Post Pi

My preservice elementary course this semester is an embedded field experience. Each week I write or find some lesson for the 3rd graders, and they teach in groups of 2 to 3 or 4 3rd graders, and then reteach in our next class period.  Each class I sit in with a group, and everyone has some time to assess and reflect themselves and the learners while I debrief with that group. Before the first time teaching, at least, we try to rehearse together. As a whole, this is how I want to teach teacher prep from here on out. We're getting to less content, but I see so much more learning.

This week I had a lesson planned for Thursday, Pi Day, that had nothing to do with π. It was on these terrific Naoki Inaba place value puzzles that Jenna Laib shared. But with Pi Day approaching, and #MTBOS talk of activities and Scrooges, how could I help but think of a lesson?

Probably won't do a pi day activity with the 3rd graders, but if I did, I think it would be to make circles as best you can with lengths of string, then measure guess how far across.



Maybe better in reverse. You lay out string for a diameter, students cut a length to be the circle, and the winner is the best circle?



Simon Gregg‏ @Simon_Gregg Mar 11

Yes, easier to start with the diameter and estimate and cut circumferences. Might be easier with thick paper strips, which have a stiffness and taped together will hold a roughly circular shape?
@mathhombre Replying to @Simon_Gregg good idea! Better visual, too.o


So I felt comfortable offering my PSTs a choice. Pi Day Lesson or the puzzle lesson. If they chose the puzzle lesson, we'd talk about reteaching it or getting back on a Tuesday first schedule. (So they have the weekend to prepare. That was the original idea, but we've had... weather.) To my surprise they overwhelmingly wanted a Pi Day lesson. Oh, crap!


For the objective, I definitely wanted learners to come away with the idea that π had to do with circles, to get to do some Visual -> Properties Van Hiele type experiences, and that it's a little surprising how far it is around a circle. Here's the lesson plan.


It starts with a quick activity that I think was first inspired by Patrick Honner, who had a lesson on a day like 11/11/11 where he had an equilateral triangle drawing contest. Who can draw the best ____ is a part of my repertoire now. It's just perfect how it goes from the visual to properties as people argue over which is best. Not without resistance. "Because it looks the most like a ____" Hmmm. So what makes a shape look like a _____?


Then the competition begins. A strip of paper cut out to be the diameter is placed, and learners try to cut out a circle that - when in it's most perfect circle shape - is the closest to having that diameter. They record the data of what they tried, and indicate which was closest. Then repeat for a longer length and then an even longer length. In the group I was watching, Sophie said at the 3rd one, "I think I want it about 3 times as long. Maybe a little longer." Why? "It's just a guess?" Did she connect with pi? Build from the data? Visual instinct? She wouldn't get more specific.





The teachers found that learners were engaged. They liked the making aspect. They definitely enjoyed the competition. A lot of good talk about circles, and a little bit about circumference. So, maybe file this lesson away for next year? 3.1420 is just around the corner.

My Oreo Lesson

Finally... my chance to do the oreo lesson!

I'm teaching one of our math for elementary education courses and the content includes measurement and statistics. I love measurement as a context which needs statistical understanding. Measurement introduces variability, and has a strong need for producing a number to represent typical. If the question is, "How tall is the ceiling?" then 2.60, 2.7, 2.725, 2.73, 2.735, 2.735, 2.74, or 2.76 meters is not a satisfying answer.

The oreo lesson, if you are unimaginably unfamiliar with it, is the brainchild of Christopher Danielson, aka @Trianglemancsd, the purveyor of much fine snack food mathematics. (All the oreo posts; this one is sort of a wrap up.)

Previous to this lesson, we investigated measurement, did an introduction to statistical typicals, and worked on statistical displays. (Two of those covered in a previous blogpost.) On the day before oreo day, I brought three packages of oreos to class: regular, double stuf, and mega stuf. Their interest was definitely piqued; it was like they could smell the sugar. Not much mathematical interest, though. So I prompted - what might a mathematician wonder about this? They immediately jumped to the idea of is it really double, and what is mega. Then we brainstormed together - what do we need to gather data on for the next day?

Their list:

OREO: data to collect

weight of the whole cookie

weight of white stuf in each cookie

height of each cookie (mm)

diameter of each cookie

weight of cookie/black sides

height of black cookie

height of white stuf

diameter of white stuf

how many of each size fit in a specific container/height

volume by displacement

compare deliciousness of different types

nutrition information

stuffing v serving size

calorie content (burning)

Not bad. Calorie burning turned out not to be viable with that short of a notice... but I'd like to see it! I made a data sheet, so that we'd have a whole class worth of data, and a google spreadsheet to share.


