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Last night, I received the following response to my previous blog entry, Finger Multiplication, the Lattice Method, and At-Risk Students: Dear Jerry, I cannot find en e-mail address to Michael Paul Goldenberg, but I would like to share the following with him in response to his mail via you. In the 1980s I was approached by a mathematics teacher who taught adults early mathematics. In his class he had a group of gypsies and they had taught him how they multiply numbers between 5 and 9 with the fingers. The teacher could not figure out why it worked and wanted me to explain it, so I did. Later I gave this task to my secondary students to solve, and I see it as a good modeling task and exercise in use of algebra for them. I have published the task in a book in 1989 called The Challenge - Problems and Mind-Nuts in Mathematics (in Swedish) and attach here the one page of that book translated into English of the task I call Handy multiplication (fingerfärdig matematik in Swedish). This see

I have begun, quite informally, an unusual collaboration with a friend who is in her first year teaching mathematics to at-risk students in Saginaw, MI. (This is not her first year as a teacher, however, as she has prior experience teaching theater in public schools). I will be posting in more detail about some of what we're doing and how it's working out for her and her students in another entry quite soon, but I wanted to look at a specific method for finding the product of two single-digit numbers from 5 to 9 that she showed me recently. The context of this method is that I had shown her how to do lattice multiplication with multidigit numbers, but she realized that many of her students were weak with the necessary single-digit multiplications that are needed to complete the lattice and hence would not clearly benefit from the lattice approach (nor from any other, since it's rather difficult to do multiplication of larger numbers by hand if you don't know the tables

"Stay away from that unproven experimental stuff. Much better to stick with the Moving The Furniture Until He Gets Better approach." Gregory House, MD. The on-going debate about content, pedagogy, and pedagogical content knowledge as they pertain to mathematics teaching and the education/ training of future mathematics teachers continues to produce more heat than light in venues where one side continues to insist that we need to focus on mathematics content only, that questions of pedagogy are closed (" One way to rule them all, One way to mind them, One way to bring them all and in the darkness bind them : direct instruction !), that pedagogical content knowledge isn't worth discussing, and that in fact all questions of mathematics teaching and learning are closed (or at least that there are no open ones on the table). Contrast that attitude with what is likely to be gleaned from the following presentation, which I plan to attend tomorrow: ========= Systemic school

It appears that folks at Blogged.com have rated a bunch of math blogs, (83, to be precise) and placed mine in the top 15 (tied for 12th place), with rating 8.3 (out of 10). They evaluate blogs based on the following criteria: Frequency of Updates, Relevance of Content, Site Design, and Writing Style. Clearly, I need to update more frequently, but otherwise I guess I'm doing okay in my first year of blogging. :) Nice to get the feedback from what appears to be an apolitical source. So here is a list of mathematics blogs , rated in a scale 0-10. If you're a math blogger, go find yours. If you're a reader of such blogs, here's a chance to find some of the best you might not know of yet.