My daughter went to senior orientation today, a sure sign summer is almost over. When I was in the classroom, I remember getting both sad and excited around this time. Sad because my holiday was coming to an end, but excited because I was revving up to start over and try some new things in the classroom. I usually spent my summers learning new tools, brushing up on skills, and reevaluating what I had done the previous year and deciding what to throw out or modify. I was, and still am, someone who does not like to do the same old thing, which was especially true when I was teaching in middle and high school. It was my summer challenge to try to come up with different ways to reach my students and bring new projects, games, hands-on tools, and of course, technology, into play in my classroom.
We at Key have been thinking about back-to-school these last couple of weeks and working on ways to help teachers who want to integrate technology get a good start for the year. Our line-up of free webinars, starting with August 28 and going through the end of September, is focused on how to start using Sketchpad and TinkerPlots with students at the beginning of the school year. We know there is a need for support and resources, especially with the current focus on the Common Core State Standards. As former math teachers, we are familiar with the struggles and stress the beginning of a school year brings. Our hope is to provide some ready-to-use resources and suggestions that focus on appropriate activities for the beginning of the year to help teachers bring something new and exciting into their math instruction through the use of technology.
Hey Sketchpad users—there’s a new version of Sketchpad available! It’s Sketchpad version 5.05, a free upgrade for Sketchpad 5 users. For you early adopters, Sketchpad 5.05 is fully compatible with Mountain Lion and will also be compatible with Windows 8 when that comes out. To update to version 5.05, select Help | Check for Updates from within Sketchpad and follow the instructions.
This week we’ve also unveiled some new features in Sketch Exchange, our community site for sharing Sketchpad resources, hints, and tips. We’ve incorporated a Search box and the ability to find activities by selecting multiple topics from the Level and Topic choices. As always, you can use the Tag cloud to browse serendipitously. And now you can also select a user name to see all of the resources posted by your favorite Sketchpad rock star.
But I think my favorite new feature is—well, “My Favorites”! When you find a resource that you love and want to find easily again, click its heart to add it to your Favorites collection. And when you click on the My Favorites tab, you’ll see that you can create an Exchange Key. Once you create and activate your Exchange Key, you can access all the sketches in your Favorites collection directly from Sketchpad. First though, you’ll need to download Sketchpad Version 5.05, a free upgrade for registered Sketchpad 5 users.
You can browse and download resources even if you don’t have an account. But if you want to upload resources, and create a Favorites collection and an Exchange Key, then you’ll need to register for a free account at Key Online. Here’s a short video that shows some of the features of Sketch Exchange:
I was at the Conference for Advancing Mathematics Teaching (CAMT) in Houston, TX last week. I was there to present on Friday, but also there to attend some sessions, go to the exhibits, and see my friend Lisa Hall who flew in from Richmond, VA to speak. The conference was great – saw my friends Jimmy and Joslyn from Mus1cnotes at the exhibits, who seemed to be having some big-Texas success with their rap math videos. I went to some terrific sessions on Sketchpad, math games, and research on dynamic geometry with technology (stay tuned for a later post on that!). All in all, a good time.
Like other enthusiasts of mathematics, I’m captivated by the way that mathematical ideas can explain things in the physical world around me, and by the way that I can carry out mathematical thought experiments in my mind and then apply the results to control my external physical environment.
But it turns out that my separation of the two elements here—the internal activity of mathematical thinking and the external sensory-motor activity of perceiving and acting upon things in the outside world—is a bit naïve. Findings from cognitive science raise questions about the dichotomy and suggest ways in which thinking is inseparably integrated into our senses and our movements. As humans we think not only with our brains, but also with our hands, our voices, our eyes, ears, touch, and smell.
For me, this was one of the main themes of the ICME conference that I began to describe in my last blog post. At the Congress, Luis Radford from Laurentian University was presented with the organization’s Freudenthal Award. In his award lecture (download), he discussed students’ early algebraic thinking, and described a “theory of teaching and learning … that emphasizes the sensible, embodied, social, and material dimension of human thinking.” His description of thinking as having an embodied and material dimension, and the examples he gave from his work with students, help to clarify the idea that thinking integrates both mental and physical aspects, and as educators we can do a better job by paying close attention to the physical aspects of student thinking.
I had the immense good fortune this year to attend ICME, the International Congress on Mathematical Education. The Congress is held every year divisible by 4, and this iteration (the twelfth) was held in Seoul, Korea. It is quite something to be at a meeting of nearly 4000 mathematics educators from 84 different countries, and to have a chance to make new friends and renew contacts with old friends in the process of exploring commonalities, issues, and differences about our shared work.
Traveling from Philadelphia to Seoul, I changed planes in San Francisco. Noticing that the person sitting opposite me could easily have been a mathematics educator, I introduced myself, and found that I was sitting next to Alan Schoenfeld, two of whose articles I assign each year for my methods class at Penn. Alan’s a superstar in mathematics education, and is the most recent recipient of the Klein award from ICME (presented just two days after I met him, during the opening ceremony). He’s also a very nice guy.
