Whiteboards for Everyone

This year, I've turned into the Oprah of whiteboards: you get a whiteboard, and you get a whiteboard, and you get a whiteboard. Everyone gets whiteboards! That hang on the walls, but can move!

Over the summer, I learned about vertical non permanent surfaces (VNPS) from Alex Overwijk, which he has explained in a blog post titled Vertical Non-Permanent Surfaces and Visible Random Groupings. The research on VNPS comes from Peter Liljedahl of Simon Fraser University, and is explained fully in his paper Building Thinking Classrooms: Conditions for Problem Solving. Both the blog post and the paper are worth reading fully, however here are the main definitions:

• Vertical surfaces are ones that hang on the wall and can be seen by everyone, such as chart paper or wall-mounted whiteboard. 
• Horizontal surfaces are ones that are placed on a desk, like a worksheet or individual whiteboard. 
• Permanent surfaces such as chart paper or worksheets cannot be erased. 
• Non-permanent surfaces can be erased or modified, and include chalk boards or white boards. 

And the main take-aways:

• Students who work non-permanent surfaces tend to start working more quickly and tend to persist longer than those working on permanent surfaces. They also tend to discuss their ideas more with their peers. This may be because non-permanent surfaces allow for corrections, and enable cognitive risk-taking.
• Students who work on vertical surfaces tend to share ideas with students in different groups (called mobility in the study).

So, it seems like hanging whiteboards are the way to go!

Some classrooms have whiteboards on multiple walls, but I did not. In fact, I didn't want one large whiteboard per wall. I thought it would be better if students (or groups) had their own large, vertical whiteboard that could be moved or re-sequenced as needed. Individual whiteboards would also fit nicely into a 5-Practice Routine framework.

To that end, I created 2 ft by 2 ft 8 in whiteboards out of Thrifty White Tile Board. They come in 4 ft by 8 ft sheets, so having the people at home depot cut it into 6 pieces isn't too bad. And, they're about the same size as the Post it Easel Pads (and much cheaper in the long run). I bordered each with black duct tape, and drilled two, 1 in diameter holes in the top, using a cardboard template to drill in the same location each time. The center of each hole is about 2 in from the top and each side. Lastly, the boards are hung with a bulk pack of Command Medium Hooks. I ended up with about 18 boards in total. In the picture below, they haven't been hung up yet, but a better picture is above.

The great thing is that I've found more ways to use them that I thought possible. I've incorporated them in timed-practice, whiteboard speed dating, stations, find the error problems, anchor charts, and more. Even better, I can put these boards on a chair and use it to teach a mini-lesson to a small group of students.

 

Recently, I've had the kids getting more involved. They've been walking over to a board in the middle of class to explain an idea. I find them teaching each other on the boards between classes. One student has started taking pictures of his boards with a cam-scanner app as a way to save his notes. Not too bad for a few dollars at Home Depot.

 

UPDATE SUMMER 2018: 

I moved buildings last year and I got to take the whiteboards with me. Most of the command strips came off easily, except those on the window in direct sunlight. Those degraded and needed to be scraped off. I was able to save all of the plastic hooks, and simply buy more command strips. Below are some pictures of my new classroom.

UPDATE FALL 2018:

The VNPS are spreading! I moved out of my room and took my boards with me, but the teacher that moved in created a set of her own. She used larger holes (1.5 inch diameter) and red duct tape. It looks great!

She also added a Calculator Caddy using the same command hooks. Now everything is on the wall!

Five Things I learned at TMC15: Saturday 7/25/15

1. Vertical non-permanent surfaces (if you want to sound smart) or wall-mounted white boards (if you want to be understood) can increase student engagement and discourse in all the right ways. Peter Liljedahl found that students using non-permanent writing surfaces such as chalk boards or whiteboards tended to start writing faster and were more eager to start, presumably because they could edit their mistakes. Liljedahl also found that vertical surfaces such as chart paper or mounted whiteboards tended to foster participation and mobility, probably because students could more easily see each other’s work.

You can expect to see me taking a trip to home depot to buy some shower board in the next few weeks. Many thanks to Alex Overwijk for the ideas.

2. Visibly random groups can also be good for engagement and discourse. The idea is that students should be in random groups each day, and they should know the groups are random (pull cards out of a hat or something similar). This promotes cross-pollination of ideas, and sends the message that students should be ready to work with anyone. And if it’s a bad grouping, then it’s only for one day. Again, thanks to Peter Liljedahl for the research and Alex Overwijk for the presentation.

