This Logic Game Needs a Name

This is a game to give Geometry students practice evaluating the truth value of conjunction, disjunction and conditional statements.

This is what one game set looks like, for use by two students:

Each set has: 36 statement cards, 18 T/F cards, a cube with logic operations on it, and 4 negation chips. (All the cards are one-sided.)

The sides of the cube look like this:

I bought unfinished wooden cubes at a craft store and wrote on them with a Sharpie (hence the bleeding.) I'm sure someone clever will comment with a better way to make these. You could also just use regular 6-sided dice and provide a decoder (rolling a 1 or 2 means "or", etc), but I was in overachiever mode yesterday. 
The kids are very much beginners in the Logic unit, so we gradually dialed up on the cognitive load by playing two easier warm-up games before the real game. I also had them set their notes from yesterday out on their desk for reference.

Warmup Game 1: Easy Mode


1) Use only the True/False cards and the cube.

2) Distribute half the cards to each player.

3) The person whose birthday is next wins when the outcome is True. The other person wins when the outcome is False.

4) Game play is like “War.” On each turn, each player flips over one card, and the cube is rolled. The players work together to determine whether the resulting compound statement is True or False. The winner keeps both cards.

5) The game is over when time is up or one person gets all the cards.

So if this happened, "True" would win the round:

But if this happened, "False" would win the round:
 

 
We only played Game 1 for a couple minutes, because it's pretty lame. Not very challenging, no strategy, also the "True" player has an advantage, because more of the possible statements come out True. On to...
 
Warmup Game 2: Like Game 1 but Harder


1) Use only the Statement cards and the cube.

2) Shuffle and randomly distribute 10 cards to each player. I gave them a few minutes to look through them to familiarize themselves with what the statements looked like, and think about whether they were true or false.

3) The person whose birthday is next wins when the outcome is True. The other person wins when the outcome is False.

4) Game play is like “War.” On each turn, each player flips over one card, and the cube is rolled. The players work together to determine whether the resulting compound statement is True or False. The winner keeps both cards.

5) The game is over when time is up, or when one person gets all the cards.

6) VARIATION: Each player also gets two negation chips. A negation chip can be played at ANY TIME, but can only be used once and must be discarded after use.

So if this happened, False would win the round:

But if this happened, True would win the round:
 

But if the False player still has a negation chip, she could opt to throw it down, and take the round:
 

So that was all a warm up to familiarize ourselves with the materials, and remember the stuff we learned about yesterday. Still kind of lame because there's not really any strategy. Finally, we get to play the very fun...

The Real Game (which still needs a good name)


1) Each player gets: 10 Statement Cards, 5 True/False Cards and, 2 Negation Chips. You will be choosing cards to play on each turn, so it’s ok to look at all the cards in your hand. (You could deal out more or less cards if you want the game to take more or less time. This number was manageable for about a ten-minute game. Most groups were able to play two games.)
2) The goal is to get rid of all your cards by making statements that work.

3) Game play is turn-based. On your turn, you select three cards and place them in the field of play: two statement cards and a True/False card.

4) Then, roll the cube.

5) Both players should agree on whether the resulting compound statement works or not. If the statement works, you discard the three cards used in the turn, and go again. If the statement doesn’t work, you keep the cards in your hand, and lose your turn.

6) A negation chip can be played at any time. Even after the cube is rolled. However, once a negation chip is used, it must be discarded, whether the resulting statement worked or not.

7) The player that gets rid of all her cards first, wins.

So if a player selected these three cards, and rolled OR, the statement works:

They discard those three cards from their hand and take another turn.
 
But if a player selected these three cards, and rolled IF THEN, the statement does not work:
 

And they return the cards to their hand, and lose their turn.
 
HOWEVER, if they still have negation chips, they could play one now:
 

and now the statement works, so they can discard these cards and go again.
 
All the kids were engaged in playing for the whole period. Some of them asked "Can we play this again?" which blew my mind. I intended to do an exit assessment but didn't, so I'll give it to them at the beginning of class tomorrow and see what they retained. If I made new games, I would make the Statement Cards a different color from the T/F cards for easier sorting. It also needs an awesome, catchy name! But I haven't thought of anything worthy yet.
 
