Math Hombre

 I was very excited when we were able to hire Joy Oslund last year. Great teacher, experienced professor, and she brought expertise in complex instruction (CI) which was completely new to our department. She wrote the book!

OK, a book, Smarter Together, which, appropriately, was collaborative itself. 

Dave Coffey and I interviewed her for Teaching Like Ted Lasso, if you'd like to hear her for yourself.

She's leading a professional development for faculty in CI here in the math department. Small group, supported by the U and by our state AMTE chapter.

There's a few texts people have for it. Everyone has Designing Groupwork by Cohen and Lotan, 3rd edition of the seminal text. The book presents the case for why group work is helpful, and examines why it so often is not helpful in practice.

Day 1

Introductions. Why are we here?

One feature of Joy's classroom is a smartness wall.  We were each asked to write one way we are smart in math. Learners add to it throughout the year or course. Lisa Hawley, another new colleague, does one at the beginning and one at the end for them to compare. She noted that they often shift from content claims to process claims, and how many more ways they think there are to be smart at the end. The decision to use 'smart', which is loaded, is that they do already have ideas about that, and using it gives us an opportunity to intervene.

Community Agreement. What do we need to have a safe classroom, where we are free to take risks?

Groupwork norms: 

• quick start, 
• no one is done until everyone understands (each step!), 
• work the whole time, (trying this year)
• call the instructor for group questions only, 
• middle space - there was a table whiteboard in the middle of the table which we were encouraged to keep open and collaborative. 

Groupworthy tasks require multiple abilities and can't be done alone. "If it can be done alone, it will be." We did an activity with instructions for folding an open-top box (not quite this one, a little simpler) from squares of different sizes and then measured volume with beans and cubes, then had to predict the volume of a different size box. There were two copies of the task instructions, one copy of the origami instructions, a few beans, a few cubes. Plenty of interest even for mathematicians and math educators to get engaged and want to keep going. 

Afterwards, we discussed what we noticed about the task. There was a lot to notice. We really could not have done it alone in the time allotted, and there was meaningful work for everyone.

Working on the task, we had roles. I have not been able to get roles to work for me before, but I've really been thinking about how I haven't pushed for them, and never really done anything to teach how to do them. These feel less made up than some other roles, and, I think, are really another implementation of the norms.

Roles

• Team Captain - fills in missing roles, moves people along
• Resource Monitor  - call instructor, distribute supplies 
• Facilitator - task gets read, everyone understands task
• Recorder/Reporter

Individual and group accountability. Joy often follows an activity with the groups sharing results, and learners writing an individual reflection, responding to one or more prompts. In addition, while we were working, Joy did a "Participation Quiz" - teacher notes in a public space on what they observed groups doing. Great at beginning of course and when group work starts declining in quality/evidencing the norms. 

Status

Painful, and familiar.  How many times have I seen similar in my class and not intervened? Perpetuating status.

One of my favorite math ed profs is Sam Otten at Missouri (and the Lois Knowles Faculty Fellow). His research is interesting and situated, he holds teachers in high regard and listens to their ideas, and he illuminates research through the Mathed podcast. He has definitely enriched my practice. In addition, he's just a lovely and creative guy, as well as a world class expert on the DC Comics film universe. Beyond that, he's a GVSU grad, so I knew him when.

He is a part of the team that produced some new professional development materials, and I had a few questions for him about it. Mathematics Discourse in Secondary Classrooms, MDISC, is based on research and developed with teachers in the field. I'm a big believer in the importance of discourse in learning, and know that secondary mathematics has been one the places where traditional teaching has included the least discourse. I also think people need support to make changes, so something like this project is needed.

What inspired these materials? Was it an idea you wanted to develop or a response to situations you saw in the classroom?
The MDISC materials came from a group of math education scholars at Michigan State University and the University of Delaware, led by Beth Herbel-Eisenmann, who were passionate about the role of discourse in math classrooms. We all believed that there was profound value in students discussing mathematical ideas and building meaning together as a community. So at its core, MDISC is a set of professional development materials that are intended to help teachers increase the quantity and quality of discourse in their classrooms.

