Solving math problems: Where and why does the solution process go astray?

This article describes a model of adaptable learning which takes account of the interaction between affective and cognitive variables in learning situations. In addition, an instrument for measuring the relevant aspects of this model is introduced. We present some initial results of the application of this instrument in the domain of mathematics learning by students in the final year of primary education. Emphasis is placed on differences between boys and girls.     

Secondary school students’ reasoning about evolution

This study examined age differences in young people's understanding of evolution theory in secondary school. A second aim of this study was to propose a new coding scheme that more accurately described students’ conceptual understanding about evolutionary theory. We argue that coding schemes adopted in previous research may have overestimated students’ grasp of evolutionary concepts. A total of 106 students aged 12, 14, and 16 took part in individual interviews investigating their understanding of evolution. Using the new coding scheme, we found that while 16‐year olds were more likely than 12‐year olds to endorse scientific concepts when answering a question about finches, their understanding of natural selection, however, did not generalize to the other four questions. Furthermore, students began to incorporate relevant terminology (e.g., adapt, evolve, etc.) and structure their explanations using relevant language at around age 14. Students often used relevant terminology without having a more advanced understanding of evolutionary theory. Instead, they used the relevant terms in a colloquial rather than a scientific sense. Implications of the current findings for teaching and theory are discussed. © 2016 The Authors. Journal of Research in Science Teaching published by Wiley Periodicals, Inc. on behalf of National Association for Research in Science Teaching. J Res Sci Teach 54: 247–273, 2017     

A comparative perspective on Finnish higher education policy

The last decades have offered social scientists an abundance of material for studies of governmental reform policy in the area of higher education. Reforms of educational politics have been legion in great parts of the world, probably in a particulary high degree in Europe. My purpose is to describe Finnish higher education policy during the last two decades in the four policy areas of (1) quantitative planning and regionalization, (2) social recruitment, (3) governance, and (4) teaching and studies as compared to the development of Western Europe. In the second part of this paper the implementation of the Finnish higher education reforms is analyzed. The third part analyzes the development of the Finnish higher education system and focuses on the various alternatives not chosen by the government. In the final part I discuss the recent trends in Finnish higher education in respect to consistency and change.     

Transient and Robust Knowledge: Contextual Support and the Dynamics of Children's Reasoning About Density

ABSTRACT— Contextual support for performance and understanding plays an important role in learning and teaching. This study investigated the temporal course of the effects of support—how it affects complexity and correctness of judgments about density in kindergarten ( n = 35) and second-grade ( n = 29) children. In the experimental group, a teacher provided support through modeling more complex reasoning about why objects sink or float. Children's complexity judgments increased sharply with support compared to no support, although their predictions about whether objects would sink or float were mostly correct from the start. Following the support event, children showed a sudden jump in complexity of explanations, which was transient for most children, who showed either rapid decrease or some oscillation and then decrease. A few sustained the high-level explanation after the jump, showing robust knowledge. That is, patterns of performance across trials were primarily nonlinear, following mostly cubic or quadratic change. In addition, second-graders had a more complex understanding of density than did kindergarteners. Findings indicate that children's concepts are dynamic rather than static, as evidenced by the strong but transient effects of support for most students. To move from transient to robust knowledge requires the building of knowledge and skill over time.     

Perceptions of university assessment and feedback among post-16 school pupils

The transition between school and university can be problematic for students. Understanding students’ expectations about the system they are entering is crucial in effecting a smooth transition. The school system involves small classes, often with teachers who know their students well. In contrast, university involves large class sizes and a degree of anonymity for the student. In the UK, National Student Survey responses for universities show that students are generally less happy about feedback relative to most other issues. The current study investigates school students’ expectations about assessment and feedback practices at university. Students were surveyed across Great Britain in 2006 and 2013. There were some significantly different responses from students between the two years of study in how coursework would be handled, but there were also many areas of consistency, demonstrating a clear pattern of expectation. For example, in both years of study 80% of students expected personal verbal feedback on their university assignments. This study discusses how student expectations may be based on their school experiences, rather than considering the reality of the university system they are entering. Misconceptions may be affecting students’ responses to surveys on assessment and feedback.     

Compliance through care and commitment: why young people do as adults ask

Although the behaviour of young people is often a focus for concern, most young people do as they are asked. This paper presents findings from a qualitative study across four educational settings that set out to explore reasons for this compliance. Forty-four young people (aged 12–21) participated in interactive focus groups and 21 practitioners were interviewed. A critical exploration of the authority relationships between the young people and the participating adults was undertaken. The research was designed to explore the relevance of the typology of authority relationships proposed by Dennis Wrong for educational settings. The findings confirmed the applicability of his work; however, the paper argues that an additional basis for authority relationships characterised by ‘care and commitment’ should be included. The results suggest the potential for long-term caring relationships, authenticity and professional competence as key factors in enhancing compliance in educational settings.     

Direct transformation of variational problems into Cauchy systems—II. scalar-semi-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational problem, the solution of integral equations, and the solution of an initial valued system of integrodifferential equations. It will be shown that a large class of variational problems requires the solution of a nonlinear integral equation. It has also been shown that the solution of a nonlinear integral equation is identical to the solution of a Cauchy system. In this paper, we by-pass the nonlinear integral equations and show that the minimization problems directly imply a solution of the Cauchy system. This second paper in the series looks at semi-quadratic functional and scalar functions.     

How to Desire Differently: Home Education as a Heterotopia

This article explores the co‐existence of, and relationship between, alternative education in the form of home education and mainstream schooling. Home education is conceptually subordinate to schooling, relying on schooling for its status as alternative, but also being tied to schooling through the dominant discourse that forms our understandings of education. Practitioners and other defenders frequently justify home education by running an implicit or explicit comparison with school; a comparison which expresses the desire to do ‘better’ than school whilst simultaneously encompassing the desire to do things differently. These twin aims, however, are not easy to reconcile, meaning that the challenge to schooling and the submission to norms and beliefs that underlie schooling are frequently inseparable. This article explores the trajectories of ‘better than’ and ‘different from’ school as representing ideas of utopia and heterotopia respectively. In particular I consider Foucault's notion of the heterotopia as a means of approaching the relationship between school and other forms of education. Whilst it will be argued that, according to Derrida's ideas of discursive deconstruction, alternative education has to be expressed through (and is therefore limited by) the dominant educational discourse, it will also be suggested that employing the idea of the heterotopia is a strategy which can help us explore the alternative in education.