Monday, August 29, 2011

Portfolio Mine

So the karma police have come calling, and after all the portfolios that I have demanded from students I have had to put one together myself.  It is for promotion to professor.

I have long thought that my scholarship choices (presentations and inservices over publishing, not that many people don't do both) meant not being a full professor, but this blog has given me a reason to write in a way that fits me to a T.  Let me take a moment to thank anyone reading this for whatever attention you've given my writing.  It was also clear in writing just how important collaboration is to me, so I'd like to thank any colleagues, IRL or Twitter/Blog who might read this. I have truly been blessed in my vocation.

Since the heart of this blog is trying to share openly and honestly, here's the portfolio. If you have questions or comments, I'd love to hear them. The university still requires a paper portfolio, and it was a job figuring out how to capture it in a binder. Which takes me back to why am I having students make paper binders again...?

By the great Charles Schultz, of course.

Saturday, August 20, 2011

Gradual Release of Responsibility

xkcd: 894
How is it possible that I haven't blogged about this? The Gradual Release of Responsibility has been one of the key ideas to help me improve my teaching. It hails from literacy education, but applies to any kind of learning, and has helped me understand why some people's best learning stories are what they are.  It's also very useful at the beginning of the semester/school year as I'm planning a course.

This is the first visualization I saw of this, from Margaret Mooney.  Fisher and Frey are also strongly associated with this idea, and their Google book preview is extensive. I was introduced to this by Dave Coffey (of course) and he has a very nice explanation on his blog.  Rather than repeat what he wrote, I'll share what it means to me.  Sometimes it's a framework for a single class period, sometimes for an entire course, depending on the scope of the objective.

When I first became a believer in active learning, thanks to the reading provided by Sue Feeley when I was prepping my first math for teachers class, I became very extreme about never telling the students anything. I was proud to hear students pass on asking me questions and work further for themselves. On student evaluations, I took their comments about frustration as statements that this kind of learning was new to them. And I do think that's partially true. But one day when a student said, "why are you asking him, you know he won't answer..." it sounded more like I was denying my students support they needed. I realized that their telling me they were frustrated was because they were frustrated. (Crazy, I know.) And humans can't learn when they are frustrated.

What was missing was demonstration. I had stopped equipping my students for tasks because I equated it with telling. What the literacy education reading let me in on was the idea of a think aloud. Authentically sharing your thinking. But the key for me was the idea that while you're doing this, the students are active observers. You let them know what to watch for and debrief them on what they saw in your demonstration.  They are still active! But they may need demonstrations on how to be observers. Early on in a class you might hear me say things like, "Oh. I hoped you'd notice how I..." Or just share my own observations. This is particularly relevant in math ed classes, but I use the idea and technique in content classes, too.  Hopefully the  demonstrations decrease in frequency and duration during a course.

The next phase for me I typically am too quick with, I think. Whole class work where I solicit ideas and suggestions from the class. It's a bit close to my novice teaching style for comfort, so I think I under use it.  You can often gauge in a demonstration when students want more responsibility, or when you've seen some developing use of your objective process.  The positive reason I skip more quickly to whole class-students lead-I support is because I want students to have the experience of trying without knowing how. If they can get used to that feeling of 'maybe I could...' it will make them so much stronger as problem-solvers. You can also do this phase in groups with active support from you, and I think this is easier with heterogenous groups.

This just makes so much sense to me as a structure, I sometimes feel guilty for having to be shown it. Of course I want my students to be independent, and of course they need to see and experience what I'm asking them to learn and of course there is an inbetween.  Gradual Release also helps me keep focused on those big goals that I want the most, the problem solving and communication. It helps me with instruction because I better know what kind of responses are available for where I assess a student to be.  A few classes have gotten to the point where they knew this for themselves; "could we get a demonstration of this?" That's an awesome place to be.

Thursday, August 18, 2011


John Hocking
From a newspaper article 1981 before a trip to China,
the year before we met.

I attended the memorial of John 'Gib' Hocking this summer, with three of my undergraduate classmates from Michigan State. Ed Aboufadel, Terry George, and Jim Koss.  By accident, my community college calc credit wasn't accepted at MSU, and it was one of the most fortunate accidents of my life.  I enrolled in honors math, met people who are my friends to this day, and completely changed my career trajectory.  He convinced me to continue on in math, and Ed is the one responsible for me winding up at GVSU.

To say Gib had a fascinating life doesn't do it justice. He went from working at Ford to the University of Michigan, served in army intelligence post-World War II, became an excellent fencer, sailor and race car driver... as well as a respected mathematician. His and Judy's home was famous for its hospitality and at the memorial many testified to the wonders of what they called Three and a Half. He bought the race car in England while on a Fulbright with the proceeds from his calculus text. (Bought by the publisher so it wouldn't compete with their top seller, said the author.)  After retiring from MSU, he worked with a grandson repairing sailboat engines, designed the first new mechanical navigation device in a century, learned how to design heating and cooling systems (and designed them), and became an expert wood worker with the third nicest workshop in the world.  (My guess is he knew the probability of meeting 3 people with nicer ones at the same time was effectively nil.)  The Topology text he wrote with his advisor Gail Young (cf. the math genealogy) was the standard for years and is still respected though old-fashioned. (Dover edition still available!) As a retiree he rewrote large section of a sailing navigation text that had stood for 100 years to simplify and clarify the mathematics.

