Solving math problems: Where and why does the solution process go astray?

This article describes a model of adaptable learning which takes account of the interaction between affective and cognitive variables in learning situations. In addition, an instrument for measuring the relevant aspects of this model is introduced. We present some initial results of the application of this instrument in the domain of mathematics learning by students in the final year of primary education. Emphasis is placed on differences between boys and girls.     

Cultural factors in the origin and remediation of alternative conceptions in physics

Over a wide range of subject areas students exhibit persistent conceptions contrary to the prevailing scientific concepts. The same alternative conceptions in physics are reported to exist across many countries, within a variety of cultural and environmental contexts. Also, many alternative conceptions show striking similarities with difficulties encountered in the historical development of physics. What is the reason for these similarities? Is intuitive science learned or triggered? And, if similar brain structures are responsible for common-sense theories, in what way then are cultural factors still important in the teaching-learning process? The influence of cultural factors will be discussed on the basis of literature available on this topic. Data collected by the authors in the Netherlands, Indonesia and countries in Africa are also taken into consideration. A distinction is proposed between alternative conceptions some of which may be universal and some dependent on culture. The same distinction is made regarding ways of reasoning and epistemology. It is suggested that the effectiveness of methods for the remediation of alternative conceptions is strongly influenced by cultural aspects of the teaching-learning process.     

A comparison of Catechesis of the Good Shepherd and Godly Play

Abstract

Catechesis of the Good Shepherd and Godly Play are the two best known variants of Montessori style Religious Education programmes. While they have much in common, there are also obvious differences. This article offers a brief outline of the distinctive features of each programme, including some analysis of their effectiveness in terms of contemporary educational research. The article identifies four areas of significant difference, namely, the understanding of the Imago Dei, the stance taken towards sacraments and sacramentality, pedagogy and the conduct of the sessions themselves. The author argues that these differences create a natural constituency for each programme. Godly Play with its heavy emphasis on the Scriptures as ‘story’ and the interpretation of the Imago Dei in terms of a ‘symbolic/language’ mediation of divine reality fits in well with the insights of mainline Protestant and Evangelical Churches. Catechesis of the Good Shepherd interprets the Imago Dei in terms of sacramentality and ontological similarity – grace building on nature through the use of the material/spiritual composition of the human person. This is better suited for use in Catholic, Orthodox and Anglo-Catholic contexts.     

Writing skills training for engineering students in large classes

First Year engineering students at the University of Edinburgh are taught Writing Skills as part of aProfessional Engineering Module. Particular difficulties are presented by the large class sizes and the generally low standard of writing skills among native English speakers at entry to the course. The course aims not only to give students the skills to communicate effectively with any readership but also to teach the conventions of engineering writing. Writer-centred, genre-centred and reader-centred approaches to the teaching of composition skills are all seen as necessary means of helping students to get the most out of their writing, for themselves and for their readers, and of motivating students to improve their writing during the four years of their degree course and beyond. The merits of lectures, handouts, surgery hours and feedback were assessed by means of a questionnaire, student interviews and analysis of feedback proformae. The indications are that structured feedback provides the key to helping individual students evolve and maintain a personal development programme for improving their writing skills to a level which meets the needs of their profession.     

Rural Students in a Chinese Top-Tier University: Family Background,School Effects,and Academic Performance

Abstract

New preferential policies in China promise to increase the number of rural students entering top-tier universities, where there is a wider path to a higher social status. While a substantial body of literature has investigated rural students’ trajectories to university, there is a dearth of systematic empirical studies on the academic success of rural students in colleges and universities. This study seek to address this gap by examining the academic achievement of representative samples of students entering an elite university in China, including their place of origin, family background, school experience, and the characteristics that align with their academic performance. The data suggest no significant difference in academic performance obtained by urban and rural students with respect to average grade point average (over four years). It also suggests that fathers’ occupations may not be associated with the academic achievements of students from different families. However, the data suggest a relatively clear school effect on the academic performance of students at University S.¹For ethical considerations, we use pseudonyms in the article. The study enriches the discussions of the inequality issue in China’s higher education sector. It also enriches the literature in sociology of education by looking at the relative strength of the relationship between the possible causes and outcomes of schooling.     

Effects of Instruction on Verbal Interactions During Collaborative Problem Solving

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving.     

Teachers’ and students’ perceptions of assessments: A review and a study into the ability and accuracy of estimating the difficulty levels of assessment items

In today's higher education, high quality assessments play an important role. Little is known, however, about the degree to which assessments are correctly aimed at the students’ levels of competence in relation to the defined learning goals. This article reviews previous research into teachers’ and students’ perceptions of item difficulty. It focuses on the item difficulty of assessments and students’ and teachers’ abilities to estimate item difficulty correctly. The review indicates that teachers tend to overestimate the difficulty of easy items and underestimate the difficulty of difficult items. Students seem to be better estimators of item difficulty. The accuracy of the estimates can be improved by: the information the estimators or teachers have about the target group and their earlier assessment results; defining the target group before the estimation process; the possibility of having discussions about the defined target group of students and their corresponding standards during the estimation process; and by the amount of training in item construction and estimating. In the subsequent study, the ability and accuracy of teachers and students to estimate the difficulty levels of assessment items was examined. In higher education, results show that teachers are able to estimate the difficulty levels correctly for only a small proportion of the assessment items. They overestimate the difficulty level of most of the assessment items. Students, on the other hand, underestimate their own performances. In addition, the relationships between the students’ perceptions of the difficulty levels of the assessment items and their performances on the assessments were investigated. Results provide evidence that the students who performed best on the assessments underestimated their performances the most. Several explanations are discussed and suggestions for additional research are offered.