In two dimensions (2D), representations associated with slopes are seen in numerous forms before representations associated with derivatives are presented. These include the slope between two points and the constant slope of a linear function of a single variable. In almost all multivariable calculus textbooks, however, the first discussion of slopes in three dimensions (3D) is seen with the introduction of partial derivatives. The nature of the discussions indicates that authors seem to assume that students are able to naturally extend the concept of a 2D slope to 3D and correspondingly it is not necessary to explicitly present slopes in 3D. This article presents results comparing students that do not explicitly discuss slopes in 3D with students that explicitly discuss slopes in 3D as a precursor to discussing derivatives in 3D. The results indicate that students may, in fact, have significant difficulty extending the concept of a 2D slope to a 3D slope. And that the explicit presentation of slopes in 3D as a precursor to the presentation of derivatives in 3D may significantly improve student comprehension of topics of differentiation in multivariable calculus.
This study examines key school reform policies and outcomes of the USA and Korea over the past three decades from comparative perspectives. Since the two nations’ unique educational problems brought divergent educational reform paths—standardization versus differentiation, high-stakes testing versus individualized assessment, and centralization versus decentralization—the study tracks international policy benchmarking efforts and potential impact on educational convergence. The study employs mixed methods, including the content analysis of research and media documents and the trend analysis of TIMSS and PISA datasets. The results indicate that, despite significant changes in policy discourse, the gaps between Korea and the USA in student math achievement and school climates did not narrow. The policy lessons from these cases and the issues of international education benchmarking are discussed. 相似文献
State and Local governments must develop an overarching legal foundation to manage critical service delivery in an electronic environment. Prior to establishing a foundation, decision-makers must first adopt a philosophy that focuses and harnesses expressions of law and public policy. The research and development community must supports the nation’s efforts with programs designed to aid in the risk assessment process. These programs must focus on identifying better ways to quantify risk, understanding infrastructure interdependency, and measuring cascading damages flowing from service outages. Finally, State and Local leaders should adopt security guidelines for industry and government service providers. Guidelines involve ten well-defined process requirements, all of which must be implemented to provide services online and in a safe and secure manner. 相似文献
Stereotype research depicts the generic immigrant as incompetent and untrustworthy. The current research expands this image, specifying key information dimensions (e.g. nationality, socioeconomic status) about immigrants. To see how perceivers differentiate among particular immigrant groups, we extend a model of intergroup perception, the Stereotype Content Model (SCM; Fiske, Cuddy, Glick, & Xu, 2002. Journal of Personality and Social Psychology, 82, 878–902), to immigrant subgroups. The SCM predicts that perception centers on competence and warmth, and relates to targets’ perceived status and competition within society. Specified by nationality, race, ethnicity, and class, images of immigrants differ by both competence and warmth, with most groups receiving ambivalent (low–high or high–low) stereotypes rather than the uniform low–low for the generic immigrant. As predicted, ambivalent stereotypes reflect target nationality combined with socioeconomic status, supporting the SCM's ambivalent stereotypes and social structural hypotheses, as well as better defining immigrant stereotypes and their contingencies. 相似文献
This study determined the degree to which the phonological and executive components of memory reflect language‐specific capacities in reading achievement. We tested whether the memory processes in a sample of English‐language learners that played a major role in predicting second‐language acquisition and risk for reading disability (RD) in Grade 1 (Swanson, Sáez, Gerber, & Leafstedt, 2004) also predicted reading performance in Grade 2. The present results showed that Spanish short‐term memory (STM) performance in Grade 1 predicted basic Spanish‐reading skills and Spanish comprehension in Grade 2, whereas Grade 1 English STM performance predicted English vocabulary and English comprehension in Grade 2. More importantly, children at risk for RD in Grade 1 differed from the counterparts in Grade 2 on both English and Spanish measures of reading, whereas their memory deficits were isolated to Spanish STM and working memory (WM). The relationship between language‐specific processes in memory and reading are discussed. 相似文献