Doing Mathematics Again

I have had an amazing night! I got to engage in Doing Mathematics! Some of my fondest memories  from college are of a group of guys (yes, unfortunately all guys) gathered around a coffee table, white board, or chalk board that is filled with mathematical scratching in a room littered with beer bottles. This is when I came to love mathematics; the active, energetic, disappointing, and exhilarating process of Doing Mathematics.

Doing Mathematics is entirely different from high school mathematics (which I sometimes call mathematish because I am oh, so clever), though with the implementation of the Math Practice Standards, it’s not supposed to be all that different. As I mention above, Doing Mathematics is an active process. Yes, we did a fair amount of sit and get in college lecture halls (I did less of that than most of my classmates. Oops.), but outside of the lecture halls there was discussion, there was argument, there was joy, there was despair, there was surprise. You could run the emotional gamut when working on a mathematical proof just as much as with a great work of literature. There is the trope of the single, solitary genius rigidly following the rules of deduction to a logical conclusion that seems inevitable, but that view is impoverished. For me, mathematics is a social activity made much more enjoyable with others.

I am currently at San Diego State University for a curriculum training to teach AP Computer Science A next year. I am staying in the dorms with many of the other future AP CSA teachers in my cohort.  We were hanging out in the common area of our suite this evening trying to get some program to install and cooperate and one of my colleagues brought out this problem:

I’m thinking of a ten-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number?

This problem was created by John Conway as part of a Pi Day promotion with Pizza Hut. I had heard about the promotion, but it didn’t really register with me. Tonight, it took hold. It started with two of my colleagues sitting on the couch discussing the problem and trying out little strategies. It escalated when they said that they needed a whiteboard. I was drawn in. It was such a joyful experience as we grappled with the problem, burned through scratch paper, asked each other to explain their thinking, and willingly explained our thinking. I don’t know how long we spent on this problem, but we got it! The crazy thing is, I don’t even know what the answer is. I don’t care what the answer is. The answer is not the important part. The important part is the process; the messy, energetic process of sense making and problem solving. At the end, when I boxed our answer, I felt a great wave of calm satisfaction. One of the other guys in the room who wasn’t working on the problem expected much more of a commotion, but I wasn’t excited, I was serene. I miss this. I don’t get this from teaching. I need to be Doing Mathematics! (or maybe statistics or computer science) In the end our triumph doesn’t actually mean much; we didn’t uncover some new piece of mathematical knowledge or win the free pizza from Pizza Hut. Hell, it was a competition for high schoolers. But that’s really not the point. It was cool and it felt good to Do Mathematics.

There is a great irony in all of this. About nine years ago, I dropped out/flunked out of a masters program in mathematics at San Diego State.  It was one of my lowest points in life. I was very depressed and unhappy. I was not doing well in the program as a result and my depression and my poor performance spiraled into one another. By November, I had stopped attending classes. I lasted a little over two months. It feels weird to even be back on this campus. I brought my Systems of Differential Equations textbook with me (one of the classes that I ended up failing) because I knew that being back on this campus would eat away at me. Right now it is sitting on the floor in the corner of the room, which is kind of what I expected, but I knew if I didn’t bring it, it would eat away at me. It feels like my redemption. Like I would be OK if I just studied some Differential Equations for two weeks in my spare time. In truth, I am living my redemption. I have a beautiful wife and daughter, to whom I am a loving husband father, respectively. We have lovely home and I have a career where I get the opportunity to impact the lives of amazing people. I still have that fucking albatross hanging around my neck, though; that little voice that says “You are a failure”, “You failed”, “You’re not as smart as you think you are”, “you blew your chance”. Man, that guy is a dick!

Anyway, thanks for the psychotherapy. There's not really a conclusion here, just an ending. Send the bill to my insurance.

Doing Mathematics is awesome! I need to do it more and I need to share it with my students.

So Much Things to Say

I had the great fortune of attending a Rick Wormeli (@rickwormeli2) workshop on Standards Based Grading. It was an inspiring and motivating two days that left me with very mixed feelings. My two takeaways are:

1. Define your beliefs, and
2. Don't be a hypocrite

Great message, but it's so hard to hear since later tonight, my plans are to be a hypocrite. I have a big stack of Algebra II tests to get through, especially since I told my students that I would definitely have the tests graded to give back tomorrow. Rick Wormeli is a fantastic presenter. He is incredibly knowledgeable and thoroughly engaging. Go see him if you ever have the opportunity, and if you don't have the opportunity, create it.

