Spiderman and Fermi

Whoa- this semester is flying by.  I know it's only the 3rd week of class, but at this rate the semester will be done before the weekend is through.  First off, I want to acknowledge Carol Cramer's helpful comments, thanks for reading and thanks for the great suggestions.  Yesterday and today, Mrs. Colwell and I began talking about how we wish we could fit in some different activities, but how we're already pressed for time as it is.  I think we're both excited to try out some new ideas in the coming weeks, so stay tuned to see what they turn out to be and how they go.

When I came into class yesterday, I was a little surprised to find out that we were having a test, as I expected that to occur on Tuesday.  Unable to help work things out, I started thinking about possible material to present during future "warm ups."  Also, I offered to help grade exams or homework, and boy did Mrs. Colwell's eyes light up!  It was like a kid on Christmas morning.  During the warm-ups at the beginning of class, Mrs. Colwell usually grades homework while the students occupy themselves with some practice problems, or listen to me ramble on the days I show up.  Mrs. Colwell had expressed interest in hearing stories of mathematicians before, and Thursdays lesson was on variation (not the statistical one, but how a function varies wrt some part.  e.g. f(x)=3ax^2 varies linearly with a, but by the square of x).  I figured it would be a good time to pull out some cool Fermi problems.

One of the new postdocs in my lab (Aaron Santos) is about to publish a great book on Fermi calculations that I had the good fortune to proof-read.  Blatantly ripping off one of his problems for the benefit of the students, today I gave them a short history of Fermi before we dove into calculating how much Spiderman would have to eat to shoot all of that web.  For those of you interested in the answer, both classes came up with 56 lbs per day.  

Both classes seemed to enjoy this storytime/problem but the after-lunch class was way more engaged, as is their full-bellied wont.  Everyone was shouting suggestions for the length of a spiderweb-shot, the number of shots per day, estimates at shot widths, and that Batman was better than Spiderman.  It was a lot of fun, and I agree that Batman is better than Spiderman- he's just a justice-loving hard-working billionaire whereas Spiderman was randomly given superpowers by a radioactive spider.  Gotta root for the hard worker.  The thing I found interesting was that this sort of silly example was actually as engaging as it was.  I always felt that such pandering to presumed interests ran the risk of insulting the student's intelligence.

Anyway, two really cool things happened today.  In my first class, Scott came bounding up to me as class began with the answer to my brainteaser from last week.  He found that the next value in this sequence:  1, 11, 21, 1211, 111221... is 312211!  I feel like I had bet everyone $5 that they couldn't find the answer, so now I owe Scott $5.  Good thing I didn't remember in class, because I didn't even bring enough money for lunch, and had to borrow some from Mrs. Colwell (let the record show I owe her $4).  After Scott impressed me with this, he proceeded to solve a Rubik's cube to the amazement of the back row (i'm serious).  I thought "holy crap- this kid is amazing!  Guess I don't need to worry about him anymore," as he beamed confidence across the room.  After my warm-up and some lecture by Mrs. Colwell, I wandered the room looking to answer questions as the kids solved this problem:

• y(x) varies by x to the 6th power
• when x=2, y=100
• find y when x=3

When Scott raised his hand, I was expecting to see one of the homework problems, him having blown through the in-class assignment.  Instead, he was still struggling with the above problem.  We worked through it twice before the "ahhhhh... I get it now" moment.  Going back to a comment I made in a previous post, I think Scott is a great example of the students in this class: they're very very smart but don't always know how to use the tools they have.  Once we show them, they're able to rock!  This is partially why I've been emphasizing group learning as a new activity- the students will be able to help each other reach the "aha!" moment while reinforcing what they've learned.  Students of this caliber may thrive with such activities (I have no data to support this). 

The second cool thing that happened today was the after-lunch class's interest in their grades.  After getting their test scores back, Mrs. Colwell was rushed by a crowd desiring to know how they're doing.  For many of them, it wasn't very good news.  But they care!  And, just like the class before lunch, they have the raw ability.  I'm hoping that our group-learning testing in the weeks to come is well-received by the after-lunch crowd.  I think their extra energy may facilitate discussions, I think the discussions may take away some of the extra energy, and I think any deviations from the traditional lecture style will be welcome for these students.  We shall see.

Also, for the record, I did not get a perfect score on the test yesterday.   

Rowdiness

Today I noticed a large difference in the level of attentiveness between the two classes.  3rd hour was great.  We got through the quiz review, everyone seemed happy with how things were going, and there was time for a couple neat examples.  After lunch, 4th hour was a bunch of hooligans!  They were loud, the exact same material didn't seem to stick, and we were rushed at the end of class to fit everything in.  It was like night and day.

Hopefully the quiz goes well tomorrow and we can make sure everyone is on the same page next week!

