Schifter, D. (1996). A constructivist perspective on teaching and learning mathematics. In C.T. Fosnot (ed.), Constructivism: Theory, perspectives, and practice (73-91). New York, NY: Teachers College Press.

Summary of Schifter article:

She first introduces two teachers, comparing their different styles of teaching. Hendry practices a constructionist approach, and has her students learn about measurement by figuring out how big the outline of a ship drawn on the floor is. Through her questioning, the children generate their own ideas about the rules of measurement and the need for a standard measuring device. Schweitzer, on the other hand, taught her students about measuring through a lecture approach, in which she gave them the information she felt necessary. Believing that students would gain more from a constructivist approach, however, she decided to change her style of teaching.

As Schweitzer quickly learned, there is no single way to teach a constructivist classroom. The most important idea is to be open to the students' suggestions, and question how they reached their conclusions. Letting them think problems through for themselves, and bouncing ideas off of each other is an important part of the learning process, and helps them to better understand and retain concepts. Constructivist teaching could be frustrating and is a continual learning experience for the teacher, but the emphasis should be on the teacher's awareness of the students' thoughts, rather than on the final outcome.

Some questions and thoughts on the paper:

There were a few questions raised by this approach:

1. How long should a teacher wait while students wander down different paths in search of a solution?

   There are certain concepts a child must grasp by the end of certain grades; how can you ensure that they get through that material? How much structure should you provide?

2. Unlike the previous article, this approach takes problems as a whole, rather than breaking them down into subgoals that must be accomplished. Which approach is more effective?

3. We have talked about the role of individuals in the classroom before; how can you know if individual students are learning if the constant emphasis is on groupwork? What about those that never talk?

4. What if the pace of the students is very different (i.e. some ahead, and some behind)? How do you work with such a diverse class?

5. Finally, how would you assess if such a classroom is successful? If you use a standardized test, that places the emphasis on tests again - which is something the constructivists want to get away from. But this is how we measure students' abilities... so how do we reconcile the two? Or does something need to be changed?