Ed and I chatted about him this week.  Ed recounts how that first semester led him to decide to be a math major. "I want to be a math professor, like that guy." Renaissance man, well-rounded. A mathematician but not just a mathematician. Excellent teacher, Ed tells how he learned a lot about teaching just from being his student. Dr. Hocking really looked at his students and saw what was going on with them. Always made eye contact, and strove to have a sense of where we were.  Further, he reached out to us, mentored us. Recommendations, advice, ... personalized our experience at Michigan State which can be rare with 40,000 students. He was a man who was very obviously intelligent but incredibly approachable. 

4 spartans in Ann Arbor
We had him for five quarters in a row, and we had no idea how rare that was.  He introduced us to topology, like the Alexander horned sphere, Möbius band, and Klein bottle. Shared what problems he was thinking about.  Ed notes how he really gave the flavor of what was in store for him as a math student.  He taught about the field of mathematics as opposed to just the topic of the day. Always used lots of applications, sailing examples.  Ed says he somewhat recently was using the idea of bearings as examples while teaching trigonometry.  I'm very grateful to Ed for both inviting him to speak at GVSU a few years ago for our seminar, and for finding out about and organizing our trip to the memorial.

I became a math major because by the time I finished all the stuff that Dr. Hocking had convinced me I needed to take, I was one class away from the degree.  The appeal of teaching - based on his teaching - led me to pick the math TA position over the physics lab assistant position.  He really formed us into a community.  The four of us from the memorial (plus Amy Crammin Shao) were my first experience in a real study group, though we worked with many people from the class over the years. He had the whole class out to his house for Christmas.  At the memorial, Bill Sledd, one of his colleagues from MSU (and another influential teacher from my past) remarked on how that group of students sent a remarkable number of people on to grad school.
Manipulative from Gib's GVSU seminar

Gib had tricks he'd pull out in the classroom, like a fancy move for drawing an extra large perfect circle, or writing behind his back while facing us. But mostly he was just tremendously authentic, sharing important stories from his life and his genuine thinking about his problems of the moment. We felt like we got to know him.  A favorite pet memory of mine is the whole class chipping together to get him a Rubik's cube (expensive in the early 80s) for Christmas.  He opens it, turns it this way an that, then says, "Oh," and solves it the first time in a minute.  What a lightning quick, fascinating playful mind he had.  Several people remarked at the memorial how much he loved games and I love to think what he might have done with games in the classroom.

Same sparkle at 90.
So raise a glass and toast to the teacher who inspired you most. Here's to Gib!

Special Thanks: Wendell Hocking, who shared the pictures of Gib for this post. And to the whole Hocking family for letting us share in the memorial.

Appendix: The American Mathematical Society shared the following notice on their "In Memory Of..."
John G. Hocking (1920-2011)
Hocking, a member of the faculty at Michigan State University from 1951 to 1987, died March 23 at the age of 90. He received his PhD from the University of Michigan in 1953 under the direction of Gail S. Young. Hocking and Young wrote a text, Topology, that was widely used. Hocking was an AMS member since 1951. Post script: the AMS has finally posted a longer notice, written by Gib's student Som Naimpally.

Monday, August 15, 2011

MCTM thinking

Marty Hogan @ Flickr
I didn't get to go to a lot of sessions at MCTM this year, as I only went one day and had to present a workshop twice.  But the three I did get to provoked a lot of thinking.

One session was a teacher sharing her structure for long division. She has a very clear and concrete worksheet style sheet they fill in.  Some people would call this terrible, some would call it terrifically clear.  What I love is that she was sharing her work that made a difference for students.  Her goal was to make visible the parts of long division that were transparent to her students.  She works with students that have failed in math before, accumulated negative attitudes and feel sentenced to math class.  With traditional long division instruction, she felt there were parts hidden from the students. Not knowing how to do those parts or even that those parts were there, they can't do long division despite being in high school.  The teacher noticed with these sheets she had developed that the students were more engaged, felt like they could do it, achieved a higher success on these problems, and were able to move on.  It connected for me with hearing Paula Lancaster talk about the benefits of structure in Universal Design. The teacher next to me asked lots of great questions: "were students able to use this structure without the sheets?" to "what was it about this structure that helped students?"

Another session was Danielle Seabold from Kalamazoo Regional Ed Service Agency. She connected the new Common Core standards for literacy to those for mathematics.  Nice for me to see was that many of the strategies from Mosaic of Thought have appeared in the CCSS and I love how those transfer to mathematics.  But more specifically, the Common Core has a Literacy in Technical Subjects component. Danielle did a great job leading a discussion about these, prompting us to look for connections and consider applications and opportunities.  She links to many CCSS resources at her blog.

