Mental Math

Confluence of reading the comments on Sarah Hoyt’s latest blog post, and a couple of observations.

Kids who do math in their heads hate showing their work. And especially since the “gifted” math students can do all the basic arithmetic in their heads, they get to about halfway through algebra and start hitting a brick wall, because they have no idea how they solve math problems and no way of formally applying the mental procedures to more complex equations. Oh, some of them will reason out the answer – in about twice as long as it takes a “less gifted” student to come up with the correct answer through using the formal process and a pencil and paper.

There was a meme about the Common Core math that was floating around on Facebook for a while, and the explanation of it (see link) actually makes sense. Except that the way people do math in their heads is not congruent to the way people communicate through the language of math on paper. 

Math is a language. Sure, if you asked me “What’s 82 times 4?” and I didn’t have a calculator or pen and paper in hand, I’d do it mentally like this: “8 times 4 is 32, so 80 times 4 is 320, and 2 times 4 is 8, so the answer is 328.” It’s a neat parlor trick (and my Dad used to do that sort of thing all the time when I was a kid and I found it totally aggravating) but it also requires you to have developed a lot of “working memory” for holding numbers in your head and remembering that the important one is 320 while you’re doing 2×4 and adding the result. I’ll often teach my tutoring students to do this if they’re already quite numerically literate and depending a bit too much on their calculators for simple arithmetic. But if I were going to show you “the math” for doing it, I would write it down and do it the “formal proof” way.

Because math is a language that has certain ways of expressing ideas. Which is exactly what I tell my students about a lot of the formulas they use – they’re just abbreviations for certain ideas. And it just helps you do your math homework/tests faster if you have the basic ones memorized… as long as you’ve internalized what they mean so that it’s not just alphanumeric soup to you. (Of course, there’s a certain amount of “fake it til you make it” that works out okay, as long as you can identify which problem type calls for which formula and where all the numbers go.)

Sure, you can do 30 minus 12 by asking yourself “How far is the distance between 30 and 12 on the number line?” – in which case, the correct answer is “eight to twenty, ten to thirty, therefore 18.” And yes, I think this ought to be taught… along with the idea that there is a “formal proof” method of expressing the operation mathematically. Because not every child is going to be able to do all that in their heads, but asking them to write what amounts to an essay on basic arithmetic is hardly any better than making them use a “traditional” method of showing their work. Unless your goal is to ensure that no parent will be able to help their child with their homework so that the kids with invested parents won’t fare any better than the kids with neglectful parents. (But they’ll be equal!)

And yes, I do believe there are teachers dumb enough to require their students to “show their work” using a method that’s meant to be entirely mental or they’ll downgrade the students. (Probably mostly boys, and the exact same ones who already think showing their work is bogus.) Especially since, as a mental technique, there are multiple ways to approach the “leapfrogging” from one number to the next. The point of having a commonly accepted way of expressing mathematical operations on paper is so that people don’t have to spend a lot of mental energy figuring out exactly what’s going on in between each step of the math problem! Especially when they have sixty papers to grade by tomorrow.

I’m sure if you threw out all the grammar and spelling rules and told kids to just make it up as they go along based on what English sounds like, there would be a lot of people screaming bloody murder, too! Thing is, nobody takes the jokes about dropping “ph” for “f” – and so on – seriously. Although I do have to admit, I have heard that there are some benighted souls who think that having their grammar corrected is racism. Hopefully that is an urban legend. But unfortunately I’m sure there are some radical Marxists who would be perfectly willing to promulgate such a belief…

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Hugo Reading: Skin Game

I’m a Dresden Files fan – though I never did really get into the TV show – who’s read all the books and a good chunk of the shorts. (I’m not a big enough fan to keep up with the shorts, so I never know when there’s more of them.) I’d read Skin Game when it first came out, and decided that I’d need to reread it in order to rank it properly against the other Hugo nominees: Ancillary Sword, The Goblin Emperor, The Dark Between The Stars, and The Three Body Problem. (This list is not in preferential order.)

I’m not entirely uncritical of the series – I thought Changes really, really, really sucked. Not because of the plot, but because the entire book was written in a sort of emotionally dissociated manner full of “telling” and not “showing” that ticked me off. Ghost Story was better, and I liked Cold Days as well, but I think Skin Game really hits it out of the park! And I think the work is especially strong because it rewards a re-reading – I didn’t remember every surprise detail but I did remember enough to anticipate the plot twist coming – without my foreknowledge ruining the suspense.

So. I’ve read all the novels nominated for this year’s Hugo Awards. Skin Game is my first choice. The Dark Between The Stars will be my second choice: I have to respect an author that can pull off the Loads And Loads Of Characters plotline without losing my interest! The others, I’m not entirely sure yet; I’ll have to mull things over and consider exactly what principles I should use to rank my non-favorite entries.

