Saskatchewan Understands Mathematics Conference

This weekend I'm up in North Country working with teachers from all over Saskatchewan at the Saskatchewan Understands Mathematics Conference. Random? Sure. Thank you twitter and thank you @park_star for organizing a fantastic two days. After a fantastic opening talk by James Tanton, I led a 2 hour sessions this morning titled Beyond Polya: Making Mathematical Habits of Mind an Integral Part of the Classroom. Here are the Powerpoint slides (I will warn you that a few of the animations did not export correctly, but it's readable). 


In short, we walked through my ten mathematical habits of mind, brainstormed what this meant to us and how we could see and teach this in our classroom, and did some math.

Starting with a personal reflection, I felt that the session went well overall. We did, however, go too quickly and we didn't spend enough time doing math. In retrospect, I should have focused on some of the habits which would have allowed for more time to engage more deeply. That said, hopefully some of the participants will come back for day two where I hope to give more space and time for participants to work. I am also finding it hard after every conference talk I do to get a real sense of whether or not my session was at all useful to people. It's one thing for people to like a session (which even that is sometimes hard to gauge across the board). It's a whole other animal for people to change or evolve. I was super jealous when I heard that The Space Between the Numbers got an email from a workshop participant at her NCTM talk on proof through logic puzzles saying that he had created a lesson around this talk the very next week. Anyway, I'm learning that conference workshops are very different from the classroom.

Technology Through Time

A visual of digital technology my 5th and 6th grade students have learned, used, explored, and/or benefited from this year. I'm proud to say that I'm continuing to increase my ratio of

using technology because it helps solve an existing problem : using technology because it's available

By the way, I created this as part of a Technology Through Time presentation to parents given by ten teachers intended to give a brief overview and scope of how technology is used at different ages and in different classes.

Escape From the Textbook Winter Meeting

Below are some lightly edited notes from the most recent Escape meeting at Willard Middle School in Berkeley. Our next meeting is tentatively set for Saturday, June 2nd somewhere in San Francisco.

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Escape from the Textbook meeting: March 24, 2012

Introductions

We spent the first part of the session exploring the game of Set. Over the course of the morning there were a few other games/ideas mentioned including Eleusis, Attributes Blocks (similar to set except with physical blocks), Spot It and Ricochet Robot.

We played the game for a bit, but then worked on solving and creating mathematical puzzles. Below are some examples:

* What is the maximum number of cards you can have without a set?

* Can you make a strip (a train) where any three cards next to one another are share the same number of characteristics?

* Games could be created with these cards similar to dominoes

* Start with some number of cards in your hand. Continue to play cards that do NOT make a set with the cards on the table.

* How many cards are in the deck?

* How many different sets can one card be a part of?

* How many different sets can 2 cards be part of? What if only 3 characteristics need to match (or be different)?

* Is it possible for all the cards to be used? What is the probability of this happening?

* Can a subset of the deck be organized in a way to make sets with no extra cards left over?

Our group then began working on "magic square" problems. We determined that if cards are on the four corners of a magic square, the entire square is determined. We then saw that this was also the case with 3 corners (and that it would be impossible to create the entire magic square if the 3 starting cards made a set).

We then shared our work with other tables and talked about. Some comments of note:

*Students who do well anticipate teacher questions and understand why they're being asked.

Ways SET can be used:

*the big picture of "Here's our universe. What is true in this universe?" Parallels other axiomatic systems.

*sorted attributes, categorizing

*union/intersection

Interesting to maybe think about how the cards are exactly the same mathematically as just having the 4-tuple (0,2,1,1) with four dimensions (four different attributes) and values that can be 0, 1 or 2 (three different options for each attribute).

Kim then shared (and asked us to reflect on how this could be done with students in a more meaningful way than just telling them) a way to determine which card is missing after playing a full game and ending up with a number of remaining cards that is not a multiple of three.

Break

Shared some summer opportunities:

Promoting Algebraic Thinking Summer Institute: Lawrence Hall of Science

Center For Innovative Teaching: Hands on Geometry

Assessment

How do we assess content learning? (I would add habits learning too)

Rigor?

How do we evaluate assessments?

Am I testing what I think I'm testing?

How can we use assessment to understand what sense students are making of instruction?

What are we looking for and how do we measure it?

Targeted, selected observation...

