Category: lessons

Total 93 Posts

Math Basketball

I was digging through the dy/dan mailbag today and found a note asking me to explain what I have often referenced on this blog but never clarified. I swear, there isn’t any activity my kids enjoy more than basketball review. Here’s how it works:

Instructions

  1. You bring in a set of questions related to the previous two week’s instruction.
  2. You put up a question.
  3. A kid stands up with an answer, either correct or incorrect:
    • If it’s incorrect, the student sits down, reworks the problem, and you wait for another student to stand.
    • If it’s correct, the student takes two shots with a miniature basketball into a lined trashcan. You award points according to a) the student’s distance from the trash can, and b) the competitive mode you’ve selected below.
  4. Repeat.

Competitive Modes

I have used four, each with their own recommendations. Listed in descending order of popularity:

  1. Class v. Teacher. The students take two shots for every right answer. The teacher takes one shot for every wrong answer. Highest point total wins either extra credit (for the class) or bragging rights (for the teacher).
  2. Class v. Class. One side of the class versus the other. Seed them by mathematical and athletic ability. Highest point total wins extra credit for their team.
  3. Free Market Capitalism. Everyone for him- or herself. Good for the final minutes of class. A student receives as many extra credit points (or pieces of candy) as he or she can score.
  4. Class v. Arbitrary Point Total. If you’re averse to classroom competition, let the class play as one, studying and shooting to pass an arbitrary point total.

Other Release Notes

  • Have the students turn in a paper with all their work on it. I make a big deal about this so everyone works the math through even if they don’t all shoot. Toss these papers after the last student leaves.
  • Encourage shy students to answer math questions and pass off the ball to another student if they don’t want to shoot.
  • Once a student successfully answers a question, she can’t answer again until the rest of her team answers, though she must still work through the problems.
  • Student conference is way out of bounds. If the idea is that everyone works hard on the math, allowing one student to source all the answers would be counter-productive. If I catch anybody whispering answers, I give the other team a shot.
  • Introduce an extraordinarily difficult and extraordinarily valuable shot halfway through the term, a 20-point shot through an open window, for instance.
  • In between the math review, toss in some extraneous nonsense. Name that flag, for instance.

    You can find these slides anywhere “basketball” is listed in my Geometry supplement.

Feltron Post-Mortem

a/k/a My Qualified Disaster
a/k/a The Trouble With Tech

previously on dy/dan

We started with four variables (text messages, beers per day, etc.) which we tracked for 2.5 months in quad-ruled notebooks attempting to transform the quotidian details of our lives into extraordinary infodesigns a lá Nicholas Felton.

This was a departure for me. A tech-driven, student-led, design-infused mathematical project. Things went wrong.

This is a comprehensive autopsy of our Feltron Project. I post it here, in its entirety, a) for my own review next year, b) for your criticism. If you aren’t in the mood for the full, bone-by-bone dissection, please scan down to the section headed What Really Happened. These are problems I don’t know how to solve.

The Lesson Plan

a/k/a What Was Supposed To Happen

  1. We selected variables.
  2. We discussed them, making them more interesting (disaggregating “hugs per day” into “boy hugs” and “girl hugs”) and more manageable (tracking “fast food I eat” instead of “what I eat”).
  3. We tracked them for ten weeks, checking ourselves for consistency every two weeks, and then we stopped.
  4. We spent one hour marveling over Nicholas Felton’s annual report, dissecting it for meaning, identifying the mathematical operations (average, maximum, minimum, sum) and the mathematical forms (pie chart, line graph, histogram, stacked bar graph, map) he used.
  5. We spent six hours entering our data into Excel sheets.
  6. We spent two hours teaching and deriving ten facts of our lives using average, maximum, minimum, and sum functions in Excel.
  7. We spent two hours teaching and deriving four graphs of our lives using pies, lines, and bars.
  8. Raw facts and graphs in hand, we spent thirty minutes discussing and distilling Felton’s graphic design savvy into the two principles I thought my freshmen could reproduce with crayons and paper if they had nothing else:
    1. colors, Felton uses a two-color design (shades of black, shades of blue) which, apart from distinguishing his hierarchy (titles in black, data in dark blue, accents in light blue, etc.) keeps down costs when designing for a large print run.
    2. grids, the kind your eyes can’t see but which your brain loves, the kind which imposes order on what would otherwise be a completely disordered data set, so while Felton jumps from music to movies to drinks you know where to find everything.
  9. We spent another two hours in class tying up loose ends in Excel and then a week designing our Feltron Projects.

