The Discovering Mathematics series (part 1)
How would you describe the philosophy behind the books?
Jim Ryan: Rather than going from a traditional book where a teacher explains the abstract and then the students practice that abstract concept, and then eventually they get to an application — which are generally called the word problems — we've turned that around for each lesson. The lessons are approached so we can try and answer that question "When will I ever use that?" before it ever gets asked. And so students see the meaningfulness of the math as the lesson is being presented to them.
Karen Coe: When we meet teachers, the way they characterize our books is we teach for understanding, or we explain the "why" behind the "what."
Can you give us an example?
Ryan: When students learn linear equations, we start off with the students gathering data, or figuring out data, so the first thing is they will put data into a numerical table, and then they'll graph that data in an x-y graph and fit a line to that data. Then they solve for the equation for that line. In the traditional materials, we present every student with the equation y = mx + b and then you give it meaning after they've seen that. So, you ask them to memorize that and then you try and give it meaning afterward.
Sounds like you're trying to lead students to an "aha" moment rather than having them memorize formulas.
Coe: That is a perfect way of describing it.
One of the criticisms of Discovering is that its investigations take too long, and that can turn off students who are good at math.
Coe: It's not our experience. And every time we work with schools on implementation plans, we work on pacing guides (materials that help teachers plan lessons), and it's simply not possible in a book for every investigation to be done in a year.
Another criticism, from students and parents, is that what's missing from Discovering is direct instruction, or very specific examples of how to do a math problem.
(read the whole article here)