Breaking the habit: engineering students’ understanding of mathematical creativity

ABSTRACT

In higher education, engineering students have to be prepared for their future jobs, with knowledge but also with several soft skills, among them creativity. In this paper, we present a study carried on with 128 engineering undergraduate students on their understanding of mathematical creativity. The students were in the first year of different engineering first degrees in a north-eastern Portuguese university and we analysed the content of their texts for the question ‘What do you understand by mathematical creativity?’. Data collection was done in the first semester of the academic years 2014/2015 and 2016/2017 in a Linear Algebra course. The results showed that ‘problem solving’ category had the majority of the references in 2014/2015, but not in the academic year 2016/2017 were ‘involving mathematics’ category had the majority. This exploratory study pointed out for ‘problem solving’ and ‘involving mathematics’ categories and gave us hints for teaching mathematics courses in engineering degrees.     

Pre-service teachers' representations of children's understanding of mathematical concepts: conflicts and conflict resolution

The purpose of this study was to investigate the extent to which research experience could enhance pre-service teachers' understanding of children's knowledge of mathematical concepts. A group of five pre-service teachers designed and conducted a study of children's understanding of fractions. As participant-observers throughout their study we gathered evidence of change in pre-service teachers' representations of children's knowledge of fractions. The focus of our observations was on the conflicts generated by the gaps between the pre-service teachers' research findings and their representations of the children's knowledge of fractions. Results indicate that research experience is fruitful in developing an inquisitive disposition in pre-service teachers and in sensitizing future teachers to children's knowledge of a mathematical concept. Pre-service teachers became familiar with the research literature regarding children's understanding of fractions, they questioned the typical instructional sequence of teaching fractions and they scrutinized methods of assessing children's knowledge of mathematical topics.     

On the nature of emotion regulation

This paper presents a unitary approach to emotion and emotion regulation, building on the excellent points in the lead article by Cole, Martin, and Dennis (this issue), as well as the fine commentaries that follow it. It begins by stressing how, in the real world, the processes underlying emotion and emotion regulation appear to be largely one and the same, rendering the value of the distinction largely for the benefit of analysis. There is an extensive discussion of how the same processes can generate emotions (i.e., are constitutive of emotion) and account for variability of manifestation of emotion in context (i.e., regulate them). Following an extensive review of many of the principles involved in emotion and emotion regulation, the paper presents implications for developmental study of infants and children, includes several methodological recommendations, and concludes with an analysis of the extent to which contemporary affective neuroscience contributes to the study of emotion and emotion regulation.     

The retention effects of an adult's emotional displays on infant behavior

The goal of this investigation was to study the regulatory retention effects of an adult's emotional displays on infant behavior. In Study 1, 11- and 14-month-old infants were tested in a social-referencing-like paradigm in which a 1-hr delay was imposed between the exposure trials and the test trial. In Study 2, 11-month-olds were tested in the same paradigm, but the delay between the exposure trials and the test trial was only 3 min. Study 1 revealed that 14-month-olds, but not 11-month-olds, demonstrated behavior regulatory effects toward the target object linked to the adult's emotional displays. Study 2 indicated that 11-month-olds were affected by the emotional displays if the delay between exposure and test trials was brief enough.     

Between the prescribed and the lived in physical education lessons

This study examines physical education (PE) curriculum development in an elementary school. Our goal was to understand the daily construction of a curriculum. We sought to analyse the theoretical and methodological framework and documents that a PE teacher uses each day while putting a curriculum into practice (lived curriculum). The data collection instruments included participant observation, interviews and document analysis. The analytical process revealed the influence of internal and external factors that affect both the authorship and the autonomy of a teacher working on the daily construction of a lived PE curriculum and that create tensions, struggles and conflicts.     

