I missed #WorldTessellationDay by a couple of days (June 17) but I figure it’s close enough to the time to celebrate it and also that I am posting to my blog for the Math Forum at NCTM for the first time! All’s right with the world.

I missed #WorldTessellationDay by a couple of days (June 17) but I figure it’s close enough to the time to celebrate it and also that I am posting to my blog for the Math Forum at NCTM for the first time! All’s right with the world.

To appreciate the significance of this is to know that it was my interest in tessellations, the webpages I learned to write as a result of participating in a Math Forum Summer Institute and the interest those pages received, that helped me land my Math Forum job. In celebration, here are a few of my favorite photos of tessellations:

Okay, true confession, I haven’t been too excited about the EnCoMPASS tool and I’ve kept thinking that it’s not quite ready to use yet. Recently, however, I changed my mind!

Max and Annie talked me into looking at five new (very short) videos. As I watched I thought of what Fawn told me quite some time ago — she would love to sit next to a programmer and have a one:one explanation of how the tool works. I promise, Fawn, that Max and Annie explain things just like you’re hoping!

In this first video, Annie gives a tour of a workspace she used to sort student submissions to find a wide range of clear, complete submissions to feature (highlight) on the Problem of the Week website.

In this second video, Annie shows how to make use of the features available to you when you are sorting student work in a workspace.

In the last three videos, Max talks out loud while he illustrates some of the different aspects and features of the feedback process. The first two end a little abruptly (we use something that only records 5 minutes and not a second more!), but the third one carries the process through to the end.

We encourage you to **Leave a reply **to let us (and others) know what you think!

About a month ago I visited an elementary school classroom. The students were working on a problem that (as my memory stored it) was something like this:

*Ricky ate 2 pieces of a pizza. He gave the rest to his friends. How much of the pizza did he give to his friends? Can you write that in lowest terms?*

The students were seated at tables, some working in pairs, some working alone. I asked one of the students if I could sit next to her. She said, “yes” and after I had introduced myself, she told me her name was Abrianna. I noticed Abrianna had already been thinking about the problem and had written something like this on her paper:

I remember thinking that from looking at her paper, it looked like she really understands what’s going on in the problem! I asked her to talk to me about what she was thinking as she wrote (and I pointed to the paper). She said that since Ricky had eaten 2 out of the 8 slices of pizza that he had eaten two-eighths of the pizza. I asked, how did you know the whole pizza had 8 slices? She patiently pointed to the picture included with the problem and said, “See the lines?” “Oh,” I said, “I see them now!” and smiled.

She continued to tell me more about what she had written but when we got to the “equals” sign she said “No, two-eighths is NOT equal to one-fourth.” I was surprised because that seemed to have been what she had written. I started wondering if “equals” meant something different to her than using the “equals sign” and so I asked her, “What are two things that ARE equal?”

She responded by saying, “Two equals two.” When I asked for another example, she said “Five equals five.”

I pointed to the two pizza pictures and I said, “What if you had eaten the pizza that we can see is gone from this first picture and I had eaten the pizza gone from this second picture, who ate more pizza?” She said, “I ate more because I ate 2 slices and you ate 1 slice.”

I tried again and said, “If you ate 6 slices from a pizza cut into 8 equal pieces and I ate 3 slices from a pizza cut into 4 equal pieces, who ate more pizza? She said, “I ate more because I ate 6 and you only ate 3.”

My visiting time in that classroom was over and I moved to observe another classroom but my conversation with Abrianna stuck with me throughout the day and as I talked about it with my colleagues as we walked back, I described the conversation by saying,

I noticed

- Abrianna’s paper included the correct notation.
- A teacher looking at her paper might assume she understood the problem.
- Her teacher would probably give her credit (or a grade) indicating she had the right answer.
- Abrianna used “=” on her paper.

I wondered

- why “=” and “equals” prompt such different responses from Abrianna.
- why does “equals” mean “is identical to” for her.
- why doesn’t “=” mean “is identical to” for her.
- did Abrianna just copy the notation as a way to “do the problem.”

I was reminded again of how important it is to unsilence students’ voices. I hope Abrianna has continued opportunities to talk about her mathematical thoughts!

This Ides of March morning I wished one of my high school classmates a “happy birthday” and as I was reading other posts on her Facebook page I realized she also just turned 65 since someone noted to her that this was a “big one.” My “big one” was on Groundhog Day and so I’ve had a some weeks to get used to being a senior citizen.

*Punxsutawney Phil and Suzanne with their shadows!*

Besides now having a special pass to use to pay only a dollar for my train commute into Philly, I’ve found myself having more than my normal amount of reflective thoughts. Recently I was thinking about my own Action Research with my students in ’99-’00. I was part of a Math Forum grant project and I was using the ESCOT Problems of the Week (*warning: there’s a lot of link rot within that group of pages but there are also still some interesting ideas/resources*) and I was interested in comparing my students’ standardized test scores from the previous year to their scores from the end of that school year. I remember when I looked up all of their scores from the previous year in anticipation of comparing them later, I noted both their literacy scores and their math scores. And, so, when I had the ’99-’00 scores for comparison I looked at both areas. The math scores were fine but it was the literacy score increases that were dramatic!

