Different ways in which students handle chance encounters in the explorative setting of a dice game

The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were tape-recorded and fully transcribed, the students were encouraged to explore strategies for winning a specifically designed dice game based on the sum of two dice. The dice game included four different set-ups of dice designed to bring to the fore different aspects of probability modelling and to offer the student the opportunity to encounter small differences in the mathematical structure of the sample space and of the probability distribution between the four different set-ups. The study describes strategies that the students use when confronted with these different set-ups, what their activities imply in terms of resources in handling random phenomena and what the dice game offers in terms of opportunities for learning probability. In order to explain such meaning-making processes the students’ activities are viewed from a perspective that takes into consideration how the students’ understanding varies with their interpretations of the situation they are confronted with, i.e., how they contextualize the different set-ups of the dice game. The results show how the students, during the course of the game, reorganize their interpretations of the mathematical content confronting them, and how a variation of guiding principles becomes the object of exploration. Approaches of extremes and a number model are described as a means for the students to identify and assign probabilities for the total of two dice.     

Academics’ Strategies and Obstacles in Achieving Collaboration between Universities and SMEs

There is an ongoing debate both in the United States and Europe about the need to develop a broader view of scholarship and the different activities connected with it, including ‘service to the community’. This empirical study reveals that researchers who are engaged in collaboration with small and medium enterprises (SMEs) encounter many hindrances within the academic structure and obstacles due cultural differences that needs to be overcome. But it is also evident that they are creative and learn different strategies in accomplishing their goals and they also bring back useful experiences and knowledge from their cooperation into their research and teaching within the academic organization. We suggest that attention should be paid to the broader and more elaborate view of collaborative knowledge production that we present in the article if university structures are to provide better support for their academic staff to interact profitably with the community, and thereby create a ‘win-win situation’ for everyone involved.

     

Researching undergraduate social science research

The experience(s) of undergraduate research students in the social sciences is under-represented in the literature in comparison to the natural sciences or science, technology, engineering and maths (STEM). The strength of STEM undergraduate research learning environments is understood to be related to an apprenticeship-mode of learning supported by more experienced (post-graduate) peers, often through ongoing research projects. Studies of undergraduate research reveal that this is not typical in the social sciences, and students report facing specific challenges to the development of their identities as researchers that include fear, intellectual confusion and emotional unsettlement. This paper examines how a social science learning environment, designed as a research study itself, fostered beginning researchers communities of practice, realised a distinct mode of apprenticing based on peers’ similarly peripheral community membership, and enabled students to reframe emotional unsettlement. It argues that, effectively mediated, talk can powerfully improve undergraduate social science research students’ experiences.     

Deaf children's use of cognitive strategies in simple arithmetic problems

Research shows that deaf children have inferior achievement in simple arithmetic compared to their hearing agemates. The reported study investigates whether the reasons for deaf children's poor achievement can be sought in their strategy development. As this is a central issue, the strategies used by deaf children when solving symbolic addition and subtraction problems are identified, classified and compared to findings from earlier research, involving both deaf and hearing children. The effect of Sign Language in strategy invention and use is the main concern in this study. One result from the present study is that structural aspects of Sign Language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but instead to refined procedural competence. This is a development in simple arithmetic that is compatible with that of less able hearing children. The counting procedures used by the deaf children involve both oral counting and Sign Language counting. Due to the small sample size, and the shortcomings of the research design, the results are more suggestive than conclusive. Thus, further studies are needed in this area.This revised version was published online in September 2005 with corrections to the Cover Date.     

Focal event,contextualization, and effective communication in the mathematics classroom

The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12 to 13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.     

Knowledge outside the box – sustainable development education in Swedish schools

Background: Sustainable development, as an area of knowledge, appears in several different places in the curriculum and does not fit neatly within the scope of traditional subject areas. In many countries, including Sweden, it has long been upheld as an important tool for increasing understanding of, and dealing with, environmental problems. It is not clear, however, what role education can actually have in the making of a more sustainable future. Even though there are several potential ways for sustainable development to be involved in education, the concept raises many questions when transferred to the school context.

Purpose: This paper investigates how teachers deal with the difficulty of defining and approaching sustainable development as an area of knowledge in Swedish schools.

Sample: This article is based on semi-structured interviews with 40 teachers, 13 of whom were lower secondary school teachers (pupil age 12–15) and 27 were upper secondary school teachers (pupil age 15–18). The study involves teachers in all subjects where sustainable development is a goal in the syllabus. The study is also based on participant observation in one upper secondary class. A total of 17 different schools were involved, from a wide range of locations in Sweden.

Design and methods: The paper builds on qualitative data and the analysis of transcribed interviews and group interviews with teachers in Swedish lower and upper secondary schools. Group interviews, involving three or more people, were conducted on eight occasions. The pupils at an upper secondary school were also observed while they were working on a course called ‘policy and sustainable development’. Data were transcribed and analysed thematically.

Findings: The analysis suggests that, according to the teachers’ experiences, the demands of equivalence and measurability in school have increased and that this affects how sustainable development is approached in teaching and learning. Three main categories of knowledge were identified. The study also presents two representations that model how teachers may approach knowledge about sustainable development – metaphorically termed ‘the Accountant’ and ‘the Adventurer’ – and their different effects on knowledge.

Conclusions: There is a tendency for complex knowledge areas such as sustainable development, which do not fit seamlessly into traditional curriculum subjects, to become oversimplified when translated into teaching situations. According to the representations that we described metaphorically, the teacher, as an accountant, is characterised by ‘knowledge instrumentalism’, which means that teachers administer knowledge and the pupils consume it. In this transactional model, the accountant is also very dependent on external governance and control. Alternatively, the teacher, as an adventurer, is characterised by authority, knowledge and self-control. In this model, knowledge sometimes grows in an unpredictable way in the meeting between people who share common experiences. For adventurers, sustainable development is a matter of commitment and awareness, and it involves an explicit stance. The metaphors can be placed on a continuum which describes how teachers manage the demands of the school system in relation to the knowledge area of sustainable development.     

Mandatory coursework assignments can be,and should be,eliminated!

Formative assessment can serve as a catalyst for increased student effort and student learning. Yet, many engineering degree programmes are dominated by summative assessment and make limited use of formative assessment. The present case study serves as an example on how formative assessment can be used strategically to increase student effort and improve student learning. Within five courses of an engineering bachelor degree programme in Norway, the mandatory coursework assignments were removed and replaced by formative-only assessment. To facilitate the formative assessment, weekly student peer-assessment sessions were introduced. The main findings include an increase in student study hours and improved student performance on the examinations. Finally, interviews were conducted by an external consultant in an effort to identify key factors that attributed to the positive outcome.