UPDATE: As I write this, there is a twitter debate going on about whether purposeful heterogeneous groups can be more useful to distribute students along gender, ethnicity, ability, etc. It seems the consensus is that “balanced” groups can be good sometimes, but prevents similar students from ever working together.

3. Today, Matt Vaudrey introduced the idea of using musical cues to direct student actions. Simply put, the teacher plays a specific song while students are completing a specific action, such as a “getting calculators” song, a “do-now” song, or a “packing up” song. Songs should play for a pre-determined amount of time, and shouldn’t be stopped early or replayed. The songs now serve as a cue for students (instead of teacher nagging) and should hopefully create a sense of internal motivation. It’s such a great idea, and I cannot do it justice with this post. Read about it from Matt here.

4. Are you teaching a math course for the first time, and don’t know the common student misconceptions? Matt Baker has created a google spreadsheet called First Like Third where teachers can note common student misunderstandings as well as what to say and how to correct them. The objective is to make the first year of teaching more like the third year of teaching.

5. Kahoot is a game based learning platform where users answer timed, multiple choice questions against classmates (teacher-made Kahoots) or students from around the world (public Kahoots). At the end of each round, students are shown a leaderboard with the top four players. Students do not need to sign in to play, and any computer or device with internet can be used. I wonder what the pros and cons of Kahoot are over other online quizzing or formative assessment websites and apps. Kahoot looks more like a game, but is there more to it? Thanks to Julie Reulbach for this one.

Five Things I learned at TMC15: Friday 7/24/15

1. John Stevens has created a Math Twitter Blog-o-Sphere Search Engine; a Google search that is restricted to blogs and other sites on the MTBoS. It is great for finding lesson materials on a specific topic, or reading reflections on a specific mathematical idea. Robert Kaplinsky also has a Problem Based Learning Search Engine.

2. Which One Doesn't Belong is a website inspired by Christopher Danielson and created by Mary Bourassa. It features sets of four figures and simply asks: which one doesn't belong. Interestingly, each of the four figures might not belong depending on the context and rational provided. A seemingly simple question can introduce ambiguity and spark rich discussion from kindergarten through calculus.

3. In the past, I have seen very rigid interpretations of standards based grading that either (1) do not allow for the grading of homework, classwork, and larger practice-based tasks, or (2) are seemingly incompatible with a traditional A-B-C-D-F grading scale. Today I found a much more open interpretation that advocates: if it’s important for students to know and do, then make it a standard. That means that there could be a set of “scholarship” standards for good student skills such as completing homework and projects in a timely manner. There could also be a set of “problem solving” standards that highlight the 8 mathematical practices. Of course, these standards would account for a much smaller percentage of a student’s overall grade, but it is possible to incorporate them within a more open view of SBG. Thanks to Anna Hester, David Petersen, and Lisa Soltani.

4. A boring lesson in person is still a boring lesson on video. While creating flipped video lessons for students introduces the ability to predict, rewind, and re-watch, we must be careful not to push mounds of procedural blather onto students. Andrew Stadel suggests creating videos that are quick and to the point with off screen preparation. He also advocates for videos with errors; complete a problem incorrectly and ask your students to find the error. Princess Choi suggests that students create their own videos as a review strategy. Whatever the method, don’t make your videos boring!

5. Pump up your class. Give everyone a high five when they come in the room. Give neuron stickers when they help each other. Let students hit the gong in your class. Create varsity math t-shirts. Build rapport. Find something you love and do more of it. Be fast, fair, friendly, firm, and funny. And remember, you can’t learn from someone you don’t like.

6. Five miles seems shorter when running with other math teachers.

Five Things I learned at TMC15: Thursday 7/23/15

1. Don’t give your students mathematical definitions. Instead, have groups of three or four students write a definition for a well-known mathematical idea or geometric figure on their own. Then, have each group pass their definition to the next group. Groups should now try to “break” their definitions by providing a counter example. Once they find a flaw in the definition, they refine the definition and continue passing the paper.

2. Here’s an idea for exit tickets. Make a grid with 3 by 3 inch boxes and write each of your student’s names in a different box. Place your grid on the wall near the door. Have your students complete their exit tickets on a sticky note, and stick them in their box on the grid as they leave class. This system makes it easy for students to hand in their exit slip and even easier for the teacher to grade. It is best used for reflective exit slips, as students could cheat on a skills-based or assessment-style exit slip.

