Since 1990, schools all over the U.S. have taken to teaching math in a "new" way. They called it "reform" math. Others called it "fuzzy" math. Much of the education community still believes in this methodology. Many parents don't.
Here is a basic list of the differences in teaching methods. This list is not meant to compare the actual effectiveness of the teaching methods.
Reform/New/Fuzzy Math
Many math topics covered at once (the day's work may cover geometry, substraction, multiplication and statistics)with too many topics overall that are covered superficially
Discovery based learning (teacher doesn't show how to do the work, students discover it themselves)
Application problems first so student can extrapolate math concepts
Standard Algorithms (like vertical addition and carrying) not taught, only more conceptual methods
Emphasis on conceptual understanding
Emphasis on explaining your work, showing how you thought about the problem
No emphasis on getting the correct answer
Group work, collaboration with other students
Spend a lot of time on one problem using hands on materials
Language oriented
No expectation of memorization of multiplication tables
No mastery of long division or multi-digit multiplication because calculators can do it
Traditional Math
One topic at a time till mastery
Fewer Topics
Teacher directed learning
Application problems shown after abstract math for students to apply their learning
Standard algorithms taught
Efficient methods taught
Emphasis on the correct answer
Individual work
Worksheets where many math problems are answered
Math oriented, not language oriented
Expectation of memorization of multiplication tables and basic math facts
Expectation of mastery of long division and multiplication by hand
