Jean and Sue and I all live in the same very small town. It’s four blocks by four blocks, or about 0.14 square miles. I met them five years ago when I learned they were hosting a monthly women’s music circle in Sue’s basement. (In fact, I logged onto Facebook just now to get the awesome Miss Piggy poster, and the first thing I see is Facebook telling me that Jean and I have been friends on Facebook for five years, and that we should celebrate our friendversary!) Other than playing music with my family and a couple of brief stints in ensembles in college, I haven’t played with other people since high school. I am a passable guitar player and singer, and would much rather play with other people than by myself, so I started going. I knew Jean’s name because I had been feeding her cat, Blake, on my back deck for years, but I’d never met her in person.

At a music circle, you basically go around in a circle, with each person picking and (usually) leading a song, either a favorite, or an original, or whatever. Many circles have pretty strict protocols around who joins in on songs and who gets to solo and who gets to sing harmony and what sorts of songs are appropriate and how much chitchat is allowed pre- and post-song. None of those things are bad, but they can make joining a circle a little scary for newcomers, especially those who aren’t as musically experienced.

Sue and Jean wanted to have a circle that was much more inviting for beginners and others who don’t “play out” (in front of other people, like in a bar or coffeeshop), was a little more free-form, and was only for women (or “gurls”, as we call ourselves). They have succeeded in spades! We’re not big on protocol, and pretty much anything goes. Some of the women play in public a lot, some have never sung in front of anyone but their family, and everyone else is somewhere in between. We even have people who just come to listen, or take pictures and post them to Facebook (hi, Carolyn!). We bring snacks and drinks, talk about kids and weddings and concerts we’ve been to, and play a lot of music. Someone might say, “Hey, can I….?” and the answer is always, “Hey, it’s Gurls Circle, so do whatever you want!” Sometimes as few as two people come (we called it The Annie and Sue Show), other times we have as many as 15. You never know who’s going to show up and what songs they’re going to lead. As far as I’m concerned, it is awesome.

Long story short, I ended up getting an electric bass and started playing that at Gurls Circle. I wasn’t that good or creative, but I had played a little bluegrass bass in high school, and I play well with others (by which I mean I can keep a beat and am good at following other people playing guitar). I got better at executing my limited skill set, even though I only played once a month at our circle.

A couple of years ago, Jean and Sue invited me to join them for a gig at a small coffeeshop, then they invited me to play with them at an open mic night they were running at a cafe. Sue invited me to play some bluegrass with her and her husband, who is a banjo player, and last summer we played bluegrass at the local farmers’ market. Jean, Sue, and I also played at the farmers’ market. This winter, I played with both “pairs” at our town music night.

This spring, Jean announced that we would be playing at a local barbecue joint every Tuesday this summer. The three of us would play from 5:30 to 8:30, with a break in the middle, during which another woman musician that Jean invites would play a short set. We played our first night on June 21.

When making the set list for this past Tuesday, Jean suggested that I take the lead and sing a few of the songs I sing at music circle. This week, Sue and I played through the break, accompanying the guest artist, Nikki, while Jean sang some harmonies. Then Nikki joined us at the end of the night to sing our last few songs. We were also joined for the whole night by Jean’s congo teacher, Karen Smith.

If you are still reading, you may well be wondering what on earth this has to do with math education, so here goes. As I was practicing with Sue and Jean this past Monday, I realized, “They’ve invited me. I’m now part of this local music party. I feel welcomed. I feel valued. This is exactly what Kaneka was talking about in her ShadowCon16 talk!”

Honestly, it was almost an overwhelming realization, that Jean and Sue have done for me (and other women) in music what I’ve always tried to do in math, and what we all need to be conscious of doing more. If you belong to a community that you value and that values you, you invite other people to join in and participate. The math community, or the “party”, isn’t any different. Just like any community, those of us who are active need to invite and nurture new members. We need to help people realize and understand that they belong and they have something to offer. Watch Kaneka’s video for more.

After we finished playing Tuesday night, we were all sitting at a table, eating our barbecue (free food and drinks for the band? I’m in!) and talking about how much fun it had been to all play together. I jumped in and said, “Hey, if I may be reflective for a minute.” I briefly told the story of Kaneka’s ShadowCon talk. Much like you were probably wondering why I was writing about music, I’m sure they were wondering why I was talking about some math thing! Then I explained the parallels that I saw in these two situations, and expressed my gratitude to them for inviting me to the party.

