Annie posted our very first Problem of the Week in December 1992. Today she continues to write problems and supporting materials for the Problems of the Week service. You’ll often find her observing teachers and students in local schools as well as developing PD for teachers in grades K-12. Follow her @MFAnnie or http://mathforum.org/blogs/annie/
The Geometry Forum began in 1992, just before the World Wide Web made the Internet accessible to a much wider audience. At that time what was your main goal for the Forum and how much has that grown or changed over the years?
Our goal was to help geometry teachers use the emerging technologies of the Internet (which then included email, newsgroups, and file sharing) to extend the learning of their students and their own professional development beyond the walls of the classroom. We also imagined that these tools might increase communication between math learners (and their parents), math teachers, and math and math ed researchers. We were also planning to write the “Forum News Gateway”, a software package which would allow the inclusion of pictures and sounds and other media within text. The introduction of Mosaic, the first popular “web” browser, in 1993 made our fancy news reader unnecessary, and we instead focused our energies on helping educators understand why they might care about “the Internet”.
We supported many teachers through local Saturday workshops and national summer workshops. As more organizations and individuals found their own way online, we shifted our focus to providing increasing amounts and types of content so that when math teachers came online, they would have worthwhile things to use and an active community with which they could engage.
Common Core is a hot button topic with teachers and parents alike. Can you give an example of how the PoWs can help teachers implement the Mathematical Practices.
MP1, “Make sense of problems and persevere in solving them,” is the focus of the activities in our Understand the Problem strategy. Often students are encouraged to reread a problem or read it more carefully. But that’s not so helpful for many students who aren’t really sure how to engage with something that didn’t initially make sense. What does it mean to make sense? What should they pay attention to? Encouraging students to re-tell a problem in their own words, act it out, or pull out quantities and their relationships gives a purpose to their rereading. MP3, “Construct viable arguments and critique the reasoning of others”, has been a focus of the PoWs since the beginning. We used the Internet to provide problems for students to solve and write a text-based explanation of their work for someone who wasn’t in their classroom. Changing the audience from their teacher to someone on the other end of the computer gives incentive to write about mathematics. So even if you just use the PoWs to explicitly implement those two practices, it will pay off in many other areas of the classroom.
You recently traveled to a classroom to take part in the video filming of the scenario: Campfire Camaraderie. Why are Scenarios* an important part of the learning/problem solving process?
Yea, I got to be a bear! See the picture at the top of this column. Scenarios are important because they present mathematical situations in which students can look for math (and other things) without feeling like they are supposed to find an answer as fast as they can. To the detriment of our students, we have long rewarded speedy answer-getting in math, instead of sense-making. By presenting a situation that doesn’t actually have a question, we slow down the process of engaging with the mathematics and encourage students think of all the math they can that might be related to the situation. It is a very powerful way to make a statement about what you value in your classroom. It also gives all students a better chance to contribute to classroom conversation, since the fast answer-getters can’t be “done” (because what does it mean to be “done”?), so everyone else gets a chance to think about the situation and share their ideas before “the answer” gets yelled out.
It also means that most of the mathematical ideas that drive the learning with and about the problem come from the students, which communicates to them that you’re interested in their ideas. When I model a lesson using a Scenario and the I Notice, I Wonder activity, once I have read the story or drawn a picture on the board, I’m done contributing “math”. The students do all of it from there on out, including making sense of the situation, pulling out any and all mathematics that might be involved, and even coming up with questions they are curious about. I’m just facilitating conversation, making sure ideas get recorded and revisited, and keeping things moving.
Can you tell me about a person who most influenced you and the way you think about teaching math?
Wow, that is a tough one. I actually did an Ignite talk a couple of years ago titled “The Teacher I Would Have Been“. It wasn’t my best Ignite talk, but I tried to get at how my teaching philosophy developed. I’ve been fortunate to work with great people at the Math Forum, but I’m actually going to pick a non-human. The Geometer’s Sketchpad software has been the vehicle through which I’ve interacted with hundreds (thousands?) of teachers (and students) over the last 20+ years, and those interactions have shaped my thinking immeasurably. I’ve worked with a lot of awesome teachers who totally get Sketchpad and instantly have ideas about why and how they would use it, but I’ve also worked with teachers who can use Sketchpad but can’t begin to envision teaching with it because they simply can’t imagine what their classroom would look like if they weren’t controlling everything. A big piece of my work has been helping teachers think about what a more student-centered, discovery-oriented classroom would look like and how you might move in that direction, even if it’s in baby steps, such as doing one Sketchpad activity in the lab one day.
*Ready to try a free scenario? Find them here.