Discovery Math and Teacher Training

As a new teacher and a parent, math has been on my mind quite a bit. In February of 2010, a Seattle judge ruled against a Seattle Public School District curriculum known as "Discovery Math".  The math program encouraged constructivist problem solving and group work as opposed to more traditional drill methods.  According to the ruling, the curriculum favored middle class students at the expense of lower income students, students of color, and ESL students (see: http://www.seattlepi.com/local/415049_math04.html).  Indeed, after the adoption of the program at Garfield High School, math scores among poor, minority and ESL students dropped dramatically. So what does this mean?



According to Kloosterman & Gainey (Students' Thinking: Middle Grades Mathematics), an approach like Discovery Math -- one based on student-led investigations -- will have a much more profound impact on students' understanding of mathematical concepts and their ability to solve problems.  Based on Information-Processing Theories of learning, this approach tries to optimize our understanding of how the brain works to store and retrieve information (short term and long term memory).  According to scientists, information stored in long-term memory is stored in an orderly fashion.  The order in which information is stored can vary from person to person and is based in part on experience.  Students will learn best (store information better) if what they are learning is related in some way to what they already know. Given that I only have Chapter 1 and the chapter does not contain a reference list, I am not sure what specific studies they are using from which to draw their conclusions.  I would like to see their references to be able to look at the evidence more carefully.

On the other hand, one question I have about the success (or lack of) of the Discovery Math program in Seattle is related to teacher training and experience.  For example, I can imagine with any curriculum, math or otherwise, it takes time for teachers to become familiar with the curriculum and make appropriate adaptations based on their student populations.  This seems like it would be particularly true in the case of a curriculum such as Discovery Math.  Additionally, on the surface, one might think that in such a program the teacher has very little responsibility --after all, the students are the ones doing all of the investigating and discovery, right?  However, from my perspective, this type of program would almost require more effort and expertise on the part of the teacher than a traditional drill and kill approach.  In a Discovery Math setting, a teacher would have to be facile enough with math to help facilitate the numerous ways in which students might approach a problem.  This would include being able to trace the path of a student's thinking and understand how that thinking works or does not work to solve the problem.  The way I was taught math -- there was usually only one "right" way to get to the answer.  That makes it much more straightforward:  either you did it that way or you didn't. Many teachers (myself included) were taught this way.  Teachers need practice and training to gain the skills to teach math in this more flexible environment and particularly, to ensure that we are able to reach struggling students.