The relationship between expert teachers' classroom behavior and their subject matter knowledge has not been examined extensively. To begin such an examination, one topic, fraction knowledge, was explored in depth as it occurred in natural teaching settings. Fractions are one of the more difficult topics in elementary arithmetic; much of this difficulty is attributable to the complex relationships among the meanings and representations of fractions and basic arithmetic operations. Despite these difficulties, many teachers are quite proficient at teaching children to perform operations with fractions. We examined expert teachers' knowledge by using extensive protocols to investigate the content and organization of teachers' knowledge of fractions. These protocols involved interviews, card-sorting tasks, and transcriptions of videotaped lessons. Semantic nets that reflected their knowledge of fractions were developed for individual teachers. Comparisons of these semantic nets showed wide variations among the knowledge of expert teachers. Some teachers displayed relatively rich conceptual knowledge of fractions, although others relied on precise knowledge of algorithms. Implications of these knowledge differences are discussed.This article explores the organization and content of subject matter knowledge of expert arithmetic teachers. Teaching is a cognitive skill and, as such, is amenable to analysis in ways similar to other cognitive skills (Leinhardt & Greeno, 1984). The expertise involved in the cognitive aspects of teaching can be seen as emerging from two core areas of knowledge: lesson structure and subject matter. Lesson structure knowledge includes the skills needed to plan and run a lesson smoothly, to pass easily from one segment to another, and to explain

This study examined memory for information that varies in typicality (relevance) to a central organizingschema. Subjects listened to scripted activities and were given recall and recognition tests after different retention intervals. Data supported a schema-pointer-plus-tag model that specifies how memory for scripted actions varies as a function of typicality, retention interval, and retrieval task. Several mathematical formulations of the model were tested in order to simulate the recall and recognition data. The model that best fit the data incorporated four properties. Fir-st, memory discrimination is initially better for atypical than for typical actions in both recall and recognition tasks. Second, recall involves conceptually driven retrieval, whereas recognition involves both conceptually driven and data-driven retrieval. Third, conceptually driven retrieval has an exponentially decreasing retention function, whereas there is a linear decrease in data-driven retrieval. Fourth, the retention function for conceptually driven retrieval is steeper for atypical than for typical actions, which supports the notion that the schema plays a more important role in guiding this type of retrieval as the retention interval increases; in contrast, the slopes of the retention functions for data-driven retrieval are the same for typical and atypical actions. A schema-pointer-plus-tag model was compared with some alternative schema-based memory models.In recent years, there has been increasing interest in developing models to explain the role of schemata in the acquisition, representation, and retrieval of information in memory (Bower, Black, & Turner, 1979;Cantor & Mischel, 1979;Graesser, Woll,Kowalski, & Smith, 1980;Hastie, 1980;Kintsch & van Dijk, 1978;Norman & Bobrow, 1979; Rumelhart & Ortony, 1977;Spiro, 1977;Taylor & Crocker, 1981; Thorndyke & HayesRoth, 1979). With regard to prose comprehension, most researchers agree that schemata are generic knowledge structures that interrelate statements in passages. For example, when individuals comprehend a passage about someone eating in a restaurant, they identify the generic restaurant schema. This schema provides a knowledge base that guides the interpretation of the text and generates inferences and expectations.With regard to the representation and retrieval of information in prose, there are several issues that a schema-based model might address. One issue pertains to the typicality of information with respect to a central organizing schema. It is rare that specific experiences are perfectly consistent with the generic schemata that This research was supported by Grant MH-33491 from the National Institute of Mental Health. We would like to thank John Black for his insightful comments on this manuscript. We would also like to thank Martin McMullen for his technical assistance on the figures and Springer-Verlag for granting permission to use Figure I and Table 1. Requests for reprints should be sent to Arthur C. Graesser, Department of Psychology, California State Univer...

SUMMARYMetabolic enzyme activities in red (RM) and white (WM) myotomal muscle and in the heart ventricle (HV) were compared in two lamnid sharks (shortfin mako and salmon shark), the common thresher shark and several other actively swimming shark species. The metabolic enzymes measured were citrate synthase(CS), an index of aerobic capacity, and lactate dehydrogenase (LDH), an index of anaerobic capacity. WM creatine phosphokinase (CPK) activity, an index of rapid ATP production during burst swimming, was also quantified. Enzyme activities in RM, WM and HV were similar in the two lamnid species. Interspecific comparisons of enzyme activities at a common reference temperature (20°C) show no significant differences in RM CS activity but higher CS activity in the WM and HV of the lamnid sharks compared with the other species. For the other enzymes, activities in lamnids overlapped with those of other shark species. Comparison of the HV spongy and compact myocardial layers in mako, salmon and thresher sharks reveals a significantly greater spongy CS activity in all three species but no differences in LDH activity. Adjustment of enzyme activities to in vivo RM and WM temperatures in the endothermic lamnids elevates CS and LDH in both tissues relative to the ectothermic sharks. Thus, through its enhancement of both RM and WM enzyme activity, endothermy may be an important determinant of energy supply for sustained and burst swimming in the lamnids. Although lamnid WM is differentially warmed as a result of RM endothermy, regional differences in WM CS and LDH activities and thermal sensitivities (Q10 values) were not found. The general pattern of the endothermic myotomal and ectothermic HV muscle metabolic enzyme activities in the endothermic lamnids relative to other active, ectothermic sharks parallels the general pattern demonstrated for the endothermic tunas relative to their ectothermic sister species. However, the activities of all enzymes measured are lower in lamnids than in tunas. Relative to lamnids, the presence of lower WM enzyme activities in the thresher shark (which is in the same order as the lamnids, has an RM morphology similar to that of the mako and salmon sharks and may be endothermic) suggests that other factors, such as behavior and swimming pattern, also affect shark myotomal organization and metabolic function.

No abstract

In 2006 I had the chance to design a physics course for students not majoring in scientific fields. I chose to shape the course around science fiction, not as a source for quantitative problems but as a means for conveying important physics concepts. I hoped that, by encountering these concepts in narratives, students with little or no science or math training might become more comfortable with them. I also thought the stories might provide the ideas with a context that would enable students to remember them more clearly than if they were reading a physics textbook.