There were too many variables in play to only give credit to the problem-solving efforts I was focused on with these students. I was teamed with an excellent language arts teacher (Rick Hartwell) and, perhaps, their gains in literacy could be attributed to his effort … but … I think it was also because he and I used similar strategies and our combined efforts had a great effect.

When Annie introduced this slide into her Sense Making workshop and also used it in a Keynote she and Max delivered (and I know she’s used it in other talks recently, too) it just brought everything into focus!

While Rick was encouraging Strong Readers, I was encouraging Strong Mathematicians and the combination worked to the advantage of our students!

A teacher in my online course, PoW Membership: Resources & Strategies for Effective Implementation recently wrote “Keeping Quiet – me, not them.” Her post was a response to the Discussion associated with the activity of reading the article, Unsilence Students’ Voices.

For some time I’ve been thinking about ways to gain minutes in classrooms so that students have more time to talk (and learn). Think-pair-share, turn-and-talk and other partner or group conversations help but invariably there seems to be a need to pull the whole class together for the whole discussion. Once we do that, though, we’re again having the “one person talk” mode — maybe it’s not the teacher doing the talking but it’s still just one voice.

BUT, here is the nugget that was suggested in the discussion post.

“**I’ve started to write down what I hear while I’m monitoring the class during their discussions and project them for all to see. Then students add any other thoughts that were discussed that I didn’t hear.**”

What a brilliant idea!

I responded,

“*As you record those comments and project them, do you find that your students refer to them? Do you still take whole class time to review those comments or might it (maybe with time and practice and suggestion) not need to be discussed as a whole? *”

Her response was,

“*I am noticing that as I post things and continue to monitor, others will say that they have the same thing. It actually seems to be encouraging discussion in groups and may be adding other ideas to continue their group discussions. I am not spending as much time on whole group discussion when I use this format.*”

I’m sure there are still moments where a whole class discussion is a good idea but this idea of projecting a compilation of ideas generated by the variety of pair/group discussants is a powerful idea!

If you try it or have already used this technique, we’d love to hear your stories!

One way to keep things rolling as a result of our **EnCoMPASS Summer Institute 2014** (August 4-8) is to:

*[reflect]***read**a blog post inspired by activities/thoughts from that week*[respond]***comment**on one of the blog posts*[inspire reflection and responses]***write**a new blog post

Here are some I’ve found in case it helps to have them in one spot:

August 7: Dandelions

August 7: Starting Anew and Regrets

August 9: Feedback for 140+

August 10: Listening to Yourself

August 23: What is EnCoMPASS?

August 8: Grateful for EnCoMPASS 2014

August 9: More Metaphors for my Teaching Journey

August 6: The choice to blog

August 27: The Professor in Me

August 24: First Two Days of School

August 1: Ignoring The Meaning of “Feedback”

August 8: How does feedback help?

August 6: People Circles

August 5: Exhaustion

August 26: Formative Assessment Responses

Here are blogs that I’ll be watching. I’ll add to the list I’ve assembled above if/when I notice any EnCoMPASS-related posts:

- Peg Cagle: Peg Cagle’s Math Education News & Views You Can Use
- Justin Lanier: I Choose Math
- Chris Robinson: Constructing Math Instruction
- Lisa Bejarano: Crazy Math Teacher Lady
- Ashli Black: Learning to Fold
- Dave Coffey: Delta Scape
- Bridget Dunbar: Reflections in the Plane
- Sadie Estrella: Who’s a Math Nerd? *raising hand*
- Wendy Menard: Her Mathness
- Jami Packer: Undefined
- Megan Schmidt: Number Loving Beagle
- Sebastian Speer: Making Sense of Numbers
- Annie Fetter: Annie at the Math Forum
- Daniel Lewis: Daniel at the Math Forum
- Tracey Perzan: PoWerful Ideas
- Max Ray: The Max Ray Blog
- Casey Sneider: Casey at the Math Forum
- Steve Weimar: Steve at the Math Forum

If you notice any posts to add, feel free to comment and/or email me directly! Thanks. ~Suzanne

Some of you know that my one (and most likely, only) Ignite talk, **Unsilence Students’ Voices**, focused on listening to students and encouraging them to talk. Along with that idea is to become more aware of what you, the teacher, say in the classroom. The best way to find out what you really said is to **listen** to it later.

**Annie’s “Phone in the Pocket” Idea**

Some time ago I overheard **Annie **suggest to a teacher that she use her SmartPhone to record herself. (Can’t you just hear Annie’s voice as she explains this!) Annie said that you should just turn on voice recording on your phone, stick the phone in your pocket and after about 10 minutes take the phone out of your pocket and turn it off. Casual. No fuss. Then later in the day when you have 10 minutes, listen to the recording and ask yourself

What do you notice? What do you wonder? … and what do you want to try next time?

