>Dear Ms. Edwards:
Thanks for this note. I’d like to make a few comments about the link you attached. The math wars, like the whole language wars of the past decade, are based on a false dichotomy: traditional education v. progressive education. Good instruction focuses on the needs of the child – every child, one by one – and no one approach meets the needs of all children.
The math issue is interesting in that the battle seems to be pitched around algorithmic fluency v. conceptual understanding. They are not mutually exclusive. Both are essential for mathematical literacy. Students who learn algorithms procedurally without conceptual understanding aren’t truly fluent because although they are able to answer questions correctly on tests (when the questions are posed in the precise format the students are used to seeing), they often have difficulty knowing whether to (and how to) apply that algorithm to new and different situations. Teaching for conceptual understanding helps children develop efficient strategies for computing. Understanding the concept that underlies the algorithm helps students know how and when to apply it, helping them to become more proficient in solving new, differently presented problems and/or more complex problems.
Programs don’t teach children, teachers do. Good teachers vary their instruction – and their materials – based on student response.