The points about measuring like a scientist (half of the smallest unit) and recording to show the accuracy measured are obviously still in progress. Also the statistical thinking of gathering and using data need more development - most were happy to answer the main question with just their measurement. "It's double." "It's more than double." "It's less than double." No one used the measurements, they went entirely by weight.

That wasn't what bothered me. I expect those kind of goals to take time.

What bothered me was that they weren't into it.

They were excited about the cookies, and figuring how many each person got, and eating the cookies afterward. But they weren't into the math.

Dave Coffey sometimes recounts (or makes fun of me for) how I want to be obsolete. Sitting back and watching students direct themselves at the end of the semester. I always want to hand off to the students. Have them make it their lesson. Look, here's a pile of data! On something interesting! What can you do with it? What else could we look into? How many ways can we come at the question?

But on this day, they said no.

My personal metaphor for this is a Smothers Brothers routine. (That's how old I am.)


(The whole brilliant bit... the show was amazing. Steve Martin got his start there as a writer, for example. They used their folk singing to make the show safe for sharp political commentary. Like we use math class as a ruse to get students problem solving and thinking critically. They were cancelled and replaced with Hee Haw.)

So this lesson felt like, "Take it, class!"
"No."

My response was to ask them to make sure they got all their group's data, and to write about the measuring and their answer to the question for a standards based grading assessment. And this is a compliant class, so they did, and did a good job on it. But that's far from the peak experience for which I was hoping with this lesson.

Part of the problem, I think, was in my desire for efficiency. By introducing the problem in the previous class and then making a record sheet, I took the initiative from them. They went into fill in the blank mode, from long habit in math class. Another part of the problem was lack of a focus, in the workshop sense. I think I should have discussed statistical thinking with them, and how that's different from single measurement thinking. It's all about the data! This is very reminiscent of the Barbie Bust. It was my problem and my lesson. "My" doesn't help me be a better teacher. (Gollum.)

Reflecting afterward, I think my high expectations helped create the sense of disappointment, like an overhyped movie.  And it led me to rush into a lesson instead of building suspense and anticipation.  I think this kind of experience contributes to teachers who "tried that once" and that was enough to turn them off of inquiry-based learning.  In the end it is the learning that needs to be the center of engagement, not the cookie.

Planning for Engagement

(This is me blogging Dave's lesson.  I like taking notes - probably the thing about class I miss most.)

We started class thinking about our six word teaching philosophies. How these can be the core of our planning, instruction and how we interact with students. Dave's - "Engagement that fosters capacity and agency."

From student blogs during the week, we know that the idea of evaluation was still in process for many of the student teachers.

Evaluation

• What can we do?
• What are we trying to do?
• What comes next?

It's natural to start with ourselves, that's what we know best.  And we may be saddled with assessment data that's not accountable nor reliable.  Eg. Star Math (as a TA pointed out) or MEAP data (Michigan's state Grade 3-8 assessments).

Dave shared his early classroom management by carrot and stick, and mostly sticks; he relates that to an instinct to control.  There's a time for that, but it's not always.  Then the cajoling.  There's a place for that, but not always.  Want to get to a classroom where it's about choice.  Students choose to be a part of class.  It's not easy.

Cambourne's Conditions of Learning.  ("Toward an educationally relevant theory of literacy learning:  Twenty years of inquiry," Brian Cambourne, The Reading Teacher, 49(3), 182-190.) (paraphrased)

Engagement occurs when learners are convinced that:

1. They are potential doers of these demonstrations they are observing.
2. Engaging with these demonstrations will further their purposes for their lives.
3. They can engage and try without fear of physical or psychological hurt if their attempts are not correct.

Students were asked to develop their rubrics on  Classroom Management:

:-)	:-|	:-(
Students do self-discovery activities. Teacher uses 10 second rule. Be able to get all students engaged. Understanding directions and interested because they see importance. The students are talking to other students about the lesson and asking questions. Creates a safe/welcoming environment and fosters an "I want to try," or "I think I can" atmosphere. Students excited to learn on their own.	Mostly teacher-centered. Ignoring actions & sometimes loses cool. Some students are engaged in lesson. Understanding, but no interest while doing work. They seem interested in what you are doing, but don't understand the lesson. Provides a variety of activities and gives learners a choice. Doing the work or trying, but not enjoying it.	Completely teacher-centered. Teacher acts impulsively. Majority of the students (or all)  aren't engaged. Lack of understanding, confused as to what they are supposed to do. The students are not talking to one another nor asking questions about the lesson. Has a controlling environments. Students not even trying.

