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Michael Froemmcke


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What does the average citizen need maths for?

I had a conventional education. In school and later at other educational institutions I was always just mediocre - but I became excellent at this - and as the years went buy I asked myself why the educational systems around the world seem to be promoting the same subjects.


Topics: curriculum

Closing Statement from Michael Froemmcke

I can understand that people, especially those who spent long years learning maths, are very passionate about the subject. Yet I am still not convinced that the actual outcome justifies the effort and, in some cases, pain associated with this subject. There seems to be widespread reluctance to even contemplate any alternatives, which reinforces my suspicion that most people are indoctrinated in believing that there is no good education without maths. I think the understanding of certain principles is far more important than an intricate knowledge of mathematics.... But this is just my opinion. Thanks to all the participants in this minor debate.

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    Jan 22 2013: Here is a link that might help: http://mathforum.org/dr.math/faq/faq.why.math.html

    One more thing also. Those trying to sell products or points of view often take advantage of people's innumeracy and insecurity about math or science to mislead them. They know that most people "check out" once mathematics is used in argument (or once someone says something about (supposed) recent findings in neuroscience or quantum physics).

    The default for people without the background to understand what is being presented tends to go in one of two ways that I have noticed. One is just to assume that anyone who talks about math (or neuroscience or quantum physics) is probably smart or at least knows what he is talking about. Maybe he knows, but maybe he actually doesn't, but without any background you can't tell.

    The other default is the anti-intellectual one of assuming that those who are experts in these areas must be frauds (the reasons vary for why this must be so).

    If you know enough math actually to review arguments critically that involve math or enough science to review arguments critically that involve that, you won't be tempted to adopt one of these default views.
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      Jan 22 2013: Good point! What is considered essential knowledge?
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        Jan 23 2013: There would be some dispute over this, in part because it isn't like there is a fence separating not enough from enough.

        It depends what you want to be able to understand.

        There would be good argument for a couple of years of algebra because real flexibility with the understanding of variables, parameters, and models is valuable in many settings and applications. Geometry is usually the easiest way to introduce the idea of deductive proof, which forever changes a students' thinking about whether a conclusion has actually been tightly defended. It can be done with number theory also, but geometry has its own additional value in understanding spatial problems.

        There is a lot of science one cannot understand without the concepts of calculus, though the calculations would not be as vital.

        John Allen Paulos, author of A Mathematician Reads the Newspaper, argues that inferential statistics is the most important part of literacy- that is, not the calculation of means and correlation but rather understanding what conclusions can be drawn legitimately from a sample or study design and what the threats are to what are called "internal validity," "external validity," and "construct validity." These are mostly logical issues and assessments that give a person who masters them lots of leverage.

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