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Still in the Thick of Math Contest Season
Much like any competetive endeavor, math contest season stretches on for months.
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I mentioned the AMC contest several weeks ago when the students were freaking out about being snowed out of the A-date and missing a chance at qualifying for a subsequent chain of events that they believe to be both necessary and sufficient for gaining admission to Harvard University. These contests are multiple choice, and the students record their answers on machine-readable answer sheets. These answer sheets are mailed to AMC headquarters where the staff there scans them and then determines the top few percent of test-takers. Those students get to take the next round of tests on Tuesday, March 6. The exams are not scored. The cut-offs have not been announced. Thousands of high strung children (and their tiger parents) are very concerned and emotional about this.
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Can we talk about MATHCOUNTS Chapter round? (MATHCOUNTS is a middle school math contest where students travel to a particular place at a particular time and do math problems alone and on teams. “Chapter” means “regional.”) And I mean that question literally, and not in some sort of “We need to talk” sort of way. Allegedly, every Chapter does its thing during the month of February. I had been told that once February is over, then the students can talk about Chapter-level MATHCOUNTS. But there are some very devoted middle school teachers who care a lot more about MATHCOUNTS than I do, and they are insisting that the students can’t talk about MATHCOUNTS.
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Let us imagine the behavior of high-achieving middle school students who are immersed in the world of math—and especially math contests—when they are in limbo about whether their AMC 10 scores were sufficient for them to qualify for next round of the competition, and they are not allowed to talk about the other competition that has been occupying their time recently.
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While each round has fewer students than the previous round, the pressure gets more intense on the remaining students. And the ones who have fallen by the wayside now get to cheer for their favorites to win it all. (Will Luke come back to win a second year in a row? Tune in this May to find out!) And while I can’t get too excited about the remainder when 90! is divided by 91 (this problem is much easier if you don’t know about Wilson’s Theorem), there are students who are totally immersed in this world, and whose enthusiasm (and propensity for trolling) is apparently unbounded.
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More Tales from the BugMaster
As long as we have students, we will have the homework bug reports. Which are real and which are fake? I’ll never tell.
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My keyboard kept glitching and entering a different number, but I actually did get 10 the first time.
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Hi, I’m on an iPad right now, and I managed to accidentally misclick and type 9 instead of 10, so I lost points. Is there a way to get them back? Thanks!
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YOU STOLE MY ANSWER!!!!!
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I am pretty sure that the answer is 10. I even checked it with a calculator.
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\(f(x)\) is in terms of x, but to get the result you have do \(f(a)\), which is a different variable.
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Is this a 24 hour clock? 12:59 is not possible on a regular one.
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\(36+(-30)\) does not equal 6.
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My sister spammed my computer and put lots of random answers.
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Please include the number of heads and legs for cows and chickens.
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I was supposed to earn points on this question. Please fix this!!! And give me points for this.
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Hello, my daughter is in your class, and I checked her work. Her answer is right, but the system says that it is wrong. Please fix this and give her back the points that she lost on this problem. Thanks! -mysterious_okapi’s mom
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My daughter is in this class, and she keeps getting her answers marked wrong even though I am sure that they are correct. I would like to talk to your manager.
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Small Successes
I took this afternoon off thinking that I would spend the time making the binding for the last of the quilts that need to be bound (bed-sized quilt to bring in to my cold office) (lots of people have blankets in the office) (when you set the thermostat to “heat,” it got colder). But that did not happen, so maybe that is not a success.
If I had known that I was going to spend so much of the afternoon sitting on the couch telling the cat how beautiful she is, maybe I could have stopped at a mall and bought myself more socks. (Or at IKEA and bought the cat the RENS that I keep thinking that I’m going to buy. Or at the Joann and bought her a few yards of fleecy material like the blanket that she is obsessed with.) But is it really a victory to buy socks at the mall? Why haven’t I seen a Facebook ad for some service that will send me socks in the mail every now and then? (Aside: I did try Stitch Fix at one point, and everything that they sent me reminded me of something that my mother would have picked out for me. I thought of my mother when I was getting dressed yesterday, as I used her descripiton of my fashion sense, “refugee from a rag bag,” to construct my outfit.)