He shared the post from miss brave, a 3rd grade teacher in NYC, on being disengaged.  Engagement as it relates to classroom management.

Finally, he demonstrated what his lesson planning was like in different stages of his career.  (Hopefully we'll have video of this, also.)  We can use the rubric as a landscape of progression.  What does it mean to plan? What am I focusing on at each stage?

:-)	"The learner will..." objectives!  Letting learners take control of their learning.  Tied everything to content, but also what you wanted your students to look at beyond that.  Evaluation process with students: can, trying, next  Better understanding of these particular learners, not just prior students.
:-|	Looked at what prior knowledge students might have and how it related. (Launch)  Started to put more emphasis on reasoning and justification - process in general.  More thinking about how students would respond. Changing questions to better suit students.  Making changes based on what happened last time.  Used words like 'construct' and 'consolidate.' More comfortable with some educational theory.  More of probing for understanding. More assessment.
:-(	Focusing on yourself and what you were doing. Teacher centered.  No objectives.  Close to what the book had in place.  There wasn't much wiggle room for how the lesson could be individualized, or varied depending on how the lesson goes.  Lesson plan is vague. A substitute would have no idea what to expect in terms of student difficulties.

We have to start by beginning with ourselves.  Those are bad words - teacher centered - but it's where he had to start.  "Constructivism gone mad," when he tried to jump right to student centered.  I go through these stages more quickly, but still go through them.

A student pointed out that there should also be progress throughout the year. Yes!  Gradual release... but that's for another day.

Throw Out Your Lesson Plans

Preamble:  the Common Core Standards for K12 Mathematics are up and available for comment.  See http://www.corestandards.org/.  My two two word reviews: too much and too little.  They just couldn't focus.  And, there's very little attention to the processes.  In related news, as Congress considers the revamping of the Elementary and Secondary Education Act, the Forum for Education and Democracy put together a pretty nice little manifesto, er, recommendations.  I glossed over it once, but Dave Coffey repointed it out to me.  Worth a look.

We were talking about lesson planning this week, and I enjoyed the think aloud enough that I thought I'd post it.

It's easy and common to confuse lesson planning with a lesson plan.  When you ask preservice teachers about planning they invariably talk about lesson plans, and most usually, particular lesson plan formats.  Then they get more classroom experience and 95/100 supervising teachers tell them that they don't use lesson plans any more and the novice teachers decide they don't them either. 

Of course, they're right.  They probably don't need lesson plans the way we often teach them.  I used to require awful things.  Huge four column Japanese style lesson plans with loads of information.  Then I started just using those to capture a lesson.  Finally, I gave up making any kind of stink about the format.  I still share those, as a way to capture a lesson.  But I make no pretense that you would use them to prepare a lesson.  As a department (okay, Dave, Rebecca and I) we are trying to get away from planning without students in mind.  Real students.  Talk about sending a bad message!


But the lesson plans are the bathwater.  Helpful.  Bubbly?  The baby is the planning.  That is absolutely essential.  And every intentional teacher I know spends time, thought and energy planning.  We may not have enough time for it, and would probably like to do more of it, but it's a crucial part of the teaching.  That's why it gets a spot of its own on the Teaching Learning Cycle.  (Adapted from the Learning Network model.)

So to try and capture the difference, this semester, I talked about both as the questions I ask myself while thinking about them.  This feels more authentic to me, because I'm constantly adding to and changing the planning questions, which feels like when I'm planning. 

Plan vs Planning:  Essential Questions

Lesson Plan

• What will help you organize your thinking?
• What physical record would be a good reference while teaching?  What details, sequencing or answers would be handy to have available.
• What record will help you keep track of what was done and what you learned from it?

Lesson Planning
What do you want students to learn?

• What do they already know about it?
• Why do they need to know this?  Or, what’s important about this?
• Consider big, long term goals and specific lesson objectives.
• Consider process goals as well as content goals.
• What do they already know about this?
• How will you be able to tell when they’ve learned it?

What experiences will move students forward towards the objectives?

• What lesson structure will be good for this?
• What mode (individual, cooperative) is good for this?
• Have you tried it?
• What’s engaging about this?

What support would help students?

• How will you equip diverse students?
• What are possible student responses or questions? Your responses to that?
• What representations will you be using?
• Would a demonstration help?
• Are there math or life connections to this?

What data will you collect?

• What does understanding look like?
• When and how will you observe the students?
• What record will you make of the data?
• How will students consolidate or reflect on their work?

What other questions do you ask yourself while planning?  What's most important to you?  I'd love to hear about it.