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Teaching statistics before calculus?

  1. Jun 11, 2016 #1
    Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

     
  2. jcsd
  3. Jun 11, 2016 #2
    I absolutely would love if statistics was taught extensively to every student. In this day and age, where half the news stories out there involve some kind of statistic, it's simply necessary to have a population that understands statistics, sort of like Sagan's "living in an increasingly technological world where fewer people understand technology."

    Unfortunately, statistics isn't often taught well. Regardless, it's so important that people be taught when to recognize bad statistics or when it's clear statistics are being used to stretch the truth.
     
  4. Jun 11, 2016 #3
    The fundamental issue of mathematics teaching is not the order with which the content is taught but the content itself. By and large the content that is taught is the routine manipulation of ready made functions, regardless of whether it is algebra, geometry, trigonometry, calculus or statistics. The reason that this is the case is that this is the only mathematics which is politically acceptable from the standpoint of our high schools being transcript/diploma mills for entry into college, which is itself a gatekeeper to the corporate workplace. If deeper thought was taught and assessed it leads to outright rebellion on the part of the major stakeholders of the public k-12 enterprise, namely the students and parents. Before long, pressure is exerted on administrators who then transfer it to teachers.

    Consider this, our high school Algebra/Pre-calculus courses should be capped off with an extensive treatment of the theory of interest. It is fairly comprehensive in terms of utilizing the mechanics of Algebra and it is even more important to our everyday lives than statistics, so why is it given only the most superficial treatment? It is too difficult and requires a algebraic competency which is beyond the abilities of the vast majority of our students precisely for the reasons stated above.
     
  5. Jun 12, 2016 #4
    Finnish high school curriculum teaches probability and statistics in course, which is situated as a pre-calculus course.

    courses for higher math in high school
    1.functions and equations
    2. polynomial functions
    3, geometry
    4. analytic geometry
    5. vectors
    6. probability and statistics
    7. calculus I (mainly derivatives, limits)
    8. root- and logarithm functions
    9. trigonometric functions, and sequences and series
    10. integrals

    optional courses (advanced courses; if I recall correctly at least one is recommended such as: the eleventh or the twelfth or the thirteenth)
    11. number theory, and logic
    12. advanced numeric and algebraic methods
    13. calculus II (advanced calculus course)
    14. rehearsal course
     
  6. Jun 12, 2016 #5
    for the lesser advanced mathematics curriculum in high schools there is also probability and statistics being taught (as far as I know)

    1.) Finnish high schools have two math pipelines generally speaking. Regular and advanced mathematics. (unless you are , in a private high school, in which case the curriculum may differ, I think)

    2.) Or if you were homeschooled at high school... but homeschooling is more rare in Finland than USA. Kids are allowed to take the high school finals after home schooling, after all.

    3. Or if you already chose trade school instead of high school. Trade schools have different curriculum compared to highs schools I think.
     
  7. Jun 13, 2016 #6

    chiro

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    Teaching statistics properly requires quite some training and the only thing that can be taught is a very superficial view of statistics.

    If people are going to interpret statistics properly then they will need a lot more than a one or two semester course on it.
     
  8. Jun 13, 2016 #7

    Andy Resnick

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    I've heard of this before, and discussed it with my Math colleagues. There is merit to teaching more/better statistics in High School, no question.
     
  9. Jun 13, 2016 #8

    Quite so.

    Clearly a couple of semester courses in statistics does not make a person a statistician. But at some point as has been previously noted people today must have a basic knowledge of the concepts and methods of statistical analysis. They must appreciate the misuses of statistics , the error in interpretation of data, that correlation does not imply cause and effect and the down right use of statistics to mislead. It is not just about definitions , procedures and formulas. I do not think that a good elementary statistics course with the aim of adequately preparing a person to appreciate the value and danger of statistical inference can be taught by just any math teacher.
     
  10. Jun 13, 2016 #9

    Mark44

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    59.3% of all statistics are made up on the spot...:oldbiggrin:
     
  11. Jun 15, 2016 #10

    chiro

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    I see what you are saying gleem but the thing missing is context.

    One can't really have that context without going a bit further and when you have a superficial form of a logic then regardless of how good that logic is it will be interpreted superficially as well.

    Take correlation can be different from causation as an example.

    The thing of this has more to do with how much variation (and co-variation) exists between the processes and this involves more than just co-variance and correlation.

    If people learned this and then said "Well the rule says this so don't believe it" then you have people parroting something they don't understand and using it in ways they don't really comprehend and (which is worse of all) making inferences that they aren't really in a position to make.

    One of the worst things you can do for people is give them a superficial, non-comprehensive form of a logic and get them to think that it isn't superficial.

    It's a dangerous thing for people to think they know something when they don't and then apply it to the world around them because they will have not enough doubt and way too much confidence and make assertions and inferences that may be out of line for what should be done.

    For the above reason I'd rather people just admit they don't understand things as opposed to thinking they did because they took an introductory course and now suddenly they think they can make interpretations on logical systems that they themselves don't understand.

    This post is not just for statistics but for any logic and it's a really bad idea to get someone thinking they are an expert when they really aren't in a position to even decide whether they are or not. To really know something takes a lot of work - and that is something small. Encouraging people to think they are in a position to make decisions and comprehend a situation they can't is a dangerous and outright irresponsible thing to do and I certainly would not encourage that myself.
     
