The Difference Between Teaching and Instruction

[michel paul]

This is very interesting. Definitely check it out, and be sure to watch the videos.

The Difference Between Teaching and Instruction 

-- Michel 

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"What I cannot create, I do not understand."

- Richard Feynman

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"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
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[Sue VanHattum]

Thanks for the link. I hadn't seen the video before. I've read a bunch of the posts on pseudoteaching before but re-read some, and read a bunch more. (Sunday morning professional development ...)

Warmly,
Sue

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From: python...@gmail.com
Date: Sat, 24 Mar 2012 22:51:43 -0700
Subject: [Math 2.0] The Difference Between Teaching and Instruction
To: hsm...@bhusd.org; mathf...@googlegroups.com

[Linda Fahlberg-Stojanovska]

@Sue

Probably more to that statement, but I really liked it even on its own: “Sunday morning professional  development”

Linda

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[Christian Baune]

Hi,

I answered on the post itself and got moderated. Nothing were wrong, I did only expose how I would teach and why.
I gave also a link to one of my YouTube videos where I explain what is a student.

Conclusion : it is one way and selective.

I gave a link to Simon's tatham portable puzzles collection. Explained that I would give these puzzles to my students, a lot of easy ones then suddenly harder ones.

Basically, I would explain using one of the puzzles how it could be solved. If they want to succeed they would have to understand that solving each occurrence in each puzzle is not the better way. So they have to think how to solve any configuration of them. While solving a particular configuration, you must not only solve it but think how you would have done in another configuration. It goes toward generalization.

I gave also example of problems which permit you to deduce what's wrong in the student cognition process.

1) Ask how many rectangles can be drawn in a 5 by 6 grid using only vertex.
2) Show that any rectangle is enclosed by two horizontals and two verticals. Thus : C(6,2)*C(7,2) yield the result.
3) Add two dots to the drawing and ask how many rectangles do not contains any of the dots.
4) Take problem 1 in the third dimension and ask how many paralepipede can be "drawn".

Depending on how they succeed on each question, you can deduce how they workout things. You can also detect which one are probably gifted.

Solving 1 with combination : probably gifted.
Solving 1 using cross sum of rectangles a*b : normal. (unless the student really find a formula from it by factorization, which makes him proeficient)
Solving 3 using the set notions : prob. gifted.
Solving 3 by adding combinations : proeficient.
Solving 4 using combinations normal.

One can be able to solve 1 and 4 but 3, that means : "monkey student".
Instructed people will solve 1, 4 but 3.
Taught ones would be able to solve them all.

If you're really good at maths, you should be able to solve all 33 in the easy level without difficulties. You may have difficulties at harder levels in some puzzles like "solo" only because of your working memory.
(in a 4*4 solo, you've to work on 16 symbols instead of 9. Like finding in these string which letter do not appear from range A...P: "BPHNCIXSGDAOKPJMFE")

When I explained things to student I coached, I always began by explaining more general concepts, then I got the the specific case the student need. They all found it odd that I tell them things not so useful and some even despered that I ask them questions that don't help. But when they succeeded and that we came back to the lesson, things became obvious. Then they notice that all exercises are ... the same!
(only words and numbers change)

Our educational system fail. So much than when I write : a/b*c to convert scales, people ask : How do you know? And some even check by trying to do the reverse operation. The rule of third is far to be mastered by people and is one of the most common need in daily life!

I Remember when I was student and that I saw many failing only because they had ton convert Km/h in m/s. You had cars going at 90m/s :-D
And not being used with this unit, they weren't shocked by the result.
Even worst, if you take the m2, most student even don't realise that this is meters*meters...It can bring odd thinking and funy results!
m2,m3 are simply units for them. A think you've to write after the number.

Kind regards,
Programaths

[dunyof...@gmail.com]

Thank you for the link

God Bless You

[Joseph Austin]

Do we ever stop to realize just how complex the base ten place-value system is?

It’s something like an n-tuple log of a polynomial—I’m not even sure we have a name for it.

If we were striving for MATHEMATICAL understanding of arithmetic,

wouldn’t we use unary?

All rational arithmetic + - * /  can be done in unary starting with Peano postulates.

And then move on to binary representation, once the concept are understood.

And if binary is not compact enough, abbreviate with hex.

Most of what is taught as “arithmetic” is algorithms for manipulating the decimal representation of numbers.

What if, instead, we taught how to reason about magnitudes and their relationships?

Equality, greater and less, similarity, proportion, logic, etc.

Or in other words, back to geometry!

Why do we persist making learning more difficult by insisting on obsolete, inappropriate representations?  Decimal arithmetic for math?  Roman alphabet and English spelling for reading and writing the American language?  An archaic kludge notation for music?  

It’s not as if we don’t have tools to make the change—the computers kids carry around in their pockets are more than enough.  I imagine we could translate the entire library of Congress into a phonetic alphabet for what we spend teaching spelling!

Joe Austin

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