As we set out to create these materials, we tried to draw on other work that already existed in the math ed literature. Some of that work was Beth's own research with Michelle Cirillo. They had worked for years with a group of secondary teachers, examining discourse patterns and power dynamics. We also drew on the work of Chapin, O'Connor, and Anderson, who wrote a great book called Classroom Discussions that focused on mathematical discourse at the elementary level. They had some really amazing results with respect to student achievement scores that stemmed from a new emphasis on discourse. With MDISC, we tried to take some of those ideas from the elementary level and reinterpret them in ways that made sense at the secondary level -- focusing on middle school and high school classes.

Overall, the MDISC PD materials equip secondary math teachers to think about discourse in productive ways and it also provides them with specific tools for changing the discourse in their classrooms so that it really empowers students. It helps move us beyond teaching-as-telling.


What are some of the different ways these materials might be used? 
The MDISC materials include a physical facilitator's guide and then digital versions of all the participant materials as well as sample videos. It could be used by a teacher leader, facilitating sessions with secondary math teachers, or by a PLC of teachers who want to work through it on their own. It could also serve as a textbook for a graduate-level course, so a teacher educator going through the activities with practicing teachers, for example in a Master's course or an Ed Specialist course. The materials are designed to be a year-long study, with connections to everyday classroom practice, but it's flexible -- so with some adjustments, it could also be used in one semester. Or people could select which components they want to focus on.

There's also an optional follow-up where teachers can be guided through some action research, if they want to continue making purposeful efforts toward shaping their classroom discourse. There are several different options, and the MDISC team is very open to communicating with people if they have questions about enactment. We've also enacted the materials many times in many different settings, so we have a lot of experiences to share. 

As you piloted these materials, what were some of the changes you saw in classroom discourse?
We have piloted the materials and had others pilot them in both Michigan and Delaware, with several different groups of teachers. They have been very well received thus far, with some teachers willingly joining in for a second and third year because once they start, they don't want to stop thinking about their classroom discourse. Some of the teachers have called it the most important learning experience in their teaching career, and this even came from a 30-year veteran.

The most visible changes have been the number of students talking in class. They open up more and share their ideas, and the great thing is that they're sharing mathematical ideas. I think this comes from MDISC's dual approach of not only providing insight into the nature of discourse but also providing specific moves for teachers to use. For example, MDISC develops six teacher discourse moves that include inviting student participation and also probing a student's thinking. These are concrete ways to get the discussion going and keep it directed toward important mathematics.

Another big change that is noticeable is that more wrong answers come to the surface -- it's not that MDISC leads to student confusion (just to be clear), it's that an increase in discourse helps more student ideas to come to the surface. And of course some of those ideas are incorrect or imprecise, and that can lead to good discussions and good learning opportunities for the group.


What’s one feature of these materials or an example experience that might help teachers understand how they will support their teaching?
One feature of the MDISC materials is that they are practice-based and case-based. So teachers will get to make constant connections to their own instructional practices and their own students. Those connections are built right into the materials. And there is also the chance to see and discuss detailed cases of other teachers. Rather than lots of little isolated examples, MDISC instead is built around larger cases of real teaching. So for example, when you're learning about the transition from small-group work to whole-class discussions, you can actually see a middle school teacher as she circulates among her students and selects certain ideas to be shared later, telling the students that she'd really like them to bring it up in front of the whole class. Then you can follow the case to see how it played out in the discussion.

Another important feature is that the MDISC materials integrate an emphasis on equity. Powerful discourse means that everyone has an opportunity to be heard and to learn from the conversations. So there is a lot of attention paid to how teachers can use a discourse-based approach to reach more students, including those with traditionally marginalized backgrounds.

What movie would you like to see DC make next?
Great question! When I'm not working in math ed or spending time with family, I love watching and analyzing DC superhero movies. I really loved Man of Steel and then I thought Batman v Superman took it up another notch, with great themes about immigrant experiences and the danger of overt masculinity having to face feelings of powerlessness. So although I'm excited about Aquaman and the Wonder Woman sequel, I would really like to see another Superman solo film make it onto the slate. And it would also be great if the Cyborg standalone would get the green light because I thought he was a really intriguing character in Justice League and I think his story could be used not only as a commentary about race in modern society but also about our increasing dependence on technology.


(Back to me) There's so much promising here. Use of real classroom discussions with connections to your own. The focus on equity. And the idea that in running it with teachers there's a measurable change in the number of kids participating in discussion, as well as the frequency and quality of discussions - that's a dream. I'd love a chance to work through this with teachers.

