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Sunday, August 13. 2017
I strongly suggest taking math, engineering, or a hard science as far as a kid can go in high school and/or college. If they only use it to read newspapers and magazines, it will train the mind and make a good impression on future employers. If a kid is a "no math creative," then I don't know what to say other than "I'm sorry to hear it."
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This is something I'm going through right now.
We homeschool our child, and she...dislikes math.
And she's almost as stubborn as I am.
And my wife had a, well, deprived childhood so she has a tendency to not say "do better on this or we cut that out".
It's not that the Child is slow--she's at or above grade level on math (she's 10). And I know that because of that putting her in a public school isn't going to help.
But she can do better.
It's easier to be a fine-art painter with a degree in mechanical engineering than it is to be a mechanical engineer with a degree in Fine Arts. I know, because I have a degree in Fine Arts.
Pick up 'The Calculus Direct' by John Weiss. It's a short book written by a community college professor.
I starts at number lines and goes through Calculus with just the essentials, but without all the aside. As such, it may give your daughter a view of the whole path up to and beyond where she's at now. Fills in those holes that happen and inhibit understanding of later math.
You might try her on How To Lie With Statistics because it's fun and she might see the point of it. Statistics is perhaps the greatest lack in math for adults who aren't working directly with numbers. A young female friend has a statistics blog "Graph Paper Diaries" which tries to answer questions she might be interested in.
PJ O'Rourke's Eat The Rich has sneaky math in it - math-thinking rather than lots of numbers, but it sets the table. You might try that on her as well. The standard math curriculum for the last century is designed for those who are going on into the sciences. But there are other maths, including probability and coding, that she might like better.
We found Singapore Math to be very useful up through about age 12. After that they don't seem to have much to offer. Maybe there's more I didn't find.
Three of the many comments I have about math and education:
•There is math itself, which is a fascinating set of ideas and tools for evaluating the world around us, then there is math the discipline which is full of crufty, awkward, out-dated, poorly thought out nonsense. The brightest kids tend to pick up on this very quickly and it dulls their interest and tries their patience.
•Math is interesting conceptually, but incredibly boring to actually do. Unfortunately one must slog through the boring, repetitious, tedious, meaningless parts to be able to do the rest. Most teaching doesn't take this into account.
•Math, especially at the college level, is used as a means of washing out students rather than as a skill to be taught. IF we really believe that math is that important, and we seem to do so, then we need to find ways to teach it rather than simply require it. This ties in with a "math culture" which is heavy on trick questions, gotchas, and put downs, and which moves at the same pace regardless of student progress. The last time I checked, STEM programs wash out a much higher percentage of participants than the Marine Corps. I believe the reason is that the marines are trying to make marines, the STEM disciplines are trying to limit the number of students they have to teach.
I was a college Math professor and a common comment I got from Freshmen taking College Algebra or 1st semester Calculus was "my middle school teacher told me I was no good at math" and that is what they remember about math...and carried through to college.
Not sure of the author but I had this quote on my office door--"In mathematics you don't understand things. You just get used to them."
"the STEM disciplines are trying to limit the number of students they have to teach."
Not necessarily. I'm an engineer and the first thing you had to do to be admitted to the college of engineering was pass the freshman calculus course. Lots of wannabe engineers couldn't do it. Calculus was a prerequisite for most engineering courses because if you couldn't do calculus you couldn't pass the engineering courses. Engineering was so much easier before Newton and Leibnitz invented calculus to confuse and befuddle freshmen.
I think you are missing my point, though maybe I'm missing yours...
Do you believe calculus to be a necessary tool for engineering? I'm inclined to think so. (Though some engineer friends of mine have called it into question...) So, if calculus is a necessary tool for engineering, why would you not teach it to prospective engineers.
Marksmanship, physical fitness, and military discipline are pretty important to marines but they don't wash out recruits who can't do those things well, they train them. Sure, some never get it and they wash out about somewhere around 12% depending on the source, for various reasons. In engineering the washout rate appears to be above half.
So, I have hypothesized, partly based on input from engineering students and professors and two or three math professors, that the reason the washout rate is so high is that simply put, the programs want it that way. There appears to be a kind of machismo in the thing too, some students who get through it have a kind of "I was tougher than you." kind of attitude which I think perpetuates the thing. But that can't be the whole reason. More "I'm tougher than you" than the Marine Corps? Probably not.
So, is math critical to STEM programs and careers? If so, should it be taught to students in those areas? Or should it be merely required? Do we really need to cut down on the number of STEM students and graduates? Are there so few classroom seats? So few jobs for the graduates? Maybe so.
How would one design the system if we perceived a national emergency which was going to require millions of qualified STEM graduates in say 5 or 6 years from now? On the other hand, how would one design the system if we knew there was an awful glut, or if STEM programs were horribly expensive to the school or to society as a whole? Any system with a 50%+ failure rate has a problem.... unless it is designed that way... hence my conclusion that they are intentionally limiting participation.
I don't "believe" calculus is necessary, it's a fact you must know calculus, period. For example, senior EE majors were required to take and pass the electromagnetics course. To pass that course you had to know calculus, vector analysis, complex variables, partial differential equations. If you couldn't understand calculus, you were going to be lost when you took the other math courses. The instructor can't teach you math, you have to learn it. As an example, I signed up for the partial differential equations course in the summer. At the first class meeting there were only 3 students and the professor said there were too few students and he was going to cancel the course. Well, we begged and whined and groveled so the professor didn't cancel the course, instead he made us students teach the course. We students were assigned sections of the book to teach and we had to stand in front of the class and teach. The professor did not allow you to use notes and he sat with the other students and asked you questions. Keep in mind the summer class periods were one and a half hours long. The professor didn't teach partial differential equations, but I learned them very well because I had to teach them.