Saturday, October 26, 2013

Teaching Proofs pt 1

There has been a lot of chatter recently about proofs. Bad drawing guy posted some interesting things. Even Dy Dan flashed a little proof knowledge.  What is boils down to is we all have our own little tricks, methods, and approaches. (Like 'mequals' ala Marshall Thompson). Some 'purists' want perfect notation and exact mathematical properties. Other 'free-spirits' just want them to learn the ways of our people proofs without the unnecessary distinction between equal and congruent.



My intentions have changed over the years, I started a bit towards the notation side and have since swung to free-spirit. There is evidence to suggest I've gotten better at it as the years add up, I can better predict struggles and pinpoint problem areas in advance. But it dawned on me that maybe I'm just better at teaching to the test, and not really getting better at teaching proof, logic, argument and reasoning.

So I set out to find a concrete reason we teach proof, and I saw it in a dirty subway station in NY city.

A subway map.



In our proofs we have a starting point (given) and a destination (prove). I liken it to needing to get form point A to point B in NY. I like proofs and in the same way I admire the transit system in NY. It is a puzzle, you know where you are and you know where you want to be, the challenge is deciding what route to take.

If you live and ride in the city every day you are probably good at the subway puzzle. Much like me completing my 7th year of teaching proofs, I see a start and an end and I know how to get there, math teachers know which routes to take.

If you live and ride in the city every day you feel safe on the subway (at least about where you are going). You are on the red line and you don't need to look at the map, you don't need to check the sign at every stop and count down in your head how many stops till yours, you just know when to get off and transfer. Math teachers are the same way with proofs, we know when the segment addition property is coming up, we don't need no stinkin' maps.

If you live and ride in the city every day you know there are a couple of routes you could take, but you know the best and fastest ones. "Oh you didn't know this was an express and missed your stop" doesn't happen to you. Math teachers don't go down wrong avenues either, we don't make mistakes and get on the wrong subway.

Our students are tourists lost in NY with a crappy map and little desire to get anywhere.


So how do we take these lost little souls and turn them into veteran subway riders. 
  • Break down the train lines (aka properties) get them comfortable with what each train line does. They should know that when they need to get to JFK they need to take the blue line. When they see midpoint use midpoint formula.
  • Start with shorter routes and work to longer ones. Confidence is half the battle, they starting feeling good on the trains they will take that next route right or wrong, instead of sitting at the station afraid to ride any trains (blank paper).
  • Do mix in long routes. Shorts are good but they usually aren't great proofs. They leave you feeling like "Why the hell did we just prove that, it was obvious and pointless." Don't let that become your first 3 days of proofs. You wouldn't go to NY and take the red line one stop for the first 3 days.
  • Remind them the lines don't change and they go both directions. Green will take you to the Bronx every time. That goddamn 'definition of congruent' ain't gonna do nothing but change from congruent to equal and back, don't use it for anything else.
  • If a student gets on all the right trains and makes it to point B celebrate that. Don't worry too much about the names of the trains, in fact don't worry at all about the names. If they can just describe the train and what it does be happy.
    • "Segment Addition Property"   -good
    • "The property that says you can take part + part = whole"   -THIS IS FINE
    • Students aren't going to use segment addition property after your class, they will use logic and reasoning though, so let them reason it out for themselves instead of jamming specific words, definitions, and theorems in their proofs.
So we have the metaphor,we just need a way to carry it out.

Stay tuned for part two of proofs.













Tuesday, October 15, 2013

Smart kids hate to ask questions

Two things have happened recently

  • We had conferences and I had multiple parents tell me students are struggling with HW.
  • Yesterday I had time in class for students to ask questions and nobody asked a thing.

Something isn't adding up. Either parents are liars... or students are good at faking it. 

I see it in most math classes I teach, if you don't see it you've got it figured out, or your students are better fakers than mine. Problem is I bang my head against the wall every time I correct a test and think to myself, "Everybody knew this yesterday didn't they?" Turns out they didn't, turns out they don't ask.

I'll let you dive into the why: Fear, laziness, social stigma, procrastination...take your pick, point is they don't ask when they don't know.

So today, the day before a pretty important test, I made every single student ask a math question about the review. No matter if you are the smartest person in the room, you had to ask a question. 

