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.