Also, one could argue about whether or not it really is a success when I went to go ask a colleague a question about the project that I’m working on, he was in the midst of solving some Google recruiting-puzzle because he had googled enough things that were interesting to Google, so after one of his searches they sent him to some page with a puzzle to solve. He closed the window with the puzzle and answered my question.
But, the real victory is that he had hidden a
unique_idcolumn in the data that he had worked with last year (the one where humans looked at 36 colorful rectangles of various sizes and then divided things into tiers based on a holistic view of the information conveyed by these rectangles), so I was able to compare the results from last year to the results that I constructed though a whole bunch of fussy queries and dull analyses. And for the most part they matched! And when they were very non-matchy, it was pretty clear why. There is one place where I need to replacethe_valuewith something likemin(the_value, fudge_factor), but aside from that, I am done with the mathy parts of the project. Next up we get to see how well the solution scales and how well we can turn the results into thousands of pieces of paper to be given out to thousands of children all over the country.
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Dull Weekend
No post yesterday because I was hoping to have something interesting to write about, but I couldn’t think of anything. Final updates from the weekend:
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Finished up the last quilt in this sequence. Yes, the reason why several of the quilts are so similar-looking is because many of the patches were originally meant to be part of a large quilt, but I never liked how it was coming together, and a whole lot of people I know are having babies these days, so those patches became three small quilts.
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So. Much. Laundry.
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The cat helped me practice my German, in particular my use of Wechselpräpositionen.
Katze, warum gehst du so oft unter das Sofa?
Katze, warum bist du so oft unter dem Sofa?
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Unanswered Questions from Trader Joe's
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Was some sort of diplomat at the grocery store at the same time that I was?
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Do other medical specialties wear varsity jackets to Trader Joe’s that have the hospital’s seal embroidered on the back with “Department of [Specialty Name]” in script lettering over it and the physician’s name and initialized credentials embroidered on the front? Or is it only surgeons who do this? (This is not the first time that I have seen a physician a UCSD Department of Surgery varsity jacket at Trader Joe’s.)
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Are the “big data” experts at Trader Joe’s corporate offices laughing at me because I am currently surviving on a diet made up almost exclusively of avocado toast and microwavable frozen dumplings?
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Bad Ideas and Machine Learning
I’ve come up with another bad idea that I would like to share.
One of the things that stops me from using machine learning (and by that I mean “machine learning that is more sophisticated than just fitting a logistic regression model”) is that most of the time I don’t have any labeled training data. I know how many clusters I want to have, and I know what I want my clusters to represent in the real world, but I don’t have a training set that can tell the computer about this.
Aside: When I say that one of my research interests is the analysis of partially ordered categorical data, that is just a dressed up way of saying that I work in education and there is a certain set of cultural expectations about grades, and I need to find ways to deal with grade data. A through F and “withdraw” is my canonical set of partially ordered categorical data. But each of our short answer items can take on one of five scores, and I don’t believe that our 0-1-3-5-7 grading scale is any more numerical than a Lickert scale. Also, what can you learn from the problems that were not attempted?
In our online school, each grade is hand-crafted by request.
However, we also have a small number of in-person learning centers, and at the end of the year, each student receives a certificate. The certificates come in tiers. (The lowest tier might actually be called “participation.”) We need to take a large number of
(student, course)pairs and assign them to tiers. And when I say “we” I mean “I.”This is a harder problem than when I was running the calculus machine. The registrar’s office handled the difficult parts of record keeping for my large lecture calculus classes at the university: They did not allow students to appear in my class most of the way through the term. When students disappeared midway through the term and got low scores because of that, the registrar’s office knew whether this was a grade to be recorded or if there was some sort of weird situation going on behind the scenes. The registrar’s office provided me with a reasonably canonical list of the students in my calculus class. How many of your university’s academic policies are set by database adminstrators in the registrar’s office? (I’m pretty sure that UT’s rule about only being able to waitlist two courses was a database thing.)
