Dan as Assessment

First day in a class on high school math with preservice secondary teachers. A rambly story, to be sure.

From The Duplex by Glenn McCoy

 We started making nameplates and forming groups of 3 or 4.  While that seems inconsequential, I leave the markers and materials up front. And it's just the tiniest bit of culture setting when someone asks "we do that now?" and "should we come up to get the stuff?" And letting them know if the groups don't meet the parameters: facing each other and 3 or 4 members. Am I really going to be a stickler? "We have 5 is that okay?" "Nope." Student 4k+1 walks in; I ask "so what are you going to do now?" I have several occasions to say, "good thing we're a room full of problem solvers."

The next activity, Piece of Me, is robbed adapted from David Coffey. I'm now calling it 2 Questions. Each person comes up with two questions to ask the person on their left in their group. Once everyone has them, ask away. Everyone has the right to decline to answer. Some of the questions were generic (how was your summer), some were trivia (Michigan or Michigan State) (Answer was Notre Dame and a story about her family) and some sparked good discussion: "why be a teacher?" or "middle or high school and why?"

The second phase is they each come up with two questions for me, one about me one about the course. Then the group picks two of those questions. As Dave documents, answering and discussing just what the students are interested in is a vast improvement over teacher ramble or reading the syllabus. (That's homework.) This day they asked about the observations they do in high school, what homework would be like, how much reading, etc. about the course. They asked if they would be teaching in class... that hasn't come up before. About me they asked about family, education, why be  a teacher, etc. Favorite question this time: "do people say you look like anyone?" They used to, when I was skinny, but fat now, so... Then the student said he asked because I looked so much like Francis Ford Coppola.

Alright!

Our first math activity was one of Sadie's Counting Circles. Regardless of how you think math should be taught, you must know what people think about math now. I shared how Jo Boaler and others have experimented with number talks to change people's beliefs about math. And how Sadie's counting circles are a good context for a number talk.

The idea of the counting circle is two-fold. One is that it helps to build a positive learning culture where it's safe to speak up, mistakes are acceptable, multiple approaches are valued, and thinking is what we want to share, and the other is to develop number sense. Sadie would probably disapprove of my choice of starter value, but I thought too easy would actually disengage this group of math majors. So we did up by 97, starting at 235. It wound up being just a little uncomfortable for a couple of people - 99 might have been better. After 1.3 times around, at 2175, I put on the pause, and asked what would Amanda say (5 people further around the circle.) When everyone indicates they have an answer, I asked for volunteers for their thinking, and then just recorded it as they spoke it, eliciting details. And I didn't take a picture!The shared strategies included noticing that the ones place went down 3 each time, adjusting from adding 100 and multiplying 97x5 and adding it to 2175. Even the computation can be interesting. 97x5 used partial products to get 485, and then he added the 5, the 400 and then the 80.

With that set up, we moved to watching Dan Meyer's TEDx talk, Math Curriculum Needs a Makeover. (It's a classic for a reason.) They were very engaged, and had intense small group discussions after watching. One of the students led the whole class discussion, which became a good assessment for me. Their beliefs about teaching stood out sharply, thanks in part, at least, to their contrast with what Dan was saying.

My notes:

Not enough time!
-planning
-class time
Some time gained from students being able to do math practice at home. Tech helps with this. 
What stus know on tech is not always helpful.

Kids need too many basics to do this kind of work

Problems like this won't be on the standardized tests
I learned this way and the standardized tests were so easy. If you're taught this way, your understanding filters through standardized fluff.

Less memorization because you've created the formulas yourself.

We missed part of the process. This leads to more general methods because of questions like: How would you figure out for a tank ten times larger? Or is there a short cut for figuring it out more easily. In a class one time, for a question on the volume of a vase, why not just fill it and see? Prof answered: "what if it was 100,000 gallons?"

This kind of activity gets across the idea that you're not always going to be right. This is just one way to do it.

Grounds the math in reality. You know students are always asking 'when are we going to use this?'