Engaging students in self-assessment

Some assessment ideas:

* Give assessments with lots of questions and then at the end tell students that their top scores on 5 (or whatever) problems will be the only ones graded.

* Ask students to solve 2 of 4 and give different point values for more complicated problems

* Have small skills, concepts, and pushing quizzes that students take weekly (with a choice of which quiz they take) and can retest until they show proficiency

Big question: assessing what?

*students making good choices

*have you learned this skill
*access

Next time, talk about different kinds of assessment. Thinking about bringing assessment questions around a particular topic/skill/concept (probably one middle school topic, maybe proportions, and one high school topic, maybe systems of equations).

Brainstorm ideas on how to make assessment a better tool for learning? What do you do after assessment?

Where's My Hovercraft? Part 3: The Typical Student Project

Welcome to part three in my N part series on technology. In part 1, I bashed Smart Boards. In part 2, I shared my Christmas wish list for improving homework logs. Since my birthday is on the 28th, I guess this could be considered my technology birthday wish list.

Right now I'm finishing up my statistics unit with both my fifth and sixth graders (moving this unit from 6th to 5th grade, so I'm doing something similar in all of my classes at the moment). I've never taught a full fledged statistics unit, and it's going really well.  Here's an overview.

The project

Our hook was this slick movie by National Geographic called 7 Billion: Are you Typical?  We then posed the following question: Are you a typical 5th/6th grader (throughout, I'm trying to keep the idea of "a typical 6th grader" light and humorous with the understanding that this is kind of a silly question)? Kids brainstormed topics and questions that would help answer this question, creating categories from after school activities to the environment. They learned how to write good survey questions and how to use Survey Monkey. They then took the survey (which ended up being a whopping 150ish questions). The data was then downloaded and kids spent time learning to summarize, convince, and predict (what I presented as the three overarching goals of statistics). We explored ways to analyze data both graphically and numerically and kids put together a portfolio of their results.

The product

My goal for after break is to make our own version of the National Geographic movie. While I consider myself relatively tech savvy and relatively proficient in editing photography, the movie making business is completely new to me. Even Dan Meyer's simple drawing of a box and a diagonal leaves my mouth agape. Btw Dan, I'd totally pay to sit in a room for a day and learn the basics of After Effects from you. I'd also be open to a list of sites/books that you would recommend for novices. Anyway, any guesses how the NG video was made? It has a Prezi feel, but alas, Prezi does not have export to movie functionality yet (really...come on already). Those of you with experience with these things, am I asking for trouble? I'd love to teach/work with my students to create something as slick, but worst case see this becoming something where each kid creates a slide or two highlighting a statistic they found and then putting it all together into a slideshow/movie in power point or keynote.

I'd love some feedback/thoughts from people with more experience.

Technology in School: Where's My Hovercraft? Part 2

Last post I talked about the difference between figuring out how to use a technology that is given to you versus looking for a technology to solve an existing problem.  Then I went all Negative Netty on interactive whiteboards. Today I'm going to talk about searching for a technology to solve an existing problem.

My students complete a short homework log every night (ah, the advantages of being in a community where everyone has computers and internet access). I use this to track how much they complete (important, since I only want them working for 30 minutes and often (purposefully) give them assignments I don't expect to be finished or don't really have a finish).  I also use this to help prepare for my lesson the following day, get a sense of what questions they have, and how well they understood the assignment. Finally, this is yet another space for kids to communicate with me.


Anyway, the tech issues:

• Right now students populate a google form and these data are transferred into a google spreadsheet that I look at. Unfortunately, I'm the only one who can see this.  It would be really nice for students to have access to their own homework logs.
• It would also be nice if this history could easily be a way for students to organize their digital work. If work could be easily linked from the log, the student and I could both look at old work.
  
• Filtering is possible, but it's slow and clunky...especially now that my spreadsheet is quite large. It would be really nice to be able to quickly filter by class, by assignment, by kid, by understanding, etc.
• At this point in time, the file in general is becoming slow and clunky. While I could start a new form, this makes filtering by student even more time consuming. 
• I wish it were easier to analyze this large (and potentially informative) data set. What's Jonny's average perception of his understanding on homework assignments? Has this increased or decreased? Is he spending more, less, or the same amount of time on assignments?
• I wish I could click on a comment by a student and have my email pop open so I can shoot off a quick and efficient reply.
• I wish my students would have an email automatically sent to them when the log is not completed...or for the ability to automatically or quickly contact parents.

