This paper attempts to create a vision of what it would be like to teach for understanding, to adopt the view of learner as constructor of his or her own understanding, and to share in the creation of an environment for reconstructing students' understanding and reasoning. Such a program is based on assumptions about the cognition of learners, aspects of curriculum, teaching strategies, and assessment consistent with these assumptions. The paper begins with a fictional story based on reform in science classroom teaching. Statements and questions provided by students are consistent with actual statements made by students as they attempted to negotiate meaning from their experiences in and out of the classroom. The vignette provides a vision of what it might look like when focus is on teaching for understanding, on helping students reconstruct their understanding and reasoning from prior ideas and experiences and from new experiences directly related to their initial ideas. Teachers who have incorporated ideas discussed in this paper have found significant change in their students' understanding and reasoning; the teachers themselves have felt revitalized with regard to their own teaching and learning. Some concerns expressed include resistance of students who believe that teachers should be imparters of information and demonstrators. Also, even when the approach is perceived as valid, it can be difficult to implement if a teacher is working alone. The conclusion is that the benefits far outweigh the costs. A discussion of the benefits and concerns derived from the teaching for understanding perspective completes the document. (LL)