I added, “You know, this is so important to me, I’m going to write about it and share it with my math peeps.” They asked if they could read it when I was done, and I said, “Sure, I’ve got a blog. I’ll make sure to send you the link.” (Yes, we finally got access to our blogs after The Long Transition.) So here it is.

As we were carrying the last few things to the car a little later, I said to Jean, “You know, I meant what I said. I really am grateful to you guys for inviting me and letting me play with you.”

Jean’s reply was better than any conclusion I could write to this story. She said, “Well, inviting people to do the next thing is the only way we all grow and get better.”

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```Why on earth is anyone giving anyone any hints? I don’t think we should be doing anything other than checking for understanding. #probchat

— Annie Fetter (@MFAnnie) May 18, 2015

I know hints are a hot Twitter topic right now, and I agree that you do, as a teacher, want to have a plan for what to say to kids who are stuck somewhere specific (that you expected them to get stuck). But most of the hints that we give are really shoves (some very gentle, some more forceful) in a particular direction. They often don’t do three things that I think are important:

- figure out what the student understands about the story
- honor where the student is and what they’ve thought of so far
- let the student do all the work and make all the decisions

As a sometimes coach in a wide range of schools/districts/populations, I don’t think that I work with students that are so unusual, and I find that when a kid asks me a question or tells me they’re stuck, probably 19 times out of 20 (or maybe more like 49 out of 50, though my colleagues would probably guess at 99 out of 100), what I say is, “Tell me something about the problem.” That’s it. There are small modifications – if they asked about question 3, I’ll say, “Tell me something about question 3.” Or, if I’m feeling radical and they’ve actually done some math, “Tell me about what you’ve tried so far.”

Yes, even if they say, “I don’t know how to start.” In #probchat, Kent asked:

```
```@MFAnnie “Ms. Fetter, I don’t know how to start.” what do you say? Nothing? At a certain point you gotta offer something. #probchat

— Kent Haines (@MrAKHaines) May 18, 2015

I didn’t mean to imply that you should offer nothing to students who aren’t sure how to get started. I just don’t think you’re doing them any good by making any decisions or doing any math for them. Sure, they might be sitting there quietly with no intention of doing math, because they know it will all be over soon and they can go to lunch. But it also might be that they honestly don’t know where to start. You know why? *<Warning: Gross generalization ahead.>* We probably haven’t taught them strategies for getting started with a problem when they don’t quickly “see” how to solve it. They might not know that any of their ideas are good. Heck, they might not even know they have ideas, or that making sense of the story would be useful. So I like to ask them about their ideas. It’s the rare student who doesn’t have any.

So, here’s an example of something I think is almost always a bad hint: “What’s the problem asking you to do?” or “What’s the question?”

The student might not even know what the story is about, because they might not have ways to engage in it and make meaning out of the story, or they might not even know that’s something worth doing. Or they haven’t even read it yet. But you’re already asking them to look at The Question and then find The Answer. Stop! Back up the truck! Unless you know they understand the story, completely, any content-related hint you give them may well be useless or, worse, confusing. In particular, a hint that focuses on The Question just perpetuates the point of math as Answer Getting, as opposed to understanding and making meaning.

Years ago, one of my colleagues, Steve Weimar (@sweimar), was working with some eighth grade students in a “low-performing” school. The students had learned the Noticing and Wondering strategy and, when Steve was visiting, were Noticing and Wondering the heck out of a math situation. Steve was watching and eventually said, “Wow! It looks like you have a lot of great ideas about this problem! How about you start thinking about the question?”

The students looked at him and said, “Whoa! Slow down. We are *not* done noticing and wondering.”

Those kids had figured out that if they did a really good job of Noticing and Wondering, they could tackle any question that came up about the situation. And they had some strong ideas about how to know when they were done Noticing and Wondering. Until then, don’t make them move on, because they aren’t ready!

Imagine how different their experience would have been had the teacher jumped in early in the process and asked, “What’s the problem asking?” I’m guessing that a lot less math might have happened in that room, and those kids wouldn’t have nearly as strong a sense of themselves as people who do math.

]]>(Did you really go play? Honest? Because if you didn’t, the latter part of this post won’t be as much fun to read.)