**Suzanne’s Addendum to Annie’s Great Idea**

During the week, change the time in the class period that you try this. So, for example, start by recording the first 10 minutes of class. The next day, try to record the second 10 minutes and then make it later into the class until you also record the last 10 minutes. Resist taping the entire class because it’s unlikely you’ll sit later and listen to the entire recording. You want it to be manageable so that you can make use of the recording.

I can’t help but point to what **Max** wrote in **Chapter 3** of * Powerful Problem Solving* and, in particular, the section titled

*The first step in creating a classroom in which students actively listen to one another is to convince students that what their classmates are saying is worth listening to.*

On **page 27** Max lists some suggestions for “*making whole-group conversations in math class more like conversations at a dinner party*.” Fun would be to pick a few of those, make your 10 minute recordings and then listen to see how you are doing.

During our recent EnCoMPASS Summer Institute (#ESI14) Fawn Nguyen‘s comment that she’ll have **140 students **this year, started me reminiscing. I, like Fawn does now, taught in southern California and having at least 140 students was normal. I usually taught 5 of our 6 class periods (at times I could have “sold” my sixth period but resisted it!) and classes could be as large as 36 students. That could mean 180 students but usually my load hovered around 150. It’s my normal mindset to think in terms of those numbers.

During #ESI14 we were talking about giving written feedback on the Problems of the Week (PoWs) either using the My PoW Work as a Teacher option of the PoWs or the EnCoMPASS software option and both of them can be daunting experiences if you are faced with 140 expectant students. *Why didn’t I get feedback?* *When are you going to look at my work?* *Why did you write to her and not to me?* Those are a few of the questions I can imagine students asking between the time they submit their work and when I promised they would have feedback … and, of course, the worst are the sad faces!

Here are some ideas I have for keeping sane!

**Feedback Buddies**

[During the Institute we talked about **Revision Buddies** (page 175 in Max's book, *Powerful Problem Solving*) and this idea can be built on it.] If you’re doing problem-solving activities in pairs, for any given problem give feedback to Student 1 of the pair. This cuts the amount of feedback in half for any given problem [**70**].

**Group Buddies**

If 70 is too great a number to handle, consider grouping pairs of Feedback Buddies and having groups of 4. Give feedback to Student 1 of the group. This cuts the amount of feedback in quarter for any given problem [**35**].

With either of the ideas for **Feedback Buddies** or **Group Buddies**, you would give feedback to Student 1 for Problem 1 and then Student 2 for Problem 2, etc.

**Random 7**

I’m thinking that if Fawn has 140 students and she has 5 class periods then she as 28 students in each class. I’m also thinking that she might use groups of 4. So, what if she used a Fast Random Number Generator app to come up with 7 students who would be receiving feedback on the PoW. She would give those seven students feedback and that’s how the groups would form to have conversations about her feedback and how they should use it to revise/improve their work. [If she happens to prefer groups of 3, then that would be Random 9 instead!) [**35**]

**Random 3**

This might be a way to start just because it’s VERY manageable for the teacher and it can be used to introduce the idea that you’ll be giving feedback and it might lead to conversations about what the process is and what the expectations are. Once the students have submitted, randomly choose 3 students’ work from any one class. (I wouldn’t pick a low, medium, high submission — I would do it randomly … or … I might not even pick one of my students’ solutions but instead lift a solution from the **Teacher Packet** and use it to generate your feedback!). [**3**] or up to [**15**] if each class is different.

I’d love to hear from you about other ways you might have thought about to handle giving feedback to help all of your students. I’m also curious to know when/if you try any of these ideas, how things went!

Last May I posted about how I presented photos from the city to have fourth graders talk to me (and, more importantly, to each other) about parallel, perpendicular, and intersecting line segments. The photos I took I included in this post:

http://mathforum.org/blogs/suzanne/2013/05/18/parallel-perpendicular-intersecting/

On a follow-up visit to that 4th grade classroom, I took some photos in their classroom. At first I just wandered around taking a photo of this and that but soon different students caught on to what I was doing and suggested things I should photograph. The most fun was when the “climate control” young man turned his back to me indicating I should photograph his shirt! He was usually focused on the discipline issues of one student assigned to him but that day they both found themselves engaged in mathematical thinking!

*click on each image to view a larger version*

On the last day of my recent vacation, I noticed some tweets from @mathinyourfeet. Malke was posting photos of “city math” and I couldn’t help but respond with some photos of what I was seeing that day at the Ala Moana Shopping Center in Honolulu. I thought it would be fun to include here the photos I tweeted that day plus a few more that I took. You can see that man-made symmetry and also symmetry in nature caught my eye!

*click on each image to view a larger version*

What do you notice? What are you wondering?

© The Math Forum at NCTM 2016. All Rights Reserved