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As for textbooks, I have been following with my own eyes and hands a grade-school math curriculum sold to schools by a certain company, and also a science program, and the first thing I wonder is where these people learned how to write English.
Horrible, horrible, horrible.
To be sure, this is a significant part of the reason why the US is behind, supposedly, in so-called STEM: lack of common-sense language in teaching basic math and science.
I am skilled at various levels in about nine languages, including three ancient ones, and often for the life of me I cannot understand what the authors of these grade-school math and science textbooks are trying to communicate to these children.
And I am talking about simple counting and addition to start with. Utterly confusing, tantamount to child abuse.
I know even professional attorneys who have difficulty in understanding what these textbooks are trying to convey to their children. Appalling.
No joke.
Or is it?
It's worse than that. I am a physicist working in a building full of rocket scientists. We've all had children in school these last 20 years. And every one of us has been unable to understand the math textbooks our kids bring home.
The language, structure, and methods in most of these elementary texts make no sense, esp considering they are supposed to be written at the elementary and middle school level. Sometimes I think these textbook companies make up their own names to try to lock schools into buying their texts for every grade because switching between programs would add even more confusion.
My tentative idea is that there IS a magic bullet, but finding, realizing and using it is hard work. The bullet may lie in the act of complete mindful absorption in the idea or task at hand - whatever the idea or task may be. This is the mental and emotional shift in focus that I mentioned.
With that bullet, we can fully enjoy pondering, puzzling, and solving almost anything, including math.
Happiness is easy when it arises, but not so easy to generate or sustain.
Mindful absorption in any particular idea or activity comes naturally to us when it lies within our native abilities and interests. It is more difficult to activate that absorption for other activities. Absorption is both a talent and skill. IQ and aptitude tests only touch the surface of absorption.
A gentleman named Jacques Ellul discussed this idea in relation to something he called "technique". Technique is a human capability that can surmount any obstacle to survival that we encounter. However, he cautions that technique may have a cost to human intuition. I think it may be possible to use technique to improve intuition, but that idea may itself be a technique trap.
I encountered Ellul's The Technological Society in an intro to philosophy course I took in the 1970's and it seemed depressing. I return to that book every couple of decades to see if my perception of it has changed. It is about time to read it again.
The reasons have all been touched on already so I really have nothing to add.
Well maybe I do.
One problem in education (I'm talking K-12 but especially 7-12), and it cuts across all disciplines, is that those teaching whatever subject were always "good" in it.
Someone mentioned how math (I think it was) always just laid out for him and it was almost intuitive. That's true in all the subjects (personal example later).
I struggled (and that doesn't even begin to describe it) in Math after switching from numbers to letters. Unfortunately in all my secondary Math classes I had teachers who would do one example, assume everyone understood it, and then assign the even numbered problems on Page XXX. Asking for help was non-productive because the teachers couldn't explain it so I (and many others) could understand it one on one, either. A couple wouldn't even do example problems, they'd have the assignment on the board and would spend class reading the newspaper or diagramming football/basketball plays.
That bled over into other subjects like Chemistry and Physics (which we took, real Physics-not Everyday Physics) in 10th Grade. Something about "Raising The Bar". This was in 1969). As a result I didn't understand Algebra until college.
Promised personal example:
Econ always laid out for me for some reason, enough so that I minored in it. When I started teaching it I always told my students the first day of class that if, as we went through the semester, they didn't understand something to raise their hand and ask me to start speaking English.
I have pleasant memories of one summer when I took only math classes and made all A's and B's. It was rewarding, but for some reason I didn't sustain it through the following years of college.
Last edited by highplainsrus; 10-18-2020 at 10:33 AM..
I think that ^^^ is a GREAT point. Math NOTATIONS seem like a completely bizarre foreign language to most (including me, BTW, even though I'm generally good at math) -- but once you get past the notations and see what PRACTICAL value the math can have, you are on your way to UNDERSTANDING those equations -- no matter how bizarre they may look.
Jourdain's Nature of Mathematics talks about the history of the symbols as being efficient shorthand for complex math ideas and theories. Each symbol can be unpacked into years of mathematical reasoning.
For me, math was hard in high-school because the problems were about kids mowing lawns and later on about physics. However, when I eventually found a subject in grad school that really interested me, environmental and resource economics, I switched majors to economics, and pretty much taught myself calculus and linear algebra and eventually earned an MS and Ph.D. I followed that up with a 35+ year career as a consulting research economist, and never looked back.
Math is taught (far too often, too much) to people who haven't mastered Arithmetic.
I agree. Arithmetic itself has a long history of development and is still studied as a solitary subject. Math builds on fundamental skills and becomes more difficult in higher subjects areas without those previous skills.
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