Rick is passionate about grading. (Understatement). He believes that a fair and accurate grading scheme is not just nice to have, but rather a moral imperative. That's very hard to hear at this point in the year. I mean, who has time to be moral. I have so much material to cover and tests that I need to get through.

I attended CMC North at Asilomar this past weekend. I got to see several excellent presentations, including Steve Leinwand, Dan Meyer, Jo Boaler, and Phil Daro. I also got to have some great discussions with my colleague @StrangeKathleen, who gave an excellent presentation as well, though I didn't attend.

On top of all that, we hosted two sessions of Hour of Code at my school yesterday. Next year, I will be teaching PLTW  Computer Science. We had a pretty good turnout and I think there's a lot of interest in the course for next year. My wife even brought our daughter along to learn to code. I don't think anything stuck, so I'll probably have to try again when she's a bit older. She is currently 12 weeks old and does not appear to be a prodigy, though she does produce prodigious amounts of drool.

I am overstimulated this week. It's got me so pumped up, it feels like Christmas! I decided that I would really like to give a talk at Asilomar next year. The only problem is, I have no idea what I should talk about. I have felt like that for a while. It reminds me of the movie Airheads with Brendan Fraser, Steve Buscemi, and Adam Sandler. The three guys are in a rock band and they hold a radio station hostage to try to get there demo on the air. Hijinks ensue. At one point, the DJ does an on air interview with Brendan Fraser and he asks him what his message is. Brendan Fraser replies on air "We just want our message to be heard." This is kinda how I feel right now. I have so many thoughts, feelings, and emotions percolating inside of me. I feel like I want to shout but the only thing I can think of to say is "I have something to say!"

*Musical Interlude*

I think this is where I will start.

It is far too much to take on tonight, but this is the guiding document suggested by Rick Wormeli to define your beliefs. It's gonna be tough and it's going to take me a while, but I believe it'll help me find my message.

#MTBOS Challenge: 3-2-1 Summary

3 -- World Series Rings in Five Years
I am a huge San Francisco Giants fan and I am absolutely beside myself over our latest World Series victory. It was smooth and it wasn't easy. I know we weren't the best team this year and I know that many people are sick of seeing the Giants in October. I'm OK with that though. The only problem is that students and other teachers feel the need to heckle me. I'm sure it's all in good fun, but after game 6, it definitely wasn't fun for me. I am so happy that the series is over and relieved that we won. It feels like a giant weight of my shoulders and I can't stop smiling.

2 -- Double Angle Identities Finally Make Sense
I took Pre-Calc in high school and I remember that we were supposed to memorize the angle-sum, angle-difference, and double angle formulas. I'd like to point out that I remember that we were supposed to learn them, not that I remember them. Last night, however, I was reading An Imaginary Tale by Paul J. Nahin and came across this:

It explains the angle-sum formula as a result of multiplying two complex number in polar form. It struck me like a bolt of lightning. It was one of those great feeling that you get when you study mathematics; that crystal clear connection between two seemingly disparate topics. I haven't had enough of these moments since becoming a math teacher. I love students but I really miss doing mathematics.

1 -- Beautiful Baby
The primary reason that I have not kept up with the blog-o-sphere is my beautiful six-week-old daughter. I hope to get back to more blogging but that means tearing myself away from this:

We shall see.

Week 5: #mtboschallenge -- 3-2-1 Sunday Summary

This was a really rough week. Well, really it was just Friday but it was rough enough to completely drain my reserves.

3 -- Number Of Multiple Choice Questions On The Test That Weren't Part Of Their Review HW
Seven of the 10 multiple choice questions were part of the review HW. I expected the minimum score on the MC part of the test to be 7. Instead the average was 6.58. Very disappointing. I haven't even looked at the free response yet, but I am skeptical.

2 -- Students In Crisis
A lot went down on Friday. Two students are really suffering right now. One probably won't get the help he needs yet and will continue to slide. One student came to talk to me. It was a good talk and I think he will get the help he needs. The part that scares me is how close I was to missing the opportunity to let the student talk. He came to talk to me at lunch but I was scrambling to handle three duties on my duty free lunch. Thankfully, the student was still in my room when I got back.

