"Three Strategies for Getting Students Engaged in Math"

Or something like that.  Dan Meyer's workshop had some or most of those words in the title.  I believe the words Common Core also appeared, but I don't care because the workshop itself was one of the most fascinating useful pieces of professional development I have done in a while (at least since last Thursday when the Math Forum crew were in Bridgewater MA!)

Anyone who has seen Dan work the room, knows what I am talking about here:  we are his colleagues, we are helping him out, we are creating a website, we are in on the joke about that "other group" a few years back that "got it wrong", and could we please share what that "other group" got wrong?

Oh. My. Word.  Six hours flew by and I have so much I want to play with, think about, create, delete, try again.  LOVE it.

The three take aways:

1. Create a fight:  cause controversy (oh yeah, hear that MP3?). If it is an opinion, no one can be wrong if answering "Which is best?"

2. Turn up the math dial: slowly!  Start with no words, no explanation (or minimal explanation, or broad question) and slowly add in some numbers, etc until they do some math or beg for a quicker way to do it.  Which leads to....

3. Create a headache:  "If the math you want them to do is the 'aspirin' (that which mathematicians use to make life easier), then what was the 'headache'?  What caused mathematicians to come up with this faster, quicker way of doing things?"

But most of all, Dan assured us that we are all good.  We work hard and not every day is going to be a stellar day and sometimes it takes 5 years to figure out how to create the headache!  But don't give up and don't beat yourselves up.  What a message of hope, inspiration, and validation.  Well done, Dan.  Thank you!

Noticing and Wondering about Systems Word Problems

The late winter was so broken up for us.  Snowstorm after snowstorm broke up the weeks: 2 days off here, 2 days off there.  Week after week this went on.  When we finally came out the other side, were hopelessly behind.  Then there were other things like state ELA tests and field trips that broke up the weeks.  So now we are further behind.

I have been trying to get my sophomores ready for the state math test. One of the things I still need to teach / review is solving systems of linear equations.  Solving by graphing was no problem.  They were comfortable graphing lines, and this made sense to them.  Any other method was like talking Klingon to these poor kids.

Finally I just went to some crazy word problems and let the kids solve them any way they could think of.  The problems were silly and funny and often involved "my friend, Max."  For years, "my friend, Max" was just a made up imaginary friend.  Maybe I was thinking about this cartoon character?

Then I met Max Ray and suddenly I had a real "my friend, Max" and HE came out to work with this particular group of sophomores early in the year.

Now every time they get stuck, I pull out "what do you think my friend, Max, would ask about this?" or "What did you do when my friend, Max, was here?"

One young lady asked if she could come after school on FRIDAY to get extra help on these systems problems.  No matter what I encouraged her to do, she was just guessing and getting lost:  we had tried drawing pictures, we had tried making tables or organized lists.  Nothing worked.

So when she came on Friday, I wasn't really sure what I could pull out of my bag of tricks.  However just the previous afternoon, the crew from Math Forum had presented at a seminar put on by the Mathematics and Computer Science Collaborative (MACS) over at a local college. (Thank you Steve, Suzanne, Annie, and Norma!)  And once again, Annie and Steve made me remember the value of Noticing and Wondering.

I pulled up some simple systems word problems from Kuta, and at first just let her read them out loud.  I wanted to see what she would do on her own.  She drew the boxes we had played with in class (for organizing some info) and then she just got stuck.  I said, "You know, there is a LOT of information in these problems.  How about we use some Noticing and Wondering here?  I am going to clean off my desk while you work on noticing some things about the first problem."  When I got back a few minutes later, she had done two problems worth!

She declared that was easy.  "Then let's sort the information.  What is the first way we could sort some of your noticings?"

"I noticed there were 2 types of shirts: Fancy and Plain.  I guess we could use those as the variables?"(she was building on discussions we had done in class).
"Sure, why not?"

"I noticed that there were 7 shirts in all."
"Cool.  What KIND of shirts?"
"Some were fancy and some were plain:  OH! Fancy shirts and Plain shirts = 7 shirts!"
"Those units of measure I keep nagging you guys about come in handy, eh?  So what else did you notice?"

"She spent $131 on shirts.  And fancy shirts cost more than plain shirts."

Here is where she got bogged down:  she said $28 + $17 = $131.  I asked her to check that on her calculator.  After some tapping she presented me with a frowny face.