Last month we were in Boston for the NCSM and NCTM yearly meetings, and as has recently happened at large math ed events, I was occasionally hailed with some version of, “We just used your video in our talk!” or even “OMG! We use your video in ALL of our PD! You’re famous in [insert state, county, or district here]! Can we take our picture with you??” Invariably, they’re referring to the very first Ignite talk I gave, which was at NCTM in Indianapolis in 2011 (though it wasn’t technically part of NCTM, since the session didn’t get accepted, so we did it in a bar). If you haven’t seen it, or haven’t watched it lately, I encourage you to check it out.

Many groups are using this video as a launch for professional development because it can start conversations about moving beyond answer-getting and instead valuing as many of students’ mathematical ideas as possible. As of this writing, the video has been viewed over 15,800 times. That’s really exciting! And I certainly don’t mind being stalked at math ed conferences.

This past year I wrote math curriculum, mentored college students doing academic tutoring, and did some tutoring myself for a group of disadvantaged high school sophomores participating in Project Blueprints, an after school youth empowerment program hosted by Swarthmore College. One thing we focused on early in the year was developing and emphasizing mathematical habits of mind and working towards getting the students to believe that they have mathematical ideas and that those ideas are important. We did a lot of Noticing and Wondering! In fact, one of the first activities we did when they got the new iPads was to play Game About Squares.

Now, these are kids who are taking high school geometry and are about to take the state’s Algebra exam for a second time (their district doesn’t have a very high success rate – one kid claimed that nobody from their district has ever passed). Isn’t this supposed to be math support? Do they really need to play a game?

Well, yes. Students opened the game and were confronted (as were you, if you followed my directions to play before reading) with this:

“What are we supposed to do?”

“How does it work?”

“Where are the directions?”

“Uh….”

Those were a few of the comments I heard from the two pairs of students I was working with that day (and the one other adult in the room, who had pulled out her phone to try playing). I just said, “Figure it out.”

Not surprisingly, they did. They noticed, they wondered, they tried things, they guessed and checked, they made mistakes, they groaned, they backtracked, they started over, they laughed, they talked to each other a *lot*, they persevered, and they were excited by and proud of their progress. What teacher wouldn’t want those things to happen in their math classroom on a regular basis?

An especially fun moment happened when Ashley, one of the coordinators of the program, came into our room. She asked what they were doing and one of the students reset the game to Level 0, handed the iPad to her, and said, “Here.”

She asked, “What am I supposed to do?”, and the students just grinned and wouldn’t say a word. I gave her a “don’t look at me!” shrug. They watched Ashley’s finger hover over the screen to see what she would click on. They snuck glances at her face to see if they could tell how she was feeling. They grinned some more. They elbowed each other gently when she made the same mistakes they had made. They watched her slowly figure out how the game worked. It was almost magical to observe them watching an adult go through the same learning and figuring out process that they had just gone through. They seemed almost entranced!

Then we talked about the game for a bit, and discussed the “habits of mind” they had employed to figure out the game – noticing and wondering, guessing and checking, persevering, struggling productively, learning from mistakes without worrying about making mistakes (since they knew the only way they were going to make progress was to make mistakes and learn from them), and working together. We talked about how these skills are as important as any content they learn in their school classes, and how they can use those skills to make progress on math problems they’re not sure how to solve. In fact, much of the math programming we did the rest of the year employed huge doses of Noticing and Wondering and generating ideas about math situations, or scenarios (a math problem with no stated question). Anecdotal reports suggest that by the end of the year, most of the students felt pretty confident that they could generate ideas about most math situations we handed them. Big win!

These days we talk a lot about the importance of implementing and practicing the Standards of Mathematical Practice in classrooms. Sometimes it’s hard to make that practice explicit, but students do need to know when they’re developing and using (and getting better at) those habits. One way to do this is to do activities, such as Game About Squares, where there isn’t any real math “content”, but there is a lot to mess around with and figure out and enough support that students can do that without a lot of guidance from any adults.

I’d love to hear about your favorite such activities, and what sorts of subsequent conversations you have with your students about habits of mind.

Now go play Game About Squares some more. After a hiatus, I’m currently working on Level 19, so I’ve got a lot of things to figure out!

]]>May the 4th was not only Star Wars Day but was also my mother’s birthday. She died in February 2014. I decided to celebrate by taking a vacation day and digging in the garden, which was one of my mother’s favorite things to do (I’m pretty good in the garden, but I swear she could weed at least four times faster than me, and yes, I totally took advantage of that by enlisting her help more than once!). I did some weeding, including the final cleaning out of this one area of the yard into which we are transplanting a bunch of irises and day lilies that our neighbor was removing from his front yard (our new neighbors are not plant fans, apparently – they have also cut down a dogwood and a Japanese maple).

