Intuitive rules in science and mathematics: the case of ‘Everything can be divided by two’

In the last twenty years, researchers have studied students’ mathematical and scientific conceptions and reasoning. Most of this research is content‐specific. It has been found that students often hold ideas that are not in line with accepted scientific notions. In our joint work in mathematics and science education, it became apparent that many of these alternative conceptions hail from a small number of intuitive rules. We have so far identified two such rules: ‘The more of A, the more of B’, and, ‘Everything can be divided by two’. The first rule is reflected in students’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.), all tasks related to intensive quantities (density, temperature, concentration, etc.), and tasks related to infinite quantities. The second rule is observed in responses related to successive division of material and geometrical objects, and in seriation tasks. In this paper we describe and discuss the second rule and its relevance to science and mathematics education. In a previous paper (Stavy and Tirosh 1995, in press) we described and discussed the first rule.     

The determinants of undergraduate degree performance: How important is gender?

This study uses data drawn from three recent cohorts of undergraduates at the University of Sussex to investigate the key determinants of degree performance. The primary theme of the study is an examination of the gender dimension to degree performance. The average ‘good’ degree rate for female students was found to be superior to the male rate. The modest raw gender differential in first class degree rates favoured women but was found to be attributable to their better endowments, particularly pre-entry qualifications. The largest differential favouring women was in the II:i classification, where almost all of the difference was attributable to differentials in coefficient treatment rather than endowments (or characteristics). The analysis undertaken also allowed the investigation of a number of sub-themes relating to the effects on degree performance of, inter alia, pre-entry qualifications, ethnicity, socio-economic background and health disability. The largest effects were reserved for the role of pre-entry qualifications with more modest effects detected for ethnicity and socio-economic background.     

The impact of teachers’ individualized practices on gifted students in rural,heterogeneous classrooms

Several factors have increased teachers’ frustrations in the regular classroom as they try to meet the needs of students with varying levels of ability. Limited educational funding, the attitude that gifted students can do without special services, and a push for increased heterogeneous grouping have all contributed to the teacher's problem. The Mustard Seed Project was developed and supported by a grant from the Javits Gifted and Talented Students Education program to train teachers to differentiate for student needs by curricular adaptations. The training for teachers modeled the process of individualization for each learner's level, pace and style. A follow‐up support system of human and material resources was implemented to sustain the teachers through the difficult transition required of change. The sites participating in this study were all rural, ethnically diverse, and economically disadvantaged. Profiles of six gifted fifth‐graders were developed using interviews and classroom observations. The research questions sought to determine the extent of the gifted child's intellectual challenge, exploration of in‐depth selected topics of interest, and social and emotional satisfaction in adapted classrooms.