Author Topic: Defamiliarization in Mathematics ?  (Read 715 times)

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Re: Defamiliarization in Mathematics ?
« Reply #15 on: November 15, 2017, 11:04:01 pm »
Thoughts inspired by my reading from The New Math: A Political History

Note about "the New Math" phenomenon of the 1960's which the Dolciani series was a reflection of:

When I promote these texts, I am not saying that the experiment was NOT a failure, but only pointing out that those texts are still valuable to anyone who desires a conceptual and structural understanding of the nature of mathematics.  After the decline of the movement, it was asserted that, for the general population, training in mechanical skills and memorization techniques was what was desired.  Hence, the movement known as "Back to Basics."

While I enjoy calculating, computing, and especially algebraic manipulation, the reason I am force-feeding myself the old "modern mathematics" is because I am still very impressed with the SMSG's emphasis on the creative, flexible, structural thinker. 

The sensibility represented by the "Back to Basics" movement epitomized the backlash against the new math in the 1970's.  Proponents of Back to Basics claimed that overemphasis on mathematical structure had impeded the ability of students to calculate, and they encouraged schools to return to the "basics" of drilled exercises and rote memorization of arithmetic facts.  (Phillips, 2015)

In other words, the masses did not appreciate the mathematicians efforts to improve their minds, but only wanted their children to develop competence in computational skills.  And yet, when it comes to the approach to mathematics I want to take now, where I am already comfortable with my computational skills, I long to develop the kind of understanding Dolciani, Allen, and the minds behind SMSG's "modern mathematics" were concerned with.  They were not interested in helping students calculate quickly or accurately. 

It's not so much that the masses want their education "dumbed down," but that they can't stand to exert energy (and money) into anything that can not be put to practical use in daily life.  Maybe this situation is related to what Vonnegut was pointing out in Harrison Bergeron from the Welcome to the Monkey House collection. 

I don't think anyone should be concerned with what works for mass society, especially when it comes to your own personal lifelong education.

These reform movements in systematic education of the youth have political motivations. 

Higher test scores and the ability to calculate quickly does not imply mathematical understanding nor mathematical maturity. 

I really think that the teachers and parents who resisted (where Dolciani and other mathematicians who were writing text books were coming from) may have had firmly ingrained ideas about what mathematics is (the computation of numbers; that is, arithmetic) and may have been put off my the mention of "abstract algebra" such as sets, fields, or rings.

I have a different reaction to being exposed to those more abstract concepts.  Suddenly I get a glimpse of an underlying structure.  Of course, when this happens one tends to slow down, to think more slowly - because you are more into it, not just mechanically calculating or memorizing arithmetic "facts".

I understand that there are far more pressing concerns for most people and that I am in my own little world, but Phillips's book was released in 2015, and I have been very obsessed with the novelty of the books I intend to study exhaustively over the next couple of years.  When I say I am revisiting high school mathematics, I ought to make it clear that it is not just any old high school math that I am interested in.

I am specifically interested in how mathematicians would present it to the youth if they were in a position to do so, and, for a brief time in the mid-twentieth century in the United States, they were.   I caught the tail end of this when I attended a private high school in the 1960's, but by the time I got to the geometry, I began experiencing emotional disturbances which must have had an impact on my ability to concentrate.

So, maybe these texts weren't so hot for kids and teens.  I don't know what to think about all that.  What I do know is that, now, as an "old man," I am ready for the "new math," or, as I prefer to call it, the "novel approach to developing my conceptual and structural understanding of the nature of mathematics."

I am someone with computational skills who realizes I have never been and will never be a "mathematician."  This does not mean I am going to stop trying to develop a deeper appreciation for what mathematics really is and to approach it in a novel way with a Beginner's Mind. 

I like to compute and calculate, but I sense there is a deeper aspect to mathematics which Mary Dolciani and others were trying to inculcate on a mass level which ended up being pearls before the swine.

Man, I know this stuff is not important compared to the everyday problems people face such as paying for visits to the doctor and making sure they have a roof over their heads with some heat coming from the pipes or vents.  I understand that access to nutritional food takes precedence over understanding set notation or the logic of algebra.

How I have come to be obsessed with studying these books offers a clue as to why I frequently refer to my day to day reality as existential science fiction.  All the politics and actual government funding that went into that SMSG phenomenon which inspired Dolciani and others to create the series of texts, of which I chose about six or seven to focus on [Algebra I, Geometry (Jurgensen), Algebra 2 and Trigonometry, Introductory Analysis, Modern Introductory Analysis, Analytic Geometry, Matrix Algebra] - it was a freak event in history, and it did not take long for the texts to be rejected.   So, when I feel this strong compulsion to pay attention to the material and how it is presented, it's as though I am in contact with GHOSTS; but not the European conception of "phantoms" or "spectres", but in the way Robert Pirsig talks about "thoughts as ghosts" in Zen and the Art of Motorcycle Maintenance.

Maybe what I was trying to express with "the Defamiliarization of Mathematics" was to force oneself to approach it in a novel way, in a way where what you thought you were familiar with appears to have deeper layers.

I think this is why it is beneficial to consider different number systems.  For the novelty.

2 + 2 = 4 in base ten.

In base 3 (with digits 0, 1, and 2), 2 + 2 = 11

Numerological Note:  This was post number 4444 at
« Last Edit: November 16, 2017, 09:43:22 am by Non Serviam »
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