When loosening the soil in the bed, I hit a rock, and decided that I’d dig it up (another thing my tenacious and hard-working mother would have done). It turned out to be two large rocks – the one in the picture that includes my foot for scale (Estimation180 anyone?) and the one leaning against the fence in the other picture (which includes a pint glass for scale).

But enough about my day off. This is a math blog, after all, so I really wanted to talk about how my mother not only persevered when faced with a giant rock in her flower bed, but also when she was designing some of her fabulous textiles. Let’s start by watching the Ignite that I did about her at NCSM last spring, shortly after she died.

She’s pretty talented, huh? For fun, and to further honor her talents on her birthday, I decided to try to reproduce that Celtic design that she found in a book. As you may recall from the video, here’s the picture that she had to work with:

I stared at it a bit and thought about what I would need to pay attention to if I was going to reproduce it using Geometer’s Sketchpad (that is another way of saying that I Noticed and Wondered). Yes, Mom worked on paper, and didn’t have any problem redoing things as often as necessary, but I believe in the power and speed of something like a dynamic geometry environment so that the tweaking goes a lot faster once you’ve set up the initial relationships!

As shown below, I took note of several things. First, the whole thing is a circle. Second, there are 12 outer points (marked in red). There are also 7 concentric circles underlying the design (marked in blue). I noticed that I would need to construct 24 radii of the outer circle, and create points of intersection where those radii crossed the concentric circles. I also noticed that one “path” through the design consisted of “diagonals” of the spaces created by these radii and circles (marked in green).

In Picture 1 below, I’ve set up the initial relationships noted above. In Picture 2 I’ve rotated that one path 11 times by 30 degrees, resulting in the beginning appearance of those 12 outer points. In Picture 3, I’ve added the “paths” going the other way. (Yes, I rotated – leveraging symmetry and using transformations in Sketchpad. In fact, I made custom transformations that rotated by 15 and 30 degrees that I could apply to any object I constructed to save a lot of time.)

It’s really starting to look like something! I can use the points along the thick radius to change the size of the circles and, consequently, the shape of the paths. One of my mom’s first sketches was a bit too “pointy”, and I’ve replicated that by making every circle but the outer one a lot smaller. (You may be able to see a couple of the circles that she drew and then erased.)

I was able to drag the points that control my circles until I got it just the way I wanted it. I didn’t see any more trial sketches in my mother’s files, but I do know that she definitely nailed it in the end!

Consider all the sense-making she did. She couldn’t just measure the picture, since it was drawn in perspective, but she took away as much information as she could. She noticed relationships and used trial and error to figure out the parts she couldn’t count. She made mistakes and learned from them. And there is no question that she persevered!

As I said in my Ignite talk, we need to be sure to look for and value these traits in our mathematicians, not just their ability to crank out answers to a lot of textbook problems really quickly. Look for opportunities for your students to practice sense making, maybe even by having them replicate some drawings!

I’ll close with one more picture of my mom’s artwork taken in 2008. She made this quilt of the Math Forum’s dragon fractal logo for us to hang in the office. Did she know what a dragon fractal is? Nope. But she had the ability to pay attention to detail enough to get it right nonetheless. Also in the picture is my husband Riz (the tall one – Estimation180 clue is that I’m 5’10″), my sister Marty, her husband Silas, and their adorable children Olivia (7), Liam (4), and Clare (8 months).

My mother inspired me in many ways as an artist and as a mathematician. We should all try to do the same for the young people in our lives.

]]>Exploring interactive applets that let students “notice and wonder”, talk about mathematical situations, and develop conceptual understandings of triangle properties, linear equations, systems of equations, and factoring trinomials.

PCTM 63rd Annual Conference, November 2014

Session Handout [PDF]

For more about the Math Forum, including information from our other talks at PCTM 2014, visit our conference page at http://mathforum.org/workshops/pctm2014/.