Find out more:

• Episode of Sam's podcast with Beth Herbel-Eisenmann and Michelle Cirillo. Also, that's Sam playing the piano.
• Curriculum available at Math Solutions

A highlight of February in these parts is Math in Action. Our local, 1 day math fest. Having been at the U for 20 years now, part of it is just great reunion, with our former students coming back to present and knock 'em dead. The last two years have felt stepped up, though, with a keynote from Christopher Danielson in 2016 and Tracy Zager, the math teacher I want to be, this year.

After taking a year off presenting last year, first ever, this year I was back at it to talk Math and Art with Heather Minnebo, the art teacher at a local charter that does arts integration. I've consulted with her, she's helped me a ton and we get to work together sometimes, too. (Like mobiles or shadow sculptures.) The focus this session was a terrific freedom quilt project Heather did with first graders. Links and resources here.

Next up for me was Malke Rosenfeld's Math in Your Feet session. Though I've been in several sessions with her before, I always learn something new about body scale mathematics. She ran a tight 1 hour session using Math in Your Feet as an intro to what she means by body scale math. One of my takeaways this time was how she made it clear how the math and dance vocabulary was a tool for problem solving. I often think about vocabulary in terms of precision, so the tool idea is something I have to think about more. Read the book! Join the FaceBook group!

On to Tracy's keynote. She was sharing about three concrete ways to work towards relational understanding. (From one of her top 5 articles, and one of mine, too.)

1. Make room for relational thinking.
2. Overgeneralzations are attempted connections.
3. Multiple models and representations are your friends. 

 The only other session I got to was a trio of teachers, Jeff Schiller, Aaron Eling and Jean Baker, who have implemented all kinds of new ideas, collaboration routines, assessment and activities, inspired by Mathematical Mindsets. I was inspired by their willingness to change and by the dramatic affective change in their students. We had two student teachers there last semester, and it was a great opportunity for them as well.

My elementary preservice teachers (PST) are exploring professional development this week. The first assignment was to do a webinar or our local conference, Math in Action. Global Math was Problem Strings with Pam Harris (awesome) and Christopher Danielson is keynoting Math in Action, so fortuitous timing, say no more. The second assignment is to find a blogpost to recommend to teachers, so I thought I would pass these along. The list of leads I gave them is:

• Marilyn Burns

• Brian Bushart

• Christopher Danielson
• Graham Fletcher
• Kristin Gray
• Simon Gregg
• Nicora Placa
• Joe Schwartz
• Tracy Zager

Apologies for any exclusions. These are all people who's work has come up so far in class. What elementary blogs would you add?

Their recommendations:
Dana -  https://mathmindsblog.wordpress.com/2016/02/11/rhombus-vs-diamond/
Summary: This blog post is about a class of students looking at four different shapes, and trying to find the odd one out.
Review: I thought this blog was great because instead of simply telling the students the names of the different shapes, the teacher let them think and reason for themselves; she allowed them to come up with and defend their answer by themselves.

Dayna - This is a great lesson to combine English and math and get students excited to learn. My response to the lesson is that I love that as a teacher you get to see the students thought process when they are working on this problem. http://marilynburnsmathblog.com/wordpress/chrysanthemum-an-oldie-but-goodie/


Kalyn - https://tjzager.wordpress.com/2015/06/06/comparisons-a-little-bit-more-older/
This post talked about how comparison problem are everywhere, even outside of school. Although they can be difficult at first, the lightbulb goes off and the problem makes sense! I really enjoyed this post and the person example that it gives of her daughter and the conversation that they had about math, but also about life. A lot of good stuff here!

Ally - http://exit10a.blogspot.com/2015/12/22-30-50-100.html
This is a great blog. It's about how is he works with "Alex", going through counting. It was a great read.

Amber - For my blog post, I chose to look at some more of Graham Fletcher's stuff. And although we aren't learning about volume right now, I thought this post was a great representation, which shows real life problem solving. It offers that children are robbed when force fed uninteresting story problems from a text book, and Graham offers an interesting 3 ACT problem as a substitute. My reaction to this concise, yet powerful read is that I would like to try a problem like the one he brings up. I bet students would be very interested in it. http://gfletchy.com/2016/02/14/im-placing-a-hit-on-the-pseudo-context/

Sarah - https://mathmindsblog.wordpress.com/2016/02/05/obsessed-with-counting-collections/ Summary: Second graders explore sorting by counting by 2's, 5's, and 10's. A similar activity is conducted with first grade students. One students has difficulty counting when there is a leftover present. Review: This post really made me think deeply and question the use of ten frames. Kristin Gray does an excellent job of questioning the thinking of students and that is something that I, personally, need some work on. 