Week 2!

Over the weekend I received a concerned email from Mrs. Colwell regarding my last post.  Most notably, she highlighted (correctly) the facts that students do need to know vocabulary to talk about math and that showing work is indeed very important.  After clarifying that I didn't mean to disparage these portions of class, but simply identified with the students we began this week anew.  

Today was the day after a quiz, so instead of giving a special talk I helped answer questions about mistakes on the quiz as well as homework problems and other examples.  There were a lot of non-passing grades on the quiz, but when I spoke with the students one-on-one we were able to clarify their mistakes.  One student said "You're my new best friend.  Always able to help when I have a question."  Most of the mistakes on the test boiled down to:

• Not knowing how to interpret the question
• Calculator error (or rather, an error from its operator)
• Not showing work

Talking through the problems helped elucidate most of the interpretation questions, and I was really surprised about how many students sounded excited to go to tutoring. 

On Thursday we're learning about sequences, so I think I'm going to give a small example at the beginning of class that covers both sequences and recursion (Friday's lecture) and proves that there are no vampires.  Hope they like it!

Showing work and memorizing vocab = BLECH

Today was day number 2.  Like yesterday, I began each class with a short lecture and spent the second half of class answering questions.  Mrs. Colwell mentioned she likes this system, as she gets to take care of beginning-of-class details while the students are getting work done.  Parallel processing at its finest!

The portion I introduced at the beginning was a practice quiz in preparation for the real thing on Monday.  This went pretty smoothly with 2 exceptions:  1)  I realized I don't really care what "domain" and "range" are.  2) I was caught in a lie.  When the students had questions about domain and range, I answered them as best I could without explicitly saying "I hate this too," but I did mention that "I'm in the 23rd grade, and even I don't always remember this."  The students jumped on this:  

students: "You've been in college for 11 years?!  How old are you?!" 

me:"umm... well I went to undergrad for 5 and I'm in my 4th year of grad school."

them: "that's 9"

me: "uh yeah, I worked for two years at Dow" (liar!!)

them: "how old are you?"

me: "26."

them:  "you don't look 26."  "wait, did you skip a grade?  how old were you when you started school..."

Pandemonium.

So... I learned that their mental math is pretty quick.  I'm thinking of applying a trick I had heard an economics professor had used.  On the first day of class you tell them that every class will have one lie.  Whoever finds the lie wins something.  It keeps them attentive, excited to win stuff, and if you mess up accidentally that gets to be the lie for the day.  Then, on the last day of class you tell no lies.  When they question this, you tell them that on the first day of class, you told them you would tell them one lie per day.  That statement, you now inform them, was that day's lie.

More importantly, I noticed that the students tuned out the subsequent discussion of domains, range, vertical line tests, etc.  These are facts about functions.  They're not really important in the real world, but they're the only things the students can be tested on.  The students also were mad about having to show their work (or rather, losing HW credit for not showing their work.)  This is something I hated too.  What matters is being able to figure the answer out, not how you did it.  Mrs. Colwell noted that this prevents the students from just copying answers from their friends.  All it does, though, is make them have to copy MORE answers from their friends, if they are copying.

A potential solution:  Don't have any homework.  Make the kids do the work in class, but let them ask questions of the teachers and of each other.  If we had a 10 minute quiz each day that emphasized just one important concept, they may very well be more engaged to learn than by having to memorize dumb facts.  Of course, this needs more thinking through, but I think the important thing is that the students learn how to use the math and how it empowers them.  Knowing what "domain" and "range" are is pointless.

A plan!

Next week, Mrs. Colwell gave me permission to tell stories about famous mathematicians, or stories about famous numbers or functions.  I think I'm going to show the students everything in the entire book.  I have trouble learning something if I don't why I need to learn it, and I suspect the same may be true for some of the students.  My plan is to show them the the only thing we're learning this semester are patterns and puzzles.  This is seriously all that's in the book:

• f(x) is how we denote a function
• pictures of f(x)
• matrices
• two equations, two unknowns
• f(x)=x^2
• f(x)=x^a  where a is an integer
• f(x)=x^a  where a is real
• f(x)=exp(x), f(x)=ln(x)
• sin, cos, tan
• polynomials
• conic sections
• series

Literally, each of those bullets is one chapter of 9-10 sections.  Why does polynomials have its own section away from x^2?  Why do they explain the names of function parts without showing cool functions?  Nobody cares that the thing in the parentheses is the "argument".  Just show me the patterns!  This book is basically a journey in finding x from f(x)=c up through f(x)=a*exp(x) + b*ln(x) + c*cos(x) + x^d.  Perhaps if they see what's coming and see that we're doing the same thing all the way through (learning about new expressions, what they look like, how they're used, and how to solve them) it may help some of them deal with the immediate pain of domain and range.  In short, the idea is to show them they can do everything in the book and that the rest of class is just filling in the details.

