Math and Reading Workshop

Last week I had the opportunity to help lead a professional development workshop on the topic of Math and Reading for middle school and secondary level teachers in the Ithaca City School District. I was invited by my friend and neighbor Dani Novak, a math professor at Ithaca College who is dedicated to bringing the joy of math to everyone, as well as working to eliminate the fear and anxiety that riddle so many math classrooms (www.ithaca.edu/dani/).

There were eight teachers who participated in the workshop. All were extremely interesting. Five were from DeWitt Middle School, and most of these did not know that the others had registered. Propitiously, I suppose, the final report of the National Mathematics Advisory Panel was released the day before the workshop (www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf). I haven’t had time to read the document carefully, but at first glance it seems very sensible, pointing to the critical importance of algebra instruction, and looking at how to focus elementary and middle school instruction to better prepare students for algebra. (A key lack now seems to be instruction in fractions.)

In preparing for the workshop I read a book called The Number Sense by Stanislas Dehaene. The book was written in 1999, but there was just a New Yorker profile about Dehaene this month, and the parent of one of my students alerted me to it. Dehaene argues that humans have a hard-wired number sense, observable in the behavior of human babies as well as in other mammals, and that a great deal of the problems children have with math instruction is because the instruction usually fails to build sensibly upon these sets of inborn mathematical intuitions.

There is much to ponder here. One of the questions I raised with the group was the difference between understanding a nonsensical and a “sensical” sentence: “The morphius is under the zinderfloss,” v. “The cat is under the table.” At first the teachers wanted to say that they didn’t understand the first sentence at all, and yet, they could all correctly answer the question “Where is the morphius?” As we discussed the matter further, the key difference appeared to be that they could make a mental image of the second, but not the first, even though they understood some purely formal, grammatical relationships expressed in both sentences. The interesting question that thus emerges with regard to comprehension of mathematics (and, indeed, of comprehension generally) is the role of mental representation. I’ll share some more of this discussion in my next post.

The teacher’s themselves came with some excellent questions, including:

• what are good ways to teach mathematical vocabulary
• how can we best help students who don’t read thoroughly and completely
• what are the underlying brain activities that are related to math
• how can we get students motivated about math
• is it wrong to give middle school students a printed multiplication table when doing their work
• what are cultural differences that influence student performance

I’ll try to discuss all of these topics as well in future posts.