Chris - http://followinglearning.blogspot.com/2016/02/art-for-maths-sake.html
Summary: This blogpost is about an "artsy-mathy" activity he did with students involving creating trees out of factor trees.
Review: I absolutely loved this post because it addressed an issue with "artsy-mathy" activities, which is that they tend to be less artsy than an art lesson and less math than a math lesson. I enjoyed how he addressed the issue by making more out of the project and creating an exhibit where the students could teach to younger students.

Orina - http://marilynburnsmathblog.com/wordpress/four-strikes-and-youre-out/ I thought this game was really interesting and fun because students have to use number sense to try to win. A lot of students are familiar with hangman and it's a math way to play a fun game.She comments at the end about how this game is competitive and can be cooperative also. Playing games can bring more fun to the classrooms, but she comments that we must make sure there are some competitive and some that are about cooperation.

Kathleen - http://followinglearning.blogspot.fr/2016/02/quadrilateral-sets-lesson.html
this teacher was trying to get her students to understand grouping and have then work together to see what made the shapes different and what the noticed in general. a lot of then saw that there are many triangles in the rectangles.

Heather - http://gfletchy.com/2016/02/14/im-placing-a-hit-on-the-pseudo-context/ I really enjoyed this blog post because it addressed the question we all ask ourselves, when will I ever use this? I like the way he addresses practical examples and being able to take those practical examples and use those for practice problems not "mind numbing" problems. (John says: "be sure to see Joe's follow up.")

Stephanie - http://exit10a.blogspot.com/2016/02/a-post-about-counting-circles.html
Summary: Counting circles can serve as more than one purpose of just counting; it helps you practice standards, recognize patterns, etc.
Review: I never knew you could do a counting circle in some many different ways; the more questions you ask your students about it, the more they will think about it, and deeply understand the material better.

I admire their taste in posts! 

The other thing is how much I want to thank these bloggers. By sharing your classroom you are having a profound effect on other teachers - and on the future. It takes time and vulnerability for you to write, and I want to thank you for it.

Edmund Harriss' logo explained

The thing I was most afraid of about Twitter Math Camp was that it could not possibly meet my outrageous expectations. I had jealously not been able to go the last two years, and was so happy to go this year, meet so many teachers whose work I love, and get to experience this community that has become such a big part of my professional life, that there was no way it could measure up.

But I was blown away.

One of the benefits of this community is that we write and reflect. The #tmc14 hashtag on Twitter might be overwhelming, but the wiki has all the presentation info and most of the slides, and the reflection blogposts (that's a partial list) capture a lot of what went on and some of what was learned.

It's a bit overwhelming to recap, so I just want to try to capture my big takeaways here. Names link to twitter accounts, more specific links spelled out.

Dance: Malke Rosenfeld
I have been a fan of her work for a while, and she was running a three day session with Christopher Danielson, a master teacher educator. Attending this session was no mistake, as it was fun, provided experience with a new-to-me concept of embodied cognition, and had so many teaching and learning things to notice...

Also my excellent dance partner Melynee, who explained all things OK to me.

Malke taught us to dance and choreograph a dance, then set us challenges to solve. This involved making a dance pattern, learning it, and then transforming it. She wasn't using dance as a representation system for mathematics, she was teaching dance, to which mathematical ideas applied. She also established the Blue Tape Lounge by the ice machines at the primary conference hotel, where participants taught what they had learned to other people, and tackled extended challenges. Christopher provided the hand-scale mathematics, manipulative contexts that connected to the dance, like his beautiful triangle symmetry ... doodads.

It was stunning how the dance created a context with lots of motivation for communication, refinement and ownership. The product was a doing not a thing to have. (No typos in that sentence, but I'm not sure how to say it, either.) There was also a lot just to observe about the teaching. Christopher is a teacher educator and was on A-level meta-teaching game. There is enormous benefit in watching someone teach well outside your content, and Malke did many interesting things. Very positive, process oriented feedback.