What Really Happened

a/k/a Help.

  1. Only 55% of my students submitted the final Feltron ProjectControlling for age: 48% of freshmen and 63% of upperclassmen completed the project..
  2. Many of the other 45% stopped tracking early in the project, which meant assigning them review work, new work, or busy work while everyone else worked in Excel.
  3. Those who kept up with the project quickly staggered their progress (based on pre-existing computer ability, typing speed, and attendance) which saw me dashing between desks, explaining and re-explaining the same procedures over and over again.
  4. Our mobile computer lab a) comprised just fifteen laptops, and b) was available for check-out only once a week, c) if that.
  5. Kids lost work. I had them send their Excel files to themselves and then download the attachment the next day. Trouble was kids sent old files to themselves or they named files computer arsenic like “<<xxxx….davidsfeltronz!!!….xxxx.xls>>” which put both Excel and Gmail into simultaneous cardiac arrestFor the record, I originally sought GoogleDocs out for this project but they maxed out at something like fifty rows where we needed hundreds..
  6. I overestimated my students’ computer fluency. Name it: locating saved files, opening programs, using a trackpad, using modifier keys, sending e-mail. These tasks all required constant, patient re-explanation. Missed that mark by a country mileThere were exceptions, naturally, but Digital Immigrants™ outnumbered Natives™ at 15:1, many of which Natives one day, I have little doubt, will grow up to be edubloggers..
  7. None of them had used Excel before. Ever. Many didn’t have it at home. One triumph of this project โ€“ recognized by a lot of students โ€“ is that my kids are now somewhere in the top quintile of Excel users. This will doubtlessly prove useful again in their lives โ€“ not in the when-will-we-ever-use-this-in-real-life? sense, like they won’t be able to find food or shelter without Excel, just that it will open up a lot of interesting opportunities.

What Mattered

a/k/a Grading

  1. Faithful Tracking
  2. Interesting Findings
  3. Clear Design

Students ranked themselves on a ten-point scale across each index. Given how deeply we had immersed ourselves in exemplary work over two-and-a-half months, with only a few exceptions, I gave them exactly the grades they felt they deserved.

What I’ll Do Next Time

a/k/a If There Is A Next Time, Obviously

  1. Host screencasts online demonstrating essential Excel proceduresincl: sorting columns, using formulas (avg, min, max, sum, countif), saving/sending work, creating new sheets, filling down the date..
  2. Strengthen our analysis. A student’s text message graph plunged for a week when her parents confiscated her phone and spiked when she pulled a boyfriend in May. Students positively thrilled to see those connections but we didn’t build any of that analysis into the project grading. Should’ve.
  3. Employ a Kuropatwa-esque rubric to better inform kids what constitutes “clear design” or “faithful tracking.”
  4. Discuss design in greater depth, incl.
    1. showing them what my own Feltron would look like with rangy, mean grids or spasmodic colors;
    2. showing off the good and bad from this year’s class;
    3. comparing/constrating Khoi Vinh’s approach to grids and David Carson’s insane anti-grids;
    4. showing them Aesthetic Apparatus’ beautiful work in just three-or-fewer colors;
    5. compare 3D graphs alongside 2D hoping a lot of students will reconsider the choices they’ve made in life.
  5. Make a more obvious point of my own Feltron Project. Playing along with your students isn’t even optional here. I made sure I ran through the collection process with my students (for empathy, if nothing else) but I should’ve made a larger point of my own struggle and process.
  6. Find collaborators. This was insane. I should not have gone at this aloneAny takers?.