Ok, so who's going to make this happen? :)

Technology in School: Where's My Hovercraft? Part 1

The #pencilchat discussion on twitter has rekindled something I've been thinking about a lot...

There's a big difference between being handed some technology and then figuring out how it's useful and having a problem and finding (or creating) a technology to solve this problem.

Let me get my Interactive SmartBoard bashing out of the way.  Just to be clear, my definition of interactive does not include a tool that:

• lives at the front of the room
• must be connected to a computer to work (and even then...) 
• freaks out when it is touched by more than two people at a time

That said, I am still trying to find ways to make this (expensive) thing that covers my whiteboard more than just a whiteboard that occasionally spontaneously erases everything (it's the only time kids are allowed to use the word "dumb" in my class). A few weeks ago I got together with three other great teachers to pow wow how smart boards could be useful.  In the end, we spent a bunch of time sharing "here's something else that's kind of neat" but someone's insightful question at the end asking if we'd learned anything brought everything back into focus. We hadn't yet found a way to make this *much* more than just a chalkboard you can take pictures of.

For me, the smartboard falls into the tech category of "here's some tech, now make it useful."  This is too bad, because I have lots of unresolved tech issues that I'll address in the next part of this series.

Asilomar Reflection

I led a workshop this past weekend at CMC-North Asilomar (this is a math conference for those of you who do normal weekend things like gardening and watching football).

Making the Common Core Standards of Mathematical Practice More than an Afterthought

This was the second iteration of the talk I gave last month in Palm Springs. About 25 people showed up, a number I was pretty happy with considering it was the last session of the day (a beautiful one at that). I feel the Palm Springs session went fairly well, but that this talk was more polished and more interactive. Three or four more times doing this and it'll start approaching good.

One of the recurring themes of the talk was promoting productive failure and a culture of working on hard problems. With this in mind, I'd like to share the critical feedback I received (thanks to those who took the time to write feedback):
Give more sources for 'good problems'
To be honest, most of the good problems I have are from a mishmash of sources: conferences, colleagues, blogs, students, and sweat. I need to start putting together a problem bank as soon as I get over feeling intimidated by Sam Shah's Virtual Filing Cabinet. That said, here are some good online sources:
Alan Schoenfeld talked about the Math Assessment Project
The Park School in Baltimore
The CME Project (a more traditional textbook in the sense that it's published)
Someone at the session recommended the book Thinking Mathematically.

Show how to connect to content standards.
Right now 99% of the resources for math teachers center on content standards. As for the standards for mathematical practice, we are the 1%. I see the discussion of habits, independent of content, to be necessarily in order to raise the status of these processes.

Heard this before. Glad will be part of standards, but didn't we already know this is good math teaching?
Maybe this comment wasn't meant as criticism, but would you prefer that I talk about and model bad teaching?


Thought it would be more about what the common core is
 I zoomed through the connections between my habits of mind and the common core standards of mathematical practice. Feel free to download the presentation, though, and take your time looking at the specifics.


a little slow
moved very slowly
I'm not sure I can drink enough coffee to keep a Steve Leinwandimo tempo (that's a bit faster than Prestissimo for the music novices). That said, I think some parts can be tightened, especially the beginning of the talk. On the other hand, I'll take "a little slow" any day if it means work/reflection time that leads to someone learning something and changing their practice for the better.

I would like to hear about or develop rubrics to assess habits of mind


I run my version of standards-based-grading where topics are broken up into skills and concepts. Kids can take each quiz as many times as they need until they show proficiency. I mostly use projects and classwork to assess retention and connections. Along these same lines, I give my students assessments of certain habits of mind (no way to hit on all 10 in one year). Here are some examples.
Assessing Collaborate and Listen: Sam Shah writes about the Participation Quiz
Assessing Pattern Sniffing: Here's one version of habits of mind quizzes my sixth graders took last year.
Assessing Tinker and Invent

Wanted to see how he views implementing the common core. Not sure the premise of conference is accurate.
Hmm...I guess I really failed with at least one person on this part. My views on implementing the common core standards is that they should be implemented. More importantly, I believe that the standards of mathematical practice should be implemented. Really implemented.