More: Malke's TMC post 1 & 2, and her Storify of the relevant tweets.

Counting Circles: Sadie Estrella 
Sadie led a session on Counting Circles. The class stands up in a circle, the teacher decides what they are going to count up by, and where to start. When the class is counting, everybody goes, the teacher records responses on a numberline on the board. ("Because number lines are awesome. And it's support for students."-SE) Count for the time you've got, then pose a prediction question to count up some number of spots more. When >everyone< has an answer, then solicit and record student thinking as they give it.

I'd watched the videos on her blog, but it was different getting to experience it. She shared how they tie into the building of classroom culture that she is seeking. In addition to the counting and number sense work, it is inherently collaborative, and leads to number talks at the end of the circle, when students make a prediction past the stopping point. ("If we kept going, what number would Judy say...") Participants quickly brainstormed a number of extensions, by extending the numbers counted, using integers, fractions, decimals or algebraic patterns. This ties in so well with Jo Boaler's research on resetting student beliefs about mathematics that I have to give it a go now.

More: Sadie's presentation page at the wiki has links to her other counting circle work, but also her first blogpost on it.

so sturdy it mostly survived packing

Math: Edmund Harris
Obviously, the days were just packed with math, but among these Edmund stood out. He was the token mathematician, I guess, but added a ton to the proceedings. His literal bag of tricks produced laser-cut paper tiles for assembling 3-D models, laser-cut beautiful Penrose tiles with matching conditions, a plastic ratio proportion engine... and who knows what else. The TMC logo was his design and he is a serious mathartist in addition to mathematician. So much fun. He also gave a terrific My Favorites on the math in dots and arrangements thereof. I learned I must never be given access to a laser-cutter.

More: his blog and the dots.

Group Work: CheesemonkeySF
Elizabeth led the Group Work Working Group, which is what I would have attended if there were two of me. Thankfully they thoroughly documented their work. I did get to sit in on a flex session trying out the Talking Points structure, and it was everything that it had seemed from reading about it. These structures are a part of her effort to push authority towards the student, and be true to restorative practices. I really think this is essential. We do not have a new game to play, and we inherit students who have experienced a lot of inequity and been trained to helplessness.

More: GWWG at the wiki and Elizabeth's references.

Just meeting them:
There were so many people whose ideas and opinions I value that I was glad to meet. I also had a handshake list - people who directly or indirectly have inspired me to dive into the MTBoS, to tweet and blog, which has definitely improved my practice and enriched my understanding. If any of you read this, THANK YOU.

Special shout out: the organizing committee, especially Lisa Henry and Shelly T, without whom this would not have happened.


Challenges:

• Incorporate more and better structure in my groupwork based on the GWWG materials. In my classes and in the departmental diversity discussions this year.
• When can I have students moving purposefully solving an embodied challenge?
• How should I implement the counting circles? Which courses?
• Edmund's Dots. Build a representation for students to notice things, or another classroom routine that builds over the semester?
• Is there a way to incorporate Heather's Cut and Grow revisions or Rebeckah's Friday letters into a university environment? (probably; don't know)
• Tweet. Less.

I caught a great talk by Eugene Peterson this week. He's a pastor and spiritual writer who gave a talk at Valparaiso University in honor of Walter Wangerin, Jr. (who was also there); the talk was "What are writers good for?" (I found a pdf of a previous iteration of the talk.) There'll be mention of God below, but really, these are my connections from his talk to math teaching. I've written one other post inspired by Peterson, Jonah the Math Teacher.

Peterson's bottom line for writers is that they can reclaim language from debasing use. For religous writers this is particularly important, because we as a society have turned our spiritual words into godtalk that is easy to ignore and not worth our time.  In other words,

Knowledge of speech, but not of silence; Knowledge of words, and ignorance of the Word... Where is the Life we have lost in living? Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information? -TS Eliot, Choruses from The Rock Poems and Plays, 96

Important ideas, I think. And amazingly close to the challenges we face in mathematics teaching.

"So what are writers good for? It is our vocation to maintain and practice this core, basic, revelational, personal nature of language, living speech.    In a world in which language has been uprooted from its originating God soil and put to the use of information or propaganda, it is the vocation of writers to represent and practice language as revelation, to re-orient language into the personal world in which men and women actually live—in their families, and neighborhoods and workplaces," says Peterson.

