Fixing Our Math Education with Context

October 6, 2011 at 8:09 am 8 comments

Sounds pretty similar to the contextualized computing education that we’ve been arguing for with IPRE and Media Computation.  The argument being made here is another example of the tension between the cognitive (abstract conceptual learning) and the situative (integrating students into a community of practice).

A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein’s famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.

via How to Fix Our Math Education – NYTimes.com.

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8 Comments Add your own

  • 1. Alan Kay  |  October 6, 2011 at 9:12 am

    Hi Mark

    “Learning happens on the fringes of what we already know” David Ausubel.

    But then what?

    Rarely do we see discussed the benefits of learning “powerful ideas” that are not like our genetic heritage, that require lots of work, that produce not add-ons but qualitative *changes* in the way we think.

    Deep thinkers about communications systems such as Innis, Ong and McLuhan have written cogently about the transformational effects of becoming fluent in new ways to represent ideas. Things that are like writing have been particularly powerful precisely because of how they are detached from our built-ins.

    And let’s put aside that most algebra courses are taught in a ridiculous manner, and prepped worse in earlier grades.

    But let’s bring front and center the idea that getting fluent in dealing with the abstractions and operations and “making a math when needed” to represent ideas is a major reason to teach it. Another is to be the representation languages for science (which is the relationships between “what’s out there” and the representations we can devise to capture meaning).

    There’s no question that much of math and science co-evolved, but they were not discovered together (the “discoveries” were about 2000 years apart), and real science is quite different and more powerful and important than it seems the authors of the Times piece understand.

    Cheers,

    Alan

    Reply
  • 2. Garth  |  October 6, 2011 at 4:19 pm

    I can see major problems with pre-service teacher education. If a student is smart enough to understand finance, data and basic engineering I cannot really see them becoming a lowly underpaid math teacher.

    Reply
  • 3. Gail  |  October 6, 2011 at 5:20 pm

    I couldn’t help but think that the contexts suggested (especially finance) wouldn’t have interested me very much. Would that have turned me off of math? What do we do when the context doesn’t work for everyone? It seems like connecting CS to media would be at least somewhat interesting to everyone, but maybe that’s making too much of an assumption if I was turned off by all of these math context suggestions. Can’t possibly please everyone…hmm…

    Reply
    • 4. Barry  |  October 6, 2011 at 9:57 pm

      Any good curriculum ought to connect the concrete to the abstract and then make the abstract concrete. In other words, start with something the student knows and derive an abstract concept out of it. If the student learns it well enough, it will become concrete information which can be used for further connections.

      Good teachers ought to be able to do this. The trick is figuring out what piques a student’s interest. That’s not something easily encapsulated in a one-size-fits-all textbook.

      Reply
      • 5. Gail  |  October 7, 2011 at 8:51 am

        I agree with this. I got the impression that each course was going to fully focus on finance (or data, or whatever), but perhaps I misunderstood. Maybe they just wanted to offer one suggestion of how to ground the context in class.

        Reply
      • 6. Seth Chaiken  |  October 9, 2011 at 1:15 pm

        The “variables” in E=mc^2, and the “unknown variable” in an equation you want solved like 100=x^2 (for finding the length of the side of a say a square garden you want to lay out with area 100) are different mathematical concepts and these concepts are both very important. I agree that teaching how to solve equations for unknown variables purely in the abstract is a very bad thing to do, but, teachers ought to understand and teach, with interesting and applicable motivations, all of the important conceptual contents of mathematics, appropriately chosen and sequenced. Of course, examples of both these particular concepts from math are to be found in any choice of contexts like finance, gardening, multimedia computing and physics.

        Reply
  • 7. Martin Roberts  |  October 10, 2011 at 6:36 pm

    Hi Mark,

    I think that Alan Kay’s response is one aspect of math education reform that does not get enough attention. If have understood many of his other articles and talks, one side of the coin is “How do we make algebra more relevant and natural”, but the other equally important side of the coin is that “the fundamental aspect of algebra is that it is not an evolutionary aspect that would naturally evolve out of general thinking”.

    The ability to conceptualize, analyze and manipulate abstract concepts is a defining part of human civilization.

    Reply
  • [...] “passion” and includes “design projects for Freshmen.”  Sounds to me that contextualized computing education, which includes efforts like Media Computation and robotics, is the kind of thing they’re [...]

    Reply

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