Not too long ago, I heard about a parent-teacher conference that I wish I’d sat in on. The story goes that this parent-of-a-struggling-student kicked off the conference by explaining how he, the parent, would teach the class.

The first suggestion was that the teacher should make the class interesting. The second suggestion was that the teacher should show how the class material related to the students’ everyday lives. Both were brilliant ideas that had never ever occurred to this teacher in all his years of teaching. And yet the third took the take:

The teacher should explain how he wished he’d worked harder in school so that he didn’t have to become a teacher. That would inspire students to hit the books, pay attention in class, and perform well on assessments.

Upon hearing this story the first time, several barbed responses occurred to me. My favorite of the bunch was “Sir, I retired when I was 28. I teach because I love teaching children.” Why? Three reasons. First, both statements are technically correct, which is the best kind of correct. Second, “I teach because…” is a positive statement that hopefully will segue into a positive, productive discussion. Third, it makes the jerk a little more insecure about his own accomplishments in life, or lack thereof.

Actually, if I’d heard that third suggestion in person, my eyes would’ve bulged out, my jaw would’ve dropped, and I would’ve been too shocked and insulted to respond right way. I’m told that the teacher kept his composure, wisely let the comment slide, and went on with the conference, which was probably the most professional way to handle the affront.

While it is true that we want our students and our progeny to have better lives and careers than we had, there are probably better ways to articulate the thought.

Ramblings on innumeracy.

Ereyesterday, I had a fun chat with my dear friend Dr. Hmnahmna regarding Common Core mathematics. Here’s a transcript, edited slightly for clarity and national security:

DR. HMNAHMNA: From what I’ve seen of “Common Core” math (the quotes are deliberate), it’s not nearly as stupid as people think. I say “Common Core” because all Common Core does is say that you should have certain skills at a certain point.

VDV: I don’t think it’s stupid, but I do think it’s needlessly complicated. They’re giving as much emphasis to shortcuts and tricks as they are to basic algorithms and tables. I think that’s a mistake.

DR. HMNAHMNA: What most people call “Common Core” is various curricula that implement those standards.

VDV: Correct.

DR. HMNAHMNA: There’s actually deep concepts buried in those “shortcuts” and “tricks”.

VDV: I don’t deny that one bit. I question the utility of the approach, and I fully expect that as these students reach high school they’ll be worse at math than current high schoolers.

DR. HMNAHMNA: Here’s an example of chunking:


Basically, this breaks the problem down into easier to manage chunks. If you’ve ever made change running a cash register, this is the way it’s done. It also demonstrates the commutative and associative properties of addition and subtraction in a concrete way. And if you’re trying to quickly subtract 712 – 648 in your head, it works much better than trying to remember the borrowing algorithm that we learned.

VDV: Again, I’m not denying that the tricks/shortcuts/alternate methods aren’t useful. I think the traditional method has far greater utility on paper. And I don’t mean “on paper” to mean “theoretically”, I mean actually on paper. The larger the numbers get, the less I’d want Joe Average to rely on a mental calculation, and the more I’d like him to rely on tried-and-true. I’ve seen a lot of students try to guess their ways through simple arithmetic work, and if they don’t guess right, the attitude is “oh well”. I shudder to think what’s going to happen when the CC wave comes through. Maybe I’m wrong, though.

DR. HMNAHMNA: Is your students’ approach a matter of not knowing the method? Or is it just trying to blow through and not caring? Because I haven’t figured out a teaching method that can overcome cockiness/laziness.

VDV: [Redacted list of SMERSH-approved torture techniques] overcome cockiness and laziness. Unfortunately they aren’t permitted by the curriculum. Seriously, though, what I meant was that training the masses to do it in their heads will lead to less patience with pencil-and-paper, and less willingness to use it.

DR. HMNAHMNA: The other big advantage I’ve seen from these other methods is that they are designed to promote a deeper understanding of what you’re doing when you subtract 712-648. And demonstrating it using teaching methods that are applied again in higher math.

VDV: When you put it like that, I think of the analogy of plumbing vs. fluid dynamics, or history vs. historiography. Or of the argument over the correct “first ten numbers” (0-9 vs. 1-10). Do they need the deeper mathematical understanding, or do they need extensive practice in efficient arithmetic calculation?

DR. HMNAHMNA: I happen to think that innumeracy is a big problem and that deeper mathematical understanding is important, though practice for efficiency is also important.

VDV: I agree. I see no reason not to introduce algebra/geometry earlier.

DR. HMNAHMNA: If I had to choose, I’d rather have a deeper understanding and slightly less efficient.

VDV: If I had to choose that for the Hmnahmnas and the [our friend who majored in mechanical engineering and is an industrial manager]s and the [our friend in military intelligence who majored in history and physics]s of the world, yes. But we’re also talking about the people who mess up your change at McDonald’s.

DR. HMNAHMNA: I think the example above will actually help the people at McDonalds not mess up your change. Note I said that it is the exact method you use to count change– count up from the total to the amount of cash handed over.

VDV: That’s why I used that example.

DR. HMNAHMNA: And hopefully, the deeper understanding will remove the blank stares when the total is $6.03 and you hand them $10.10.

VDV: May I propose a minor flaw with the analogy? If chunking, cashiers don’t have to keep track of how much they’re handing back (i.e., the difference). They just have to keep adding bills and coins until (price + change) = (initial payment).

DR. HMNAHMNA: Maybe I don’t understand people that are stupid at math, which is entirely possible.

Dr. Hmnahmna has a doctorate in mechanical engineering. It’s entirely possible.

Byzantine arithmetic is not unique to our era. About a month back, I picked up an 1877 edition of Ray’s New Practical Arithmetic: A Revised Edition of the Practical Arithmetic. Four bucks at a flea market. Here’s some Core-esque material from page 29:


I shouldn’t have posted this. Someone, somewhere, might get some ideas.