I will be keeping an ear to the ground, as far as the anti-Sad-Puppies politicking goes. Because as much as I want to be an idealist like Brad, idealists do not make the rules, and when idealists play against ideologues like the SJW CHORF crowd, they always lose – because idealists play fair, and CHORFs think “fair play” is for their opponents, not themselves. If there is still an anti-SP contingent campaigning for “No Award” scorched-earth against the SP3 works when the ballot deadline rolls around, I’m going to play hardball right back at them. Because I don’t make the rules. THEY make the rules – after all, haven’t they been claiming that the Hugo Award belongs to them this year? (After spending two years claiming that it’s a popular award for all of fandom!) And if they think it’s fine for their side to vote for a Hugo Award according to politics, then that’s exactly what “the rules” are for this competition. At least I can say I’ve read all the works, which is more than they’re willing to do.

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Hugo Reading: A Single Samurai

As far as I know, this story isn’t available for free online anywhere, but Baen is a generous publisher so I’m sure it will be available in the voter packet. I actually own the anthology containing this story – just hadn’t gotten far enough in it to have read it before it was nominated. By people other than myself, in case anyone is wondering.

Well. It’s very… Asian-flavored. My favorite quote about Asian movies goes something like this: “Like King Lear, only more depressing.” And I happen to be a fan of anime like Mononoke, in which (invariably) a lot of (deserving) people die, too.

Meeeeeeeeeeeeeeeeeeeeeeeeeeh. It lacks a certain lyrical quality that the best shorts possess. I could overlook the story type not being my favorite if the prose “sparkled” more. I’m not even sure how to describe sparkly prose, though – obviously I have not studied enough Lit courses.


Continue reading

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Hugo Reading: Totaled

I was poking about on the internet, ending up on Mars Is through MHI, and I saw a link to “Totaled.” Being a little ADHD in my internet consumption (“browser tabs” was either a great invention or THE WORST, I’m not sure which) I decided I had to go read it RIGHT THEN.

Wow – I gotta say, if you’re going to do tug-on-heartstrings soap opera scifi, that is the way to do it. The human pathos is intimately intertwined with the speculative fictional elements in a way that neither one can be extricated from the other – which is precisely what I want to see out of award-worthy works. Great writing is great, for sure – but a scifi/fantasy award needs to go to a scifi/fantasy work. Not a work with only a limp, meaningless gesture towards scifi/fantasy elements.

I didn’t cry at the end, but my eyes definitely prickled.

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Hugo Reading: The Goblin Emperor

The blurb printed on the front of this book reads “challenging, invigorating, and unique.”

I’m afraid I’m not impressed in the slightest. I found no aspect of the novel challenging, except keeping track of particular name-forms: there is an appendix in the back, but as the table of contents is excessively large and I didn’t read all of it, I wasn’t aware of this resource until I finished the book. *looks* Oh wait, it’s not even listed on the TOC! How… unique. 

As far as invigorating, it is quite a passable bit of entertainment, but nothing more. Not boring, but not a compulsive page-turner either. It doesn’t have a downer ending, though – perhaps some readers accustomed to gloomy depressing books like The Three Body Problem and find a hopeful ending invigorating.

As far as unique, there must be some new definition of “unique” that means “checks all the boxes” – we have the dark-skinned half-breed (racism, check!), the proto-feminists in a patriarchal culture (sexism, check!), the abused orphan victim who’s suddenly the most Important Person Of All (victim-worship, check!), and the Understanding Foreign Cultures box, due to a guest “appearance” by the Mongol Horde in court discussion, which is mentioned in the book solely to check the multi-culti box. I’m serious. They serve absolutely no function in the plot whatsoever, except to show that Harry Potter I mean Maia, is A Good Person!!!

This book is court intrigue, and that’s all it is. Literally. There are no pressing concerns outside the court: the rest of the world sends the occasional representative, but all of them are bit-players in the grand tale of Blossoming Mary Sue Maia, the Goblin Emperor, who appears to go from a half-educated political exile to Emperor Secure On His Throne in the space of a single season. *cough* I guess I’m being a little too hard on the only character in the entire book, though. If you were expecting to get to know any other side characters as well, unfortunately you’ll be disappointed. None of them get enough screen time for the reader to get to know them. And Maia isn’t allowed to have any friends, because he’s the emperor.

