Mathematics teachers from 3 school districts watched a 50-minute mathematics lesson video taped in Japan. Participants were asked to compare this lesson against the vision of improved practice promoted by the National Council of Teachers of Mathematics (NCTM). Use of the video as a concrete referent clarified participants' interpretations of ubiquitous catch phrases such as "learning facilitator,""mathematical connections," and "problem solving." Results suggest that many teachers: (1) are unfamiliar with lessons which juxtapose teacher centered and student centered instruction; (2) associate open-ended problem solving with group work, but not with making mathematical connections; (3) link use of technology (calculators) with a reduction in numerical competence; and (4) interpret their new role as a "facilitator" in ways which limit the use of directive practices they believe to be valuable. Practical barriers to the implementation of perceived NCTM recommendations were a common concern. These barriers revolved around lack of motivation, self discipline, and computational proficiency on the part of students. (Contains 10 references.) (Author/ASK)