Whiteboards in Math

Recently, I tweeted out a link to Nat Banting’s post on whiteboards. It reminded me that I was going to write a post here about my experiences with them this year. I’ve been trying them out. I’ve done some things well. I’ve learned some things.

The three things I like most about having students use whiteboards in class, probably in order, are:

• How their work “pops” off the boards so that I can see it easily. As I circulate, it’s so easy to provide feedback.
• How comfortable students are working on a dry-erase surface. They are not afraid to try things. They are not afraid to make mistakes.
• How easy it is to group and pair students to give and receive feedback from peers when their work is on whiteboards.

The things I learned, I learned by making mistakes, and by asking you questions. Here’s one I threw out in the middle of a class in which I was making mistakes. I was having students do questions on the whiteboards, and then copy them into their notebooks. Of course, they hated it. They were doing everything twice. The high school math teacher in me is having a hard time letting go of the mentality that I must write it on the board and they must copy it down, or they haven’t learned it. I still want them to leave my class with something useful and correct written down in their notebooks for future reference. Please don’t judge me for that.

In the middle of that class, I put the call out on Twitter.

The responses were immediate and helpful. Talk about real-time formative feedback! My pocket was buzzing in the middle of the lesson. You can see all the responses here.

Christopher Danielson (@Trianglemancsd) saw right to the heart of my question and threw back at me, “Also, how much needs to?” That’s really what I was wrestling with.

Consensus was that between none and very little of what is written on whiteboards gets transferred directly elsewhere. This whiteboard work is the learning phase. It’s messy. It’s getting transferred to their brains, honest. One suggestion what to have students take a photograph of their work if they think they will need to look back at it. Frank Noschese (@fnoschese) suggested Lens Mob as a way to create an album they could all send their work to. Jacqueline (@_Cuddlefish_) uses them a lot, and I respect her experience. I wish she blogged (too busy geocaching, I suspect). She tried to convince me to let go of the need to have stuff written down.

So the question, then, becomes what do they do AFTER they have finished the messy learning on the whiteboards? Some teachers go straight into practice. Nat Banting (@NatBanting) and Bowman Dickson (@bowmanimal) talk about having students reflect on their whiteboarding at the end.

One teacher I work with this year helps her students summarize a few key things in a “Student Study Guide” that she provides. Heather Kohn (@heather_kohn) does something similar by giving her students a guided notes page for things that she feels need to be formalized. Of course, there’s always the textbook for future reference.

I’m in the middle of figuring out what I am going to do next year. If I land back in a classroom, I will make sure I end up with a set of mini whiteboards. I may still make kids write some stuff down on paper. Don’t hate me for that.

Old Friends and 101qs

Around about 4th grade in the early 1980’s, I was walking home from school and saw the new kid in my class following the same path. We got talking and realized that he lived just around the corner from me. The proximity law that governs childhood friendships dictated that Andrew and I would become best friends.

Andrew and I had a lot in common. We were both smart (although too modest to tell people that, until today). We both loved reading trashy horror novels (Stephen King and Dean Koontz were our favourites). As a team, we rocked the junior high debating circuit in Alberta for a couple of years.

Andrew and I grew apart a bit in high school, and then he moved to Ontario. I saw him once in the early 1990’s when I drove across Canada. A year or two later, he showed up at my parents’ house one day when I just happened to be there. Five or six years ago, one of us managed to track down the other, despite Andrew’s aversion to Facebook. We correspond infrequently by email, and occasionally update each other about our families. Last weekend, I got an email from Andrew. He is not a math educator (I think he does government training), but he reads my blog. He sent me this:

Source: http://imgur.com/JDZ1WDk

That’s the thing about curiosity and perplexity in mathematics. You don’t need to be a math teacher to know a good 101qs when you see one. Everybody wonders about things that can be explored mathematically.

I wonder if Justin lost or gained followers when he got arrested.

I wonder if this growth is linear. I wonder if I could have a couple more data points.

I wonder when and if Kim will pass Justin.

I wonder why Andrew knows more about what I do than I know about what he does. I’m a terrible friend.

SUM2014

Last week, I had the privilege of being allowed to take my road show to Saskatoon, SK. I presented at, and more importantly, I got to attend SUM2014, the annual conference for math educators in Saskatchewan.

It came at a time when I really needed it. It was a great two days hanging out with math educators. I learned a lot, and had a lot affirmed.

Steve Leinwand‘s keynote was a joy. If you haven’t had the pleasure of hearing him speak, check out this presentation (from another conference). As Dan Meyer says, “this guy breathes fire.”

