Posted on 04/21/2020 9:55:55 AM PDT by Olog-hai
Those were necessary for more advanced algebra, e.g. parabola, hyperbola, logarithmic equations etc. but for long division?
I could see using log-log paper to perform a division.If you could get fourth-grade students understanding logarithms . . .
‘course the real issue is understanding the concept of quantity apart from the concept of numbers.
I was in the middle of my engineering coursework when I had a required course in analog computation. And the first thing we learned was how to wire op-amps to perform addition. Then we used the hardware, and did a little lab work - and I wrote a report.
My report said that “well, it did work as advertised - but it isn’t practical because adjusting the input voltages and reading the output voltage was cumbersome and imprecise. Much easier to use elementary arithmetic instead." My critique was absolutely correct - and entirely beside the point.
Because although when you are talking about integers - counting numbers - there is such a thing as perfect precision, much of what matters cannot be precisely quantified. So perfect need not be allowed to be the enemy of the good. The “good” in analog computation lying in the fact that it could add, subtract, multiply, divide, do direct and inverse trig trig functions and logarithms - and integrate and differentiate vs time - at high frequencies. And do many instances of many of those things simultaneously. And especially sixty years ago, that was nothing to sneeze at.
What I learned in reflecting on that is that is that quantity and numbers are not the same thing, This shows up in the nomenclature “analog to digital conversion.” A friend tried to research what “analog” meant in that context - and I explained that if you want the sum of the lengths of two boards, you can measure each board with a tape measure, and add the two numbers to get the sum. Or you can simply abut the end of one board to the end of the other. In the former case you have performed two “analog” to digital conversions and an arithmetic sum of the two numbers. In the latter case you have performed an “analog” addition - and the result isn’t a “digital” number but a physical length.
The confusing thing to explain being that the physical length is the very thing itself - not an “analog” of anything else. But my friend got it. :-)
I have to admit math is a weakness with me. Moreso now since my MS. I was very fortunate in my last job to have as my supervisor a very, very smart man who was excellent at explaining math concepts I had not visited since I left high school. He also introduced me to the excellent text “Practical Mathematics (For beginners For those who have forgotten)” by Hobbs, MacLennen, and Dalzell.
I do like that the method you demonstrated is practical and has obvious field application.
Provide names of flunked out former homeschoolers? I must demure. Homeschooling is great, but some people can screw up anything.
My experience of homeschooling is zilch. But IMHO nothing is beyond some people’s ability to SNAFU anything.Even so, in the process of failing a lot of learning (by the parents) will have gone on.
And any school administrator who presumes to think that her school can educate a child well without parental support is smoking something fishy. Homeschooling is obviously the limiting case of parental involvement in a child’s education.
My bottom line on homeschooling is that the parent is the adult who is responsible - “responsible,” in the sense of being affected by the successful or failed result - for her child’s education. Schools - all government institutions - eagerly grab for authority. But “authority” and “responsibility” are two different things.
Separating responsibility from authority is the cardinal sin of management. Therefore when it comes to schooling, the parent is always right. Even when she is wrong.
Heard that teachers are deliberately making online cumbersome in order to discourage parents and make them think educating children is some mysterious task that only government schools can accomplish.
Well, we homeschooled our three children, and I followed a rather laissez faire method. They are all now successful, well-adjusted adults. One of them has a Ph.D in toxicology and is a cancer researcher. BTW, I let him spend a great deal of his school time reading Japanese history, because that interested him.
Children are born learners. Traditional schools destroy curiosity and love of learning.
Thank you for your thoughtful comments about the many complications of the distance learning that is going on right now.
Where did you hear that? It sounds like the “some say” lead in.
Great news, millions can say the same for public school. Again, some (terrible) parents are letting their kids down by not teaching them at home and not letting them go to school.
I heard this from a person who follows many bloggers who are now teaching their kids at home due to the school shutdown. These parents complain that teachers are demanding all kinds of silly projects, like building a bridge using computer paper, which would require using up most of the paper they have in their homes.
Some of these moms have 3 or 4 kids, and each of their teachers require that the kids sign on to zoom at a certain time of day without considering what the other teachers require.
The teachers are foisting silly “science” projects on the students that require materials that most people don’t have at home, and each teacher piles these projects on one after the other. They do not care if the parent has more than one child they are teaching at home.
In other words, the teachers are making parents jump through hoops in an effort to disguise the fact that schools are mostly busy work and that children get very little of a teacher’s time and attention one-on-one. What schools waste 8 hours a day doing can be accomplished in very little time at home. For that matter, if teachers have a child in their care all day, 5 days a week, why is there homework? The answer is to make it look like a whole lotta educating is happening.
Teachers’ unions are not interested in the children or education. They only care about protecting their jobs and preventing competition from private schools and home schools.
Although he was an old hippie, and had some screwy ideas, John Holt had some great insights into what schools do to kids. His book, How Children Fail, is a good read.
It’s sad, but there are some abusive parents who claim to be teaching their children at home so they can hide the abuse. This is quite rare, though. Most people who homeschool care very much about their children and education.
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