Monday, December 21, 2009

Favorite comments of '09: bky on invented algorithms

Re: Math problems of the week: 6th grade Connected Math vs. Singapore Math, bky writes:

When the curriculum has students invent algorithms for basic mathematical operations, to me the message is this: none of this really matters -- that's why we're letting 10-year olds make the decisions.

What if you teach them how to add fractions and build it up by: (1) giving a good foundation of what a/b means (b partitions of [0,1], count up a of them), (2) using that foundation to show, very common sensibly at this point, how to add fractions with like denominators, then (3) give a good foundation for understanding equivalent representation of fractions (e.g. why 2/3 = 4/6), and then (4) very naturally lead to the general algorithm for adding fractions with different denominators ...? (that sentence started out as a question) Then the message is that adding fractions is so important (and the students are so important) that we want the kids to really be able to do it and understand how it works.