Discussion: Keynote Part 1

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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 4-8 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
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?
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