Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective

This study describes an elementary teacher's implementation of sociocultural theory in practice. Communication is central to teaching with a sociocultural approach and to the understanding of students; teachers who use this theory involve students in explaining and justifying their thinking. In this study ethnographic research methods were used to collect data for 4 1/2 months in order to understand the mathematical culture of this fourth‐grade class and to portray how the teacher used a sociocultural approach to teach mathematics. To portray this teaching approach, teaching episodes from the teacher's mathematics lessons are described, and these episodes are analyzed to demonstrate how students created taken‐as‐shared meanings of mathematics. Excerpts from interviews with the teacher are also used to describe this teacher's thinking about her teaching.     

Teaching and Coherent Science: An Investigation of Teachers’ Beliefs About and Practice of Teaching Science Coherently

This article is about an investigation of six middle school science teachers’ beliefs and instructional practice about the coherence of the science they teach as articulated by National Science Education Standards ( NRC, 1996 ). Many well intentioned reform efforts focus on improving content knowledge of teachers, but many classroom teachers regularly miss opportunities to provide conceptual connections within the science ideas building the sense of coherence in science. This investigation involved a quasi experimental study to examine the efficacy of a method for collecting data about middle school science teachers’ thinking about science and to determine if they teach science coherently. The teachers were surveyed, interviewed, provided concept maps about their thinking of the science they taught, and observed to investigate whether their practice reflects their beliefs. An examination of the teachers’ beliefs, stated and unstated curriculum, the connections among topics and the nature of science revealed that one, the observation tool may have merit for identifying the content and connections among science topics, and two, that teachers ‘stated beliefs consistent with the National Science Education Standards’ vision for coherent science, did not match their demonstrated practice. The content taught could be characterized in three ways; coherent content and few connections, coherent content and connections, and not coherent content. This indicates for this group of middle school science teachers that knowing how they think about science and how those beliefs are reflected in their teaching is complex. This study can inform teacher education and professional development efforts about the need to move beyond just content enhancement to examine prior beliefs about the connections of concepts within science.     

信息论教学实践的探究

分析了当前信息论教学现状,提出应对策略,论述了信息论教学实践,在教学中取得了很好效果.     

Subtraction From a Historical Perspective

The algorithms used for subtraction vary. In the United States, three different algorithms were used almost equally until the 1940s: the equal additions, the decomposition, and the Austrian method. After William Brownell modified the decomposition algorithm, the use of other algorithms was practically eliminated in mathematics textbooks. Today, some texts introduce the equal additions algorithm, but the decomposition is still the predominant algorithm. This article reviews the historical use of each of the three algorithms in the United States, discusses the modification to the decomposition algorithm, and gives a brief overview of the current status of subtraction algorithms.     

Constructivist Beliefs About the Science Classroom Learning Environment: Perspectives From Teachers,Administrators, Parents,Community Members,and Students

This study examines the perceptions of teachers, administrators, parents, community members, and high school students about the science learning environment. The participants were active members of a grant project aimed at creating community action teams. Varrella and Burry‐Stock's (1997) Beliefs About Learning Environments (BALE) Instrument was used as a theoretical model for constructivist belief identification and comparison. Two primary questions were explored: (a) What are the beliefs of the teachers and other school community members about the science learning environment? and (b) How do these belief structures compare? Analysis of the BALE responses indicated that, although beliefs varied greatly, the administrators and teachers possessed the most constructivist beliefs. The authors suggest that identifying the beliefs of teachers, as well as those of the entire school community, is crucial. If the school community does not believe in (or understand) the recommendations, the chance for long‐lasting reform is improbable.     

数学建模教学工程的理论与实践

本文探讨了普通院校数学建模教学工程的理论 ,给出了一种分层次进行数学建模教育的新教学模式 (即整合模式 ) ,并介绍了安徽省安徽机电学院施行的四年三阶段的新教学模式 .