First day

Today was the first day of class.  I was simultaneously nervous and confident:  nervous because I had no idea what to expect from my first class, but confident that I would be able to help Mrs. Colwell had asked.  The assignment was seemingly simple "talk about how functions are used in engineering."  I thought it would be a breeze!  Just sit down, make sure everyone knew the notation, and then talk about some famous functions used in the real world.  Easy, right?

Wrong.  

As I took the projector for the first class, I didn't know what the kids knew or didn't know, so I just started talking in the hopes of feeling out unfamiliar waters.  Whereas I thought the discussion of nomenclature would just be a side note, a preface to real engineering functions, it turns out that this was actually the lecture for the day!  After I fumbled for a while, Mrs. Colwell took over and began the day's real lesson.  The kids copied down the answers to the previous day's homework, and then Mrs. Colwell explained Euler and Mapping notations for functions.  A couple of examples of these, and then BAM, it was homework time. 

During Mrs. Colwell's lecture, I tried my best to run around the room answering questions that the kids had as she went.  This seemed to work well- she had fewer interruptions to deal with and I was having fun being useful.  The kids asked good questions, were typically interested, seemed motivated, and had good attitudes.  Maybe it's just because it is still the first week, or maybe because they're not used to having a new person in the room answering questions, but I was pleasantly surprised with how well-behaved the class was.

With lunch between classes, I get a chance to sit down with Mrs. Colwell, which I think will be a great asset in the future.  We should be able to talk about how things did or didn't work, and then adjust for the second class.  Today, she asked "when were you going to talk about engineering?"  Before class, I thought that it would just "come up" as I talked about functions in general.  As this answer left my lips, I thought "boy do I sound unprepared." 

In the second hour, I was way more comfortable with being up in front of the class and set out to give my 20 minute shpeel about functions in engineering.  I sat down, introduced myself, and found myself talking about why they should care about math as a preface to "real engineering functions."  When I said math was beautiful, one student (who may be a bit of a disruption, we shall see) said "you mean math is sexy!?"  I went off on a tangent about the golden ratio, explaining how it appears in proportions for things that are aesthetically pleasing, like faces, buildings, and bodies.  "So yes, math is sexy."  One student asked if I would measure the ratios of her face before I realized I had probably run out of time and hadn't mentioned much in the way of engineering.

Again, Mrs. Colwell stepped in and delivered the lecture as I attempted to help out with questions as they arose.  On average, the attentiveness and attitude of these students was the same as the morning class, but their distribution is much more broad.  There were both more kids working hard and more kids causing disruptions.  

After class ended, Mrs. Colwell asked "so, can you talk about engineering tomorrow?"  I chuckled to myself a little bit- as impressed the students had been with "sexy math," none of them realized that their new teacher had failed at his homework assignment.  Now that I think about it more, it's a hard assignment.  How do you talk about math in engineering in a way that is both accessible to neophytes in the subject and sufficiently interesting?  Also, what is the goal of talking about functions used in engineering?  Is it to show them that they can be engineers?  Is the goal to show them real-world applications of the work they are doing?  What if they don't care about engineering?- is it possible that such a talk may turn them off from math?

The impression I got from the students today was that nobody hated math, but that none of them really loved it.  I think that rather than just showing them what math can be used for (like engineering), we should be emphasizing what they can do with it.  Show them that math is just playing with patterns and that playing is fun.  It's my hope that they can learn all the necessary test material at the same time, but we'll see how it goes.  Today I learned that they have the ability.  The challenge, of course, lies in taking the rote memorization of "dependent, domain, and argument" and turning it into something they can actually use and talk about.  

Teacher selection

Today we met with math and science teachers from Ypsi high school for Fellow-Faculty pairings.  I was paired with Doriane Colwell and I'll be teaching algebra and advanced algebra this year!  Sounds like we'll be getting into the classrooms soon, but I still don't think I have any idea what I'm getting into.  

first post

Hi.  This is the blog for Eric's experiences as he teaches (or, attempts to help teach) a high school class this year.  On Monday we meet with the teachers whose classrooms we can potentially serve in- and I'm pretty excited.  Right now I think I'm leaning towards math, but with all the idiocy about creationism in the news it might also be fun to teach biology.  Regardless of the subject, I hope I'll be helpful and a good example of a scientist.  Just look at what one 7th grade class thought of scientists before they met real researchers at Fermilab!  As a side note, if you look through all the pictures in that link, many students seem to have chosen a man with a striped shirt and goatee as their new canonical scientist.  I wonder who they met at Fermilab that fits this description.