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Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.  相似文献   
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As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the generalization of learning. In this article, we posit “noticing” as a plausible transfer process and investigate both individual noticing and the social organization of noticing via the focusing framework. Specifically, we relate the nature of students' reasoning on transfer tasks with what students notice mathematically in classrooms when many sources of information compete for their attention, and then we account for noticing as socially situated in classroom discourse practices, features of mathematical tasks, and the nature of mathematical activity.  相似文献   
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ObjectiveTo assess long-lasting effects of childhood trauma on the functional outcome of adult patients diagnosed with schizophrenia.MethodNinety-nine stable patients with schizophrenia followed in an outpatient program at a public university hospital in Porto Alegre, southern Brazil, were investigated for childhood traumatic experiences by the Childhood Trauma Questionnaire (CTQ) and for functional impairment by the World Health Organization Disability Assessment Schedule (WHO/DAS). The schizophrenia diagnosis was assessed by ICD-10 and DSM-IV criteria according to the Operational Criteria Checklist for Psychotic Illness (OPCRIT).ResultsChildhood trauma in general was associated with increased disability in adulthood, reflected by impaired Overall Behavior (p = .023) and Global Evaluation (p = .032). Analysis of specific traumatic domains revealed that increased childhood physical neglect was associated with functional impairment in Overall Behavior (p < .000), Social Role Performance (p = .037) and Global Evaluation (p = .014). Higher emotional abuse was associated with impaired Overall Behavior (p = .026), and higher emotional neglect with poor Global Evaluation (p = .047). Additionally, earlier onset of illness was associated with lower level of functioning evidenced by impairment in Overall Behavior (p = .042). Linear regression using WHO/DAS sections (Overall Behavior, Social Role Performance and Global Evaluation) as dependent variables and CTQ subscales indicated that only physical neglect had an effect on adult functionality.ConclusionsChildhood trauma was associated with functional and social impairment in adult patients with schizophrenia. Specific types of abuse and neglect, such as physical neglect and emotional abuse and neglect, influenced disability, and the most robust association was physical neglect. Studies involving more patients, with normal controls and additional measurements of biological liability, should be conducted to confirm this association and to increase the understanding of gene-environment relationship in schizophrenia and pathways to disability.Practice implicationsFurther investigation is warranted to clarify the association between childhood trauma and disability in schizophrenia, as well as to develop standardized instruments for the assessment of trauma and earlier detection of risk along with education of patients and families about adequate care, in an effort to reduce the incidence of disability in schizophrenia.  相似文献   
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Learning Environments Research - The four-component instructional design model (4C/ID) has been increasingly used in face-to-face and online learning environments. We present a meta-analysis on the...  相似文献   
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