"If you type in $28, how many shirts is that?"
"One fancy shirt."
"Yep, how many shirts did be buy for the $131?"
"Seven shirts."
"Hmmmm, could she have bought more than one fancy shirt? or maybe even several?"

She played around with the calculator for a while and then said in frustration ,
"But I don't KNOW how many fancy shirts she bought! And I noticed that she bought plain shirts, too!"
"Hmmmmm, do we have a way of saying 'I don't know how many?' "
"Oh! we could call it x !"

And then she was able to make more sense of all the algebra we had been doing the last couple of days / weeks.  She had been blindly "doing the math", with no understanding why she was doing it.

"We should have done Noticing and Wondering all along, " she informed (admonished?) me.  "It makes a lot more sense now!"

Here is what she presented me with:

One thing that came up during our chat was a question that really threw me for a loop.  As she worked on noticing and wondering she asked aloud:  "How many legs do chickens have?"  I have to tell you: we don't live in farm country out here, but we are not exactly city dwellers either.  It took a lot of restraint to not have surprise register on my face.  I answered her question and she was happy with that.  "And pigs have four, is that right?"

Later, I told her I was giving her one problem that would count as a "quiz" to see if she could really do this on her own.  Here it is. Look carefully at the Wondering column.  She had a question about goats :)

Which One Doesn't Belong and MP3

If you haven't been playing with Which One Doesn't Belong then get thyself over to Mary Bourassa's blog and read up on it and its origin.

The short version:  you are given 4 pictures, graphs, shapes, whatever, and you have to decide which one doesn't belong.  The coolest thing?  There is no right answer!  Or wait, yes there is: there are FOUR right answers!!

Try this:  Which of the 4 words you see below doesn't belong.  WHY? (oh yeah, that WHY is the very best part, the frosting on the cake so to speak!)

Last Tuesday on the Global Math Department, Mary and fellow collaborator Chris Hunter presented Which One Doesn't Belong? They encouraged us to participate with them as Chris was showing how he comes up with the four items that will make up the WODB.

My Geometry class has been doing investigations with special parallelograms.  I thought it would be fun to get them to a WODB on that topic.

Before I go on, let me tell you that my professional goal this year was to listen more and to get students to REALLY work on the eight Standards for Mathematical Practice.  In particular, I wanted them to be really comfortable with sharing their thinking and be able to critique their own reasoning as well as the reasoning of others (MP3). I want them to understand that critiquing includes telling what you thought was great and what you are confused about, not just disagreeing with what was said (though that, too, is an important skill.)

I introduced the students to the "game" of WODB by showing them the slide above, then.....

with MP3 in mind, I presented this slide:

I tweeted this slide out, too, and got some WONDERFUL comments about it and how to improve it.  I want to explain why there are no angle marks, no parallel markers nor tic marks:  I wanted to see if they "got" it.  Would anyone call me (or one of their classmates) on it?  One of my four class rules is Don't Make Assumptions.  

They had a blast: so engaged.  Kids who never say anything were practically jumping out of their seats (and I number the squares as though they were quadrants, btw, because I find that these cherubs don't know about Quadrant I, II, III, and IV!). 

"The one in Quadrant III has only 1 set of parallel lines.The others all have 2 sets."  

"Quadrant I is the only one with all equal sides."

"It appears that the one in Quadrant IV is the only one with diagonals that are not congruent."

We decided that I would have to go fix the "rectangle" in Quadrant II, so it would have something unique to it.  It originally had the dotted diagonals, same as the others. We just couldn't figure out how else to make it unique, though just as we about to give up, one student jumped up and said: "It's the only 'tall' one!  Taller than it is wide!!"  The others clapped.  One suggestion to "fix" the rectangle was to change how the diagonals were made, and another suggestion was to change its color.

This was all happening just before the bell and I praised the student who said "It appears....." because that was the closest to admitting there was no proof that any of these were any thing more than mere quadrilaterals and that almost ALL of us had broken Palmer's Rule #3.

After watching the conversation about this on Twitter (I was too busy at school today to be able to do more than glance!), I thought I would make a second slide with the marks on it:

When I do this with next year's class, I may just show the unmarked slide and then this second slide, and ask them which is better and why?

Which do YOU like better?  Is too much information too much??