The american educational system is a hodge-podge of ill-conceived,
poorly executed "ideas" (a polite way of saying "experiments")
Imagine a control system with sufficient lag in which you are
continuously changing the control criteria *and* making decisions
about those changes before the results have filtered through to the
output.
Then, seeing sub-optimal (by some definition of "optimal") results
and using that to justify still *more* changes.
And, others pointing at lack of progress from YOUR changes and using
that to justify changes in yet another direction.
"We need more testing" -- as if testing (measurement) was a panacea.
(how are you going to adjust your process once you have those results?)
"We need smaller class sizes" -- as if fewer students meant better
instruction.
"We need a laptop per student" -- as if reading on a screen magically
improved comprehension.
"We need increased parental involvement" -- as if one could magically
change the motivation of (and resources available to) parents.
Etc.
I "help" (avoiding the term tutor as that's an ongoing, structured
relationship) many of my friends kids. I suspect "individual attention"
can be credited (by folks who advocate smaller class sizes) with
their resulting successes ("Look, Don, I got a 92 on my math test!").
But, I think my knowledge of them, as individuals, is more to credit
for these successes.
As I know their interests, I can present ideas in ways to which they
can more naturally relate.
TL;DR
A neighbor's high-school son was having problems with trig. Dad asked
me, on the QT, if I could help him out -- cuz I'm not seen as a "parental
authority" and he's more comfortable talking with me, than them.
(Oh, if they only knew of the stuff he's confided in me, over the years!)
I stopped by a few days later and asked him (kid) if he could give me a
hand for a few minutes.
"I want to cut down this tree in front of the house. But, as you can see,
if I fell it THAT way, it will crash into your house, your trees, your saguaro,
etc. If I fell it the other way, it crashes into Tim's stuff. And, I
certainly don't want to drop it on MY house!
So, the only option is to drop it directly away from the house and lay it in
the street! But, even there, I have to worry about those neighbors' properties
across from me.
How tall do you think it is?"
"Gee, that's hard to say. At least 50 ft! It looks like it's going to be
*close*..."
"OK, we'll have to measure it, then."
I dug out a folding chair and set it up on the far side of the street,
opposite my tree. Then, asked him to crouch down so his eyes were level
with the top of the chair's back. And, look directly at the top of
the tree.
"Now, I'm going to stand between you and the tree with my hand held above my
head. I'll walk away from you, towards the tree. I want you to tell me
when the tip of my fingers APPEARS to be located at the top of the tree."
I then measured the distance from that point to his "eyes". And, the
height of my fingertips above the roadway. And, the distance to the
tree. Then, announced the height.
"How did you do that?"
"The tree is ~8.25 times farther from your eyes than I was (40'/4'10").
So, the tree must be ~8.25 times taller than me!"
"Yeah, but you're 6' tall; wouldn't that make the tree 50 ft? Yet,
you claim the tree is only 47.5 ft!"
"But the tips of my fingers are much higher than my head! Seven and
a half feet!"
"OK, then that would make the tree closer to *60* feet!"
<grin>
"Yeah, but your eyes weren't at the level of my feet! They were
two feet off the ground. So, you were only comparing 5.5 ft of
'me' (7.5-2) to the tree!"
"But, still, that means the tree would be 45 feet!"
<bigger grin>
"But, you're not including the lower 2 ft of the tree in that
comparison!"
So, I fetched a piece of paper/pen and made a sketch.
"Similar triangles..."
No mention of sines, or cosines, or tangents...
Now, it looked like one of his homework problems. I could
almost hear the gears sliding into place in his mind...
I bumped into his dad a few weeks later and he commented on
how much more confident his son was in his math class. And,
how quickly his test scores had climbed.
"I don't know what you told him, but it sure worked!"
A couple of years later, when the son was headed off to college,
he mentioned that he had previously wanted to get a liberal
arts education, "because that would be the most flexible"
(I bit my tongue). But, had decided, instead, to go into
engineering. He could *see* how that sort of education
could be directly applied to problem solving. (like figuring
out the heights of trees without climbing them!)
[Sadly, he died, suddenly, a year and a half later]