The conference was to begin on Sunday, July 8, and I made a point of arriving on Saturday in order to ease my adjustment to the time change; Seoul time differs from Philadelphia time by 11 hours. I had been in contact with my up-till-now virtual friend Nate Burchell; we had corresponded but never met in person. Nate used to teach in India, and is now at an international school in Seoul. Nate and his wife Joie very kindly invited me to dinner the evening of my arrival.
Ms. Walter, my junior high math teacher, sure knew how to get my attention on the first day of class. She told us we would be studying all about sex. Well no, let me restate: She said we’d learn about sets, but my seventh-grade ears heard otherwise. It didn’t take long for my confusion to clear, and, needless to say, I was disappointed.
My junior high experience aside, I think sets generally get a bad rap in elementary mathematics. Proposing that young learners study sets invariably raises the specter of the New Math movement’s misguided emphasis on set theory in the 1960s.
I propose giving sets a fresh look by considering a new Sketchpad model that I designed as part of the Dynamic Number project. Start by downloading the Set Puzzles activity. Below is a sample puzzle.
We were so impressed by Jamila Riser’s talk at NCSM a couple of years ago that we asked her to present an Ignite! for us this year. Now, we’ve asked her to guest blog so we can share even more about the amazing work she’s doing in Delaware. Jamila is the Director of the Delaware Mathematics Coalition and one of the leaders in her state who is driving change through P-Cubed (Powerful Pedagogical Practices).
P-Cubed Teachers Hard at Work (and Play)
The Delaware Mathematics Coalition and its higher education partner at the University of Delaware were fortunate to have one of the lead architects for the Common Core State Mathematics Standards, Bill McCallum, at our recent summer professional development institute.
McCallum led participants of the Coalition’s Toward A New Normal in High School Mathematics Institute in a discussion of the meaning and use of the Common CoreStateStandards. “We teach mathematics, not individual standards,” shared McCallum.
Today I get to introduce you to our next guest blogger, Andy Martinson, which seems appropriate given that we not only share the same initials, but significant chunks of both our first and last names!
In any case, Andy is a high school teacher and technology coach from White Bear Lake in Minnesota. He is also a Sketchpad and Fathom user, as well as one of our online course moderators.
Social networking, blogging, interactive whiteboards, going paperless, student response devices, cloud-based computing, netbooks, apps, yadda-yadda-yadda. These terms and phrases have been rattling in my skull this year as I took on the role of one of our high school technology coaches. The one topic on the front of my brain since December has been the Flipped Classroom. My working definition for a flipped classroom is one that sends all students home to watch videos and interact online. They are doing something more than traditional homework—watching videos, reading articles, listening to lectures. When they arrive the next day, they have already watched the base lecture or video, and the teacher can go deeper and expose students to richer content normally shoved aside due to time constraints (since the base lesson was the entire lesson in a non-flipped class). Sounds like a pretty good plan!
As part of our guest blog series, we bring you a post from Kathryn Shafer. A former middle school and high school math teacher, Kathy is now an Assistant Professor in the Department of Mathematical Sciences at Ball State University, Indiana. She’s done a variety of work for Key, including presenting webinars, moderating online courses, and delivering face-to-face professional development workshops.
This summer, the teachers in my probability and statistics course used TinkerPlots to complete an exercise on the Law of Large Numbers. An engaging discussion took place, as a few of the teachers wanted to discuss their interpretations of graphs, and others extended the problem beyond what was required. The resulting discussion focused on simulation models and multiple representations, hitting the mark with regard to the Mathematical Practices.
A coin flip experiment can be modeled used the Sampler Engine in TinkerPlots. Set the Sampler options to capture the running percent of heads. The Spinner device can be used to simulate a fair coin. The spinner shown at right will simulate flipping a fair coin 50 times.
Ken Gordon has written our first in a series of guest blog posts from people working with Key Curriculum products in schools. Ken teaches Precalculus and Calculus in an accelerated program at Sisler High School in Winnipeg, Manitoba, Canada. He has been using The Geometer’s Sketchpad since first seeing it at an NCTM conference in 2004. Ken is also a consultant for Key Curriculum and moderates online courses with The Geometer’s Sketchpad.
One of the major hurdles for most teachers when they are trying to incorporate more technology into their courses can be the availability of computers or computer labs. This is something that we have struggled with at Sisler High School for many years. In 2008, new mathematics curriculums were introduced at all Western Canadian schools, beginning with K–8. Grade nine was added in 2009, ten in 2010, eleven this past year, and the new twelve will begin this fall. At Sisler, we have viewed this as an opportunity to try and incorporate more technology into the courses as we are implementing these new curriculums. Last year, we were quite successful in adding many labs and demonstrations involving The Geometer’s Sketchpad (GSP) to the new grade ten “Introduction to Applied and Pre-Calculus Math” course.