The final version owes a big debt to my colleague Dina Kushnir who talked through the game play with me, and came up with some of the basic mechanics. I'd also like to thank Maria Andersen for all her writing and insights about what makes a good math game - I don't think this would exist without her.

Here are some resources so you can make your own games. Enjoy!

Good News Postcard

Here is a picture of the postcards we use that I talked about here. Unfortunately I don't have a digital file used to produce them, but at least you can see what they look like. I find the hand-holding-pen clipart very helpful, don't you? (Oh! That's what I'm supposed to do. Write on it. Thank you, clip art.)

Project Spiky Door

Ever since Riley and I had this exchange, I've been dissatisfied with my classroom's plain door that is not covered in spikes. Well, like, lo:

This took three days of class time (129 minutes) for a non-honors Geometry class of almost all tenth graders. Many students also needed some additional time outside of class. The goal was for students to get hands-on grokking for the meanings of height, slant height, surface area, and volume. They designed the net of a pyramid and labeled dimensions, calculated the total surface area and volume of their design, and constructed and decorated the model.

I offered a bonus for a base that was not a square. I also suggested making a cone instead, but none of them chose to make a cone, so next time I should make the cone worth a bonus as well. I specified a target range for the area of the base, and a target range for the volume, mostly so that the door would look cool.

Here is the project description and scoring sheet.

In order to make grading less ultimately-annoying, since they were given lots of flexibility in choosing measurements, I programmed my TI to do calculations for me (link goes to TI-Nspire .tns file.) The vast majority made a square pyramid, and just about every student first decided on the length of a base edge and the slant height, and went from there, so the program takes these measurements as inputs, and returns all the other values they were supposed to calculate. This way, if their numbers match my numbers, I can just move on, and only have to spend more time inspecting their work if there is a discrepancy.

Here is an example of what a student turned in. Since they had to organize their work, I had to say things like "Label EVERYTHING! Make it REALLY EASY for me to grade! I am VERY LAZY and I DON'T CARE if you get a good grade!" That sounds awful but it's funny only because they know neither of those things are true. It would be easier to grade these if you gave them like a template where they had to fill in stuff, but I think there's a ton of value in them deciding how to present their work sometimes. This is hard for me to explain, but when they are in filling-in-blanks mode it's different from figuring-stuff-out mode.

This was pretty fun and a nice break from the usual. I believe the goal of reliably distinguishing both slant height from height, and volume from surface area was achieved. And my door is looking pretty badass. I'd do this again.

Shoulders this project stands on:
Mimi
Riley

Good News from FM High School

Realizing that "make positive phone calls home" and "reinforce positive behavior" are on every teacher's to-do list, and that some of you regularly do these things, and that I'm not patting myself on the back too much because many of you are more virtuous than I...

But also recognizing that these behaviors being on my good intentions slash nice if I have time list and being on my checked-off list are two different things...

And also not judging myself too harshly for six years of failures in virtuosity...

I'm happy to report that the school providing me with a fresh, stiff pack of yellow postcards that have address blocks on one side and "Good News from FM High School..." on the other side has prompted me to send at least three of these every Friday afternoon to children's homes for...

acknowledging determination to not drop out of a class that is a challenge for them
or he is a cool kid and he volunteered to partner with the kid everyone thinks is a little weird
or because she had a rough start this year but she is killing it this quarter
or something I halfway made up but I know they have been having conflict with their parents and could use a boost

has been, I wouldn't call it transformative, and I may be imagining it, but I have noticed an additional warm fuzziness, a we're all in this together, a patience in my room with each other and with me...

and I'm going to keep doing the postcards.

A More Auspicious Beginning to Surface Area and Volume

For a few years, by the time December rolls around, I am so beat up by daily grading, making copies, paperwork, being a good example for the youth of America, etc etc, that my Surface Area/Volume unit has always been just fantastically awful. Although it's been a long December, I was determined to make this at least a little better.

I start with surface areas, because we just spent tons of time working with areas of composite figures and shaded regions, so it makes sense to extend that.

So to start out, instead of this (try not to barf:)

I sneakily ask them to calculate some composite areas.

I am not super-thrilled with these. In the future I would make them bigger and use more integral values, and not use such a tall, skinny cone.

As they were working, I asked them to write how they calculated the area in the middle of the shape. So in that last one they might write "Area = 1 rectangle and 2 circles."