Students On Feltron

Just do a month.

โ€“JG, smart; we’ll multiply a month by 12 to extrapolate for a year.

Everyone should track the same thing because it’d be really cool to see which people are like you.

โ€“BP, also smart; resolved, then, that we’ll select three variables independently of the class and then select a common classroom variable for the fourth.

I like the chalang. It feels like I acopolished something hard and it made me feel good.

โ€“BS, sic sic sic; whose mother, in an IEP meeting, said of his Feltron notebook, “He carries it everywhere.”

Felton On Feltron

Nicholas Felton consented to an e-mail interview on his process which will appear in this space tomorrow.

Gallery

I have installed student work โ€“ everything from awful to exemplary, but mostly exemplary โ€“ into a Flickr set.

Handouts

  1. Feltron Project Outline
  2. Nicholas Felton Analysis Sheet
  3. Excel Chart Illustrations
  4. Excel Formula Sheet
  5. Map Infograph Template
  6. Final Review Sheet

To Conclude

This was a different, necessary kind of insanity for me to finish my fourth year teaching even a little eager for a fifth. The price tag was steep. To accommodate this time-sucking project-based learning, we skipped a third of our logic unit in Geometry and fully jettisoned last year’s Platonic Solids project.

If I weren’t already guzzling away at this barrel of standards-based Kool-Aid, I’d write something agitated and truly inexcusable here about curriculum narrowing or the time cost of NCLB, but I remain convinced we need to settle on a list of necessary skills and then decide horse-in-front-of-cart-style on the best tools and projects to teach themNoted here: Jay Greene’s j’accuse directed at teachers who complain that NCLB exigencies leave them with no time for fun project but who also wile away the last month of school with parties, assorted time wasters, etc. We didn’t start computer lab work with Feltron until after our round of state assessment.. I do not know if this was that.

There are twenty-four hours. No exceptions. I’m uncertain Feltron was the best use of our time.

I put Feltron to rest now, surely the weirdest assignment I’ve concocted in a four-year career. I post this here to solicit the usual gallery of critique and construction but also because, at some point in this whole blogging thing, I forgot how else to end a project if not with rigorous and public self-critique.

On Math And Breaking A Guinness World Record

a/k/a Because It Was There

The Ingredients

[left to right]

  1. me, twenty-two years old, anxious.
  2. paperclips, 60,000, sponsored by OfficeDepot in exchange for (full disclosure!) t-shirt advertising.
  3. a cable spool, begged off a Sacramento Municipal Utilities District back lot.
  4. wax paper, lots, to keep layers of paperclips from tangling on the spool halfway through the task, because that is a very very disappointing thing.
  5. a CD-R, burned with one essential Excel spreadsheet.
  6. measuring wheel, ’cause no one cares about your paperclip chain unless you can measure it end-to-end.
  7. a log book, signing me in and out of bathroom breaks.
  8. Starbucks Double Shots™, nine, the most expensive component here, to push me through the 9PM to 6AM corridor.
  9. Digital-8 cassettes, 24 hours worth, because Guinness requires nonstop video coverage.
  10. food

My Best Case

This is my best case for math education.

Not that, “hey kids! if you learn your fractions you, too, can accomplish something of very questionable value, like chaining paperclips together for 24 continuous hours.”

Rather, that math can uncomplicate the complicated, that an understanding of math leads to a richer understanding of the world.

For Example

In 2000, Ms. Jeanine Van der Meiren of Belgium chained together 22,025 paperclips in 24 hours.

If you are innumerate, your best response here is “that’s a lotta paperclips.” Which is how most of my students responded to this prompt the last week of school. But if you are numerate at even a basic level, you have only one option here.

You have to answer the question: how fast is that?

The question is irresistible.

By Hand

Jeanine set the record with 3.9 seconds per clip!

Think about that.

Mime it.

Use your hands.

“Clip two three four … clip two three four …. ”

The numerate math student realizes that the record is really, really slow. If he is also a little socially disordered, his next steps are predetermined.

