Stepping off a polygon

[Moby Duck]

I am still using my old HP45 calculator that I purchased new in 1973 for USD395. (Wiki tells me that in 2017 terms that was the equivalent of USD2178).
It was the first scientific calculator that I had ever heard about, and I had visions of it changing the world.
I can read it in poor light, because unlike modern calculators it has a red LED display.
Apart from its speed advantage, I found that the RPN also had a distinct advantage in a work environment, because nobody ever asked to borrow it more than once.

[Paul Jones]

Moby Duck,

I like your story about the HP-45. I remember it well. In 1973 I started graduate school for MS and PhD degrees in geophysics. The geophysics department owned an HP-35 and HP-45 calculators that we shared among 10 grad students. Other than using a Wang calculator (the one with the cool Nixie tubes) in an undergrad statistics class, I never used an electronic calculator before 1973 and only used a slide rule starting in 1962 (and still know how to use mine). Wow, what a world of difference these wonderful HP calculators made for our work. By 1975 the cost of simplest electronic calculators had become affordable and I bought one at the local Kmart store. Years later I bought an HP-65 programmable calculator with storage for 100 keystroke instructions (in its time this was a big deal) and still have the calculator as a museum piece. Almost all of my grad work was preformed with computers using FORTRAN code for research but the HP calculators were great for double checking our work.

Regards,
Paul

[DIYer]

Thanks mklotz! We've added your Divider Stepping Method to our Measuring and Marking category,
as well as to your builder page: mklotz's Homemade Tools. Your receipt:

Divider Stepping Method by mklotz

tags: divider

[volodar]

"Stepping off would be faster..." Any student with grade 11 math should have no trouble applying the cosine law to a simple diagram - which anyone should have no trouble sketching...not much understanding required.

[mklotz]

"Stepping off would be faster..." Any student with grade 11 math should have no trouble applying the cosine law to a simple diagram - which anyone should have no trouble sketching...not much understanding required.

I'm inclined to agree with you.

Nevertheless, most posts involving anything remotely mathematical beyond the four functions will have posters with little on-topic to offer advertising, as if proud of it, their ignorance of mathematics.

How is it that the educational system(s) have failed so miserably to instill an understanding of elementary math below the calculus level?

Everyone will have his own answer to that question so I'll offer my own thoughts on the subject to get the ball rolling.

From my own experience, teachers fail to answer what the first slide in any presentation should be: Why do you want to learn this? Admittedly, in math it's difficult to answer if the student doesn't yet know how to use what's being introduced but, by re-answering the question as each bit of new knowledge is presented, some degree of communication can be effected.

Still, the student has to apply himself and learn. I think a large part of that problem stems from the fact that math is the first time he is faced with a subject that is absolute, offering no opportunity for interpretation. You can argue endlessly about what the author of Catcher in the Rye meant or what the impact of the North's victory at Vicksburg was on the Civil War but the solution to a polynomial equation provides no opportunity for self-expression. Students denied the opportunity to manipulate the subject react by mentally retreating from it. (OTH, they could just be typically lazy kids who don't want to learn anything. :-)

Finally, a society that denigrates intellectual achievement makes it difficult, bordering on anti-social, to demonstrate learning. Sports achievement outweighs any learning that might be useful in the world most students will enter.

[Jon]

From my own experience, teachers fail to answer what the first slide in any presentation should be: Why do you want to learn this? Admittedly, in math it's difficult to answer if the student doesn't yet know how to use what's being introduced but, by re-answering the question as each bit of new knowledge is presented, some degree of communication can be effected.

Agreed. They have also failed to address the reasonable question posed by non-technical students: "When will I ever use this in my life?"

When I hear kids asking this, I say: "If you're asking that question, the answer is that you will probably never, ever need to use this specific bit of mathematics in your entire life." This backs them into saying: "Then why am I wasting my time learning this?!"

Then I explain that, for non-technical people, the benefit of math is not necessarily the math itself, but the problem-solving techniques:

-Acknowledging the existence of a provable, immutable, and universally-accepted answer, devoid of nuance and opinion.
-Using knowledge as stepping stones, where each level builds upon the previous one.
-Understanding that some components of life are mechanistic and deterministic, and you'll never change that.

And the most important:

-Doing something difficult, hating every second of it, and completing it anyway.