The purpose of this study was to determine the nature of the supervisory functions that both teachers and principals of "open space" elementary schools in the Edmonton Public School System consider desirable in order to improve classroom instruction. A 77-item questionnaire was sent to the principals as well as to the 4th, 5th, and 6th grade teachers under their supervision to elicit their opinions and observations. As a result, the author makes several recommendations for improved supervision, which principals and teachers in all schools might consider. For example, he feels that staff members should focus on cooperation, involvement, collaboration, and communication in their daily interaction; that principals should give teachers more responsibility and authority for making decisions which directly affect teaching and learning; the threat of classroom visitations as a supervisory technique should be removed; demonstration teaching should be considered as a useful technique; and that principals should help teachers achieve a sense of worth and dignity in their work. (Author/Editors)