He has to break it.

In The Classroom

  1. Groups of two or three.
  2. Show them a few pictures and make sure they realize what a few gracious friends can do for you here.
  3. Count how many clips one person can chain in one minute.
  4. Ask: is that rate fast enough to bring Jeanine down? They will take one of three routes to get there (proportions, rates, unit conversion) but most groups will determine that yes, they could.
  5. Discuss the assumption they’ve made, that they could maintain that monotony for 24 hours.
  6. Have another member take a turn for five minutes.
  7. Play it dumb: “Oh man, Alyssa crushed Kyle by 47 paperclips right there!” Kyle will correct your error (indignantly) before you finish the sentence.
  8. Have them answer the question, then: who is faster and by how much?, pointing out that the answer isn’t, “Alyssa is faster by 47 paperclips.” because a paperclip isn’t a measure of speed.

California says you’re done with rates now. Nice.

Stretch This A Little Farther

Suggest that Alyssa is faster than Kyle by .1 second per paperclip. She has trained just a little more and can chain ’em just a little faster. Ask if it matters.

It surprises no one that, yeah, any small gain positively explodes over 24 hoursThis is why I went through boxes of paperclips before the actual attempt, looking for the best way to chain two clips, looking for the best way to position the clips in front of me, looking to shave off any fraction of a second., but the exact increase is kind of shocking.

Now wrap your head around the relevance of rates to your life. If your boyfriend drags your self-esteem down by tiny increments daily, you’re going to stagger away from him after a year.

Get In / Get Out

It’s essential to know when to get out of a good story, joke, or learning moment. There was more to talk about but we didn’t, choosing instead to leave a few ends hanging.

One of those ends was a spreadsheet I cooked up for the occasion using formulas my students all know from our Feltron days.

My former-housemate-now-commenter Steve would enter in a) my clip count and b) the current time, and my Excel sheet would tell me:

  1. my pace over the attempt so far,
  2. my pace over the last 1,000 paperclips,
  3. my expected total clips after 24 hours,
  4. my expected total chain length after 24 hours,
  5. the exact time, given my pace, I could expect to break Jeanine’s record.

See: I don’t know how you attempt this record without those last three. Without math, you’re just clipping in the dark, just sorta sure you’ll bring the record down before the clock expires, just sorta sure your pace isn’t steadily slackening.

What I’m saying is that basic numeracy makes everything a little less confusing and, at the same time, a whole lot more curious.

Which is why I teach.

For The Record

Final Exam Question For The World History Class I Don’t Teach

You are unexpectedly transported to England in the year 1000 AD with what you are wearing, what you know, and nothing else. What challenges do you face? Specifically, how do you survive?

Such a fine summative question there, visceral, compelling, offering a gradient of responses all the way from “I wouldn’t.” to some of the comments at Marginal Revolution, demonstrating extraordinary command of local geography, sociology, and economy.

You’ve got people arguing for trebuchets, crop rotation, and bookkeeping while others argue that trebuchets, crop rotation, and the printing press are all ideas that’ll get you incinerated for sorcery.

And after dozens of serious vectors on the question, this gem:

Only what you are wearing and what you know? Well, I’m wearing a fully-comped Springfield DA in a shoulder rig, counterbalanced with three extra mags. I’ve got a Spyderco Police Model in the back pocket of my jeans, a pretty extensive magpie board in my wallet, and I know how to make grain explode. So, me, I’m headed straight for my new castle, comprende?

Comprende.

Peer Editing In Math

Todd Seal, elite member on my list of Bloggers Who Don’t Blog Enough, makes the wait worth our while with some great peer review strategies, which I’ll co-opt for math as soon as possible:

“Create two piles,” I said. “Which ones passed and which ones did not? There will be three paragraphs in each pile.”

Great conversations ensued, both in the small groups and as a class. Some shocking revelations occurred (“That one didnโ€™t pass!?”). This was worth my time.

Once again, great teaching and free weekends prove mutually exclusive.