1 -- School Day Until My Daughter Is Due
I really thought she would come this weekend. I guess that gives me some more time to plan for my absence.

180 Blog: Day 12

AP Stats

I stumbled into a great way to give good feedback and cut down on time spent giving feedback! Last week, I assigned the class two FRAPPYs on surveys and sampling (04B.2 and 11.3). Coincidentally, each problem had two parts. Students are seated in groups of four, so I decided to give feedback on one part for each student. Every student received feedback, and, in aggregate, every group got feedback on a full problem. Tomorrow, as part of the review, the students will get together with other students who received feedback on the same part of the problem. They will compare and rewrite their part, and then return to their original group as experts on their part. The goal is to have students rewrite their original work and experience writing a clear, complete, and concise solution. I know this is just repurposing jigsawing but, as any AP Stat teacher will tell you, grading writing and giving good feedback is incredibly difficult and time consuming. I guess putting things off and being lazy really gets my brain juices flowing.

@druinOK is doing Chalk Talk with experimental design tomorrow because of my post yesterday. It is a great feeling and incredibly validating to know that my practice can spark something for another teacher (even though I stole the idea from an article that she posted). I can't wait to read her reflections on the activity. You should too.

What are your feedback hacks?

Algebra II

One of the saddest parts of my day is when I'm done with second or fourth period and I have to erase the board. Today, it was beautiful. One idea flowed to the next. everything was color coded. Clearly, some great teacher talking had just happened. It's sad because I don't like being the only one talking about math in my classroom, yet that's what happens most days. Then, I erase the work and repeat the exact same stuff two periods later, and then again the very next period. I have been entertaining the idea of a flipped classroom for a while and this lesson just might be the impetus that I need to make it happen. With a flip, I would only spend 30 minutes talking and time editing instead of 90 total minutes talking.

Are you flipped? What are your essential tech pieces? What does your daily class look like?

Algebra I

We had a test today. One of my focus students still hasn't turned in any homework yet. He was wearing a Jimi Hendrix shirt today, so while he was taking the test, I wrote a new homework assignment for him. His assignment is to listen to "All Along the Watchtower" and "Like a Rolling Stone" by Bob Dylan and "Like a Rolling Stone" by Jimi Hendrix. Bob Dylan is my absolute favorite and Hendrix is incredible. "Like a Rolling Stone" is my absolute favorite and "Like a Rolling Stone" by Hendrix is incredible. I love how the two versions have entirely different feels. Dylan's is acerbic and cutting, while Hendrix's is heartbreaking and ambivalent. It's amazing to me how the same words can be so distinctive. I am determined to make a connection with this kid, but I need a victory, no matter how small. I hope he does his homework. I'd love to know what he thinks of the songs.

I attended a JMP workshop this summer and learned a lot about the program. Here's one of the things they showed me:

You can find more Residual Sur(Realism) here.

What is your favorite Dylan song?

180 Blog (do I have to rename it now): Day 11

Aficionados will undoubtedly recall the opening words to this 180 blog, but for the rest of you, here is a reminder: "I fully intend to fail at maintaining this 180 blog." Yesterday, I lived up to my word. I have enjoyed sharing and reflecting on my classroom but yesterday was wholly unremarkable. As I sat down in front of my computer yesterday, the only reason I could think of to write was to say that I wrote so I decided not to write. It was a nice feeling. I felt like I got time back which I could fritter away watching The League. I also finally got around to reading "Thinking Made Visible" (#eduread a week or so ago). I forwarded the article to a colleague, who immediately tried the Chalk Talk strategy, so I felt I should at least finish the article. After I finished the article I decided I would try Chalk Talk as well.

AP Stats
We did Chalk Talk today on the four principles of experimental design. Students are seated in groups of 4, though not all tables are entirely full. I started by placing four markers (one red, blue, purple, and black) on each table. I had two posters for each principle of experimental design (Control, Randomize, Replicate, Block) with each principle written in a different color. Students chose their marker from their table. The color of their marker indicated their starting principle. They conducted a 4 minute silent conversation with their marker group and then rotated to the next principle. We did a total of 5 stations, so that students ended on the same principle that they started with, but the alternate poster. Here are some of the results.

