Things We Need You to Stop Saying, part 1

There are a couple of things we really need you to stop saying. The first:

"The right answer isn't important. It's knowing what you're doing."

No matter how you parse this, it's ridiculous. The right answer is the whole point of doing the problem ... has always been, is now, and will always be. The "knowing what you are doing part" leads to the right answer. If it doesn't, then you don't know what you are doing.

Variations on this include: "It's the concept that matters" and "We're putting the emphasis on the method." It shows up as sarcastic responses from Institute Professionals and college professors, too:

@MathCurmudgeon Good thing math is only about answer-getting, then! Phew!
— xxxx (@xxxx)

What we should be saying is "The right answer is vitally important ... so important that we also want students to explain the method and how we all know the answer is correct; they must be able to detect an error if it occurs and describe how to fix it so that the solution IS correct."

If you go to the trouble of having the students communicate, verbally or in writing, how they solved a problem, then you are focused on the right answer ... there would be no need to explain anything, or fix errors, if you didn't care about it. You'd take any randomly achieved answer as long as it was correct, and move on.

Just cancel the 6s.

Does anyone ... ANYONE ... seriously think that the right answer doesn't matter here? I don't consider this a "right answer" even though it looks like it.

I'm going with "No."

You'd take a wrong answer that looked like a right answer if you weren't paying attention.

Just cancel the x² from numerator and denominator.

One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from.

That is a far cry from "The right answer isn't important."

For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge.

You can't detect errors unless you know the right answer, or at least have a sense of what that right answer should be.

Even the infamous "Letter to Jack" assumed that the kid could get the right answer, then could find the error made by the other kid ... the assignment went two steps beyond the right answer: explain the error to the other kid and help him fix it.

JD2718 banned FOIL, Dan Meyer used immediate feedback, countless teachers rearrange PEMDAS (as BEDMSA) to avoid this:

We need them to explain what and why.

I often "let them in on a secret" and share the mnemonics after they get the understanding ... especially if the mnemonics speed up computation so we can get on with what we are actually doing, but every teacher worth his salt knows that you have to periodically make sure that random, blind luck isn't at play.

The last reason that we need to stop saying "The right answer isn't as important as knowing what you're doing" is that too often we teachers are speaking to people who don't know that it is merely step 1, namely school boards, administrators and parents.

I watched a young teacher from another school give a presentation to her school board. Among other weird things, she came out with this statement ... immediately, board members latched onto it.

"What do you mean? Of course the right answer matters."
"I've been in business for forty years; every time, the right answer matters."

She doubled down ... "No, they need to know HOW they are solving the problem." No one was buying it, nor should they have. Whether she didn't understand their concerns herself or honestly didn't believe that the right answer was so vital, she certainly couldn't communicate her stance to the Board.

A blind acceptance and repetition of poorly-understood Twitter broadsides and mindless slogans is the rhetorical equivalent of canceling the sixes.

That makes us all look bad and we're gonna need you to stop saying it.

Doing Things the Hard and Expensive Way

So this school had an election. Desperate to justify their purchase of enough TI-Inspire Navigator calculators for the whole school, they used them for voting for StC, because apparently:

• the cellphone that every kid carries around were ... IDK ... banned, 
• the free Socrative.com website was shut down undergoing maintenance at that exact moment, as were all of the similar, related websites, also free. .. like SurveyMonkey.
• Google Forms was suspiciously locked and inaccessible ... 
• the supplies budget didn't allow for 100ct note card pack at $0.39 per ...

but did allow for the Inspires:

For this misuse of funding, we hereby award them the US Armed Forces Monetary Memorial Medal, emblazoned with the image of Our Rich Uncle Pennybags.

How cool is this? HS students used the TI-Nspire Navigator to cast their votes for the Student Council Board: http://t.co/tr8WEjJKI0 #edtech
— TI Calculators (@TICalculators) April 16, 2014

Snap Judgements

I love the kinds of conclusions people make on Twitter.

