Formulation of stable difference schemes for systems of initial-value partial differential equations

A general system of initial-value partial differential equations is classified into four categories based on the partial differential operators which define the equations. Specific combinations of the operators are termed “invariants” since they are common to all finite difference approximations to the system of equations. The “invariants” are used to a priori determine if one may formulate a stable difference approximation to a system of partial differential equations. This is in essence a numerical existence theory.     

Four dialogues and metalogues about the nature of science

We analyse and explore, in the form of dialogues and metalogues questions about the dialogic nature of beliefs and students belief talk about the nature of science and scientific knowledge. Following recent advances in discursive psychology, this study focuses not on students' claims but on the discursive resources and dialogical practices that support the particular claims they make. We argue that students' discourse is better understood as a textual bricolage that is sensitive to conversational context, common sense, interpretive repertoires, and textual resources available in the conversational situation. Our text is reflexive as it embodies the discursive construction of knowledge and undercuts any claims to authoritative knowledge. The very conception of “belief” is itself an expression or construction from within the mundane idiom.... We learn to use “belief” in conditions when the “objective facts” are unknown or problematic and we want to indicate the tenuous character of our claim.... The notion of “real world” or “objective reality” is embedded in an extensive, pervasive language game which includes as an intelligible move or possibility the use of the very concept of “belief” itself. (Pollner, 1987, p. 21)     

Relations between teachers' approaches to teaching and students' approaches to learning

This paper reports on an empirical study which shows that qualitatively different approaches to teaching are associated with qualitatively different approaches to learning. More specifically, the results indicate that in the classes where teachers describe their approach to teaching as having a focus on what they do and on transmitting knowledge, students are more likely to report that they adopt a surface approach to the learning of that subject. Conversely, but less strongly, in the classes where students report adopting significantly deeper approaches to learning, teaching staff report adopting approaches to teaching that are more oriented towards students and to changing the students conceptions. The study made use of a teaching approach inventory derived from interviews with academic staff, and a modified approach to learning questionnaire. These conclusions are derived from a factor and cluster analysis of 48 classes (involving 46 science teachers and 3956 science students) in Australian universities. The results complete a chain of relations from teacher thinking to the outcomes of student learning. Previous studies have shown relations between teachers' conceptions of teaching and learning and their approaches to teaching. Numerous studies have shown correlations between students' deeper approaches to learning and higher quality learning outcomes. The results reported here link these two sets of studies. They also highlight the importance, in attempts to improve the quality of student learning, of discouraging teacher-focused transmission teaching and encouraging higher quality, conceptual change/student-focused approaches to teaching.     

The costs of secondary schooling in developing countries; patterns and prospects

This research is concerned with the problems that may arise in paying for the costs of secondary school places in developing countries, which have experienced a rapid increase in primary school enrolments since the World Conference on Education for All at Jomtien. Many, but not all, of these countries are in sub-Saharan Africa. Case studies are being conducted six African and Asian countries. The basic argument is that cost structures, which may have been appropriate for systems that had low gross enrolment ratios and modest transition rates from primary to secondary are unlikely to be sustainable as enrolments become universalised. The challenge is to identify opportunities to expand quality secondary schooling to meet new needs while reducing costs to levels which can be afforded. Access to and quality of secondary schooling is likely to dominate the educational planning agenda in many developing countries in the early part of the twenty-first century.     

Teacher behavior, student interest and affective learning: putting theory to practice

Students of Project Adapt (PA), an instructional program for at-risk middle school students in Brooklyn NY, have displayed startling improvement on cognitive outcome measures. Teacher given grades and standardized tests illuminate the progress students have made since entering the program. The current investigation attempts to analyze PA on students' affective responses in a pre/post-test experimental design. Upon entering PA, students completed measures of interest, affect, and their previous teachers' behavior (pre). These ratings were then compared to end of year ratings on the same instruments (post). Results indicate students' perceive PA teachers utilizing different behaviors than their previous teachers. Additionally, student affect and interest increased significantly. Results of this study have implications for both instructional researchers and educational practitioners.     

Effect of verbal instructions and image size on visual search strategies in basketball free throw shooting

We assessed the effects on basketball free throw performance of two types of verbal directions with an external attentional focus. Novices (n = 16) were pre-tested on free throw performance and assigned to two groups of similar ability (n = 8 in each). Both groups received verbal instructions with an external focus on either movement dynamics (movement form) or movement effects (e.g. ball trajectory relative to basket). The participants also observed a skilled model performing the task on either a small or large screen monitor, to ascertain the effects of visual presentation mode on task performance. After observation of six videotaped trials, all participants were given a post-test. Visual search patterns were monitored during observation and cross-referenced with performance on the pre- and post-test. Group effects were noted for verbal instructions and image size on visual search strategies and free throw performance. The 'movement effects' group saw a significant improvement in outcome scores between the pre-test and post-test. These results supported evidence that this group spent more viewing time on information outside the body than the 'movement dynamics' group. Image size affected both groups equally with more fixations of shorter duration when viewing the small screen. The results support the benefits of instructions when observing a model with an external focus on movement effects, not dynamics.     

Using stroke removal to investigate Chinese character identification during reading: evidence from eye movements

We explored the effect of stroke removal from Chinese characters on eye movements during reading to examine the role of stroke encoding in character identification. Experimental sentences were comprised of characters with different proportions of strokes removed (15, 30, and 50%), and different types of strokes removed (beginning, ending, and strokes that ensured the configuration of the character was retained). Reading times, number of fixations and regression measures all showed that Chinese characters with 15% of strokes removed were as easy to read as Chinese characters without any strokes removed. However, when 30%, or more of a character’s strokes were removed, reading characters with their configuration retained was easiest, characters with ending strokes removed were more difficult, whilst characters with beginning strokes removed were most difficult to read. The results strongly suggest that not all strokes within a character have equal status during character identification, and a flexible stroke encoding system must underlie successful character identification during Chinese reading.