(In my remake of The Graduate, Mrs. Robinson will teach Benjamin about databases.)
Here, this is my problem. Policy states that students can appear at any time during the academic year. Students can switch courses and sections at will. I have spent a significant number of hours negotiating with the
enrollmentstable. My life is a tangle of SQLWHERE dropped_at IS NULL OR switch_id > 0and such. I have a regex to deal with thenotesfield because sometimes there are very special cases that I need to know about.Last year this was a much smaller problem, and someone came up with a bespoke solution using an Excel spreadsheet and overrode any anomalies with institutional knowledge.
Do you know what this Excel spreadsheet is? IT IS A TRAINING SET! Instead of worrying about which students are legitimately in the course and which weeks’ of homework scores are fair to count in the grades and all of that, I can just feed the
enrollmentstable and thehomework_trialstable and whatever other tables I can find into a machine learning algorithm and have it generate grades with the same finesse as the internet recognizing pictures of cats!But this is a terrible idea, so I won’t do it. (Unless I have some free time after I solve the problem for real because I am sort of curious of what the algorithm would tell me about my data.)
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Staring at the Sun (Part 2)
There was a total solar eclipse in North America on Monday, August 21, 2017.
The last time I wrote about a solar eclipse, it was really a story about migraine aura.
Again, the dates don’t really line up quite right, but this time they are a bit closer. The last time I experienced a truly unusual migraine aura was on Tuesday, August 22, 2017 at 9am. Six months ago today.
If you asked me about the way that I think, I would start out by telling you that there is a running commentary, in English, in my head. Or, if you had asked me this roughly six months ago, that is what I would have opened with, and it would have taken a lot of follow-up questions to push me away from that idea. Sometimes when I think about math, it is in some sort of indescribable way; it only turns into words when I start to think about writing down the proof. Maybe this is why it is so hard for me to do math or other technical things when people around me are speaking English (but not around other sounds). Maybe I only remember the thoughts that are streams of English words because I am using that mode of thinking to prepare for some future interaction with people.
On Saturday, August 5, 2017, I stopped at Trader Joe’s after knitting group (same shopping plaza), and as I was heading back to my car, the part of the sky in the upper right corner of my vision flickered just a little bit. A few pulses that reminded me of some sort of digital artifact. Like you might imagine a glitch in the matrix. I drove home, although in retrospect, I probably should have gone back into Panera and asked someone from knitting group to call 911. But I thought that this was some minor variant of the flashing rainbow crystal, the unusual (but harmless) migraine aura that I had befriended over several weeks in the spring of 2015.
By the time I got home, the upper right corner of my visual field was flickering and refracted. It was as if someone had drawn a diagonal line and had applied some dynamic version of the photoshop clone tool to everything above it in a somewhat haphazard way. When I got home, I saw a neighbor in the alley and had a weird conversation. I just could not find the words to say any of the things that I was thinking. It was similar to the feeling when you are speaking a foreign language that you aren’t very good at and you know what you want to say, but you don’t know what the words are. But I didn’t have access to words in English, and there was no fall-back language. I had thoughts, but there were hardly any words; all I had were some well-practiced stock phrases. The neighbor clearly knew that something was wrong; she blamed it on the hot day and suggested that I should drink some water and rest. I knew that it was far worse than that.
When you lose your ability to speak, you can’t call 911.
Fortunately, I live in North Park, and it was the early afternoon on a sunny Saturday. North Park is filled with crazy homeless people and very popular and crowded hipster brunch places with plenty of outdoor seating. I walked half a block to the nearest brunch restaurant and harrangued the hostess: CALL 911! CALL 911! I NEED HELP! I couldn’t explain what was wrong, but it was pretty clear that I was upset and something was wrong. I needed to get to a hospital. The hostess wanted me to stop causing a scene in front of her restaurant. It was in both of our best interests for her to call 911.
