
Teaching binary to 3rd Graders using the Socratic method - scorchin
http://www.garlikov.com/Soc_Meth.html
======
alxp
One day after a visit to the Computer History Museum, my SO and I got to see
the live demo of the analytical engine they have there. We watched the gears
turning and stopping to add up numbers, saw the complex mechanisms to handle
carrying digits, and she asked me how this would work if it was binary and I
just said "much more simply". Then she admitted that, even though she has been
working as a developer and manager of developers for years, she never learned
binary.

When we got home I got out a pad and pencil and got her to write down 0, then
1, then asked her, if you only had two digits, what would come next?
Tentatively she wrote 1 0. THen I asked her to add 1 to it. We more or less
carried on the way this transcript went, except instead of using aliens with
two fingers I introduced AND, OR and XOR 'boxes' that 0s and 1s go in and come
out. I hadn't planned any of this but by the end of it she was just about
drawing the circuit diagram of a full adder with carry bit.

I'm sort of thrilled to see that what I was doing is precisely the socratic
method. I love teaching, never really did much of it until I gave a course in
Unix and shell scripting at an old job but for a week I had more energy at
work than I ever did just programming or in meetings.

~~~
DrPhish
I'm also a member of the "Taught my wife binary just for fun" club, but I used
fingers in a different way than Rick Garlikov did. I told her that there was a
way to count to 512 using just your fingers, and let her work through how it
might be possible using a similar question-answer trial and error approach.
Once she realized that each finger had 2 states (up or down), she naturally
recreated a binary counting system. It's a neat trick, and even comes in handy
when trying to keep track of a large count of something. With kids, however,
you may end up with behavior problems around the numbers 4 and 132 :)

~~~
gort
"a way to count to 512"

1024 (or 1023), surely?

~~~
Raphael
She wanted a sign bit.

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docmarionum1
Reading this gave me a warm, fuzzy feeling.

I can't imagine trying to teach 3rd graders binary using a standard method - I
even have peers in college that struggle with it. Probably because it was just
taught to them as something different - this weird language computers use,
instead of them developing an intuitive sense for it. But whenever I try to
explain it to them, or anyone else, I always try and explain it as "just like
decimal, exactly what you already know."

The Socratic method really is much more interesting and captivating for
students. For example, Walter Lewin's physics lectures (Which are well worth
watching, even if you're not taking a physics class), which I'm currently
watching to "supplement" my actual physics class in which the professor stares
at the board and rambles.*

*Not to say that his lectures are the Socratic method - that's probably not feasible with a lecture hall of hundreds of students. But the way he teaches makes you feel like you're discovering everything again along with him.

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ericHosick
This is a great way to teach and Mr. Garlikov did an amazing job. It is hard
work to "teach" this way because it requires student/teacher interaction
(which is a lot harder than just standing there and lecturing). Coming up with
the content is equally difficult.

But it there are so many more things students learn using this method.

One is they learn how to create new ideas from existing ones: "inventing". It
really gets me when I hear people tell kids "don't re-invent the wheel".

~~~
Chocobean
>One is they learn how to create new ideas from existing ones

This is how our brains are wired to work: the more places we can cross-
reference the material from, the more likely we can "derive" it again quickly
even if we can't memorize it.

"shut up/memorize it/some things just are" kills the intention to learn faster
than a speeding bullet to the brain.

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drblast
This is wonderful.

My wife homeschools, and the math curriculum she uses uses a very similar
method from the beginning.

My daughter knows "12" as "One-ten two" and "33" as "three-ten three" and says
it that way. She also knows those mean twelve and thirty-three, but for the
purposes of the math program she uses the place terminology.

We can only hope that it will give her a better understanding of what's going
on than pure memorization, and the jury's out until she's older, but it's a
fascinating way to teach.

