Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.     

Parental beliefs and their role in child-rearing

Beliefs have been a topic of considerable interest among researchers in various fields. In this article 71 articles reporting a study on parental beliefs and published in the course of fifteen years (1980–1995) are reviewed. After clarifying the term ‘belief’, the topics and the methodological solutions of the studies are discussed. Throughout the discussion the question of the origins of parental beliefs and the belief — behaviour dilemma are dealt with. Finally, the implications of the findings and suggestions for future research are presented.     

Conflicts of interest: an indispensable element of education for sustainable development

A central concept introduced in the Nordic debate on sustainable development is ‘action competence’. The concept has been defined as a competence of learners, i.e. the ability to take into consideration the social factors and human conflicts of interest that lies behind environmental questions and sustainable development. The concern of this article is the role of such conflicts for making meaning in relation to sustainable development. With this aim, we analyze a series of interviews with seven high school students. Our analysis takes its point of departure in the works of Dewey and Wittgenstein. It shows that the dialogue partners in this study continuously put one another in the position of having to make communicative choices in the dialogue. Moreover, the choices facing these dialogue partners can be translated into human conflicts of interest of a broader kind. A conclusion we draw from our work is that value judgments dealing with human conflicts of interest are a foundation upon which the dialogue on sustainable development is constructed, and that they seem to be a prerequisite if the dialogue is not to come to a standstill. We discuss the consequences of this finding for education for sustainable development.     

Linguistic Resources Used in Grade 8 Students’ Submicro Level Explanations—Science Items from TIMSS 2007

Explanations involving submicro levels of representation are central to science education, but known to be difficult for students in secondary school. This study examines students’ written explanations of physical and chemical phenomena regarding matter and changes in matter, in a large-scale test. This is done in order to understand linguistic challenges in constructing submicro level explanations involving the particle model of matter. Drawing from systemic functional linguistics, the lexicogrammatics used in explanations for realising experiential meaning in student explanations were analysed. We used answers to two partly constructed response items from the Swedish part of Trends in International Mathematics and Science Studies 2007, grade 8, to sort out explanations referring to the particle model of matter. These answers (86 from 954) were analysed regarding choices of vocabulary and grammar to distinguish between macro and submicro level of representation. The results show that students use a wide variety of lexicogrammatical resources to realise what happens on both macro and submicro level of representation, with greater diversity of verbs on the submicro level of explanation. The results suggest an uncertainty about the distinction between macro and submicro level of explanation.     

Governing through non/recognition: the missing ‘R’ in the PLAR for immigrant professionals in Canada and Sweden

Despite claims that prior learning assessment and recognition (PLAR) can act as a transformative social mechanism and a means of social inclusion, this study reports that PLAR has become a serious barrier to adult learning rather than a facilitator. Drawing from Foucault’s concept of governmentality, the study examines the difficulties that immigrant professionals have experienced in having their foreign credentials and work experience recognized in the contexts of Canada and Sweden. Using document analysis and interviews, the study analyses how PLAR has created a system of governing through technologies of power and technologies of the self which work as dividing practices in discounting and devaluating immigrants’ prior learning and work experience. The study concludes that PLAR has become a technical exercise and a governing tool rather than a form of social transformation.     

Number of Judges when Scaling Attitude Items

Sjödahl, L. 1974. Number of Judges when Scaling Attitude Items. Scand. J. educ. Res. 18, 183‐197. When constructing attitude scales for measuring patient‐centering among student nurses the author has carried out a series of studies of the method of attitude scale formation. The article presents one of several methodological studies published by the same author in Ped. psyk. problem (nr. 184). Scale values, interquartile range, interval position and the selection of items for the final scale are studied as dependent variables when varying the size of the judging group. The results show that correlations between series of scale values from judging groups of varying sizes can be very high but that we can still get quite a different selection of items for the final scale, depending upon which judging group we use in the scaling procedure. The stability of the interval placements of the statements is shown to vary with the intervals along the scale.     

Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms

Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students’ attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.     

Cross‐Country Skiing

The purpose was to study the adaptation to speed in the temporal patterns of the movement cycle and determine any differences in velocity, cycle rate and cycle length at the maximum speed level in the different classical style and freestyle cross‐country skiing techniques. Eight skilled male cross‐country skiers were filmed with a digital video camera in the sagittal plane while skiing on a flat cross‐country ski track. The skiers performed three classical style techniques the diagonal stride, kick double poling and the double poling technique and four freestyle techniques paddle dance (gear 2), double dance (gear 3), single dance (gear 4) and combiskate (gear 5) at four different self‐selected speed levels slow, medium, fast and their maximum. Cycle duration, cycle rate, cycle length, and relative and absolute cycle phase duration of the different techniques at the different speed levels were analysed by means of a video analysis system. The cycle rate in all tested classical and freestyle techniques was found to increase significantly (p < .01) with speed from slow to maximum. Simultaneously, there was a significant decrease in the absolute phase durations of all the investigated skiing techniques. A minor, not significant, change in cycle length, and the significant increase in cycle rate with speed showed that the classical and freestyle cross‐country skiing styles are dependent, to a large extent, on an increase in cycle rate for speed adaptation. A striking finding was the constant relative phase duration with speed, which indicates a simplified neural control of the speed adaptation in both cross‐country skiing styles. For the practitioner, the knowledge about the importance of increasing cycle frequency rather than cycle length in the speed adaptation can be used to optimise a rapid increase in speed. The knowledge about the decrease in absolute phase duration, especially the thrust phase duration, points to the need for strength and technique training to enable force production at a high cycle rate and skiing speed. The knowledge that the relative phase duration stays constant with speed may be used to simplify the learning of the different cross‐country skiing techniques.     

Lab Work and Learning in Secondary School Chemistry: The Importance of Teacher and Student Interaction

Laboratory work is considered essential in promoting students’ learning of science and of scientific inquiry. What the students perceive as important to learn from a regular laboratory exercise is probably affected by the teacher’s objectives. We study the extent to which one teacher’s objectives are fulfilled during lab work, and how teacher–student and student–student interactions contribute to developing learning experiences from the laboratory exercise. Do students encounter opportunities to learn in agreement with the teacher’s objectives? This explanatory single case study includes use of a palette of methods, such as pre- and post-interviews, observations and video documentation from an experienced secondary school teacher and her 8th grade (aged 13–14) students’ laboratory work. Our results point to the importance of teacher involvement to help students understand what to look for, how to do it and why. Especially teacher–student interactions during lab work seemed to influence what students perceived as important to learn. In the laboratory exercise in this case, the teacher helped the students to observe and to use their observations in their explanations. The lab work included learning experiences other than those addressed by the teacher, and the teacher’s intentions were partially fulfilled. Not only what the teacher says, but also how the teacher acts is important to help students understand what to learn from a laboratory exercise.     

Questioning two myths in innovation literature

Which knowledge is most important in the completion of innovative processes? In which contexts does such knowledge develop? The combination of an in-depth case study, theory and reasoning formed the platform from which conclusions could be drawn. One conclusion is that the strategic knowledge necessary for innovation not only concerns technology. It is rather about business intelligence, funding, marketing and other non-technical areas. Moreover, the production and development of frontline knowledge and research is not the sole province of universities. In many areas, companies are far ahead of universities. Both conclusions differ from the assumptions in mainstream innovation literature.