**Types of Triangles** – Annie Fetter

Link above includes handouts, sketch, and Sketch Explorer version

*Key technology strengths: exploring dynamic models of different triangle types, allowing students to develop intuition about different classes of triangles and what characteristics they do and don’t have.*

**Runners** – NCTM e-Examples from Principles and Standards

*Key technology strengths: developing intuition about distance/rate/time and the concept of slope, without needing to know the formal vocabulary at all, as well as the ability to try things and get it wrong, and get instant feedback without fear of judgement by others.*

**Galactic Exchange** – The Math Forum’s ESCOT Project

Galactic Exchange Handouts (PDF)

*Key technology strengths: the applet does the recordkeeping for you, and students can explore systems of equations without needing to know that they’re doing that, or even knowing that such a thing exists!*

**Algebra Tiles** – National Library of Virtual Manipulatives

*Key technology strengths: the variables actually vary!*

Annie Fetter, The Math Forum @ Drexel University, Philadelphia, PA

Session 12 Handout [pdf]

**How This All Started – Formative Assessment
**

- Constructing Quadrilaterals Activity (see handout)
- Making Movies Using Jing – Instructions [PDF]
- Kathy’s Movie
- Danielle’s Movie

**Where it Went from There – Summative Assessment
**

- Red Shirt’s Movie
- Christina’s Rubric (see handout)

**Then Debbie Got Involved**

Annie is the Problem of the Week Coordinator and Professional Development Specialist at the Math Forum. She also teaches three courses in Drexel’s Math Learning and Teaching Masters program,

The corner deli sells roses in bunches of 6. If Dylan buys 3 bunches of roses, how many roses does he have?

A. 3

B. 9

C. 18

D. 24

Almost half the third graders (46%) in a group of schools I was supporting chose B. The correct answer, C, was chosen by 31% of the students. I don’t recall being all that surprised, but as I have thought about it over the years, I’ve come to see it as one more piece of evidence that many students do not do “sense-making” when they’re doing math. They look for numbers and guess what operation they’re supposed to do (addition is very popular). I have a theory that if you had asked those same third graders to draw a picture of the story, many more of them would get the problem correct. So the problem above becomes this task:

The corner deli sells roses in bunches of 6. Dylan buys 3 bunches. Draw a picture of the story.

To informally test this theory, I invite anyone with access to students in grades 2-5 (or older kids if you think they might be good subjects) to run a small experiment for me. I’ve written two sets of questions, one math and one drawing. Each has three questions. The math questions are taken directly from some Grade 3 benchmark tests, but I can see them being used in grades 2-5 for the purposes of this experiment (though you are welcome to use them with whomever you want – it’s an experiment, after all, not hard scientific research).

Since I am interested in how students solve problems when they think they’re supposed to “do math” versus when they might not realize they’re engaging in mathematical thinking, I’d ask that the math questions be given during math instructional time and the drawing questions be given during literacy instructional time, or, barring that, any time that isn’t math, and that the two sets of questions be given a couple of weeks apart.

The attached PDF contains 26 copies of each set of tasks (labled Student A through Student Z), instructions, and a roster sheet so that you can keep track of which student corresponds to which letter. (If you have more than 26 students, be creative.) You can report results through an online survey or send me copies of the completed task sheets (as a scanned PDF, or toss them in an envelope) or both.

Download the files: Fetter Sense-Making Experiment v1 [PDF]

So, wanna play? I hope so!

]]>- Lani Horn facilitated the session. Her research focuses on mathematics teacher communities and professional learning, and she focused the discussion on longstanding issues at this cross section in the novel context of social media.
- Ashli Black (@Mythagon) was a young teacher in search of greater professional engagement, which she found through reading other math teachers’ blogs. There, she has found research articles and lesson ideas that have helped her refine her own ideas about teaching.
- Hedge (@approx_normal) was one of about 8 teachers who taught AP Statistics in her entire state. Although she tried building collaborations with them, she found little traction. Finally a friend told her that Twitter was the best “math department” she’d ever been a part of. Ever since, she has blogged and collaborated with many teachers online.
- Justin Lanier (@j_lanier) is a teacher who blogs to reflect on his practice and whose social media presence helps to build the mathematical literacy of teachers and students by sharing the diverse mathematical resources that can be found on the internet.
- José Vilson (@TheJLV) teaches in a large urban district and is a prolific and widely-read blogger who focuses on mathematics pedagogy, race, and educational leadership. His work is featured on a number of online outlets. (He didn’t actually get to join us in person, but Lani talked about his work and some of the issues on which he is active.)
- Nicole Bannister (@CUMATMathDrB) is a teacher educator at a large university who has begun to experiment with using social media to solve the “two-worlds” problem, the divide between student teaching placements and university coursework.