The last session I got to attend was about implementation of Standards Based Grading by Amber Cross and Jason Gubeno from Dansville High School.  Very exciting.  Entirely teacher-led, with great support from administration and buy-in from parents, they have replaced traditional grading over the last three years, inspired by professional development with Carol Commodore and reading including Marzano on grading practice and purpose. They are very happy with the changes this has helped bring about in their students' learning. It has correlated with modest increases in test scores, but more importantly has changed student attitudes and focus.
From PAEC SBG course

Jason and Amber referenced the parachute example to support their intuition about why make the change.  They have a pretty clear system, one reassessment, a lot of emphasis on student accountability.  And they have modeled some excellent reflection in considering what worked and why, and how they might adjust.  I would love from them to write something up for the web about both their practice and their journey.

I was going to send them this great xkcd comic, but then Frank Noschese wrote a great little SBG post on it so I could send that instead.

Friday, August 12, 2011

Teaching: Hard or Easy?

It's been interesting on twitter this week, in itself not unusual; a recurring topic has been teaching hard or easy. A colleague was almost politely flamed for a statement which caused the reader to infer that teaching was easy.  It was funny to me because a long-running joke is that we want t-shirts with "TEACHING HARD." Then an internet colleague started tweeting and wrote about how teaching is easy.



I agree with both?

(Once again, I wish I was a graphic designer.)

On the Teaching Easy side is Aristotle's argument. (HT to Matt Wyneken who is a good spokesman for this.) Teachers, gardeners and doctors have natural work. People learn, plants grow, and bodies heal. These professions seek to encourage them to it better.  The principles of learning are something with which we all have familiarity, since we have all learned.  And I do think if my preservice teachers can just learn to assess student's understanding and reflect on their practice, that no matter where they start they will attain teaching excellence. That's a pretty simple recipe. Learning is exciting and furthers our purposes and people really enjoy it when it's authentic.

On the Teaching Hard side is the Problem. Each class is composed of 30ish (or more) individuals with completely different experiences, preferences and purposes that we are supposed to guide to an equal understanding of the same objectives.   We often don't get to pick the objectives, or our materials, or our consequences, or our pacing chart or... And the people who have the most say about our conditions seem opposed to listening to teachers because they are partisans on the matter.

Furthermore, the individual problem of the most challenging students is , finding problems for them, determining effective support for someone who seems to learn so differently than you, overcoming years or decades of negative and false feedback in a culture that says our subject is impossible for all but a select few and irrelevant.  You have to solve entry problems to get an opportunity to work on your essential problems.

Frankly, the difficulty of the problem puts most mathematical problems to shame. Reminds me of one of my favorite quotes: "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."  ~John von Neumann

It is real work. A true vocation. I'm so blessed to both be a teacher and work with teachers.

same as it ever was
Love to hear what you think: hard or easy?

Photo credit: Richard Masoner @ Flickr

Sunday, August 7, 2011

More GeoGebra 4 Teachers

I presented two 1.5 hour workshops for teachers at the Michigan Council of Teachers of Mathematics annual conference yesterday Thursday, and thought I'd share a few quick thoughts.  Here's my session page/lesson outline. All handouts are attached.  Even in a computer lab with somewhat slow connections, running Internet Explorer, we were able to have the GeoGebra 4 beta installed and running in 10 minutes.

EDIT: Later I used those materials to share GeoGebra with the Muskegon Community College Math Tech Bootcamp and a workshop with at the Kent Intermediate School District. The materials are updated from that, and feedback from all three groups are below.

It doesn't take a lot of experience to introduce teachers to GeoGebra. I mostly just gathered resources, talked about the basics, then let them explore. It's worthwhile for me, too. In a room where many people had not even heard of it before (yet they are at the session - I love teachers' exploratory spirit) they found new corners and features for me to think about. I am no omega-class expert, but I've spent some hours with it. This is a rich program they're giving away for free.

The basics to me are:
  • understanding the main areas:
  • Tool bar, including pull down tools. Emphasize the selection tool, the move graphics view and zooms
  • Graphics area
  • Algebra view and the View menu for axes, grid and algebra view
  • Input Bar
  • The selection arrow
  • Undo
  • Object properties/Right-clicking objects
Just a few minutes and people are ready to roll. I made up a page adapted from the 2-day workshop of introductory algebra and geometry tasks, and then had options for further exploration of either. All the handouts are attached to the session page.  By the end of each workshop, most teachers had made something that impressed them. A few just thought it would be valuable for making images for tests and handouts, and I think that's a proper way to start for some people. But most were digging in deep, and several got some math learning out of what they did. "Oh, that's why..." was overheard a few times.

The teachers recorded their comments on a Google doc (benefit of a computer lab session) and they're embedded below.  If you are a GeoGebra user - share it with your fellows! If you are not, give it a try. You'll find it worthwhile within an hour.

Or I'll double your money back!

MCTM Feedback

MCC Math Tech Bootcamp Feedback

Kent ISD Feedback