3. Mathmistakes.org is a site is about compiling, analyzing and discussing the mathematical errors that students make. It is edited by Michael Pershan, a middle school and high school math teacher from NYC.

4. Manifold is an origami style game by The Incredible Company. It challenges players to take a small sheet of paper with scattered black and white boxes and fold it such that all the white boxes appear on one side and all the black boxes appear on the other. While it isn’t tied to any topic or standard, this is a fun activity in spatial reasoning that will either frustrate or leave you addicted.

5. Another game about spatial reasoning that will either frustrate or leave you addicted. Okay? is a simple iPad and iPhone app that challenges users to bounce a ball off a series of blocks in one shot. Best of all, you pay what you want for this app.

6. (Extra Credit) Dueling Piano bars are the best.

Five Things I Learned at PCMI: Friday 7/17/15

1. When you set goals, set them in stone. The RoP staff asked us to set goals for the upcoming school year as a result of our experiences at PCMI. They asked us to consider possible solutions to challenges we might face along the way. And then we made it official; we made and submitted a video of us explaining our goals to be reviewed later in the year. Although it is a bit awkward to create a video of yourself, I doubt I will forget my goals any time soon.

2. All of the afternoon working groups presented today. Our group presented Geometry Transformed, a webinar style professional development to help teachers transition to Common Core geometry, which relies heavily on transformations. There were also a number of other professional development resources presented, and I will be exploring them all very soon. Most notable were the presentations about growth mindset, the social dynamics of math discussion, writing in math, and a problem set from Ben.

3. Bowen Kerns demonstrated the math games at http://solveme.edc.org/. There is a Mobile puzzle that develops intuition for solving equations, a “who am I” game for number sense, and Ken Ken style puzzle that imposes higher order thinking on the basic operations. Each game also gives students the ability to make their own puzzle.

4. I learned how to transform an algebraic function if the rule is in this form: (x, y) -> (f(x), g(y)). I also learned about how permutation groups and symmetric groups relate to reflections and rotations of regular polygons. There are so many connections between geometry and algebra; you would think it was the focus of the conference. Wait a second…

5. The MAA held a "debate" over the relative merits of the transcendental numbers, pi and e, at the Family Weekend for Williams College in 2005. The debate is largely humorous, but does hide some important mathematical ideas. Thomas Garrity, who served as e's champion, was one of the faculty members at PCMI.

Part 1: https://youtu.be/whpAX30vjoE
Part 2: https://youtu.be/i1hYL0ccqm0
Part 3: https://youtu.be/DytqTMmi_os
Part 4: https://youtu.be/9CCBqinb744
Part 5: https://youtu.be/Xp_znceoeWo

6. (Extra Credit) The cheese and ice cream from Heber Valley Milk & Heber Valley Artisan Cheese is delicious. Two vans full of teachers drove down from the Zermatt to eat some ice cream and see the cows. I split the south west cheese curds with matt, and most of us walked back to the resort.

7. (Extra Credit) The people I have met at PCMI are some of the most amazing, thoughtful, dedicated, and human educators that I have ever met. Darryl and Bowen helped me remember the highs and lows of being a student again. The entire Reflecting on Practice staff facilitated sharing, discussion, and reflection about pedagogy. In my afternoon working session, Gabe and Jim gave me more insight into transformational geometry than I ever had hoped to have. Every single one of the participants at PCMI 15 was willing and eager to share their ideas both in and out of sessions. The entire three weeks served as an open forum for refining old ideas, gaining new ideas, and plenty of time in the pool.

On the last day, most of the TLP got all of the leftovers together for one last meal, one last volleyball match, one last hot tub, and one last late night card game. I hope to see you all again soon.

Five Things I Learned at PCMI: Thursday 7/16/15

1. I learned a great deal from Dylan Williams. See the full post here: http://mrjanesmath.blogspot.com/2015/07/dylan-williams-at-pcmi.html

2. Chris introduced me to a question structure for inquiry. After students have become familiar with a problem, scenario, or task, they should be asked to generate at least one or two questions in each of the following categories. Level 1 questions are questions that they know the answer to, level 2 questions are ones that they don’t know the answer to but have an idea of how to approach it, and level 3 questions are ones that they don’t know how to approach. All three levels are important. It might seem trivial to write down questions that students already to know the answer to, but it is important to parse out what information is known and what is unknown. Besides, it also helps validate student thinking. Chris also noted that throughout the activity, questions should be moved from one level to another as they are answered, or more insight has been achieved.