I sometimes wish we were all born with eight or sixteen fingers, but that's
just the CS/EE bias in me talking.

~~~
Chocobean
I'm very very interested in considering homeschooling. How did the article's
method differ with your child, since the "class size" is reduced to one? Your
child won't have the benefit of being "filled in", but maybe she feels that
she owns 100% of the achievement?

By the way, "one-ten-two" and "three-ten-thee" is literally how the Chinese
would pronounce their numbers (一十二，三十三）. In a way I think it's helped me
understand place values earlier.

~~~
drblast
The Socratic method can be frustrating with one child, because when she
doesn't get it, she really doesn't get it, and it takes a lot of questioning
to lead her down the right path again. Sometimes you just want to bang your
head against the wall when you ask the simplest leading question and she gets
it wrong. At least with a group most of the kids will get those questions
right.

I think my wife and I use that teaching method quite naturally. I'm never
inclined to just give our children the answer; they only learn when they
arrive at the answer themselves.

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elviejo
I love to learn using the Socratic method. One of my favorite books is: "The
Little Schemer" which is great and twists my mind in ways that I didn't think
where possible.

Anyway do you know of other books, on any topic, that use the socratic method?

~~~
Chocobean
Plato's Republic?

~~~
gort
There must be shorter, easier Socratic dialogues one could read. Maybe
Euthyphro, or something:

<http://classics.mit.edu/Plato/euthyfro.html>

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measure2xcut1x
I learned how to count in binary using my fingers as digits probably about
third grade. The pinkie is the 1. At that age, I thought it was pretty cool
that I could count to 31 on one hand, and it stuck with me to this day. I'm
sure I'll teach my son the same.

~~~
Chocobean
=) then you can tell people you are _this_ many years old this year, up until
you're 31.

~~~
jasonkostempski
Genius! I can use that for another 4 months, then it'll have to be a pinky and
a fist, but that's a little too suggestive for normal conversations.

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whozman
Captivating. Understanding something by answering questions on your own (even
if guided) always feels more like true understanding. But what happens when we
come to a point that requires mental leap beyond what a student can do? Is
there a set of problems, or a set of students that are more suitable for
Socratic method (3rd graders seem to do just fine at it)? Or is there a set of
teachers that are more adept to teaching this way? Please give your answers
through questions only.

~~~
kalmi10
If it requires a mental leap, then you are doing/teaching it wrong. Every
large leap is just a bunch of small leaps.

~~~
kenjackson
Absolutely.

The hard part about teaching is recognizing when you've introduced a large
leap for a good percentage of the class.

There's a famous math story that goes:

"A professor was at the chalkboard writing up a proof for his class. At one
point he comes to a portion of the proof and says, 'And it's obvious this must
be X'. At which point he pauses, the class waiting. Stares at the board for a
minute. Then leaves the class without saying a word. He returns fifteen
minutes later, continuing, 'Yes, it's obvious this must be X'."

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charlieflowers
This is amazingly similar to Test Driven Development. In the purest form of
TDD, you don't write a single line of code until you have a failing test. The
failing test is the unanswered question. Then, you write the code that
"answers that question." This means that each step of the way, you are
confirming that prior principles are correctly understood by the human and the
computer before building on those prior principles.

As the Agile theory puts it, this approach "maximizes feedback".

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ars
This is very cool, and I'm going to try it when I can.

But just to nitpick, he did actually tell them plenty of things, it was not
just questions.

2 Examples:

> Could it be because we have 10 fingers?

> No, only to you guys, because you were taught it wrong [grin] -- to the
> aliens it is two. They learn it that way in pre-school just as you learn to
> call one, zero [pointing to "10"] "ten". But it's not really ten, right?
> It's two -- if you only had two fingers.

Not a criticism, just a nitpick.

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nbashaw
This gives me an idea. What if there were a virtual university that was
entirely conducted via chat? Like Quora meets Convore.

~~~
Chocobean
I'm unfamiliar with Quora. How is it different from, say, yahoo answers or
stackOverflow??

~~~
nbashaw
Quora is of greater intellectual merit than Yahoo Answers, and isn't siloed
into verticals like Stack Exchange.

