Sunday, July 29, 2012

El Tenedor

I have been going back and forth with whether to just keep everything here, or put all the non-math non-teaching related things elsewhere. I settled on elsewhere. I think the mathematicians and teachers could handle the other stuff, but my family and friends will not appreciate the math. So, if you want to keep up with Kate's descent into abject Yerba mate addiction, road to international tango stardom, and relentless pursuit of penguin viewing, go follow this ugly tumblr by your favorite method. If you don't, do nothing! Ciao!

Quick and Dirty Unit Conversions

Part of getting used to my new city is acclimating to new units of measure. Which have rather annoying conversions to perform mentally on the fly. In time, I won't need conversions, because my internal sense for these things will calibrate, so that I know what 10C feels like, and how painful it is to pay 15 Argentine pesos for a good cup of coffee (not that painful!), and about how long it takes to walk 3K. In the meantime, I have noticed myself devising some "good enough'" estimation shortcuts. Of course, I've also analyzed the reliability of these shortcuts, because I'm like that. And when you're a Precalculus teacher, everything looks like a function transformation.

For example, I have never been able to reliably remember the formula to convert between Celsius and Fahrenheit. I know it has a 5/9 or a 9/5, and I know you add or subtract 32, but good luck remembering what goes where when you need it. And then mentally working on a number that is not a multiple of 9 or 5? No thanks. (Dear mansplainers: before you head to the comments to mansplain this to me, I can look up formulas any time I want. And yes I know I can use my phone here in any number of clever ways. The point isn't exactness - it's estimation with good-enough accuracy while simultaneously not dying in traffic.)

My first tactic was to devise a quicker formula. Mostly, I am having to hear a temperature in Celsius, and convert it to Fahrenheit, so that I know whether I will need a jacket or whatever. So I need something close to F = (9/5)C + 32. Okay so 9/5 is pretty close to 2, and 32 is pretty close to 30. "Double it and add 30" is a function I can work with, even after two glasses of Malbec. Let's see how useful this is with a graph.


The two rules give the same result, 50F, at 10C. The estimation is worse the farther you get from 10C in either direction, but how hot/cold does it really get here? Even at extreme temperatures for Buenos Aires, we are not that far off. 0C should be 32F, but with the new rule it's 30F. (And yep that's as cold as it gets here. Feel free to hate me. I did my time.) 40C is really 104F, but with the estimation we get 110F. I don't know about you, but I don't know the difference between what 104 and 110 feel like, because they both mean "ermahgerd, stay inside and have a beer or something." We can also summarize this with a difference function: 2x + 30 - (9/5)x - 32 which simplifies to (1/5)x - 2. Let's put this on our graph.


So there's a picture of what we just said in words. The x-intercept at 10C is when the difference is 0. The graph shows us how far off the estimation is for any temperature. Looking at x (celsius) values from 0 (hace frío) to 40 (hace mucho calor) we don't get far enough away from the x axis to matter for our purposes.

Converting in the other direction is not as useful to me, because I'm not generally hearing Fahrenheit temperatures and needing to know what they are in Celsius. However, we can use our knowledge of functions to realize we don't have to go through this analysis again. We can easily picture the inverse estimation function, "subtract 30 and halve the result" along with the inverse of the actual formula by reflecting both over the line y = x. Therefore the differences will have the same distance, therefore we're safe to use the estimation going the other way.

A second tactic I have found myself using is to mentally carry around a table of anchor temperatures. If I remember…
0C = 32F
10C = 50F
20C = 68F
30C = 86F
40C = 104F

…I can do a good-enough mental interpolation to know how it's going to feel outside. But that doesn't make for as fun a blog post. It's about the best I'm doing now with pesos to dollars, though. I just think of $100ARD notes as $20US notes (but I'm dissatisfied with that -- see below.)

Your assignment:


1. Any suggestions for quickly turning Argentine pesos into US Dollars at a rate of 4.5ARD = 1USD? Currently I am dividing by 4, and then dividing by 5, and then arithmetic mean, which works great but it's too many steps, and annoying for numbers that are not divisible by 4 or 5. An alternate method is to divide by either 4 or 5, whichever is easier, and then bump the result up or down a little bit by an arbitrary amount. I am never confident in results from this method, and find myself digging out my phone and dividing by 4.5. You have a successful technique when you can decide whether to spend $23 on breakfast in the time it takes to cross a street. You must also make it to the other side alive, assuming Frogger rules: no car will slow down to avoid hitting you.

