If you feel like watching mathematics learning in progress, check out the classroom videos at the Inside Mathematics website. But don’t stop there; inspiration can also be found from the interviews with principals and the “coaching conversations.” I’ll be spending a lot more time watching these videos in the near future.
The website is from the Silicon Valley Mathematics Initiative, a project of the Noyce Foundation, which “was created by the Noyce family in 1990 to honor the memory and legacy of Dr. Robert N. Noyce, co-founder of Intel and inventor of the integrated circuit which fueled the personal computer revolution and gave Silicon Valley its name.” The participating schools are from a bunch of districts in the Bay area, including the Berkeley Unified School District, where my sons attended school in 2000 – 2001. The younger boys were in fourth grade at Leconte Elementary School, and I noticed that there were a couple of bilingual classes in the earlier grades. At the time, I wondered what math instruction in such a classroom might look like. Now I know — check out this video (clip 2, Number Talk).
There’s a Mathematics Teaching Rubric available for download on the “Tools for Coaches” page. Under “Teacher’s Role in Discourse,” the rubric’s description of “Exemplary Teaching” includes this (page 3):
The teacher listens carefully to the students’ ideas and discerns mathematical reasoning and relevancy from student responses. Students are asked to clarify and justify their ideas orally and in writing. The teacher decides what to pursue in depth from among the ideas that students bring up during a discussion.
Remember that joke about how Ginger Rogers did everything Fred Astaire did except backwards and in high heels? Well, Katie Arrillaga of Ruus Elementary School in Haward does everything any exemplary teacher does, except in two languages at once. My favorite part is near the end at around 8:45, where she asks “¿Donde está el diez y seis?” (“Where is the 16?”), and then asks the student to be specific. Once she gets the clarity she wants, another student, referring to the “carried” 1, calls out “Pero no es uno, es diez” (“But it’s not one, it’s ten”). Perfecto.