Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education

This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to adjust their instruction to the students' thinking. But, the point of departure is that if justice is to be done to the input of the students and their ideas built on, a well-founded plan is needed. Design research on an instructional sequence on addition and subtraction up to 100 is taken as an instance to elucidate how the theory for realistic mathematics education (RME) can be used to develop a local instruction theory that can function as such a plan. Instead of offering an instructional sequence that “works,” the objective of design research is to offer teachers an empirically grounded theory on how a certain set of instructional activities can work. The example of addition and subtraction up to 100 is used to clarify how a local instruction theory informs teachers about learning goals, instructional activities, student thinking and learning, and the role of tools and imagery.     

Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education

This article focuses on a form of instructional design that is deemed fitting for reform mathematics education. Reform mathematics education requires instruction that helps students in developing their current ways of reasoning into more sophisticated ways of mathematical reasoning. This implies that there has to be ample room for teachers to adjust their instruction to the students' thinking. But, the point of departure is that if justice is to be done to the input of the students and their ideas built on, a well-founded plan is needed. Design research on an instructional sequence on addition and subtraction up to 100 is taken as an instance to elucidate how the theory for realistic mathematics education (RME) can be used to develop a local instruction theory that can function as such a plan. Instead of offering an instructional sequence that "works," the objective of design research is to offer teachers an empirically grounded theory on how a certain set of instructional activities can work. The example of addition and subtraction up to 100 is used to clarify how a local instruction theory informs teachers about learning goals, instructional activities, student thinking and learning, and the role of tools and imagery.     

网络计划法中作业间逻辑关系的自动确定问题

针对作业具有重要特征的一类工程项目,提出了作业间逻辑关系的自动确定问题,并给出了确定作业间逻辑关系的搜索算法。     

Science and Mathematics Instruction in a Reform‐based Teacher Preparation Program

This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform‐oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi‐experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform‐oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform‐oriented instruction. Implications of results for large‐scale reform of science and mathematics teacher preparation are discussed.     

Almost Everywhere Convergence of Bochner-Riesz Means On The Heisenberg Group and Fractional Integration On The Dual

Let L denote the sub-Laplacian on the Heisenberg group H_n and the corresponding Bochner-Riesz operator. Let Q denote the homogeneous dimension and D the Euclideandimension of H_n. We prove convergence a.e. of the Bochner-Rieszmeans as r 0 for > 0and for all f L^p(H_n), provided that . Our proof is based on explicit formulas for the operators with a C, defined on the dual ofH_n by , which may be of independent interest. Here is given by for all (z,u) H_n. 2000 Mathematical Subject Classification: 22E30, 43A80.     

The Effectiveness of Schoolyards as Sites for Elementary Science Instruction

This study compared the impacts of traditional classroom and outdoor schoolyard instruction on the environmental science content knowledge and attitudes of 285 third‐ and fourth‐grade students. A modified Solomon Four Group design, including control, classroom treatment, and schoolyard treatment groups, was used. Both the indoor classroom and outdoor schoolyard treatments consisted of corresponding 10‐day units focusing on plant and animal ecology. Valid and reliable content knowledge and attitude assessments were administered before and after instruction. Analyses of variance and post hoc analyses of posttest scores and gain scores indicated that elementary students learned significantly more about selected environmental science topics through outdoor schoolyard experiences than through traditional indoor classroom experiences. Both classroom and schoolyard treatment groups developed more positive environmental attitudes as a result of instruction, but the attitude posttest and gain scores of these two groups were not significantly different from each other.     

Computational Construction as a Means to Coordinate Representations of Infinity

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of infinity-related objects (infinite sequences, in particular). We present episodes based on four students’ activities, seeking to illustrate how the available tools mediated students’ understandings of the infinite in rich ways, allowing them to discriminate subtle process-oriented features of infinite processes. We claim that the microworld supported students in the coordination of hitherto unconnected or conflicting intuitions concerning infinity, based on a constructive articulation of different representational forms we name as ‘representational moderation’.

例说函数图象在解题中的作用

借助实例说明如何利用函数图像突破解题思路、设计解题步骤并完成问题解答。     

关系营销中的心理逆反和顾客忠诚研究

关系营销是企业提升顾客忠诚度,维持与顾客长期稳定关系的重要手段.研究引入心理逆反理论探讨了关系营销的负面作用,在文献综述和理论推导的基础上,以商业银行高端客户为样本,分析关系营销策略对顾客状态逆反与顾客忠诚的影响.实证结果表明非物质层面的关系营销策略正向影响状态逆反,而物质奖励可以降低状态逆反;关系营销策略正向影响顾客忠诚,而顾客状态逆反负向影响顾客忠诚,降低了关系营销的效率;顾客的营销契合度对联系沟通与状态逆反关系有着正向的调节作用.结论从一定意义上解释了关系营销效率变化的问题,同时也为商业银行营销行为提供了参考依据.     

Intentional Integration of Mathematics Content Instruction with Constructivist Pedagogy in Elementary Mathematics Education

The purpose of the research was to improve the effectiveness of instruction in constructivist pedagogy in a college elementary mathematics education course through intentional integration of instruction in mathematics content. Instructors of this course previously used examples involving mathematics content on an ad hoc basis in an attempt to illuminate desirable constructivist pedagogy but discovered that they were ineffective because students experienced difficulty with the mathematics content itself. An instrument was created to assess students' mathematics content knowledge required to understand these examples. Based on the outcome of the assessment, intentional instruction of mathematics content using anchoring examples was integrated with pedagogical instruction. Results showed significant improvement in mathematics content knowledge and confidence in that knowledge with a better understanding of constructivist pedagogy.     

计算机辅助教学的初步尝试

本文介绍了我校引入北京大学“高等数学练习系统”(AMES),在部分学生中初步开展计算机辅助教学(CAI)的情况,分析了CAI 对高等数学教学所产生的积极作用.并针对使用AMES 过程中存在的不足之处提出了相应的对策.