Monthly Archives: October 2011
Folding Stories and Math
One of my goals this year is to add different “evergreen” activities to my teaching toolbox that can be for used for basically any topic, especially ones that are less open to application and need drill type skill practice. Especially for these topics, I always feel like I need things to break up the routine and find ways to get students more involved. Here is one that we did today which the class really enjoyed:
FOLDING STORIES:
A real Folding Story is one where you start out by writing two lines of a story. Then, you fold the paper so the next person can only see the second line and pass it on. Based just on this last line, they write the next line of the story. You keep going for a while and then in the end open up to read the whole thing. They are usually very funny because the story quickly veers in different directions.
The idea in the math classroom is similar, but using a step by step math problem instead of a story. I put them in groups of three and gave them derivative problems involving negative and fractional exponents. The first person rewrote the expression to put it in a power-rule friendly form, the second person differentiated it, and then the third person rewrote the expression back into one with exponents in the denominator or radicals instead of fractional exponents. They folded the paper down each step of the way so that they could only see the step above theirs. Then in the end, they opened up and checked the final answer with the answer I gave them at the top. As a group of three, they attempted to find and fix their errors.
I had three rounds ready that got progressively harder, so when a group finished I would just hand them the next round. The groups worked at their own pace, but most did 2 rounds in about 15 minutes and then got partway through round 3 when class ended.
REFLECTIONS:
- Students are often really bad at diagnosing their own errors, but I think this is because we have never trained them. They had a tough time at first finding their errors in this exercise, but I think the step by step nature of it helped them figure out which part of it that was wrong and follow it up to the step where it got messed up. I want to do this more often to help them diagnose their own mistakes.
- My role was reduced to “person who hands out the next round of three when the group finishes,” which I loved. I answered a few questions individually, but for the most part, people helped each other and talked math.
- Lots of students cheated by opening up the paper to make sure the step above theirs was correct. Don’t know how to avoid this, but maybe it’s not the worst thing in the world.
- I think that next time I might hand out colored pens too so that when they get to the mistake stage, they correct it with a different color and can more easily see where they went wrong. The correcting stage this time just involved lots of scribbling all over the strips (as you can see above).
- The only thing I didn’t like is that the students left with nothing in their notebook to review afterwards. Some students took the completed strips, and I will post the whole exercise on our course website, but that is always less than ideal for me.
- FINAL REFLECTION: Keep this one in my toolbox.
Bonus Question Humor
We all need a little bit of math humor in our life. In the teacher edition of the geometry textbook that our school uses, there are math jokes every ten pages or so (which is hilarious, because the textbook publisher thought that corny jokes would be of great use to classroom teachers). My favorite joke from that book: Why was the math book so sad? Wait for it. Wait for it. Wait for it… Because it had so many problems. Feel free to use that one all you want.
One of my favorite places for humor is tests. Last year, I had a question involving the movie ticket revenue of Avatar and slipped this in as part e:
e. Avatar was a [ great movie | good movie | ok movie | bad movie | didn’t see it ]. (Circle one)
When I corrected the tests, I corrected their answers as right or wrong (the correct answer was “good movie” not great movie – I didn’t even accept didn’t see it). Obviously this did not count in their point totals, but one student submitted this in a feedback form “Please make it more obvious what the answers should be to personal preference question e.g. is Avatar a good movie?” I almost died laughing when I got that one.
On the first test we had for Calculus this year, here was the Bonus question:
BONUS: Draw a piecewise-defined function below that makes the most beautiful picture I have ever seen. The only rules are that it must be piecewise-defined and it must be a function and it must be the most beautiful thing I have ever seen (or else I will rip up your test and not grade any of it).
Needless to say, I got lots of great submissions for this, with the only negative being that a few students spent like 10 minutes drawing instead of checking their test. Building up to the good ones, first here were some that were unsuccessful. I should have gone through with my threat of ripping up their test, but I guess I was in a good mood when I was grading (what?). About half of the submissions were similar to this one – just a random assortment of lines thrown across the page:
I mean, a piecewise function, sure, but beautiful? Why? Is it abstract expressionism or something? I guess I should be happy that it was at least a mathematically sound submission, unlike this one:
I mean, really? There were like two rules and you messed up one of them. Regardless of how wrong something can be, I always give mad props if a student can at least make me laugh:
Is this what you are feeling after the test? Was that little explanation picture in the top right corner necessary? This one also made me laugh:
I didn’t notice it the first time around but caught it when I was just briefly going over the tests for a second time… If you didn’t notice either, because it seems like the page is blank, very small in the bottom right-hand corner she wrote “(hint: it’s abstract)” which actually made me laugh out loud. BUT, some of the submissions were mathematically functions, and undeniably beautiful:
This is from THE student artist at the school. She really is quite talented. On the left is a fisherman who is casting out for a fish on the right. She cleverly used the x-axis as the sea level. Love it. Unfortunately though, that was still not the winner. (Trumpets sounding) And the winner was…
This student drew a picture of a bow and arrow. She did this for me because I am Bowman, man of the Bow, the archer, Rami in Arabic (that’s what’s written towards the top). I don’t know how she figured out so quickly that the way to win questions like this is to reference me, but kudos for her for getting this so quickly. Far better than the sideways B that won last year.
Side note: Don’t know how comfortable I am with the fact that she wrote “cute asymptote” on it. I just sincerely hope that it was just an opportunity for a wonderful math pun, and not a reference to me.
An Arab Bow Tie
If you haven’t read about my bow tie saga yet, this would be a good time. The short story: I randomly wore a bow tie one day and people liked it so much that I decided it would become my thing at this school. Since then, I have tried my hardest to introduce bow ties to the Arab culture – I got the school to manufacture school bow ties and started “Bow Tie Thursday,” where (so far) just barely more than a handful of kids sport a bow tie. It has been slowly catching on – I randomly see kids I have never talked to strolling around in bow ties on Thursdays. One of those moments happened last Thursday, so I tweeted this out of excitement:
And I got this response, which I actually agreed wholeheartedly with:
But, but, but, hold the presses. I think I might have actually outdone myself. BEHOLD! The keffiyeh bow tie!
For those of you that don’t know what a keffiyeh is, it’s a beautiful traditional Arab headdress found throughout the Middle East. They protect from the harsh desert sun and also do well in the bitter desert cold. They come in many colors, which often signify various groups and countries – the red ones are associated with Jordan. Most have a very distinct, stately checked pattern. They have come to really represent the region and are a symbol that is still a huge part of Arab life and a point of genuine, unassuming pride. Students at school wear them as scarves when it’s cold out, many older men wear them daily. Lately, they have become somewhat trendy in the American hipster circles too. Here’s a run down of how to tie one on your head.
And in a wonderful blend of American and Jordanian culture, I now have a keffiyeh bow tie!
Here’s how this wonderful creation came about:
- I went into Madaba with one of my bow ties and showed it to a tailor to see if she could sew something similar with any cloth. Of course she could.
- I bought a keffiyeh from a nearby store for 2.50 JD (around $3.50) and brought it back to the tailor.
- In less than a half hour, she cut it up, and sewed it while I drank tea with my barber whose shop is about 3 shops down. All for 2 JD (about $2.80).
So for less than $7 and less than 45 minutes, I got myself a beautiful, custom made bow tie. I wonder how expensive this would have been in the US. Needless to say, I’m freakin’ pumped to wear it to school tomorrow (even if it’s not bow tie Thursday).
Bowman in Arabia 