The cylinder was VERY interesting, since there's really nothing given about the height of the rectangle, but by now they tend to assume that if they need a dimension, there should be a way to figure it out. Some kids realized we were going to turn it into a cylinder and used the circumference of the circles, but some kids estimated that the height of the rectangle was about three circles, which I didn't anticipate but hey, pi is about 3, and that's kind of awesome.

Anyway, so now we are going to cut these out and hold on to them for a few days.

Hopefully avoiding the phenomenon of having no idea which dimensions we need or randomly plugging given numbers into given formulas.

I don't really know where we're going to go from here. I might freak out and go back to a traditional approach, but at least more kids might have a better idea of what those formulas are all about.

Math Lesson Formula

Okay so, seven years in, and I feel I am finally cracking this nut: how do you make any math lesson work for most kids under most circumstances? Throughout the year I have been tweaking most of my lessons to follow the same basic formula. Not that we do the same boring thing every day - there are infinity variations to make it work for me or a particular group of kids. Not that I'm saying teaching doesn't require a whole mess of skills besides knowing how to set up a lesson. Anyway.

I will illustrate with the most frustrating of topics : log laws. I can't think of a topic that seems more boring and pointless to most math teachers and students. I know their virtues as well as you, but let's be honest, 99% of your kids don't really need to know them for anything they are likely to do for the rest of their lives. I posted about it last year, but there was a piece missing, and now it really sings. To believe this works, you have to believe that the one doing the work is the one learning. Nobody gets much out of Miss Nowak doing dramatic performances of math problems and proofs other than Miss Nowak learning how to do dramatic performances of math problems and proofs under the withering attention of 24 bored and irritated teenagers. I don't want to give the impression that I'm giving them a worksheet and being all like, "You're on your own, kids! Time for me to kick back and drink coffee." Because I'm running around, scanning for common questions or points of confusion or missed connections, re-capping with the whole group every five to ten minutes, encouraging and validating, etc. But if you believe "teaching" = "lecturing" then you are not going to see the validity of this approach, and I can't help you.

Phase 1: Productive Struggle
Hook the new thing to something they already know or know how to do. Then make them do it. A few times. Let them discuss and work together. No reason this has to be done in silence. Whether calculators are allowed depends on whether the calculator will let them avoid the things you want them to remember and see. (This particular lesson is no-calculators.)

Phase 2: Generalize. Make them write whatever they have been doing with letters. This is harder for most kids than you'd probably expect, especially if they've never been asked to do it before.

Phase 3: Use it. Presumably this new thing you've discovered is good for something. Even if that something is obviated by ready access to a shmancy calculator.

Phase 4: Prove it. The hardest part for kids, and the hardest part for me to figure out how to get them to be the ones doing the work. I have had some success with this approach of setting up an organizer and basically telling them what to write. But they still need lots of hand-holding. But at least they are doing more than watching/copying a dramatic performance.

Phase 5: Lots and lots of practice. I want them to understand, but I also want mental automation of relationships and procedures. Because later they are going to use this stuff to learn something new.

I would like to say Phase 6 is apply it to a novel and interesting problem, but I'll be real, I'm not there yet with log laws. Though I am there with good projects on some other topics that lend themselves to applications. Give me another seven years.

All I Really Need to Know about Teaching

Dave started it. Here's mine: It's been on a bulletin board at eye level at my desk for seven years. It's a little embarrassing to share because it's more than a tad hubristic. But I think it helps me be better. I don't really need to have it hanging up because I can recite it from memory. Like a mantra. But it's comforting to have it there. Like a talisman.

“I have come to the frightening conclusion that I am the decisive element. It is my personal approach that creates the climate. It is my daily mood that makes the weather. I possess tremendous power to make life miserable or joyous. I can be a tool of torture or an instrument of inspiration, I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis is escalated or de-escalated, and a person is humanized or de-humanized. If we treat people as they are, we make them worse. If we treat people as they ought to be, we help them become what they are capable of becoming.” ― Johann Wolfgang von Goethe

(There is a teacherified version floating around by Haim Ginott. I like the original better.)

I don't take away from this "it's all about me." The take away is more like, "There is a ton that is in my control, and that makes all that happens here my responsibility." Which is maybe a little oppressive and maybe a little "duh." But I still like reading it every day.

