posted by:

Royce Page
on May 15, 2003
at 8:43PM

subject:

Content Knowledge for teachers and planning PD

Several questions come to mind when I try to think of what content knowledge is appropriate in mathematics for elementary teachers. If we look at text books used at universities for math methods courses, then an inevitable question from the perspective Kindergarten teacher may be: why do I need to know how to construct a "box and whiskers plot," when this has nothing to do with Kindergartners? I was heard Liping Ma state that teachers in China knew much more about the mathematics they were supposed to teach at their grade levels then did US teachers. So, what specific math content should elementary teachers understand? Should each have a working knowledge of arithemetic? algebra? calculus? We had a state initiative in CA a few years back that sought to update the content knowledge of 48 teachers because the CA Math Standards now require 6th graders to be able to: "Explain the meaning of multiplication and division of positive fractions and perform the calculations," (Mathematics Framework for CA Public Schools Grade Six Math Content Satandards Number Sense 2.2), Solve addition, subtraction, mutipication, and division problems that use positive and negative integers," (NS 2.3); "Write and solve one step linear equations in one variable," (Algebra and Functions 1.1) along with about 60 other standards. We found that most upper elementary teachers were not able to perform the calculations involved with these standards let alone begin to have the knowledge of how to teach the concepts behind the calculations. And, while specific content sessions were designed to help teachers begin to use mathematics they hadn't used since high school, little carry over effect was seen in class rooms. I observed a 6th grade class recently where the teacher modeled to students why 3 + 6 = +3.
In one of our staff development institutes we gave teachers the task of writing a story problem to fit 1 3/4 divided by 1/2. Most did not even attempt to do so, and of those who did, only two out of 30 were able to write a problem that fit. So, I know I'm long winded here, but what is to be done? Isn't it reasonable to think that if a 6th grade CA tchr is required to teach students about division of fractions that he/she ought to be able to write a story problem to fit a division of fractions problem? Who trains teachers in such? How is this to be done? Should there be specific content competencies at each grade level that teachers should demonstrate before being allowed to teach mathematics at a paricular grade level? Shouldn't conceptual understanding have to be demonstrated as well? How do we best address these issues?