Then there’s me: “Annie Fetter (@MFAnnie) works for a well-known online site dedicated to providing professional resources for mathematics teachers. This site was one of the first to attempt to cultivate online teacher community.”

Since I got to go last on the panel, my piece was somewhat of a retrospective of “How did we get to this place that these educators are in right now, and what part might the Math Forum have played in all that?” As senior member of the panel, I feel the historical perspective was an appropriate task.

In the late 1980s, I was part of an NSF-funded project at Swarthmore College called The Visual Geometry Project. In addition to writing some engaging and perpetually-on-sale-in-the-Key-Curriculum-Press-catalog workbooks and computer-animated videotapes exploring three-dimensional geometry, we were also the group who wrote the first version of the *The Geometer’s Sketchpad* software (which, by the way, made its public debut at the NCTM Conference in New Orleans in 1991).

While working on this project, one of the programmers said to me one day, somewhat incredulously, “You don’t have *email*??” So he gave me my first email address, on the Computer Science department’s system, and I became immersed in the world of usenet newsgroups (now Google Groups) about bicycles, motorcycles, cooking, homebrewing, and other fascinating topics. (Disclaimer: No grant-funded time was spent pursuing these non-grant-related topics of interest.)

As the VGP grant wound down, we considered possible next steps. None of us wanted to get real jobs, so we figured we had to write another grant. We thought that this Internet thing might be useful for geometry educators, so we wrote a grant focusing on the development of a site on the Internet devoted to geometry and geometry education.

Note that this is before the advent of the World Wide Web, so communication was done via email and newsgroups, and resources were shared via FTP and Gopher. But we could sense that this Internet thing could become an incredibly valuable resource for educators, so we wanted to build an electronic database of resources so that when teachers got access to the Internet, they would have somewhere professionally useful to go.

We also claimed that we would develop a community of users of the database. Teaching is a very isolating experience, and time was that you would come to a conference such as NCTM, meet all sorts of great people and be exposed to great ideas, and then go home, back to your little cinder block box, and tough it out by yourself until next time. But with the Internet, it could be like having access to great people and great resources all the time, without having to leave your school or house (or even take off your bunny slippers!).

We started building this database and developing the discussion groups, and we figured that maybe we should hire someone who knew something about teacher professional development. So in 1993, we hired Steve Weimar to help run workshops to teach teachers how to use these new tools and resources. We held Saturday workshops at Swarthmore for local teachers and week-long summer institutes for a more national (and international) audience. We also helped local teachers get connected by giving them dial-up accounts at Swarthmore, coming to their school or house to configure their computer, and even, in one case, running phone wires up the outside of a school building so they could have a connection in their computer lab.

That third item in our grant proposal might need a bit of explaining. Basically we thought we were going to write a web browser. We didn’t know it was a web browser (there was no web, after all). We just thought of it as a smarter way to interact with newgroups and FTP and Gopher archives. It would allow math to look like math, and make things easy to search out and get, and would use hypertext. Sounds great, doesn’t it?

In mid-1993, the first version of Mosaic came out. Mosaic was the first popular “web browser”. We downloaded it and thought, ah, um, okay…I guess we don’t have to do that part of the project any more! We shifted all our energies to developing our “database” and our community. We wrote our first web pages in 1994 in a hotel room during the NCTM Annual Conference in Indianapolis.

In 1995 we wrote a grant to expand and continue The Geometry Forum. The grant was nicely focused and specific as you can tell from its title: *Mathematics Education and the World Wide Web*.

In 1996 we changed our name to the Math Forum and came up with a new logo. We were also cited in a white paper that described what we were doing – and continue to do! (And which very much captures the potential of the Internet.)

To this day, we’ve continued to expand our “electronic database containing a great deal of useful information on geometry and all its aspects [and other parts of math!]” and to cultivate online community in many forms. As math teachers (both new and old) increasingly turn to the Internet and the web for professional purposes (in addition to the personal purposes they’ve been using it for), we’re still a destination they’ll want to visit.

We’re active on Facebook and Twitter, we have a number of newsgroups and community discussion areas, and, as you know since you are reading this, we’re blogging.

We were each supposed to end our brief presentation (I talk fast, so it was sort of brief when I did it live and in person) with some lingering questions we have about using the MathTwitterBlogoSphere for our own growth and development. I don’t remember what I actually said at the time, but I’m thinking it was something about wondering in what ways the Math Forum can continue to support and contribute to this growing community. I’ve enjoyed being part of the development of what really was the first social network for math teachers, and I’m looking forward to being a part of whatever happens next.