3. We discussed “My Favorite No” today. I’ve seen this before, but I want to incorporate this in my class. Rather than boring you, let’s go straight to the source: https://www.teachingchannel.org/videos/class-warm-up-routine

4. We have also discussed 5-Practice Routines for the past two weeks, but now is a good time to bring them up. Again, the source a la Christopher Danielson: https://christopherdanielson.wordpress.com/2011/08/26/five-practices/

5. Marty talked to me about The SimCalc Project at UMass Dartmouth. The objective of the project was to create software that allows students to collect data on computer simulations relevant to algebra and calculus classes. The software and curricula are now available online for purchase: http://www.kaputcenter.umassd.edu/products/. However, Marty cautioned that other programs that used more hands-on simulations and data collection had more success. I’m not teaching calculus next year, but I’ll pass this one on to my colleague who is.

6. (Extra Credit) Beth A Herbel Eisenmann is a mathematics education researcher at Michigan State University who focuses on promoting student discourse. Her book Promoting Purposeful Discourse was recommended to be by a colleague at PCMI.

Dylan Williams at PCMI

Dylan Williams spoke to the PCMI Teacher Leadership Program today via webinar. He answered questions, one of which was mine. Here are some major take aways and quotes:

- There are only two recommendations that educational psychologists can agree on. First, mass practice is less effective than distributed practice. That is to say, we should integrate our topics such that students have many opportunities to practice a particular skill. This notion is closely aligned with Ebbinghaus’s Forgetting Curve. Distributed practice also helps with truant students because no topic is addressed in only one day, making it easier for the absent student to catch back up.

- Second, frequent testing without giving grades helps students because it helps them practice retrieval. Students often practice memory storage when they hear a lecture, experience an activity, or study for a test, but they do not regularly practice memory retrieval. It seems that testing, when used the right way, can significantly benefit learning.

- Having students predict an answer before learning how to complete a problem, even when they have no obvious entry point, has been shown to increase student learning. The thought is that by predicting an answer, they cognitively struggling. This, in turn, leads to greater learning (more on that later). This is connected to test corrections. Even if students don’t perform well on an assessment, the act of trying and correcting their work aids learning.

- Higher levels of cognitive struggle lead to higher levels of learning. This can manifest itself simply: a student trying to solve a novel problem unaided will learn more than a student completing a procedural problem whose solution is already known. However, other types of cognitive struggle also impact learning. In a psychological study, students who were given a smudged print out of a story were better able to recall the story than students who were given a clean copy because they struggled to read the smudged copy.

- There is no psychological evidence that catering to individual learning styles helps students. In fact, it may lead to lower learning since it would lower the cognitive demand and struggle. Yet, this is not permission to ignore learning styles altogether. Working in a learning style that is not your own is tiring, and so teachers should frequently vary the style they use to ensure equitable learning for all.

- In both Japan and the United States, lessons often start with the teacher demonstrating how to solve a certain problem. In the United States, this is often followed by procedural practice. However in Japan students are challenged to find other solution methods. This leads to natural differentiation because higher achieving students can be prompted to find more complex solutions while the teacher scaffolds more basic solutions for students who are confused.

- The advantages of formative over summative, or comments over grades, is not absolute. The only thing that matters about feedback is what students do with it. If a student in AP Calculus would learn the most from seeing a number grade out of five on their practice test, then they should receive a numerical grade. If a student would benefit the most from teacher comments, then that is what should be done. Moreover, any assessment can be used as a formative or a summative depending on how you use it. Groups of four students could individually take a standardized test, then all pool their ideas as a group to create a fifth “best version” of the test. After finishing, the teacher would find any common mistakes and have groups present their solutions to each other. In this way, a traditionally summative assessment has become formative.

- The goal of feedback is either to give students information about where they are at currently, or how they can improve. However, it is disadvantageous to give both at the same time because students tend to focus on one type and ignore the other.

This talk gave me a great deal to think about, but I’ve tried to come up with a few succinct action steps to improve my teaching. These probably sound familiar:

Integrate the topics in my curriculum more, and don’t hesitate to expect students to remember essential topics from previous units.

Let students predict answers to novel problems before they start them, and allow them to struggle within a well-thought scaffold. 

Use more quick formative assessments. Even if I don’t grade them myself, the act of taking the assessment is important, and it can give students the opportunity to reflect on their peers and on themselves.