Pre-schoolers,pre-school teachers,and interpersonal problem-solving skills: a comparative study in Turkey and Belgium

Interpersonal cognitive problem solving, one of the most crucial social skills, is a life-long competency that must be supported from the early years of life. In this study, the opinions of 55 Turkish pre-school teachers and 53 Flemish pre-school teachers who work with 3–6-year-old children in private and public pre-schools in metropolitan cities of both countries were obtained using the Teacher's Interpersonal Problem Solving Questionnaire. When the results were considered, it was noticed that Turkish pre-school teachers tend to solve problems as soon as they emerge. They usually prefer to suggest a solution to the problem or give advice. On the contrary, pre-school teachers in Belgium express that they analysed problems together with the children and guided children to produce various solutions. It was revealed that few Turkish and Flemish teachers have specific training in improving interpersonal problem-solving skills in children.     

Building middle school students' understanding of proportional reasoning through mathematical investigation

This article describes and shares an innovative pedagogical practice that holds promise in contributing to the teaching and learning of proportions in middle school. The teaching and learning of mathematics with understanding framework was used as a vehicle to help 21 seventh grade students reason proportionally. The findings of this unit suggest that the classroom culture, which encouraged the students to make connections between their existing and new ideas and reflecting and communicating their thinking, contributed to their emerging understanding of proportions. The use of an authentic and non-routine task involving liquid measurements also heightened their interest, curiosity and enthusiasm, thereby contributing to their excitement about the mathematics they were learning.     

What underlies successful word problem solving? A path analysis in sixth grade students

Two component skills are thought to be necessary for successful word problem solving: (1) the production of visual-schematic representations and (2) the derivation of the correct relations between the solution-relevant elements from the text base. The first component skill is grounded in the visual–spatial domain, and presumed to be influenced by spatial ability, whereas the latter is seated in the linguistic–semantic domain, and presumed to be influenced by reading comprehension. These component skills as well as their underlying basic abilities are examined in 128 sixth grade students through path analysis. The results of the path analysis showed that both component skills and their underlying basic abilities explained 49% of students’ word problem solving performance. Furthermore, spatial ability and reading comprehension both had a direct and an indirect relation (via the component skills) with word problem solving performance. These results contribute to the development of instruction methods that help students using these components while solving word problems.     

A Teacher Who Left His Mark

Abstract

Discussion of the nature of critical thinking and the ways in which it can be enhanced has increased in recent years among social work educators, and yet little is known about the impact of MSW education on the critical thinking of students. This paper examines the nature of critical thinking, presents an adult cognitive developmental model, the Reflective Judgment Model (King &; Kitchener, 1994), which holds promise for enlarging social work's understanding of critical thinking and examines approaches to teaching which enhance critical thinking. The Reflective Judgment Model focuses on the development of assumptions about knowledge and the process of knowing as development occurs through adulthood. Specific implications for creating classroom and field learning environments are detailed, including characteristics of effective teachers and of effective assignments.     

非齐次代数特征值问题的计算方法

给出了两个半无限区间内解存在的充要条件,同时,把求解问题限定在确定的有限区间内,然后,设计了求解算法,并用算例进行了验证。     

浅谈数学解题教学

论文介绍了数学解题过程寻求解题“引子”的几种常用方法     

Web-Based Student Assessment for Program Evaluation

As part of an overall evaluation of the Global Learning and Observations to Benefit the Environment, (GLOBE) program, we designed a Web-based assessment environment to measure students' environmental awareness and data analysis skill. It was expected that students who were identified as high implementers in the GLOBE program would outperform low implementers in their ability to construct environmental inferences and the degree to which they could analyze environmental data. Seven high and middle school classrooms were identified as either high or low GLOBE implementers depending on the amount of atmospheric data they had collected during the year. Within each classroom students were assigned into smaller learning groups of three students per group. A total of 32 groups participated in this study. Analysis of students' responses to the tasks revealed that the students differed in their performance. Overall, the results showed that students in the high implementing classrooms were more likely to construct higher-level environmental inferences than students in the low implementing classes. Contrary to expectations, middle school students were more likely than high school students to solve the data analysis problem correctly. However, upon further analyses, high school students constructed more data graphs and were more skilled in providing correct evidence to support their decision making than were middle school students in GLOBE. This study confirms the viability of using technology-based assessments for measuring students' environmental awareness and data analysis.     

巧用构造法证明不等式

阐述了巧用构造法证明不等式的意义和一些常用方法     

A Critical Examination of Three Factors in the Decline of Proof

Proof seems to have been losing ground in the secondary mathematics curriculum despite its importance in mathematical theory and practice. The present paper critically examines three specific factors that have lent impetus to the decline of proof in the curriculum: a) The idea that proof need be taught only to those students who intend to pursue post-secondary education, b) the view that deductive proof need no longer be taught because heuristic techniques are more useful than proof in developing skills in reasoning and justification, c) the idea that deductive proof might profitably be abandoned in the classroom in favour of a dynamic visual approach to mathematical justification. The paper concludes that proof should be an essential component in mathematics education at all levels and compatible with both heuristic techniques and dynamic visual approaches.     

论数学解题的自然性

以自然结构为理论依据,分析、研究及推广了历史名题Ｃａｕｃｈｙ－Ｓｃｈｗａｒｚ不等式,并简述了数学解题的自然审美观和研究问题及发现问题的思维方法．