Other highlights for me were:

• Reconnecting with David Coffey and Kathryn Coffey, who I first met two years ago in Edmonton.
• David and Kathryn’s session on literacy and math. We’re into that here in Alberta, too, so it was timely.
• Meeting Nat Banting in person. Watch this kid. He’s a rising star in math education.
• Reconnecting with Park Star. I now know (and remember) her real name, but it’s more fun to pretend I don’t.
• Meeting Lisa Lunney Borden. We only had a few moments to chat over breakfast and before the conference started, but now I know about CMESG, which I think I will attend.
• Briefly disengaging from David Coffey’s session on engagement and convincing the woman beside me to join Twitter.
• I enjoyed my sessions. Some of the participants were kind enough to let me know they did too. That kind of feedback is always appreciated. Keep in touch.
• Having supper with Steve, Anne, David, Kathryn, Nat, Michelle, Jacquie and Allison. It was a great meal, and I got Leinwand’s ear to myself for a bit. His bloggable advice on the current math debate is to build bridges. Connect with math professors. Listen to each other. He’s wise. He’s been through this before. I appreciated him listening to me.
• Steve Leinwand referred to me in the closing session as “That dude from Alberta.” I felt like I had arrived.
• A panel discussion with (L-R) Kathryn, David, Me, Steve. Terry Johanson was also on the panel, but we took this before we started (notice Steve’s engagement level), and she wasn’t there yet.

We ended with Steve Leinwand modelling practice. One of the panel questions was “How do you coach or teach subversively?” We all answered (except me – my voice was gone). Then Michelle was wrapping up. She asked the audience if they had any questions. They didn’t. There was time left. Steve jumped up, asked the audience to take 2 minutes to share their conference “take-aways” with a neighbour. Then he asked them to share back with the whole group. One person shared back something he learned in my session, thereby earning a beer on me next time I’m in town. Other people shared what they learned. Steve took over the wrap up and modelled a large group reflection. That’s subversive coaching, right there, folks.

Radical SNAP

I take no credit for this idea at all. I was in a classroom this morning, and the teacher had the students play a game of Radical SNAP. The students were totally engaged, and were enthusiastically converting between mixed and entire radicals. It’s pretty simple to set up.

Materials: You need one deck of cards with the 10, J, Q and K removed for each pair of students, and one giant square root symbol per pair of students. This one should do the trick: Giant Root

Pair off the students in your class. Each pair gets a deck of cards, and should remove the 10, J, Q and K. Shuffle the remaining cards, and deal them so that each person has half the deck, face down.

Mixed to Entire

The students flip over their top cards. The student on the left puts his in front of the radical, and the student on the right puts hers under the radical. The first student to correctly convert the mixed radical to an entire radical wins the round.

Entire to Mixed

The students flip over their top cards, and put them both under the radical. The first student to correctly simplify the radical or to identify that it can’t be simplified wins the round.

 

2013 in review

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 36,000 times in 2013. If it were a concert at Sydney Opera House, it would take about 13 sold-out performances for that many people to see it.

Click here to see the complete report.

Same Problem, Two Presentations

In my quest for a good Three Act Problem for elementary level students, I’ve come up with two more ideas. It’s actually the same idea presented in two different ways. It’s going to hit division at the grade 3 or 4 level, I hope.

Hay Bales – Act I

Cars – Act I

These videos are rough. The car one could be fantastic if a car lot would let one of us come by with a video camera and film them loading a carrier. The hay bales one would be great if we could get a farmer to let us film him loading a truck. In the past week, I have driven to Calgary and back, Stettler and back, and Red Deer and back. I’ve seen a ton of those bales in fields. I haven’t, unfortunately, come across any of them being loaded up or hauled along the highway.

Engineering Effective Discussions

In the spring, I was working on a series of posts about formative assessment in math class. I got sidetracked by starting a new blog, and kind of let it drop. This morning, however, I read this great post from Max Ray about questioning, and it brought me back to formative assessment.

One of Dylan Wiliam‘s 5 Key Strategies is “engineering effective discussions, questions, and activities that elicit evidence of learning.” From Dylan William’s book, Embedded Formative Assessment:

There are two good reasons to ask questions in classrooms: to cause thinking and to provide the teacher with information that assists instructional decision making.

Max is right. Good questions that cause thinking in math are tricky. Most of us lean towards asking recall and simple process questions. With practice, we can learn to throw out deeper questions as easily as we ask recall questions.

Max’s post contains a number (26 to be precise) of great questions that prompt discussion. My two favourites are:

• What do you notice?
• What do you wonder about?

Questions like the two above feel safe to students. They don’t have to worry about being wrong. They can think and respond without fear.