In Which Ben Articulates My Reasoning Better Than I Could

...and then some.

Read.

#takethetest

#passiton

I'll add, since I didn't provide much in the way of explanation. The NY Algebra 2/Trig test is a horror show. It tests many things. Notation. Vocabulary. Procedures. Graphing calculator button sequences. It is not a test of mathematical understanding. I am pretty sure any reasonably mathematically-literate adult would sit down to take it, and within twenty minutes be all like, "What the HELL is all this CRAP? And WHY are we inflicting it on our young people? Get me the Governor! Oh wait, I am the Governor!"

I just want the guy to know what his organization says is important for college-bound kids to know. Thats all. I'm not even totally anti-test. I'm anti horrible, very-bad, no-good test.

"Favorite No"

Just a quick share - I have tried this a few times this year, because I was looking for ways to more frequently but still quickly assess a whole class. It works really nicely. I don't have anything to add - Lea covers it all. Just watch.

This Journey to Wherever...

...is about to get slathered in chimichurri. If you keep up with me on Twitter this is old news, but everyone else: I accepted a position at an International School in Buenos Aires for 2012-2014. Reactions fall into two camps: 1) Awesome! 2) WHY IN THE WORLD WOULD YOU DO THAT? so, here goes. While a young pup Navy officer I spent great chunks of time overseas, predominantly Italy and Bahrain (which seems like an odd pairing only if you've never been a Med/Gulf Sailor,) and hearted it. I like being a stranger in a strange land. I like navigating mysterious cultural waters. I like spending twenty minutes of gesticulating to communicate the idea "I think this thing is awesome but I am not willing to pay 20 dinars for it." "Okay fine you can have it for 15." "10." "12." "Fine."


So when I started teaching in 2005 the idea of an International School really appealed, but at the time, the reputable schools wouldn't consider teachers with no experience. I hear that's not always the case these days, but at the time, it was off the table for a few years anyway. Cut to seven years later, and you'd be right to wonder what took so long. I wonder that, too.


It took me about the past three years to Get Serious about making this happen. There was comfort with the known and fear of the unknown. There were two boys who captured my attention for a time but things just didn't go that way. I had to improve my math teacher fu. I had to gain and lose fifty pounds. Would that it had all not been so painful but it was all probably necessary. There were excuses but once I Got Serious I realized my excuses were really no thing. 


For instance, I was all concerned about What Would Happen with the Cat, but here is what my point of contact at my new school said when I asked if it would be reasonable for her to join me: 

YES!!!! Bring Kitty! (what is his/her name....that is very important for me to know!) I came here many years ago with 2 young German Shepherds and an old grumpy cat!  So you KNOW I understand bringing your little furry friend! 

So yeah, excuses loom large in your mind but sometimes go poof when exposed to daylight. And they are just that, excuses, i.e. not the real reason you are hesitating. I think my real reasons (mostly fear) were alleviated by meeting and talking to and reading the blogs of teachers currently working at International Schools. These are real people not that different from you and this is their life. I have to especially thank Mimi who spent lots of time patiently answering my questions at PCMI and afterward, and offered lots of good advice.


So when I finally Got Serious I was looking for three things in a placement: 1. a non English speaking country so I could become fluent in another language 2. a stable, reputable school committed to supporting and developing their faculty and 3. a major urban center, for all the reasons people like living in cities. Beyond that I wasn't even particularly concerned about what continent I would end up on.


I joined Search Associates and joyjobs. Search Associates turned out to mostly be useful for demonstrating to potential employers that I was "serious" - since I interviewed and accepted an offer quickly, and never even had to go to a job fair. Joyjobs is a source of lots of good information, and frequently updated vacancy postings, and worth the small fee in my opinion. 


In conclusion.... I'm ridiculously delighted with the way things turned out, and I can't wait to get there. This placement has lots to be excited about - the probability of teaching IB or AP, a block schedule, much smaller classes, no fire drills, no Regents nonsense...not to mention I won't have to scrape ice off my car any more. Considering that my new school hasn't hired a math teacher in five years, maybe all the delays make sense in the grand scheme. Now for a long six months of trying to learn Rioplatense Spanish and find new homes for all my stuff. (But not the cat. She's coming.)