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!

*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!

*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 PowerPoint slides [pdf]

I’m not making the handout available because there isn’t much to it!

I may add a few thoughts after the session.

]]>This is posted in support of the mini-session I’m leading at CMC-North Mini-Conference. A session description for those who might stumble across this post:

*Many topics in math seem difficult to address conceptually and tend to be taught procedurally. We’ll explore technology tools that encourage students to “notice and wonder”, talk about and make sense of mathematical situations, and develop conceptual understanding of triangle properties, linear equations, systems of equations, factoring trinomials, calculus concepts, and more.*

My thanks to everyone who came to the session. As promised, here’s a copy of the session handout [pdf].

- iPad: Types of Triangles sketch – Annie Fetter
- iPad: Quadrilateral Pretenders – Key Curriculum
- Laptop: Runners – NCTM e-Examples from Principles and Standards
- Laptop: Virtual Algebra Tiles – National Library of Virtual Manipulatives
- iPad: Mellow Yellow – Interpreting Graphs – Key Curriculum
- iPad: Graph Dancers – Key Curriculum
- iPad: Wuzzit Trouble – Inner Tube Games

- PowerPoint Slides [PDF]

My thanks to those of you would came to the session. I enjoyed the conversation a lot. Unfortunately, I did not remember to take a picture of the list of reading lesson objectives that we generated, but I have to say that I was excited to learn a new word that was the topic of one person’s reading lesson objective last week: Syllabicate. When we reviewed the list and talked about analagous topics and foci in math instructions, someone pointed out that syllabication is sort of like place value. That was brilliant! Decomposing and recomposing numbers is an important part of numeracy, and of course place value is one big part of that.

I hope some of you will send me mail or leave a comment here about ideas they will or have already tried in class as a result of our session.

]]>