Sometimes, questions can be improved by turning your lesson around. I spoke to a teacher last year who was working on 3-D shapes with his class. He had the nets all copied and ready to have the students cut out, fold, and tape. It seemed more like a lesson on cutting, folding and taping, so he scrapped it. Instead, he brought out models of the 3-D shapes, and asked the students to create the nets that could be folded up to make the shapes. It ended up being an incredibly rich discussion.

One of my favourite conversation-extenders comes from Cathy Fosnot. When a student responds to a traditional question, extend the conversation by simply stating, “convince me.”

The more we can engage students in conversation with each other through effective questioning and planned activities, the more likely they are to come to their own understanding of the topics.

69 Children

Here’s another attempt at an Elementary-style 3 Act problem. No photos. Just a story. I got this one from my 8 year old daughter, who likes reading the Guinness Book of World Records. This story fascinates her. In class, I’d read right from the Guinness site for Act I.

Act I

The greatest officially recorded number of children born to one mother is 69, to the wife of Feodor Vassilyev (b. 1707-c. 1782), a peasant from Shuya, Russia.

http://www.guinnessworldrecords.com/world-records/3000/most-prolific-mother-ever

Act II

Depending on what the students wonder about, you could go in some different directions here. My daughter wonders about how many of this woman’s children didn’t have a twin. In that case, the information to provide is that the 69 births contained 16 pairs of twins, 7 sets of triplets, and 4 sets of quadruplets.

Act III

The payoff here is that when students do the math above, they will discover that there was not one single case where only one child was born out of all 27 of the pregnancies. That fact makes the whole story seem suspect.

Sequels

• How would you know if the total number of children is even or odd, based on the information about twins, triplets and quadruplets?
• Others?

I may have missed the mark here. It is entirely possible that pregnancy is a topic to be avoided in Elementary school. So far, my daughter has played around on the math on this one for a day or two now without asking me any questions that I don’t want to answer.

Ticket Roll Elementary Style

I get asked frequently if anyone is compiling 3-Act Math stories in the style of Dan Meyer or learning through problem solving activities specifically for elementary school. I’m not aware of anyone cataloguing them at the elementary level, probably because most elementary school teachers have to teach everything, not just math. It’s daunting, and probably hard to focus so much on one subject. Here’s the thing that occurred to me, though. Because Act I is typically completely visual, and we ask students what THEY wonder about, won’t they automatically wonder about things at their own level? I think that many of the ones presented on this blog would work in an elementary classroom with minor tweaks to Act II (and maybe Act III). I’ll use the ticket roll video I posted yesterday to explain.

Act I – Same Video Used for High School Students https://vimeo.com/69124531

I assume elementary school students will also wonder how far Sarah will get. The high school kids will get dimensions of a ticket and work with area and volume to determine how many tickets are on the roll. What if we just change the Act II information we provide for elementary school students?

Act II – Modified for Elementary School Tell the students that there are 2000 tickets on the roll, and show them the video below. https://vimeo.com/69173213

Act III – Same Video Used for High School Students Play the same answer video from my previous post. The answer is the same. The payoff is the same. The math is more elementary. https://vimeo.com/69123114 The answer the will come up with (by dividing) is actually a little too close. I was hoping it would be messier in the end so the students could discuss why it might not have been so accurate.

Ticket Roll Reworked

The first time Dan Meyer came to Edmonton, he had us work on this problem. It was engaging, and a room full of teachers dug right in. The second time he came to Edmonton, he explained his 3-Act Math format. During that session, which was almost two years ago now, I came up with an idea for a video Act I and Act III for the ticket roll problem. My idea was to film a roll of tickets unravelling along a marked football field. The math remains the same.

I didn’t film it for a number of reasons. Marked football fields that don’t have Eskimos playing on them are scarce in Edmonton. It would require several cameras, and I had only one. It would require editing above my level of ability. This week, it all came together for me. We are doing more and more video editing in our work at AAC. We recently hired a NAIT student to do some of that work for us, and bought a shiny new computer and the Adobe suite. One of the student’s jobs was to teach us how to use some of that fancy equipment.

The way I learn technology is to immerse myself in a project, and seek support when I need it. Today, I did just that. I put together my vision of Acts I and III for this problem, with the NAIT student nearby for support. I learned a lot about video editing. It was a great day of learning for me. The videos are not perfect, but they’re better than I could have done last week at this time.

Enough Preamble. Here’s what I did. I give you Ticket Roll Reworked. Presented in 3 Acts, of course.

Ticket Roll Act I

Ticket Roll Act II

As near as I can tell, Canadian ticket rolls are identical to the American one Dan photographed. His Act II information should work out perfectly here. I have a different Act II filmed and not posted yet. I’m on it. I’m hoping it will take this problem to an elementary level.

Ticket Roll Act III

Sequels

Dan has sequels listed here.