Yesterday I was told by another friend, who has operated cash registers far more recently than either Dr. Hmnahmna or I have, that many modern cash registers have dedicated buttons for each denomination of currency. That means that a present-day cashier can get away with not knowing how much cash the customer handed over. If the customer gives the cashier two twenties, the cashier can just press the $20 button twice.

I replied that even that might prove too complicated one day. What if the cashier doesn’t recognize the digits on the bills or coins, or can’t tell the difference between Grant and Franklin, or doesn’t understand that a $20 is worth more than a $10? I mean, looking at two digits is so much tougher than looking at one. We need to make counting bills and coins as simple as humanly possible. Therefore I recommend that henceforth, all portraits and other decorative images on American currency be replaced with symbols from video game controllers. Problem solved, and we’re one step closer to pure idiocracy.

My proposal also eliminates any possible debate about controversial figures appearing on our currency. Honoring Andrew Jackson by putting him on the twenty is questionable for several reasons, but what did or  ever do to anyone?


A coupla weeks back, a student asked an odd question. She asked how the members of the Second Continental Congress got to Philadelphia to work on the Declaration of Independence. Before I got the chance to answer that question, she asked another, much braver one: “Did they have cars?”

I hope I stopped the teasing and tittering before it got started by explaining that cars, as we recognize them today, wouldn’t be invented for another 100 years or so.

Anyhow, that “silly” question got me thinking. Consider that to the average teenager, cars have always been around. Their parents and grandparents grew up in a world with cars all over the place. We can easily grasp the idea that cars haven’t always been as advanced as they are today, but visualizing a world without cars– and I mean going beyond the intellectual knowledge that cars haven’t always been there, I mean really visualizing what life was like as if we were there– grows increasingly difficult with each passing generation. (Consider also that there isn’t much history taught in elementary school, and if you haven’t sought out this sort of information, and if it hasn’t come up in a history class by the time you’re in my classroom, it makes sense you wouldn’t really know when the automobile came around.)

Look at telephones. Today’s high school seniors were born in a world where cell phones weren’t ubiquitous, but they probably don’t remember it well. I remember pre-ubiquity pretty darn well: it was much more difficult to get in touch with people, cordless phones were a big deal, you used pay phones more often, caller ID was less common, prank calls were more common, and so on. My parents remember the days of someone from the telephone company coming over to install or repair your AT&T phone– and you were stuck with AT&T because there were no other phone companies. My grandparents, once they finally got phones, had party lines.

I remember a time before cell phones (yes, they were invented before I was born, but they didn’t trickle down to Joe Average until 10-15 years ago). I can imagine what the world was like without any sort of phones, but I don’t think I can truly appreciate what that world was like. And I think that makes it harder to count the ways in which the world is more awesome than ever before.

The faster technology advances, and the more that people are born into an increasingly advanced world, the harder it is for people to understand their ancestors’ everyday lives and to appreciate the material progress of mankind.

I probably wouldn’t have liked this when I was a teenager, but I’d like to see some sort of lesson or ritual or holiday that involves living with the technology of generations past. Some people might call that “camping”, but that’s not what I’m talking about. I mean a 1963 day (and night) where you live with the technology of 1963– no cell phones, expensive long-distance calls, music from the radio or the record player, a black-and-white TV, etc. (“Kids, this is how your grandparents lived.”) I mean a 1923 day with a party line phone, limited indoor plumbing, limited access to cars, no TV, maybe a pre-talkie movie, and no microwave or fast food. (“Kids, this is how your great- or great-great-grandparents lived.”) I mean an 1873 day with no cars or TV or phones or electric light. Let’s even throw in the clothing of the time, though I wouldn’t throw in the medicine or lack thereof of the time, because we’re trying to cultivate a sense of history here, not bring back the plague. Maybe we could also get the town/city/surrounding community to tone down the light pollution at night so we could actually see some stars.

Living that way for a day and night (though three to five days per time period would really drive it home) would do a much better job of showing kids how we used to live than any course or lecture or dinnertime story. It would be a far more powerful way of envisioning and connecting to our pasts. Sure, it’d probably be miserable to live through as a kid, but take solace in imagining your own grandchildren griping about “2013 Day” and having to make do with a smartphone that wasn’t built into your hand or not having a heads-up display projected on your contact lens.

When I went to college, I had a PS/2 with 4 MB of RAM and 128 MB of hard drive space when I went to college. When my dad went to college, he used punch cards to write simple addition programs on a computer the size of a room. When my grandfather went to college, he had a pencil, a slide rule, and some paper. My great-grandfather didn’t go to college; he had a shovel and a railroad wrench.


We’re three days in to the new year, and all three days I’ve had a vague and nagging feeling that something was just plain un-right. I wasn’t able to place it until this evening.

I spent a good chunk of pre-planning trying to determine the best layout for my classroom given the increased class sizes. In all that time I spent trying to figure out how to arrange 35 desks in my room, and which other pieces of furniture to rearrange or remove in order to accommodate those desks, and where to move the items that once sat upon the pieces of furniture I had to remove, and which desks were too badly broken to re-use, and where to get replacement desks from, and whether I felt like cleaning the desktops before the angels put their heads down on them, and where to put the small desks, and where to put the big desks, and where to put the red desks, and where to put the blue desks, and how to implement feng shui and optimize the flow of ch’i through my classroom and whether I was spending way too much time on the whole matter when I should have been goofing off… I forgot one small detail.

I forgot to hang my flags– Bennington, Washington’s Standard, and Gadsden. Those flags have adorned my classroom walls since time immemorial. ‘Twill be rectified tomorrow.