The results of a second operation for tumor removal in 24 adult patients with supratentorial glioblastoma multiforme or anaplastic astrocytoma were analyzed. The median survival time after reoperation was 14 weeks. Five of the 24 patients lived 6 months or longer after reoperation. Only three of these patients maintained a Karnofsky rating (KR) of at least 60 for 6 months or longer after reoperation. Preoperative neurological status (KR) is the most significant determinant of survival after reoperation (p = 0.02). When the KR is at least 60, median survival after reoperation is 22 weeks. When the KR prior to reoperation is less than 60, median survival is 9 weeks. Only one of 13 patients with a KR of less than 60 prior to reoperation survived longer than 6 months after the second operation. The interval between first and second operation is significantly related to survival (p = 0.03), but when adjustment is made for the KR the interoperative interval is no longer significantly related to survival after the second operation (p = 0.39). Age, sex, and location of tumor were not significantly related to duration of survival. This study suggests that reoperation is most likely to produce the best result when the KR is at least 60 and the interval between operations is longer than 6 months. Using these criteria, one-third of the patients could be expected to survive with a KR of at least 60 for 6 months. The study indicates that reoperation should not be carried out when the KR is less than 60.

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Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self‐identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.