to be inconclusive because the result depends on what you use as a measure of wealth. If you use GDP, you could get a certain answer, but that answer would ignore the fact that a big segment of the population (the slaves) had nothing. BTW, slavery is not the opposite of education. There were many educated slaves in the ancient world. In the antebellum US, during the early period of slavery, it was not uncommon for slaves to be educated, sometimes very well educated. That didn't changed until the end of the slavery period, when it became illegal to educate slaves.

    About education and democracy, I would be interested to know if you could come up with a counterexample. That is, has there ever been a country with (a) a healthy, sustainable democracy; (b) widespread lack of education, and (c) universal suffrage? In the examples I know where a and b both apply, they were a long time ago, and c didn't apply. E.g., in the early US, suffrage was reserved for white male property owners.

    Note that my argument about Hacker's proposal doesn't actually depend on the truth or falsehood of the belief that education is a social good in general. I'm simply arguing that even if it is, there is no reason to believe that numeracy is a social good.
     
    Last edited: Mar 5, 2016
  26. Mar 5, 2016 #25
    I have no basis for my claims in terms of studies.

    I do note anecdotally that from a teacher that taught in China for years streaming kids heavily has made great gains.

    The low ability kids are identified and redirected rather brutally for productive but menial futures to contribute to the economy while the flashy whiz kids get redirected and stupid levels if resources thrown at them.

    In the west streaming is generally considered the greatest evil in education due to alleged impacts on self esteem.

    I think the assumptions on streaming kids needs to be put on an objective basis and less ideological.
     
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