"Which looks more like a 21st century classroom?"

Neither. They're booths at a conference. I understand that the snap judgement goes against the top booth because the 21st century classroom isn't supposed to be about one person "lecturing" and 30 students quietly absorbing new information without "collaboration"; it's also missing a lot of misunderstood 21st Century Learning New-Age Idealistic Pedagogical Folderol.^tm

But I digress.

In the Upper portion of the composite photo, we see a booth set up to present a lot of information. The people are encouraged by the layout to be seated, which means that they can all see because they out of each others way; no one is standing in front of the screen.

Think about this for a second. TI has a mission: sell calculators, at $150 each, with crappy screens and SLOOOOOOOW processors. They need to get you in a seat and show you the WOW factor. They need to get you past the basics fast and sell you on the tech because that $4500 classroom start-up fee is huge.  "Those regression functions don't come cheap, and aren't in any other package."

This is crying out for exactly what they've got here: a booth with a presenter who knows the machine inside and out, delivering information to as many people as they can, as efficiently as they can, in as little time as possible.

You put them in a seat where they can set down their stuff, see the big screen, write something down if they want to, hold the Inspire, swap out the faceplate, photograph it with their phones, set it down and tweet about it ... tables and chairs arranged in an efficient pattern, making best use of the space. Additionally, once seated, it's tough to leave politely before the end of the spiel and it's easy to control the technology and prevent theft.

Over on the side, some tall tables (which don't force you to lean over) for people who are browsing and don't want the whole presentation, or who want to stand and watch from the side.

BOOTH SCORE: 8 out of 10. Great for information transfer and for sales promotion. This booth is designed to have you linger and explore, try out and figure out, and to convince to you agitate for a major purchase back at your school.
CLASSROOM SCORE:  7 out of 10. "Boring" if you are looking for new-age learning styles, but effective as an organized setting for 30.


In the lower one, there is a guy on the left, holding a laptop in an awkward stance. One of the people he's talking to can see the screen. The other one can see the keyboard and be part of the conversation but unless he leans in and gets in the way of the other listener, he can't see much.

In the lower right, three people are crowded around a computer that desperately needs to be on a higher platform because all the people who want to look at it are standing -- it should be at eye height or, if not eye height, at least not "lean over and peer through the top part of your bifocals and then crane your neck back so you can see through the lower half of your bifocals" height - as the guy in white shorts is being forced to do.

In summary, a badly designed booth for this function, unless that function was "quick information shot and move on." This booth is designed to NOT allow you to linger and deeply explore the product.

There is no marketing director here trying to maximize anything, because there doesn't need to be. They only need to let you convince yourself that Desmos is cool - it is its own selling point. The website is free and doesn't have a large initial classroom purchase required, as TI does.

As a classroom, this booth is crap, too. There's nowhere for people to get comfortable. There's a giant graphic with some expression art. The displays / workstations are placed too low without any chairs so students have to type at weird angles. If the intent was for people standing, there should be some podiums so they can set down their devices and use both hands. If the intent was for people to sit, then the tables are at the right height, but there are no chairs.

This would be a horrible "classroom" for teacher/guide or for students.

BOOTH SCORE: 3 out of 10. (or 8 out of 10, depending on intent)
CLASSROOM SCORE:  1 out of 10.

But I guess I don't see things in the same way as other people do.

Oh dear! RT @calvinballing: @Desmos and TI at #NCTMNOLA. Which looks more like a 21st century classroom? pic.twitter.com/SgcWBPUgSu
— Christopher (@Trianglemancsd) April 13, 2014

Volumes

Thanks to a sale at Jo-Anne Fabrics, I got this heavy-weight craft paper, 100 sheets of 12"x12" for about 5 bucks. Unfortunately, they were out of heavy weight linen for fighting tunics and cotton duck for banners. Satisfy one addiction, develop patience for the other.

Print the base functions.

Shells.

Same function photographed with foil crane. Looks creepy, doesn't it? Like Giant Spider in a Colosseum model.

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