What are math teachers called to do? To recover the debased math, practiced in schools for years, to bring it into the world in which the students live, to share math as it's truly done, to share learning that will make a difference in our students' life.

So how does a writer do it?  For Peterson, the illustrating example is the middle parable section of the gospel of Luke. A lot of Jesus most powerful teaching. Stories with no explicit mention of God, no direct lesson. A story about fertilizing a tree instead of cutting it down. Told in Samaria to people who are not interested in his religion, and not fond of his people. He might as well have been a math teacher.

Not to double up on poetry, but Peterson also went to Dickinson.

Tell all the Truth but tell it slant – Success in Circuit lies Too bright for our infirm Delight The Truth’s superb surprise As Lightning to the Children eased With explanation kind The Truth must dazzle gradually Or every man be blind -Emily Dickinson

(Fantastic art by  David Clemsha. Shows up in my Reader the next morning as a wonderful coincidence.)

How well does that capture the essence of good teaching?  Peterson notes, "A parable keeps the message at a distance, in the shadows, slows down comprehension, blocks automatic prejudicial reactions, dismantles stereotypes. A parable comes up on listener obliquely, on the slant." A writer does this by having the reader come to them, going slow, countering the impatience of the age.

This leaves teachers the challenge of knowing what is best, in a culture that wants what is lesser. When we propose that there is better, they want solutions that are immediate and rushed. How can we convince them that the answer is slow? Real stories, finding the way themselves, experiencing the superb surprise. I think we have to just persist. Write our real lessons. Participate in the community. Share our success stories that will buoy us through a dozen bad days.

"The Truth must dazzle gradually."

It's our vocation to tell it slant.

I had one of those great twitter moments yesterday, completely by generosity of tweeps. This captures one aspect of why I introduce twitter to our preservice teachers in hopes that they will either enter in or give it a go later.

My summer intermediate algebra class is leisurely (12 weeks instead of 6) picking its way through the summer. Linear, quadratics, exponentials with tons of technology use, simulation and experiment and a dash of art. And then comes logarithms.

My emphasis on introduction is as a way to undo exponentiation. Not a big emphasis on inverse functions, because though we're using the language, we haven't really dove into function language yet. But doing and undoing we talk about a lot.

But after that reasonably good start, we come up against the log rules. Our introduction was Kate Nowak's log law introduction (which I found through Sam Shah's Virtual Filing Cabinet; why bookmark? Let Sam do it for you.) The idea is that you see lots of examples and then try to generalize into a pattern, which is the log law. Nice pedagogy!

Yesterdays lesson included connecting the exponent rules to the log laws.





Tough going.  In terms of gradual release, we had to back up to a lot of teacher support. But the most useful law was the toughest. So I came back from class and just tweeted, to ... vent, I guess. Commiserate. (Which is definitely a purpose of twitter.)

 Wasn't expecting any real response. But then, the great feedback and constructive suggestions began immediately.

This is where we should start. We - as a teaching culture - are so steeped in general then specific, abstract before concrete, that this is a good first check.

 They did understand the multiplication to addition rule better. Look for areas where students understand and build off of those. Connections strengthen learning.

 This is the connection I'm going to follow up on. Look for a way to get it across.


 Think about the broader context. How the logarithm lives as an inverse function, with a nice concrete place to start.


 Support that this is challenging, and not me just being stupid. Of course, I'm happy when people point out I'm just being stupid, too, since I don't want to be stupid.

Neat post.  It gives a lot of good thinking about introducing logs, being intentional, and paying attention to students making sense of notation. This is very close to how I introduce logs, and how it looks like Kate Nowak introduces them, too. I use to think this was inappropriate for high school but okay for college (because of their bad early experiences), but I'm beginning to think that's how we should handle bad math notation. Use constructive notation and then transition the students to traditional.

 I don't think this is accessible (YET), but I'm going to mention this, too. Part of the class is getting the students more comfortable with symbolic methods, and I like how this emphasizes the operational part of logarithms.

A reminder of where to start. This is the fundamental relationship for logarithms, and connecting back to it well and often is important for learning in both directions.