2. Do you have any favorite shortcuts for converting units?

3. Challenge : I still need to get a good photo for this, but seeing gas station prices in ARD/liter and trying to mentally calculate how expensive that is, is breaking my brain. I suppose I would care more if I had to buy gas.

Update
I'll swear on the deity of your choice that I didn't see this first.

Tuesday, July 24, 2012

Twitterers and The Human Resistance and Radical Preschoolers

A few things I want to get down here for the sake of f(t) serving as my professional timeline.

#TMC12, y'all.
One word: surreal. I showed up a little late to dinner the first night, and this is what happened. Walked into restaurant, was greeted warmly by everyone, had a seat next to @cheesemonkeysf and gave her a quick one-arm shoulder hug. Then we all fell into and picked up on conversations we had been having for three years. Except I hadn't met any one of these people in person in my life. I had a little bit of an out of body experience, looking around the table and seeing all the avatars come to life.

After that, it just got better. In some ways, it was a teensy bit like a NCTM conference, except where everyone is invested to the nth, and you know ahead of time that every presentation is going to be killer (okay, so maybe not like a NCTM conference at all.) Part of the reason I'm struggling with what new things to try out next year is, I know about so many great things to try out. Foldables! Interactive notebooks! MOAR GEOGEBRA! MARSHMALLOW GUNS! Plus we got to do math in the morning, which why isn't there more of that in my life? Those four days were a testament to the quality of interaction and learning that a bunch of smart, generous professionals with pure motives and a sense of humor can pull off on a shoestring. Seriously I have a major nerd crush on every one of these people:


It was a privilege to attend and participate. For more detailed reflection (because they are poets, too) go read and read and read (that last one has links to all the other ones so I don't have to get obnoxious with this.) And check out our legitimate press coverage.

We Might Not Be Replaced by Robots After All
Finally, the forces for good are managing to gain some traction pushing back against the Khan hype. Go see this extraordinarily well-articulated piece by Karim Ani at WaPo's The Answer Sheet blog which presents a focused critique of KA's pedagogical issues, but also rightly places blame square at the feet of the breathless, undeserved mainstream hype. Being mentioned in the same sentence as Frank Noschese is making me feel prih-tee-kewl, but I'm more excited that finally an argument has been laid down that I can point to and say "THAT is my problem with this. Right there." Also, holy bananas, Diane Ravitch is on it.

My Family is Awesome
Some of them went to Poland recently, and brought me back these:


Um, pass the sharp scissors? I think I have a new hobby.

I got to spend a little time with the most outrageously wonderful three year old around, who will now come out with "gotta get UP to get DOOOWWN!" without prompting (#auntwin)


And my Dad is an artist. Who happens to work in cheese and ham and tomatoes and basil:



I am one. lucky. girl.

And Finally
I realize this is gratuitous. Believe me. I am sick of myself. But how many times in your life do you get to type the sentence: I am moving to Argentina tomorrow!

See you on the flip-hemisphere.

Monday, July 2, 2012

#mtt2k and my own version

Here's both an entry to the #mtt2k contest, and a humble submission for a better video that provides instruction for this concept.

The target is the Coordinate Plane video. I used a tool called Popcorn Maker to add comments to it. I don't think this can be embedded, so please click here to go watch.

Before y'all get out your flamethrowers and head to the comments, I'd like to say a few things. I'm neither vitriolic, panicked, nor bitter about Khan Academy. I think it's a great resource and it's an excellent place to see a demonstration of procedures. I send my own students to it during exam review time, and they report that it is helpful.

Where Khan and the Gates Foundation overextend their claims, though, is when they suggest that the Khan Academy can serve as standalone instruction in Mathematics. Enduring learning requires productive struggle and time to noodle out unfamiliar problems, posed by a teacher who knows what you're ready for, and can provide expert scaffolding. Lecture-only instruction focused on mastering procedures is an impoverished substitute for doing Mathematics, and it doesn't matter if that lecture is in person or in a video.

Given that, I do think that the instruction provided in the Khan Academy could be improved with some better planning and basic pedagogical technique. It's already a good resource for some purposes, and I'd love to see it get even better. It's my hope that the key players involve will calm down, cut the drama, and work together to improve the available resources. It's math, people. Not the opera.

I made a video intended to instruct on the coordinate plane. Although I'm certain it could be improved since it hasn't been subjected to editing by anyone but me, I think it's better than the Khan Academy offering. First, it provides motivation for graphing quantities in two dimensions. Second, it asks questions of the viewer at key points, with the idea that the viewer would take a moment to think and respond before continuing. Here you go: