Wednesday, January 30, 2008

Dilemmas of Discourse-Oriented Teaching in One Middle School Mathematics Classroom

http://0-search.ebscohost.com.library.winthrop.edu/login.aspx?direct=true&db=aph&AN=9702073598&site=ehost-live
This article illustrates the use of discourse-oriented teaching through a single case study. This reform creates a shift "from a view of the teacher as dispenser of knowledge to a view of teacher as facilitator of knowledge production." This practice, as described, is vaguely reminiscent of the Socratic Method, in which parties involved ask questions and are encouraged to use reason to arrive at answers or hypotheses that can either be proven or contradicted. The first dilemma that this article discusses arises from the fact that the teacher must facilitate true knowledge. Thus it is the teacher's responsibility to guide or lead the discourse, which can easily revert to a dispensation of knowledge. "The pupil's task is to come up with the correct solutions to problems seemingly spontaneously, while all the time trying to discern in the teacher's clues, cues, questions and presuppositions what that required solution actually is." The point is made that students may not completely grasp the required mathematical understanding simply by watching another person work out the problem. Rather, they must ask questions to understand the process, and in order to show understanding of the process, they must be able to explain it in their own words to someone else.

How does this case study fit in with Tyack and Cuban's perspective on reform? Most aspects of this particular classroom fit very well with T & C's Grammar of School. The class is self-contained, concentrates on one subject (mathematics), lasts for a set period of time, incorporates familiar manipulatives, and involves group work. The most notable deviations from this grammar lie in the fact that the teacher elicits mathematical concepts from her students rather than dispensing them and that there are no textbooks. The students were not shown how to work problems nor were they given example problems. While the mathematics class involved in this case study seemed to perform (in class) at least as well as in a traditional setting, I would have difficulty as a student without the retention of a textbook (or really thorough class notes) to aid my learning. As we have discussed in class, no school reform can possibly result in a utopia of perfect learning. The authors of this article end on a similar sentiment, "We have concluded that there is something going on inside the minds of students and realized that students learn only information that is meaningful to them. Thus, students must be involved in a fundamental way with their own education."

2 comments:

NakiaPope said...

This is an excellent post. It briefly but adequately summarizes the article, places it in the context of our course discussion, and does both in a clear and well-written manner.

Do the children get to take notes? You made a brief comment about that in the summary, but not allowing the children to write anything down (even their own observations about what's happening) seems a bit odd.

Kristan and Michael McKelvey said...

It does not explictly say whether or not they are "allowed" to take notes. However, from my understanding of the reading, there is not much to take notes on in the traditional sense (meaning teacher lectures, example problems worked out, etc.) Students may possibly have journals where they record what they have learned or their thoughts on the day's discussion, but most of the learning seems to take place not by recording or referring to notes. Instead, discussion and interaction with manipulatives such as 'mats' that represent an area of measurement is the main focus. The teacher sometimes asks probing questions to help steer individuals in the right direction, but does not provide much academic scaffolding to the class as a whole.