Pros:
  • I talked to every kid in my room, rarely do I do that. 
  • There was a more even distribution of wealth (my support).
  • Whinny kids (yeah I said it) knew my time was sparse and they needed to figure some S out on their own.
  • Too cool for school kids had to ask a decent question which means they had to do decent work.
  • Too scared for school kids timidly raised their hand and asked a question out of fear that I would dock them 1 million imaginary points if they didn't.
Cons:
  • I answered the same question a lot which can be frustrating.
    • I way value answering it individually compared to answering it with the whole group, but it is still exhausting
  • Smartest kids were under utilized
    • As soon as a girl asked me what she should do when she was done and there was 20 minutes left I should have said, "Help people with hands up." Instead I said "Get a job."
    • No I really said, "Work on the assignment for tonight." 
Try it for yourself, it started as kind of a whim, hey lets makes these nerds ask some questions, but it really turned into something that was noticeably different in my classroom.

Good Luck


Monday, October 14, 2013

Teachers Teaching

The district I work in has had some rough years. We've tried implementing standards based grading and it happened poorly. We had poor leaders who had lost touch with what happens in a classroom. We had decisions being made by people that don't have to implement them. There were teacher groups that were supposed to 'guide' the practice but it turned into a "thanks for your ideas but we'll take it from here' kind of guiding.

The same thing is happening at our staff developments.
(insert funny picture of something funny and witty because I'm both those things...)

Friday we had a workshop and it was brutal. I'll admit I stayed up late the night before, yeah I spent some time at a bar with some friends watching any and all sports but I was there Friday morning on time and I ready to go.

Que music teacher teaching us about rubrics from a script created by people that just learned what a rubric was the night before (maybe at the same bar). Across the district (across the 3 high schools at least) we all sat through the same terrible presentation.

Highlights include:

  • A 50s TV show reference from Dragnet that went over everyone's head because anyone old enough to watch and understand TV in the 1950's is well retired or will retired after that terrible workshop day.
  • an arbitrary out of place Cyndi Lauper audio file.
  • Scripted jokes forced in by a teacher who just isn't funny.
  • Coloring activities where we identify the noun, verb, capital letters and punctuation.
It was bad followed by worse..."courageous conversations" came after lunch and I can't even describe how painful an experience it was listening to someone not talk about the achievement gap for an hour. 

Enough complaining though, what was good?
  • We got work time. Year after year, workshop after workshop they ask for our feedback and we tell them "we need work time" they are starting to listen.
  • Our teacher coaches presented and actually made it seem like they know how to speak to adults. More on that later
  • Pizza buffet for lunch with great co-workers.

How do we improve it?

It is an embarrassment that a group of teachers can't get together and teach. 
  • Some people have a hard time in front of a large groups of their peers. If that is you STOP PRESENTING. 
  • Do the same things in staff workshops we are expected to do in class everyday.
    • Differentiate.
    • Adapt to audience.
    • Find out prior knowledge and encourage growth where ever a student is.
    • Student centered
    • AGE APPROPRIATE learning
The last one is what is going to get me in trouble some day when a professional asks a group of high school teachers to color code something. That kind of crap works with high schoolers because they can't handle more then one thing at a time. Some high school students will drop out, some will become doctors, there is a wide variety of skills in a high school classroom you need to keep it general.

EVERY TEACHER WENT TO TEACHER SCHOOL

We are a group of adults concerned about student learning, that is what unites us. We also all have our undergrads or better, we can all read at or above a high school level, we can focus for more then 2 minutes, and we can think and reflect on something without having to fill time with meaningless coloring activities.

We need our leaders to allow people who can speak to adults do the presenting. This starts with hiring the right people in the right positions. Then letting them present appropriate things based on the group they have.

Thanks.







Friday, October 4, 2013

So why not post right now.

Things I like that I'm doing:


  • Three-acts Dy/Dan style which I am sure you know about if you are reading a math education blog.
  • Keeping grades fresh and updated.
    • I hate grades but they make me keep them so I might as well keep them updated on the hour every hour
  • Only yelled at my student once.
    • I'm not sure why yelling makes me feel better, its an odd relationship I have with teaching. I don't like it some days. Some days I love it. I like to think I spend more time on the like to love side rather then the dislike side, but each year is it's own adventure. I don't think I'm alone in this description.
    • They deserved it.
  • Weekly calendar is staying updated.
    • I plan only as far as the hour that is happening. Sometime my colleagues don't work well with that. Often time my favorite copy lady doesn't like that. But it is who I am. I tell me students at the beginning of the year to use their planner but I am such a hypocrite when it comes to planning.
  • Alternative Assessments
    • Had a colleague that was pushin' portfolios but I wasn't buying it. His seed grew into "Alternative Assessments" which take the place of in class tests. We've done some 'sequels' off the 3 acts. We had a sketch-up assignment where students build a 3-d model of something. I don't know if they are hitting everyone but I am happy if one student enjoys it. 
Future Matt reading back: keep these things going.