Learning group isomorphism: A crossroads of many concepts

This article is concerned with how undergraduate students in their first abstract algebra course learn the concept of group isomorphism. To probe the students' thinking, we interviewed them while they were working on tasks involving various aspects of isomorphism. Here are some of the observations that emerged from analysis of the interviews. First, students show a strong need for canonical, unique, step-by-step procedures and tend to get stuck of having to deal with some degrees of freedom in their choices. Second, students exhibit various degrees of personification and localization in their language, as in I can find a function that takes every element of G to every element of G vs. there exists a function from G to G. Third, when having to deal with a list of properties, students choose first the properties they perceive as simpler; however, it turns out that their choice depends on the type of the task and the type of complexity involved. That is, in tasks involving groups in general, students mostly prefer to work with properties which aresyntactically simple, whereas in tasks involving specific groups, students prefer properties which arecomputationally simpler.     

On fractions and non-standard representations: Pre-service teachers' concepts

The present study examined the reasoning strategies and arguments given by pre-service school teachers as they solved two problems regarding fractions in different symbolic representations. In the first problem, the pre-service school teachers were asked to compare between two different fractions having the same numerical representation, and in the second problem, they were asked to compare between different notational representations of the same fraction. Numeration systems in bases other than ten were used to generate various representations of fractions. All students were asked to provide justifications to their responses. Strategies and arguments relative to pre-service teachers' concepts of fractions and place value were identified and analyzed based on results of 38 individual clinical interviews, and written responses of 124 students. It was found that the majority of students believe that fractions change their numerical value under different symbolic representations.     

A second chance for higher education: Academic preparatory programs in Israel

The Israeli academic preparatory programs (APPs) challenge the sorting regime of regular education by offering a genuine second chance for higher education to youngsters who have failed to acquire the necessary prerequisites via the mainstream. The study analyzes the success of the APPs to produce changes in their students in light of the failure of a different second-chance framework, the community college, to do so. The analysis of a sample of APP graduates indicates that background characteristics and high school history, powerful sources of differentiation upon admittance to the APPs, lose their discriminating power after graduation. All graduates join any postsecondary educational framework, regardless of their initial disadvantages. The success of the APPs in eliminating initial gaps among the students is assigned mainly to their nonconformity to the selection criteria of regular education. The purpose of this research was to assess whether second-chance educational programs that challenge the sorting criteria of the mainstream succeed in enhancing social equality in education. Outcomes of the challenging second-chance academic preparatory programs in Israel are analyzed in light of the reported failure of community colleges to moderate inequalities in higher education.     

Establishing Sociological Imagination before Blame in Historical Events

Although finding fault with someone or something is part of human nature, blame is merely a perception. Before assigning blame in the causation of historical events, students should be given the opportunity to look past textbook generalizations and establish sociological imagination, or the ability to recognize history's connection to society and its people. By instituting sociological imagination, societal and cultural factors could be emphasized, various perspectives could be examined, and empathy could be evoked from the voices of people who lived during, or participated in, these historical happenings.     

Knowing where we Stand: Mapping Teachers’ Conception of Reflection in Service-Learning

Innovative Higher Education - Reflection is fundamental in experiential pedagogies, and many studies have been carried out to investigate its impact and benefits on student learning outcomes....     

定量负荷运动下体育生与非体育生心率变异性比较研究

目的:探讨体育生与非体育生在定量负荷运动中心率变异性指标是否有差异,为提高大学生的心脏功能提供科学依据.方法:随机选取山西师范大学体育专业女生15名,非体育专业15名,分别进行安静状态下、定量负荷运动过程中、运动后恢复期的HRV测试,应用MEGA心率变异性仪器进行记录与分析.结果:在安静状态下体育生心率变异性大于非体育生,但没有显著差异;在运动过程中,非体育生迷走神经降低程度大于体育生,且具有显著性差异;在运动后恢复期,非体育生交感神经张力大于体育生,且具有显著性差异.结论:体育生的心率变异性大于非体育生,非体育生要加强体育锻炼,促进身体健康.     

Stuck on convention: a story of derivative relationships

In this article, we explore the responses of a group of undergraduate mathematics students to tasks that deal with areas, perimeters, volumes, and derivatives. The tasks challenge the conventional representations of formulas that students are used to from their schooling. Our analysis attends to the specific mathematical ideas and ways of reasoning raised by students, which supported or hindered their appreciation of an unconventional representation. We identify themes that emerged in these responses and analyze those via different theoretical lenses—the lens of transfer and the lens of aesthetics. We conclude with pedagogical recommendations to help learners appreciate the structure of mathematics and challenge the resilience of certain conventions.     

The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments

In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose.This revised version was published online in September 2005 with corrections to the Cover Date.