]]>The Math Forum used to host an Internet Math Hunt. Long before Google, Bing, Ask Jeeves, and even AltaVista showed up on the scene, finding things on the Internet was actually challenging. In our very first hunt in September 1995, we asked these five questions:

- In what town is the Geometry Center located, and what is it?
- Annie Fetter, the person who runs several of the student projects at the Math Forum, has pictures of her cats on her home page. What are their names?
- Name four members of the Swat Team, which staffs the Dr. Math project, who have home pages.
- What school runs the Great Penny Toss? (Extra: where is the school located?)
- There is a History of Mathematics site somewhere in the United Kingdom. What university hosts it, and where in the UK is it exactly?

The second question got a lot of attention, and even now it persists on Answers.com in two different places:

- Answers.com > Wiki Answers > Categories > Jobs & Education > Education > School Subjects > Math and Arithmetic (This one remains unanswered)
- Answers.com > Wiki Answers > Categories > Animal Life > Mammals > Land Mammals > Cats (Felines) > (This one is answered correctly)

Eukie and Ivan started coming to the office in 1994 when they were only a couple months old. We were then housed in the math department at Swarthmore College, and the cats had free range of our office, the hallway, and the Fishbowl, which was a seminar room across the hall with floor to ceiling windows on three sides (hence the name “Fishbowl”).

(FYI, Ivan is the one with the spot on his back.)

One day I went to retrieve Eukie from the Fishbowl before a psychology seminar, and the students looked at me imploringly and asked, “Can he stay? Please?” I looked at the professor and he shrugged, so I left Eukie there. For the next three hours, Eukie slowly circulated from one lap to another to someone’s notebook. At one point I glanced over (our office had windows out onto the hallway and right into the Fishbowl), and a student was making an impassioned argument, gesticulating with one hand while the other hand was petting the furry mass lying on her notebook.

Eukie and Ivan loved to sit on the trash can next to the water fountain outside one of the big lecture halls when class was about to let out, because they knew someone would turn the water on for them so that they could have a drink. (One morning the housekeeper reported that she had seen a student holding one of the cats’ paws against the button, trying to teach them how to turn it on themselves.) When the department secretary argued that this was unsanitary, the housekeeper explained that she just wiped it down with some disinfectant when they were done.

Eukie and Ivan have long been fixtures of our Math Tools library gallery, with Eukie chasing the isocahedron screensaver (shown above) and Ivan doing trig with his TI-92. Eukie’s enthusiasm for chasing screensavers at the office didn’t abate as he got bigger, though sometimes all that chasing is tiring.

Ivan often engaged in the age-old cat responsibility of confirming the continued existence of gravity by knocking things off shelves, such as this tissue box (but, fortunately, not the octahedral wooden puzzle), and both dutifully entertained visitors.

A few years later, we hired someone who was allergic to cats, so the cats retired to a life of leisure at home. They both continued assisting with important mathematical work, such as my technical editing of the first version of *Exploring Calculus with the Geometer’s Sketchpad* and helping with the Geometry Problem of the Week #GeoPoW.

They also spent time on the deck lounging and watching the squirrels, blue jays, starlings, raccoons, and other neighborhood cats eat the dried food that we ostensibly put out for the resident cats.

Naturally, all this work makes one tired, so they also did a lot of what cats do best, which is nap and look wicked cute at the same time.

We haven’t even mentioned the origins of their names. Eukie’s real name is Euclid, of course, while Ivan is actually Nikolai Ivanovich Lobachevsky – a fitting pair of names for cats belonging to someone then working at “The Geometry Forum” if ever there were. While Eukie and Ivan aren’t the most famous cats on the Internet, they’re long-lived fixtures. We’ll miss them, but their mathematical contributions will live on.

]]>*The very first Mathematical Practice, “make sense of problems”, includes many ideas that have long been foci of literacy instruction. Yet when “math” starts, both teachers and students often leave those good habits behind. We’ll look at examples of this and explore how to translate literacy routines into good mathematical practices.*

Download the handout [pdf]

Download the PowerPoint slides [pdf]

Visit the Math Forum’s NCSM & NCTM conference web page to learn more about our talks, view videos that support Max’s book *Powerful Problem Solving*, download free samples of our Problems of the Week support materials, and more!