高校教师综合分析评价专家系统的设计与实现

基于T—S模糊模型的神经网络结构,通过在模糊辨识中引入3级知识库,并采用2级模糊推理技术的方法,提出了一种以高校教师为研究对象的综合分析评价专家系统的体系结构和方法。     

Unrealistic responses to realistic problems with missing information: what are important barriers?

Abstract

It is a well-documented finding that students tend to neglect their real-world knowledge when solving word problems, even when realistic assumptions are needed. Although studies have successfully shown the extent to which students tend to provide unrealistic responses, the question of where this tendency comes from has yet to be answered. We focused on two major steps needed to solve realistic word problems: noticing missing information and making realistic assumptions. We conducted two studies with fifth graders (Study 1, N?=?108; Study 2, N?=?60) in which we compared students’ (un-)realistic responses to problems that differed in how obvious the missing information was. Study 1 fostered only students’ ability to make assumptions. Study 2 fostered this ability plus the ability to notice missing information. The results indicate that, if the missing information is not obvious, students’ failure to notice it seems to be what prevents them from arriving at a realistic solution.     

Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

数学直觉思维探索

首次提出了数学直宽思维模式，讨论了它的一些特定的研究问题（例如灵感问题）。     

The curriculum potential of Darwin's Theory of Evolution

Unity and diversity are best reconciled by Darwin's Theory of Evolution. Two major dilemmas related to the study of Evolution are described. The first, concerning pedagogy, can be solved by teaching the topic at an elementary level in the middle school so that the Theory may serve as an advanced oragnizer and returning with in-depth study in the last two years of high school. The second, concerning Faith, is a sensitive issue. Some successful approaches are discussed. The place of Darwin's Theory in the all-elective high school biology curriculum is described as well. The role of the Theory regarding explanations is especially highlighted.     

An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of combinatorial reasoning. We finally analyze the implications of the theoretical model and type of analysis presented for mathematics education research and practice.     

论汉语言对亚氏的逻辑思想的应用、阐释与发挥

亚里士多德逻辑思想的光辉照耀了人类几千年，作为有着悠久的逻辑发展史的中国自然与其有着千丝万缕的联系。着重把亚氏的逻辑思想与当今汉语言教学联系起来，以期从中发现它对当今汉语言教学的启发与引导。主要把汉语言知识中的语音、词汇、语法与逻辑知识中的概念、判断结合起来分析。     

直言命题变形推理特例分析

传统逻辑学的演绎推理是在一定的条件限制之下进行的。直言命题变形推理形式"SAP→SOP"的成立,超出了传统逻辑理论中"前提中不周延的项在结论中不得周延"这一普遍规律的限制。我们可以把"SAP→SOP"这一推理形式看成直言命题变形推理中的特例,但不应该把它看成亚里士多德开创的传统逻辑学的缺欠和不足。     

Using Exploratory Talk to Enhance Problem-solving and Reasoning Skills in Grade-7 Science Classrooms

This study investigates whether the generation of exploratory talk in grade seven, second-language science classrooms in the Eastern Cape Province, South Africa, has a positive effect on learners in terms of their problem-solving and reasoning skills and whether socio-cultural milieus (urban, peri-urban and rural settings of schools) have an effect on any cognitive gains that may be made by learners. The findings were that there is a clear and statistically significant improvement in the mean test scores on problem-solving and reasoning of pupils who participated in the classroom discussion initiative (exploratory talk) over those of the comparison groups. This result was consistent in both the first- and second-studies that were undertaken. There was also a significant difference between the gains in problem-solving and reasoning test scores of the three socio-geographical settings in which the participating schools are found.     

推理链：科学发现的逻辑新论

科学发现有没有逻辑的争论,由来已久.有人称其无,有人说其有,还有归纳派和演绎派的形同水火.究其实,争论是由逻辑观--传统形式逻辑和现代数理逻辑的不同引起的.其实,归纳派和演绎派各执一端,各有长短,彼此是相通的,类比、归纳和演绎整合的推理链,才是科学发现的逻辑.