  12. Jun 15, 2016 #11

    mfb

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    Yeah, but how often does that happen if the topic is not directly politics but with political implications?
    Knowing that you don't know things needs some education as well. Also the knowledge that you can easily make up statistics that sound great until you look at the details.
     
  13. Jun 15, 2016 #12

    Andy Resnick

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    That sounds nice and neat but is completely untenable. People go through their day continuously making decisions based on incomplete information, and even more, people engage in many activities of which they are not an expert. Is it irresponsible of me to have a garden, since I am not a master gardener? Of course not.

    I suppose you would ban procreation.....
     
  14. Jun 15, 2016 #13

    chiro

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    I'm saying it has to be put in its proper context.

    One of the worst things you can do for someones intellect is to get them to believe something they aren't.

    Incomplete information always exists and that is a certainty - but that doesn't mean it's an excuse to just say superficial logic is ok.

    Politics is a screwed up system anyway and causes so many problems when it comes to decision making so that alone is already bad enough as it is.

    If you are gardener you don't want to apply pesticides and weed killer incorrectly since you might kill all of the healthy and wanted plants.

    Same thing with statistics - you don't want people taking their new found knowledge and making inferences that would destroy far more truth than it creates.
     
  15. Jun 18, 2016 #14

    Andy Resnick

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    Who am I to tell someone who they are or what they can (or can't) do?

    Edit- let me elaborate a bit more, because now we are getting to the actual rationale for formal education: evaluation of student efforts by experts. Indeed, I do tell my students what they can or can't do within the context of my class.

    Education should not have a 'value'. I realize this is contrary to societal trends during the past several decades, especially in higher education. Currently, a college degree is often treated as a commodity- something that is purchased by a customer, sold by the institution, and confers some sort of value- future job earnings, prestige, etc. When education is treated as a commodity- something that can be bought and sold and has value (monetary or otherwise)- institutions are transformed into service industries with all the concomitant negative associations- customer satisfaction requirements, administrative oversight of academic functions, accountability requirements, etc. Only by resisting the commodification of education can educators truly ensure that students have an opportunity to gain proficiency and master skills.

    On one hand, the goal of introducing basic statistics earlier in the math curriculum can be phrased in terms of 'educational commodity' by producing smarter consumers- consumers of *information*. But fundamentally, providing formal instruction of statistics at any level should be the same as any other formal education exercise- student efforts are evaluated by experts. One may be tempted to argue that (for example) a junior-high school teacher is not a sufficient expert to provide proper evaluation, but that's clearly a false argument since with few exceptions, no primary school educator has a PhD degree (or even a MS degree in something other than education).

    Educational curricula must be adaptable to accommodate changing needs. One current need is for the adult population to have appropriate intellectual tools to critically evaluate biased information- news feeds, press releases, etc. Schools are in a essential position to provide the necessary evaluations to *prevent* someone from growing up thinking they are more of an expert than they in fact are.
     
    Last edited: Jun 18, 2016
  16. Jun 18, 2016 #15
    Is this your view of education? Don't educate, because if you don't teach them enough to be experts, then you've done more harm than good?

    Guess I shouldn't have taken any literature classes, lest I fall into the trap of thinking I can have opinions on books without years more of training.

    The entire point is that in the modern world, people need to understand at least vaguely that not every statistic they read is the complete truth. They need to know the common techniques used to mislead people.
     
  17. Jun 18, 2016 #16

    chiro

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    My value is to get people to differentiate the limits that an education can provide.

    I'm all for education but when people take it out of context things can go very sour.

    Identifying context (which is the main point here) is far more important to having that context retained and it's often lacking in people's minds based on the effort it actually takes to clarify it.

    If you don't have that context you create people that think in a more absolute way and that contributes to poor logic, reasoning and inference.

    As educated people surely you must understand this.
     
  18. Jun 23, 2016 #17

    MarneMath

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    My only quam with this is that in my experience, most students end up taking a statistics course before they ever take a calculus course. I think the problem is that if you study STEM, then the inverse is true, so the professor has a view that that is the norm. I, on the other hand, know far more people who have taken Intro to stat methods or business stats or econometric stats, or some other name for stats before ever taking a calculus course (if they ever do take a calculus course).

    While I understand completely that there is a portion of students whose end goal is to take calculus in high school, I don't think that ends up being the majority of high school students. I could be wrong though.
     
  19. Jun 23, 2016 #18

    chiro

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    The calculus is definitely necessary for the calculation aspect but I think most people in this thread are debating the sort of conceptual offerings as opposed to doing the "nitty gritty" stuff you would need to make any sort of real thorough assessment.

    If you are wondering how you could do it without calculus you could just get lots of statistical tables and get the student to use them rather than do the calculations with the calculus techniques - and that is exactly what a lot of introductory statistics courses do.
     
  20. Jun 23, 2016 #19
    Today's SMBC reminded me of this thread
    1466693822-20160623.png
     
  21. Jun 23, 2016 #20
    That may explain why I am such a poor consumer. So are we all (physicists/mathematicians) poor consumers?
     
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