Sunday, October 15, 2017

NWMC 2017

Holy Cosines!  A lot has been happening in the math world in the three years since I had my first child and my life was consumed by this entropy machine.  I just attended my first professional conference in 4 or 5 years and my mind is abuzz.  I need to write it all down before I forget.

First I attended Tom Reardon's "Problem Solving: All-Time Favorite Mathematically Rich Precalculus Activities, Individualized- with Complete Solutions".  Here are some things I want to remember:

  • We started with "the great applied problem" which involved a cylindrical tank lying on it's side partially filled with water.  The goal is to figure out how much water is in the tank, and how much water is needed to finish filling up the tank.  He asked us first to ask him for the information we'd need to solve the problem.  I never do this in class because I'm always in such a hurry.  What a super important first step when tackling any problem.  This was consistent through all the activities he showed us.
  • Then we did a bunch of other fun problems and we played with graphing calculators a lot.  My classroom has a set of donated calculators I scrounged up from the app Next Door this summer, so I don't know how much of this fun my kids will get to have, but it reminded me of how powerful they are, and how intimidating they are.  He had us doing stuff with them I never new was possible. But remembering how to do all the little steps and where all the different buttons were was hard, and I use TI-84s every day.  I almost asked him if it was worth it teaching students this way or if we should just switch over to Desmos, screw the standardized tests, but I was too chicken.  

Then I did Dan Meyer's "Charge Up Your Classes with Free Desmos Technology."  I have to insert another Holy Cosines here!  Dan sat next to me at one point.  I was too star dazzled to say a single word to him, but I was 2 feet away!  I actually haven't always been a big three act fan.  I've followed Dan's blog for a long time, but I was too overworked to implement any of his ideas.  I'm not tech saavy and when he was first posting his three act videos I thought they were super cool, but I couldn't see how I could make any, didn't have the technology in my classroom to even show them, and I also didn't think I could spare the class time to really do them justice.  Also I was teaching 14 preps so really didn't have the planning time either (yes, it really was 14 preps.  Isn't that insane?)  But in the few years I've been away he's made Desmos into a lean, mean three act machine.  Some things I don't want to forget.

  • He did this super cool thing where we made a list of values from -5 to 5, then he defined points like (L, L) or (L, -L) or (L, L^2) and had us predict what the graph would look like.  What a super super super cool way to finally cement the idea that when we graph a function like y=x^2, the ordered pairs will be: (x, x^2).  I've had such a hard time getting my students to understand that (x,y) means the same thing as (x, f(x)) which means the same thing as (x, whatever f(x) is defined as, like x^2, or x^2 -2x+7)
  • I MUST go back and finish the desmos scavenger hunt then use desmos all the time.
  • Dan said something during the presentation that rubbed me the wrong way and I'm still trying to make sense of it.  He had this shtick of playing super dead-pan and skeptical of anyone's answer.  He said he worked hard to make students doubt any answer they presented.  His point that we want students to justify their thinking, to be open to alternate solutions, and to really own their answers even in the face of doubt is well taken, and maybe if I'd been taught with someone like him as a teacher, someone I trusted, I would have learned more confidence.  But I have too many experiences of being ignored or doubted when I was right in less trusting environments to be comfortable with this teaching style.  

Then I was tired and the next day we had staff development for my school so I played hookie and didn't go to any of the Friday sessions.  Which was a huge bummer.

Then I did a 7:30 AM (ON A SATURDAY!) breakfast keynote with Fawn Nguyen titled, "What if We've Been Teaching Mathematics All Wrong."  WOW.  There is so much from this that I want to remember that I wish I'd video taped it.  But I've already forgotten so much of it.

  • First, I want a poster that has three rules on it.  Rule #1: Never give up.  Rule #2: Never give someone else an answer.  Rule #3: Love being stuck.
  • She used visual patterns in ways I'd never thought about before.  Of course I can't remember them anymore!  She did a cool paper folding activity where you take a strip of paper and fold it in half.  Then unfold and count the creases.  Then fold it back in half and then in half again.  Count the creases.  Repeat.  I've seen this activity before, but I'd forgotten about it so hopefully this blog post will make me remember.  
  • I need to play WAAAAAY more with visual patterns and between 2 numbers and everything she's ever done ever.  

Then I did Andrew Stadel's "Lessons that Make Math Stick."  Again, he may have made me a groupie for life.  Things I want to remember:

  • Give every activity the 3-C test; each one should be conceptual, spark curiosity, and should connect students to real experiences.  He had a great video of a girl on a see-saw.  She put a milk crate on the other side of the see-saw and started filling it with bricks.  Each brick weighed 5 lbs.  The obvious questions was how many bricks it took to balance with the girl.  What a really cool way to model division and multiplication.  He had so many of these great videos that made me see how truly important it is to spark curiosity.
  • He talked about how baseball players who practice three kinds of hitting in blocks learn less than those who do mixed practice.  Then he advocated for Steve Leinwand's 2-4-2 homework model.  Here's a link to a blog post talking about it.  I really really really want to try this with my pre-calc class.
  • Finally he talked about meaningful feedback- whether feedback should be immediate or delayed.  I post all my answer keys online for students to look at.  I need to give this question a LOT more thought.  

Finally I did Jeff Crawford's "Visual Algebra: Current Research and Practical Applications."  Oh my gcf!  He had us looking at visual patterns in such cool ways.  Blocks are sooooo cool.

  • I want to investigate proofs without words, Jo Boaler videos and youcubed (which I'd never heard of before!) and open-up resources which I'd already started playing around with for my 6th grade math class.
  • He talked about Finger gnosia which is crazy and I want to experiment on my toddler with.  
  • He showed us all the different ways our brains see patterns and how while all those different ways can be distilled into the same algebra expressions, they are beautiful in their uniqueness and the different ways we see them can lead to some understandings of the function's that are more useful than others.  (Particularly in tracing the patterns backwards)
  • The key to functions is identifying what stays the same and what changes.  Then when it changes, how it changes.  
  • I need to have students prove why sqrt(a^2+b^2) IS NOT a+b with blocks.  Because they KEEP making this mistake.  
  • I need to read PEAK.
Whew.  I'm pooped.  Maybe later I'll come back and fill out more details but I've got the heart of the sessions distilled for future me to enjoy with tea and biscuits.  

Tuesday, October 3, 2017

Inverse Function Activity

Here's a quick activity to develop the idea of inverse functions for my algebra 2 students.  We just learned composition and domain and range.  I hope it'll be fun.

Here's a word version: inverse functions game

Update: We just did this activity.  The game was GREAT.  The worksheet was terrible.  I need to tweak it.  I'll upload a new version once I think it'll work better.

Update update: Here's a new version of the worksheet.  I'm actually kinda proud of this one.  I want to go back in time and kick myself.  Or at least hand this over to past me and make me teach it this way instead.
  And here's a word version