Even though I did not have the words to express complex thoughts, I still knew that both the ability to speak and the right part of my visual field are controlled by the left side of my brain. I also knew that people with a history of migraines are statistically more likely to have a stroke than the general population. I had all these thoughts without having any access to words like “brain” or “blood” or “probability” or “stroke.”
A few hours later, still in the emergency department, words started to return. While I was in the MRI machine, the word “localizer” was one of the first to come back to me. They did a bunch of test: CT, CT-A, MRI, EEG. No signs of stroke. No signs of seizure. A perfusion study that was consistent with migraine. An EEG pattern that was consistent with migraine. A vascular feature that is probably nothing but they wanted to get a better look at just to be sure (it has either been there since I was born or else is a result of that time I was hit by a car in October 2002). I have a history of migraine. I have such a history of migraine that when I could speak again one of the first things I volunteered to the neurologists is that one of the photo albums on my phone is a CT-A of my brain from about ten years ago. Diagnosis: Migraine with aura, not intractable: G43.10. I spent the night in the hospital.
Everything is performance. I wanted nothing more than to be declared to be better so that I could go home. When the herd of neurologists came by on rounds on Sunday, I was sitting up in bed doing the New York Times crossword puzzle. I explained that I was still having trouble with visual processing. In order to do the crossword puzzle, I had to put a finger from my left hand on the clue and a finger from my right hand on the box because otherwise I could not look back and forth between them correctly. I was also having trouble with my phone; it was really hard for me to read anything that was on a phone or a computer screen. (And, yet, the newspaper was fine.) I had to stay another day just in case and also because of the way that imaging resources are allocated in our current health care system. The MRI venogram got me some pretty cool images. One of my friends helped me section the images into an STL file so that I could 3D print the vascular tree. Sadly, 3D printing something so complicated is above my skill level.
You can feel remarkably good when you are sitting around a hospital bed, and you don’t even realize what you can’t do until you are home. Or until you try to go back to work. Visual system was definitely still off. I was much more aware of the work that my brain was putting in to resolve figure vs. ground. Reading screens was still quite challenging. Every now and then, the upper right part of my visual field would start flashing, and things would feel slightly off. For example, during the time that the flashing was going on, it would be really hard for me to do subtraction in my head.
So, um, yeah, a few days later I went back to work. I told my colleagues about the hospital and showed them the MRI images. I told them about the weird flashing—which was taking place rougly once every 20 minutes, as much like clockwork as you might expect from an organic process in the human brain. 7:10am, 7:33am, 8:04am, 10:10am, 10:32am, 10:52am, 11:39am, 12:10pm, 3:21pm, 3:43pm, 4:31pm, 4:50pm, 5:24pm. My colleagues are fascinating people, so they told me that the next time one of these flashing events happened they would see if I could draw.
Do you remember how some people were not impressed by the president’s ability to draw a clock? My colleagues told me to draw a clock. Ignore the curve in the lower left; it is part of a different drawing. The “clock” is the arc in the upper right and the diagonal line segment.
Could I draw a compass? (Not in the Euclidean geometry sense. In the orienteering sense.)
OK, so I couldn’t draw. But could I copy a drawing? The next time I saw the flashing, a colleague drew a picture of a cat (while I watched), and then I tried to copy it.
(I am such a good neurology patient. I come to appointments with complete logs of the times and duration of my symptoms as well as DVDs full of imaging studies and drawings like these. One of the doctors I saw is also a neurology professor. He made a copy of my notes and drawings to use in his class.)
Eventually these weird migraine auras stopped happening. (The day after the eclipse. If you make the movie version of my life, we can change the dates.) I can now draw clocks and cats and other simple figures whenever I want.
One of these days I want to take all of my migraine drawings, my MRI images, and my EEG data and sew it into a quilt. There will, of course, also be eclipse imagery.
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