Teaching Math


Guiding principles in teaching math:
  • This is important
  • You can do it!
  • I won't give up on you.

:) Relax, Math can be fun!

Math as a human product, an extension of how humans think, using sense.
Goal: to foster a deep understanding of mathematical concepts in children.
Work on math pedagogy. Teaching math, but focusing on how you are teaching.
Class will utilize doing math as observing how we learn to gain insight into how children learn.

Principles and Standards for School Mathematics (c. 2000, National Council for Teachers of Mathematics)
Curriculum Focal Points (NCTM) says what you should be teaching at every grade level

Standard 6: Problem solving, Baserer's "Toolbox"
  • Be aware of your own "toolbox"

Floor function: |_ _| meaning the greatest whole number equal to or less than
Ceiling function: the opposite, the least whole number equal to or greater than...

Class Notes 6/30

  • Prime numbers, has two distinct divisors of 1 and itself
  • 1 is not a prime number, because if it were considered a prime, it would present an infinite number of prime factors
  • Marsenne Prime = 2 to a power, minus 1 (but not in every case)

Class Notes 7/2
Natural numbers are the counting numbers, 1, 2, 3, 4, 5...
Four main operations in elementary school mathematics
  • operations have more meanings than one simple meaning
  • these meanings are often connected
  • there are many algorithms ("borrowing" e.g.)
  • knowledge of base ten is important to understand these algorithms

Addition:
Teacher talk: if you add 3 ones and 8 ones, you get 11 ones. You want to compose 1 ten from that, with 1 left over

Class Notes 7/16
Whole numbers, fractions and particular aspects of geometry and measurements are the Critical Foundations of Algebra

By end of Grade 4: identify fractions and decimals

Rational number: a number that can be expressed as the ratio or quotient of two integers, a and b represented as a/b where b is not 0
Fraction: a number that can be expressed as the quotient or ration of any two numbers, a and b, represented as a/b, where b is not 0

Class Notes 7/21
Objectives of teaching math:
to expand participants' comfort zones with mathematics content
to broaden participants' conceptions of mathematics teaching and learning in the elementary grades
to increase ... there's more.