Conditional inference and advanced mathematical study

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one’s ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts students. The mathematics students in the study were found to endorse fewer invalid conditional inferences than the arts students, but they did not endorse significantly more valid inferences. We establish that both groups tended to endorse more inferences which led to negated conclusions than inferences which led to affirmative conclusions (a phenomenon known as the negative conclusion effect). In contrast, however, we demonstrate that, unlike the arts students, the mathematics students did not exhibit the affirmative premise effect: the tendency to endorse more inferences with affirmative premises than with negated premises. We speculate that this latter result may be due to an increased ability for successful mathematics students to be able to ‘see through’ opaque representations. Overall, our data are consistent with a version of the formal discipline view. However, there are important caveats; in particular, we demonstrate that there is no simplistic relationship between the study of advanced mathematics and conditional inference behaviour.

The POE in the primary school: An evaluation

The POE (Predict-Observe-Explain) is a technique for identifying students' knowledge and understanding of science concepts. It has mainly been used for physical science topics at secondary and tertiary levels. In the present study, 60 preservice teachers each implemented and evaluated POEs with groups of primary children. The children were studying a range of topics from the NSW Science and Technology K-6 Syllabus and represented a range of year levels. The evaluations were generally positive. The children responded to the technique enthusiastically and the teachers were able to identify both their understandings and their process skills development. The main problems were the difficulty of inventing suitable POEs in some topics, especially topics on communication, and problems caused by the use of oral rather than written responses. The study concluded that it is a suitable technique for primary science.     

Exploring the relationship between homework task difficulty,student engagement and performance

This article considers the relationship between differential homework task difficulty, student engagement and performance across four Irish post-primary school sites. A total of 236 participants completed all elements of this study. All participants were junior cycle students, aged between 12 and 16 years. The study employed a standardised test–retest approach, with a one week interval between tests. Between testing, participants were randomly subdivided into three cohorts. Each cohort received homework questions of different difficulty levels to complete for one week. The results of this study found that Cohort A, who received the least difficult homework tasks, completed the most non-compulsory questions. Although Cohort A demonstrated higher levels of engagement, no statistically significant difference was found in the change in performance scores of the three cohorts. The results highlight the negative impact of increased task difficulty on student engagement with independent homework tasks. The findings suggest that in order to support student engagement it is important that teachers afford ample opportunity for student success when designing self-directed tasks such as homework.     

The pedagogical value and the interdisciplinary nature of inductive processes in forming generalizations: Reflections from the classroom

The tendency to generalize from specific experiences leading to new, more abstract concepts is a natural aspect of human thought. Generalizations are the end result of an inductive process that begins with the identification of similarities in seemingly disparate situations. It is the existence of such generalizations that makes it possible for us to understand each other and the world around us. It is pedagogically weak to present generalizations to students and expect them to know how and when to apply them. On the other hand if students experience the inductive process in classrooms and discover generalizations, they are likely to remember and use this process when tackling other problems. The authors illustrate the pedagogical value of such an approach and the interdisciplinary nature of the inductive process by reflecting on teaching practices in English literature and mathematics in a high school classroom. In particular the authors reflect on how the inductive process was applied to four short stories and four problem-solving situations, which resulted in high school students arriving at generalizations that characterized the stories and the problems. A conceptual model that illustrates how inductive processes facilitate generalizations in the classroom is presented.     

The governance of sustainable socio-technical transitions

A quasi-evolutionary model of socio-technical transitions is described in which regimes face selection pressures continuously. Differentiated transition contexts determine the form and direction of regime change in response to these pressures. The articulation of pressures, and the degree to which responses are coordinated and based on resources available within the regime, define the transition context. Four alternative contexts are described: endogenous renewal; re-orientation of trajectories; emergent transformation and purposive transitions. Agency and power in the governance of regime transformation are analysed. Power to affect change depends on regime membership, the distribution of resources for change and expectations.     

Grief – The Expression of Romanian Artistic Spirituality

This paper expresses a personal point of view of the main features of Romanian artistic spirituality based on the writings of Romanian philosopher, Emil Corian, on personal knowledge of Romanian folk art, of the art of the initiated, and on teaching and art-making experience.     

Students' application of the concept of interdependence to the issue of preservation of species: Observations on the ability to generalize

One of the aims of science education is that students should be able to apply scientific principles to contemporary issues. Individual interviews were used to investigate the way in which students (63 12-year-olds and 60 16-year-olds) applied the ecological concept of interdependence of species to the issue of preservation of species. Students were shown a list of items representing a range of living things and were asked to select those which they would want to save from extinction and explain their reasoning. Although most students used the concept of interdependence for some items, they did not apply it in a scientifically consistent way to all types of living things. Three probable reasons for this lack of consistency were anthropocentricism, mixed reasons (students appeared to spontaneously choose another type of reason depending on what image the item immediately provoked), and opposite reasons (students interpreted the idea of interdependence as applying to some types of living things but not to others). J Res Sci Teach 34: 837–850, 1997.