So now I have a place to go Monday, following this up as I promised the students.  Maybe I would have had some of these insights on my own - but I don't have to work and think alone about my teaching or the mathematics. It also really sparked some thinking to me about whether logs should be introduced as a function or an operation. I feel like exponentiation goes from being notation, to an operation, to a function. Logarithms could do the same. I'm thinking:

Anyway, excellent teaching advice. I am so glad to be connected to these excellent teachers. And even though I can't go to Twitter Math Camp, I still get to have the home game to play. Why don't you play along?

(Here's my brief intro to twitter for math teachers. ) Here's the activity I put together for the next class:

So we had a small group in for GeoGebra learning this week, and I want to share what I've learned. One of the best ways to learn anything is to try and teach it, and this was true this week.  This post is a review of our approach with links to the materials, and some description of what the intermediate users were interested in: images, buttons, input boxes, and more.

http://bit.ly/ggbgv

First up is our revamped website. I'd really like this to be a resource for anyone learning or teaching GeoGebra to others, so please send feedback. The old website had gotten pretty clunky, as we modified and added to our materials, and it was time to start fresh. The website also includes a page with all of our handouts, and a nice Resource section.  Besides the website, we started a local GeoGebra Facebook page that we could use for links and resources.

This site has a clearer direction through it. Whether you are introducing GeoGebra to people with some time - say a two or three hour block - or in a quick one hour presentation, this is how I'd recommend starting:
The program is so intuitive to use, that many teachers can go from there. GeoGebraTube is such a huge sell, that I tried starting with it, but it turns out that it's even bigger when people know how easy and free the program is to get. They can explore the sketches on the tube better with just 5 minutes on using the program first. I separated that out into three pages at the website: Start Up, GeoGebraTube, and the Quick Introduction.  I asked participants to record the Tube finds they liked the best on a Google doc, but I've also just asked them to write the Tube number on the whiteboard.

If you'd like to add to the Google doc with your favorite Tube Finds, be my guest! (Here's the link.)






We covered search, tags and user profiles, all of which enable finding cool stuff.

For the Basics, the list of intro tasks has gone through several iterations and seems to work pretty well. Getting through those gave users a fair amount of control. The first non-basic topic most people are interested in is usually is using images in sketches (often inspired by the Dan Meyer inspired Dan and the Ball sketch). If it's not images, teachers are interested in the spreadsheet view. So we've got a guide to using images and a starter for the spreadsheet.  It's also important to cover the export menu.

Once users have gotten to making some pretty impressive setches, most of what the teacher or trainer has to provide are the commands to help in what they want to do. The two that have come up the most for me are:

• RandomBetween[ ⟨ minimum integer ⟩ , ⟨ maximum integer ⟩ ] - does just what you'd think it would. Very useful for generating targets or random polynomials using this for coefficients. You get new values by choosing Recompute All Objects from the View menu.
• Function[ ⟨ function ⟩ , ⟨ start x-value ⟩ , ⟨ end x-value ⟩ ] - limits the ___domain of a function. Best technique for this is often to define a function f(x)=... then make a limited version of the function using the Function[] command.

It seems the next matter for most users is to get experience with the Action Objects Tools,  sliders, input boxes, check boxes, and buttons. (That's the intuitive order for me.)






Richard Wade shared with me a neat challenge that provoked some good work as well as some instructions on animation, etc. This is my entry for a dynamic Olympic logo. I also think they should include a purple and orange ring, but I understand the importance of tradition. I wanted an interlocking rings effect, but couldn't figure out an over/under trick.

A note about embedding animated gifs: some services are weird about it. If you're having trouble, upload it to a photo sharing site (I use the mildly annoying photobucket) and put in the image by URL.

The main feature that's come up that we don't have a guide for yet is the dynamic text. Text is next.

Whenever you get to work in a group with GeoGebra you learn something. The two tidbits I found most useful this time was the Corner[ ] command, which we found in an Anthony Or (orchiming on GGBT) sketch.   Someone asked "Well how did he make two sets of axes?" and the answer was clever use of the corners.

The other was instigated by a participant: looking into what that student option is in a GeoGebraTube collection. When you click Create version for students, you get a menu of choices.

You get a palette of sketches for students, like this.

That's going to be a great feature.

Hope this can be of use to you for your GeoGebra learning, or with fellow teachers or with your students.  I'm happy to share any materials electronically, or in person if you're within driving distance.  What would be helpful for you?