I’m not quite convinced that this novel qualifies as fantasy, honestly. Elves? Goblins? Other than some references to ear-twitching and eye color, their society is human-vanilla. Completely. There is magic, but nobody ever uses it for anything significant that couldn’t have been just as easily accomplished with readily-available technology. (The tech-level is steam-powered industry, but not much of that appears in the novel either.) There’s minor hints of divine intervention from the local pantheon, but that all happens to somebody else offscreen, not our sole character Maia. There’s no mystical or technological McGuffin, no arcane powers. Not even any quirks in “elf” or “goblin” society that makes them any different than any fictional human society, either.

So basically, this book is the opposite of challenging or unique. Which doesn’t mean it’s not entertaining, if coming-of-age stories and court intrigue plots are your thing.

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Hugo Reading: The Three-Body Problem


Depressing. Highly reminiscent of all the YA SF I read as a child from the library, in which The Entire Planet is DOOMED Because Humanity Sucks. Good characterization, which is a relief because the book is nothing but characterization. It’s not that literally nothing actually happens, but it certainly feels like nothing happens by the end. Not quite a waste of time but not a book I’d recommend to anyone; the work is simply not to my taste. It will be last on my ballot, unless The Goblin Emperor manages to be terrible but not quite bad enough to get kicked off my ballot entirely, which I am not sure is possible. (I tend to like political intrigue plots.)

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How to learn to do the crown braid

No, not how to do the crown braid – you can Google that and find a YouTube video that you happen to like. I’m going to tell you how to learn to do the crown braid. Because it looks freaking difficult to do yourself if you’re just starting out, and to be honest it is not the easiest braiding hairstyle for a beginner. So I’m going to give you instructions based on how learned how to do it. Over the course of several years.

First, of course, you have to know how to braid in the first place, but since fingering habits are important, I recommend you learn to do a French or Dutch braid. (I prefer Dutch, also known as inside-out French braid.) On your own hair. I have a Klutz book that shows specific fingering that allows you to easily hold all three strands in one hand at a time. Do this braid on yourself until you can do it half-asleep before your first infusion of caffeine, because your fingers remember how to do it, and your arms don’t ache while braiding because you can do it fast! (You can easily adapt the fingering patterns of French or Dutch braids to braid a ponytail, and won’t pick up any bad braiding habits this way.)

Got the Dutch braid ingrained in muscle memory? Good. Now, do braid sideways across the front of your hairline, starting from where your hair naturally parts. (The larger side, if your part is asymmetrical like mine.) You can start out by taking this sideways braid and just braiding it straight down next to your face once you get to your ear. Next is the tricky part: once you get to your ear, figure out how to switch hands from “braiding in front of your face” position to your typical “braiding behind your head” positioning. This is where the fingering depending on only one hand holding the strands at a time is crucial. Continue braiding behind your head but just go straight down your back like a normal braid.

Now you’re at half-crown, and you’ll have noticed a lot of extra slack in the off-side of your hair if you try to wrap the straight braid around your head, and possibly you’ll think your hair is too short for a crown braid. That might not be true: a full crown braid wraps a lot farther than you’d expect if you’re going off of how far a straight-back braid will reach.

Gotten to the point where you can do the switchoff at the ear consistently without losing your place? Good. Practice parting your hair farther and farther to the side, until you’re starting your half-crown at one ear and braiding next to your hairline all the way around to the other side of your head. I lean over sideways to accomplish this, since the hair above my “start” ear definitely doesn’t want to stay lying flat when I brush it to join the rest!

Once you have gotten to this point you have all the basic skills. Now, you just have to learn to do a second switch off behind your head once you reach the back of your ear, the one you started at, in order to move your arms back to the front of your head. (At this point you’ll probably only have one or two more sections of hair to pick up into the braid, and these will be the “loose” ones if you didn’t braid tightly enough to your head. You can use bobby pins to secure the extra if you need to, though, so don’t give up if your first tries aren’t perfect!) After that, you can finish braiding the length of your hair and wrap the rest of it around your head, securing with bobby pins. Try to braid as far down as you possibly can: you want the smallest unbraided tail you can get, to make tucking and pinning it easier. I recommend the second switch-off because it’s quite hard to take up the slack and braid “to the front” of your head if your arms are still both behind your head. I certainly always had sub-par results before mastering the second switch-off.

With this training regimen, you can take yourself from basic braiding skills to doing crown braids yourself, without a lot of frustration. If you work up to it, it will seem really easy, while it looks quite difficult! Crown braiding definitely feels like an uber-feminine style to me whenever I wear it. And it attracts a lot of attention! One other useful thing about it – with application of hairspray, bobby pins, and a silk scarf, you can actually get multiple days out of a single braid before it starts going too “fuzzy” to continue to wear in public. It also keeps your hair from swinging and getting into things it shouldn’t, when you’re working on dirty jobs! I think it’s especially good for travel, since unlike a bun, it doesn’t stick out on the back of one’s head and get in the way of seat head-rests.

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