Affective Reorganization in the Infant, the Mother, and the Dyad: The Role of Upright Locomotion and Its Timing

Clinical theory is replete with rich observations that the onset of walking engenders an enhancement of emotional expression in the infant. Yet, no empirical research exists on this subject. Moreover, the importance of normal timing variations in the onset of developmental transitions has not been a topic of investigation in most developmental research. In this naturalistic home study, "earlier" and "later" walking groups were delineated on the basis of timing of entry into this developmental transition. Age-held constant analyses indicated that earlier walkers and their mothers generally showed a rise in positive exchanges as well as "testing of wills" across the transition to walking. These changes were less clear for the later walkers. Differences were observed also between the two groups even prior to walking. These findings suggest that future studies should take account of timing variations in the onset of a developmental transition.     

The Structure of Temperamental Fear and Pleasure in Infants: A Psychometric Perspective

Despite the prominence of temperament constructs in the study of infant development, little evidence exists about the internal structure of temperament. We assessed temperament both via questionnaire and in repeated laboratory visits for 168 9-month-old twins and singletons. Mothers' and fathers' agreement on temperament questionnaire scales was low, except for scales tapping negative emotionality and activity level. The factor structure of mothers' and fathers' questionnaire scales also differed, with fathers tending to associate higher motoric activity with hedonically positive behaviors. We measured fearfulness during 2 visual cliff episodes and a stranger approach, and we measured joy/pleasure during a series of 4 games. For both fearfulness and pleasure we found moderate cross-situation generality, short-term stability, and convergence with specific temperament questionnaire scales. Parameters of response, such as latency, duration, and intensity, intercorrelated within--but not across--response types. Fearful distress and avoidance proved to be uncorrelated. The results suggest that the component behaviors of infant fearfulness and pleasure are structured in a fashion consistent with a temperamental interpretation.     

Transversal traits in science education research relevant for teaching and research: A meta‐interpretative study

This study is a meta‐interpretative analysis that focuses on research conducted and published by other researchers. Concepts central to this study include global practical relevance, curriculum design, and formative situation. We analyzed 35 studies selected from 374 published studies in the years 2000 and 2001 in three journals referenced in the International Scientific Index. Using a replicable methodology developed specifically for this research, we found evidence of s clusters of variables that suggest the existence of transversal traits in the 35 science education research studies. These results form a reference framework of theoretical and practical knowledge relevant for research and practice pertaining to teaching and learning science. © 2008 Wiley Periodicals, Inc. J Res Sci Teach 45: 574–599, 2008     

Primary and Secondary Students’ Understanding of the Rainfall Phenomenon and Related Water Systems: a Comparative Study of Two Methodological Approaches

Rainfall is a key process in the water cycle, the most structured scientific knowledge about water movement on Earth. Nevertheless, despite being a common topic covered in school science, it entails several cognitive difficulties for young children. This study uses a pictorial task and semi-opened questions to examine primary (11/12 years old) and secondary (12/13 years old) students’ understanding of the elements and processes involved in the hydrologic cycle and how they are integrated into their explanations regarding the rainfall phenomenon. Overall, we have found that the studied children’s (n = 246) conceptual knowledge increases with age. However, they have an incomplete perception of the mechanism of rainfall and its integration into the water cycle. In fact, not all the students have a cyclic notion of water dynamics; they also miss the inclusion and role of groundwater in water systems and present misconceptions regarding key processes, such as condensation and evaporation. Regarding the two diagnostic tools (drawings and questionnaires) used to study children’s understanding, although questionnaires seem more appropriate for assessing lower conceptual levels, each methodological approach is useful for detecting different key concepts and misconceptions related to the rainfall phenomenon and related water cycle. Consequently, a mixed research design using different methods is advised for a comprehensive study of students’ conceptions.

     

International Comparisons in Higher Education Funding

The use of appropriate indicators of public and private expenditures, from which statistically significant differences in funding policies can be identified, constitutes a solid foundation in which the assessment of the role of governments in promoting higher education can be grounded. Based on a carefully selected set of Organization for Economic Co‐operation and Development indicators, this paper explores the effects of education funding policies, along with research and development expenditures and tax levels, on the entry rate to higher education. The results from the statistical analysis of the data confirm the existence of two distinct approaches to higher education funding, the Scandinavian approach and Anglo–American approach, and help to define their characteristics.