Welcome to our first episode. Recently, in the halls of School University, some teachers attempted some selfdirected professional development, encouraged by their principal and given hope by Sal Khan, a man described as "Bill Gate's favorite teacher" (from a TED endorsement), "very popular," "extremely popular," "an educational revolutionary," and being like "like a nerdy, South Asian-American Seinfeld." (I'm not making any of those up. The last is from Wired.)

Here's what happened.





So, obviously, as comedy improv actors we're a couple of math teachers.

We're very interested in your comments. What do you think of this video? Of the teaching? What did we miss in our commentary? 

Dave was the instigator here, but is too smart to put it up at Deltascape.

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

My current logo attempt.

I had a great experience this summer co-leading with Michelle Bunton a GeoGebra workshop for teachers. We decided to do a loose structure, emphasizing algebra one day and geometry the second. People were free to register for one or both days. We got about 22 teachers, with 14 for both days. One teacher was bitterly disappointed because they wanted premade activities, and our focus was on learning the program.  Though we tried to connect people to plenty of resources and the wide-world of GeoGebra sketches, this teacher left before that.  Most of the teachers took the freedom and ran, and it reminded me of what a joy it is to be in a room full of independent, motivated learners working on stuff that matters to them.  I learned a lot, which is typical of such situations.

We decided to run the workshop using GeoGebra 4, as it's being released at the end of the summer.  Unfortunately - I was a novice on it.  I'm an enthusiastic GGB 3 user, but have been weak on spreadsheet use. Adding more novel features was a little scary. Turned out well, as it made us co-investigators with the teachers.  And the program is great. I mean it was great, but now it is greater. They've managed to add features without making it perceptibly more complex.  That's rare; I love this software and its developers. Guillermo Bautista's GGB4 sneak peek series was very helpful. (Of course!)

We structured the workshops with time to get software loaded. And I wanted the teachers on Twitter to converse on backchannel through the day.  That was hit or miss, due to Twitter's tendency to ignore new users as an anti-bot measure. I wound up having people follow me so I could follow them, then retweeting their tweets. This made some people show up but not others... mystery.  I thought it was important because I get some of my best GeoGebra support on Twitter. And, in fact, during the workshops we got some excellent input from @mike_geogebra and @lfahlberg .

So startup, a demonstration sketch to show some of the potential for classroom use, an overview of the program parts (tool bar, menus, views, etc.), specific tasks to figure out how to use, and then free explore time. The workshop website has all of our materials (see the workshop page), plus the sketches created by participants. One exciting feature is that participants spent time sorting and classifying sketches by standards strand in a Google spreadsheet with links to the sketches.

One problem were still working on is the "now what?" We're trying a Google group and want the website to morph into a place for teachers to share sketches. (If you are interested in joining the page to share your materials, just drop me a line.)  Teachers also wondered aloud what made this experience useful in comparison to some other professional development, and that's worth looking into.

As I said, I learned a lot: about professional development, workshop development with a new partner, and a lot of GeoGebra. The GeoGebra knowledge I could put into a sketch!  Note that the sketch links below use GGB4, which can download as a Beta.

Dave made a nice height vs time projectile sketch that used text box inputs. (That is my favorite new feature so far.) Cristine got me thinking about more subtle show/hide condition with her beautiful Unit Circle.  One of the participants made a face sketch for which he figured out how to limit the ___domain of a function. (Which he seems to have never uploaded!) @lfahlberg taught us how to make a reset button for a sketch.  Chris and Jason just pushed and pushed and explored in general. I can't remember why we figured out that sliders can have calculated min and max now.... I was seriously impressed at what good use everyone made of their time. 

After the workshop I made this projectile sketch to practice. It's a projectile in the x-y plane, where the slider advances or animates time. You put in the initial height by textbox, set the vector of your throw by dragging the vector, and can do target practice to a garbage can or by throwing at a seagull. (No actual seagulls were harmed yotta, yotta.) The button resets the targets.  This was fun to make. 


The big screen shot is an animated gif - one of GGB's new export formats. Go ahead and click on it!  The garbage can was inspired by Dan Meyer's WCYDWT ball toss, which is also a sketch.

GeoGebra is a supertool, which even has the power to get more powers, and I definitely want my students and preservice teachers skilled in its use.