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Just got a card from a student who has been having a rough year. She was having a great deal of trouble until I started showing her how to really USE a calculator. (It's algebra and geometry not arithmetic, and she knows the algorithms just makes SO MANY little mistakes)
Since then she's really taken off. I find very few people who could benefit from calculators know how to use them effectively, and there is a lot of snootiness and stigma in the way of this happening.
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I generally agree that up to around grade 7 there isn't much use for calculators. But from there out if you understand place value and can estimate being consistent and accurate doing long hand calculations is kind of overrated-- I'm always a little shocked that once I tell the grade 9 students they can use calculators they somehow keep making arithmetic errors... (HOW) not this student, though!
She might even like math now. Imagine that.
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@futurebird
Loving all of this post!
You have planted a seed. You have increased the chances of her liking math. And if she likes math, she increases the number of career paths she can take.
It is one of things I sort of get bummed out about is that schools (in general) do not teach how to use tools. Tools that are widely used in industry.
You rock!
I've heard teachers complain "my students put things like 6*8 in the calculator"
I always think "so?" I mean if they know it's around 50 and are worried they've mixed it up with some other fact why does it matter?
You are teaching calculus who cares?
(It's 4 ... 12s which is helpful if you know the 12s but if you didn't learn them young... anyway it's kind of a distraction from the problem at hand. Get the correct result. Use the tool. )
@futurebird @snacktraces
Yes! Normalize redundancy, verification, and checking external sources, instead of encouraging the arrogant practice of refusing help to demonstrate knowledge! It’s a fragile ego that refuses “measure twice, cut once.”
@inthehands @futurebird @snacktraces Great advice.
Recently my son had CS coursework that involved converting a bowl-of-spaghetti logic diagram into a C++ program. Me, with 40 years of C experience, independently wrote my version of the program, he wrote his in C++. I asked him to send me his output and I sent him mine.
They didn't match, and sure enough I had messed up an AND gate.
@stacey_campbell @futurebird @snacktraces Joe Groff (of the Swift compiler team at Apple, wow do I miss him on here) once remarked that unit tests and static types have in common that they are a form of •systematized redundancy•: both ask engineers to express their understanding / assumption / intent in two forms, and then a second actor (the machine in both those cases) checks that the two forms agree. I love that way of seeing it.
@inthehands @stacey_campbell @futurebird @snacktraces so type inference is counter to that. Which is useful to say out loud when wrestling with type inference gone awry, as often happens when chaining many function calls together
@paddlefish Maybe counter, maybe just pushes it back a few layers. At best, it lets the developer push those explicitly stated assumptions back to the places where they’re actually worth stating (as opposed to “yes, I explicitly think that int plus int is int). At worst, they turn code into a Sudoku-like logic puzzle of a build error.
Case in Point - I “melted” UI developers minds who insist on TypeScript for coded static type checking by extending/mutating said types in running JavaScript browser code to demonstrate prototype-based inheritance.
Unspoken assumptions should really be replaced with stated presumptions with %age of occurrence in a specific context and time range. Useful friction, overcome by required potential energy.
@dahukanna @paddlefish
Runtime type creation and static verification are always in tension. Anyone who tries to pretend there’s no tradeoff there is too much inside their own bubble.
> “Runtime type creation and static verification are always in tension.”
Nicely said. How does this get missed and ignored?
@dahukanna @paddlefish Exactly!! Seeing tradeoffs is the heart of engineering. Yet somehow our human nature always makes us want a single best answer for everything….
Every situation is on a spectrum i.e. has more than one value & I’ve never understood the need to have to have “the contextless only one”.
@dahukanna @paddlefish It’s a lonely world for people like us, Dawn.