I would summarized their talk as: "It would be more engaging, but..." I maintain that I do not want this course to be about me telling them how to teach, but giving them experiences that can equip them to construct their own vision of teaching and learning. Resources, reflection and a focus on student understanding lead to good teaching. But this experience helped me understand where we are starting and some of the barriers to where I want us to get.

We continued class by looking at 101qs.com and generating some questions. (Aside: read Pershan on learning to ask questions. We'll be tackling this later.) 

This led into launching the meatball three acts. We watched the video, and got to our estimates, and low and high guesses.

This was cut short because we had a presentation on Lisa Kasmer's excellent study abroad program in Tanzania .  I'm interested if anyone worked farther on it.

I was moved to write this up, because I tend to think of asking questions to get assessment data, and this wasn't intended to be assessment. I might not have noticed as well if I was running the discussion, but as an observer, it put me into notice-mode.

Postscript:
Part of the homework was to look for a 101qs prompt they found interesting. What they found interesting is in turn interesting to me! Here's a few:

• Jennifer: Bowling for Pennies. "Would this be cheaper to make than buying a 'mirror ball'?":  Nicole Paris asked: Would this be cheaper to make than buying one?
• Brittany: Waterkracht "centrale". Water power plant. How fast is the stream flowing?
• Greg: Beatlemail "How many letters would each band member have to answer?"
  Ken Meehan asked: How many pieces of fanmail?? What is the first question that comes to your mind?
• Sam: Brita How many water bottles are need to go around the earth once?
  Dan Meyer asked: How many times around the world would all those bottles wrap?
• Kevin: NFL JumboTron HDTV's How many 60" televisions does it take to fit in the Texans television?
  Nathan Amrine asked: How many 60" TV's would equal one Texans TV?
• Molly: Packing Box What is the total area of all boxes?
  Elaine Watson asked: What combination of small boxes and medium boxes can fill a large box?? What is the first question that comes to your mind?
• Joshua: Angry Birds Can knowledge of quadratics improve your Angry Birds accuracy?
• Jerry: Okay, this is the first one I found: Stuck Truck This reminded me of a story I once heard of about a semi-truck that came to the opening of a tunnel only to realize it was a couple of inches taller than the opening. Having to stop in the lane with no way to turn around, the truck had traffic backed up for miles as everyone had to consolidate down to one lane and everyone slowed down to gawk at the truck to see why it was stopped there. The police and the truck driver were all standing around the truck trying to figure out how to get the truck through the tunnel or turned around and had discussed numerous things but none of them seem to be the right answer. Then a little boy leaning out of the window as his dad drove by yelled out, "Why don't you just let some air out of the tires?" The question the original poster seemed to be thinking along the same lines, "How much beer would he have to drink to allow the driver to get the truck free?" However, my question had to do with how often this happens at this spot. Either it happens often and they should fix it or there is a sign and the driver just did not see it.
  Fred Jaravata asked: How much beer would I need to remove to help free the truck?? What is the first question that comes to your mind?
• Dakota: Cylindrical Tunnel How many windows are in this tunnel?
  statler hilton How much glass is needed for this?
• Jim: Pickle Stack How tall can you build a pickle tower?
  Krista Keats asked: What is the question?
• Brody: Keep 'Em From Fallin' How tall is the main structure?
  Michele Thomareas asked: How wide apart are the columns?? What is the first question that comes to your mind?
• Amanda: Waterworks at Legoland How far will the water spray?
  Rod Bennett asked: What happens to the trajectory of the water if she pedals faster?
• Christopher: Roulette Wheel What are the odds of that many 19's in a row?
  Joe asked: What are the odds of the same number coming up 7 times in a row?
• Anika: Circle Square How many circles are there?
  John Golden asked: What is the function for number of circles after each step?
• Nick: 2010 Guatamalan Sinkhole How deep is the hole?
  Robert Kaplinsky asked: How much material will they need to fill the sinkhole?? What is the first question that comes to your mind?
• Brooke: Firing Range How many lasers are there?
  statler hilton asked: How far away is the target they're shooting at?? What is the first question that comes to your mind?
• Leesha: Perfectly-timed photo How high is the plane?
  Johanna Langill asked: How high is the plane?? What is the first question that comes to your mind?