Wednesday, October 12, 2011
Sunday, April 17, 2011
I really enjoyed Bill Jasper’s session on Concept and Vocabulary Acquisition. Though the importance of enabling ELL students was a thread through his presentation, he didn’t include this in his title, because his theme was that the same techniques that are useful for ELL students actually bring significant benefit to all students. He made a very good case for this position, with lots of examples, pages of basic principles and specific suggestions, and even manipulatives that he passed out to the audience. The emphasis on manipulatives was important to his theme of acquiring vocabulary and concepts because students’ use of manipulatives gives them concrete experiences to write and reflect about in the process of developing conceptual understanding.
I particularly liked his story about Ramon. At the end of his first day of summer school (after failing math), his math teacher asked the class to write about what they had learned that day. He told her “I don’t write English.” She encouraged him, he repeated that he didn’t write English, so she told him to write in Spanish. He was still reluctant, but she persisted until he had written several sentences in Spanish. She then told him to translate his sentences into English. After several iterations of Ramon’s reluctance and the teacher’s encouragement, she managed to get him to write down the English translations of as many of the Spanish words as he could. This continued, day after day, until Ramon realized that he was doing twice the work of the other students at the end of each class, and decided just to write the English translations. By the end of summer school, he not only passed the math course, but his teacher’s refusal to let him off the hook resulted in a huge leap in his skills in writing English.
Near the end of Bill’s presentation, he showed some Sketchpad projects several of his students had done in their geometry classes, and it was delightful to see how he’d used these projects to get them to write in detail, right next to each construction, the mathematical observations that they had made from these constructions and their reflections about the construction and about the mathematics.
Bill also encouraged his audience to join Todos (www.todos-math.org), the NCTM affiliate that works on issues related to equity for all students, with a special emphasis on Hispanic/Latino students.
Having spent the last twenty years of my career working on The Geometer’s Sketchpad, it would be inappropriate for me to comment on the substance of Jeff Hall’s presentation comparing Sketchpad and GeoGebra. But I will say that I came out of the session reflecting on two related issues that I consider much more important than a feature-by-feature comparison.
- How do we bring the benefits of general-purpose interactive mathematics tools into as many classrooms as possible? Even when computers are readily available, it’s a challenge for many teachers to adopt the technology. How can others who see the value (whether fellow teachers, department chairs, or supervisors) support those who are reluctant, convince them that the use of such software is not an optional enrichment activity, but is essential to developing students’ mathematical reasoning? What features of the software itself help or hinder this effort?
- Related, how can we use such tools most effectively in developing students’ reasoning and sense-making, and how can we encourage students to incorporate the tools into their own mathematical repertoire, to turn to the tools on their own when they want to investigate a mathematical question? How can we best use them to stimulate students’ curiosity and to encourage them to write about and reflect upon the math?
Jeff’s session wasn’t designed to address either of these questions directly; I’m raising a different issue than the one he undertook.
But I do think these are the most important issues, and at the same time more difficult to address. Nobody has the answers, but I would certainly love to attend a session next year presented by someone with experience acting as a change agent, describing both successes and difficulties in related to these related issues. How can we best encourage reluctant teachers to use such tools and to use them most effectively in developing students’ reasoning and sense making? Any takers?
Thursday, April 14, 2011
She modestly acknowledges that she has studied more math than most artists (BS Mathematics, Yale University, summa cum laude.) Her further education shows that she has also studied more art than most mathematicians -- a stone carving workshop in Italy, study at the New York Studio School for Drawing, Painting and Sculpture, and an MFA in Sculpture from the University of Pennsylvania.
Her list of past exhibitions traces a path across the country, around the world, and through venues and themes that sound like technical science fiction. It’s a journal of the artist’s twists and turns of curiosity, research, and resolution.
Visit www.bathsheba.com and you will find a richness and diversity of content that is not often seen on an artist’s website. Or a manufacturer’s website. Or an art gallery’s website. Explore thoroughly. The site features not only sculpture, jewelry, laser-etched glass, and hardware, but also very clear descriptions of the technical processes she uses: 3-D Printing (now that’s right out of Star Trek) and Laser Etching in Glass.
This promises to be a Closing Session and speaker worth hanging around for. You will leave our Annual Meeting with stimulating images floating in your head and a wonderful sense of “What if …?”
Saturday, April 16, 12:30-1:30 p.m.
Be there or be a Borromean Ring.
Research Presession 132: Research on Technology in Mathematics Education: Current Efforts and Future Directions
Steve Hegedus set the stage by using a beautifully composed slide show speculating about how technological change affects what his son (now 6) should learn in school, through the lens of what skills and qualities might be needed for his son to live a successful and satisfying life between now and his retirement in about 2070.
Nathalie Sinclair followed up with a presentation that involved classroom video to emphasize how teachers can use dynamic mathematics software to stimulate student conjecturing and to present students with cognitive opportunities not available using other media.
John Olive finished with a video interview of students exploring “scooting tick marks” (from the Dynamic Number project) to deepen their understanding of fractions, illustrating how a sketch initially used for one specific task becomes a generally useful tool for the student.
My overall takeaway from the session was that it brought home (a) the enormous potential that educational technology has to change what and how we teach, (b) the importance of research to help us figure out when and how to use technology effectively, and (c) the urgency to do so both wisely and quickly at a time when technology is rapidly changing both the world outside our classrooms and the future in which our students will live.
(Full disclosure: Professors Sinclair and Olive used Sketchpad for their work with students, and Prof. Olive is the evaluator for the Dynamic Number NSF project.)
(Shameless plug: I will be showing our Geometric Functions work from the Dynamic Number project in session 373 on Friday morning. Many Dynamic Number activities are freely available at www.kcptech.com/dynamicnumber.)