A longitudinal analysis of estimation, counting skills, and mathematical ability across the first school year

In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3 monthly intervals. Correlations between the 3 types of ability were evident, but while the quality of children's estimations changed over time and performance on the mathematical tasks improved over the same period, changes in one were not associated with changes in the other. In contrast to the earlier claims that the linearity of number representation is potentially a unique contributor to children's mathematical development, the data suggest that this variable is not significantly privileged in its impact over and above simple procedural number skills. We propose that both early arithmetic success and estimating skill are bound closely to developments in counting ability.

Can childhood neglect be prevented through parenting skills training?

Child neglect continues to be the most prevalent form of child maltreatment, yet it has received less specific research attention than other forms of maltreatment (Zuravin, 1999). It is only in recent years that neglect has been seen as a phenomenon that needs to be conceptualised separately to other forms of abuse (Gershater- Molko et al., 2002). Although the term ‘neglect’ is used generally when children do not receive minimal physical and/or emotional care, there is no single agreed definition; one possible reason for this is the lack of consensus about minimally adequate standards of childcare either within professional groups or existing research (Rose and Meezan, 1996; Stone, 1998).

Teaching and cognitive outcomes in A-levels and Advanced GNVQ's: Case studies from Science and Business Studies Classrooms

The purpose of the paper is to demonstrate how a research diary methodology, designed to analyse A-level and GNVQ classrooms, can be a powerful tool for examining pedagogy and quality of learning at the level of case study. Two subject areas, science and business studies, are presented as cases. Twelve teachers and thirty-four students were studied over a four-week period in May 1997 and contrasts were drawn between lessons from three A-level physics teachers/three Advanced GNVQ science teachers and two A-level business/economics teachers/four Advanced GNVQ business teachers. Lessons were analysed within a cognitive framework which distinguishes between conceptual and procedural learning and emphasizes the importance of metacognition and epistemological beliefs. Two dimensions of lessons were identified: pedagogical activities (e.g. teacher-led explanation, teacher-led guidance on a task, question/answer sessions, group discussions, working with IT) and cognitive outcomes (e.g. structuring and memorizing facts, understanding concepts and arguments, critical thinking, problem-solving, learning core skills, identifying values). Immediately after each lesson, teachers and students (three per class) completed structured research diaries with respect to the above dimensions. Data from the diaries reveal general and unique features of the lessons. Time-ofyear effects were evident (examinations pending in May), particularly in A-level classrooms. Students in business studies classes reported a wider range of learning activities and greater variety in cognitive outcomes than did students in science classes. Science students self-rating of their ability to manage and direct their own learning was generally low. The phenomenological aspects of the classrooms were consistently linked to teachers' lesson plans and what their teaching objectives were for those particular students at that particular time of the year.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.