I really don't know what to make of this. I can tell that they have a sense of humor, but think Control only means control group. I tried to debrief, but, as pointed out in previous posts, I am not adept at facilitating classroom conversation.

In the end, I'm fairly ambivalent about the day. I think it's a potentially good activity, but I'm already disappointed in the level of the class. We have a test on Friday and I think it's going to be a wake up call all around. I really hate relying on grades as motivation, especially because there are so many really cool ideas and applications. I'm frustrated because I have obviously not engaged them.

Algebra II
Test

Algebra I
Practice test. Test tomorrow.

Week 4: #mtboschallenge -- 3-2-1 Sunday Summary

My wife was at the grocery store this weekend and she saw her old photo teacher. She said "Hi, Mr. Allman" and he immediately replied "Hi, Kat." My wife graduated 11 years ago! It was such an amazing experience for her. During their chat, her photo teacher said that he still has some of her pictures on his wall (he is at a different school now) and that he still uses them as examples. I have a t-shirt from my union that says "Educators affect eternity."

While I still think eternity is overstating it a bit, we can and will have a long lasting effect that goes far beyond our classroom, beyond our careers, beyond our lives, maybe even beyond the lives of our students. What you do is important. What you do is meaningful. Have a great week and yield your awesome power for the good.

3 -- Tests This Week
I am testing in all my classes this week. Algebra II is Tuesday, Algebra I is Wednesday, and AP Statistics is Friday. I worked on writing the Algebra II and AP Stat tests today. I am weirdly proud on the Algebra II test; I have no idea why. I had already decided to allow for test retakes in Algebra I and Algebra II for students who score below 75%, and, after writing the stat test today, I think I will allow for retakes in that class as well. Last year, my tests consisted of 20 AP style multiple choice questions and 3 AP style free response questions. This year, due to the change in our schedule, I have had to cut the length of the tests way down so know it is only 10 MC and 2 FRQs per unit. This is nowhere near enough questions to get an accurate measure of their knowledge, but I don't want to give a unit test over multiple days, and I don't have enough time to entirely rewrite my tests or to give chapter tests.

How are your AP Stats tests structured/timed/scored? Do you/have you used retakes?

2 -- Runs This Week
I used to be a pretty good athlete, but I've never really had good health and fitness habits. I like running and it is an important part of my mental and physical health. It helps me clear my mind and helps me be less exhausted during the school year (Napping is also an important part). I really wasn't prepared for the rigors of teaching and I haven't adapted to it too well. The negative issues like poor interactions with students, parents, and coworkers, paperwork, and bureaucracy really exact a mental toll, and poor health habits combine to make the job incredibly draining. I've been working on a couch to 5k program and I'm right at the end of week 6, which is awesome except that I've been working on it for 9 weeks. The plan is for three runs a week but I've been averaging two. I'm planning on a run this evening to start the week of right.

What do you do to stay mentally and physically energized for the long school year?

1 -- Week Until My Daughter Is Due
She's due on the 16th. I feel pretty comfortable with becoming a dad, or at least I'm redirecting my anxiety. I am planning on taking two weeks of to be at home with my wife and the baby, but I am not at all ready to leave my classroom for two weeks. Two weeks seems like an eternity to be gone from the classroom, but a nanosecond to be with my growing family. My experience has taught me that it will all be OK, but I know I don't have two weeks of sub ready lesson plans beginning at some unknown date. I also don't see the point of leaving sub ready lesson plans since they have NEVER been executed properly when I have. Last year my sub instructions were literally to give the students a handout with instructions for an activity and select a few volunteers to help make the graphs. It was supposed to be entirely student run. All she had to do was pass out the stack of handouts that were sitting on my desk with the note labeled "Sub Instructions." When I got back to school the next day, I noticed the graph didn't look quite right and the sub comments didn't make sense. I asked the students how far they got on the activity. They stared at me blankly. I then asked what step did you get to on the handout. Finally, someone spoke up and asked "What handout?" I was dumbstruck. I'm afraid that I'll come back after two weeks and the same thing will have happened. It's especially frustrating since I take the time to actually write sub ready lessons. That activity wasn't just a time filler, it was an introduction to sampling distributions.

Have you subbed? What are your recommendations for leaving sub plans?