Cabinetmakers’ Workplace Mathematics and Problem Solving

This study explored what kind of mathematics is needed in cabinetmakers’ everyday work and how problem solving is intertwined in it. The informants of the study were four Finnish cabinetmakers and the data consisted of workshop observations, interviews, photos, pictures and sketches made by the participants during the interviews. The data was analysed using different qualitative techniques. Even though the participants identified many areas of mathematics that could be used in their daily work, they used mathematics only if they were able to. The cabinetmakers’ different mathematical skills and knowledge were utilized to their skill limit. Cabinetmakers were found to constantly face problem solving situations along with the creative processes. Being able to use more advanced mathematics helped them to solve those problems more efficiently, without wasting time and materials. Based on the findings, the paper discusses the similarities and differences between problem solving and creative processes. It is suggested that the combination of craftsmanship, creativity, and efficient problem solving skills together with more than basic mathematical knowledge will help cabinetmakers in adapting and surviving in future unstable labour markets.     

‘I <3 my high-performance dog’: love for the sport in agility coach representations in social media

In contrast to its inception as intermission entertainment at the Crufts Dog Show in the UK in the late 1970s, dog agility has become a worldwide steadily professionalized and entrepreneurialized sport with reputable coaches and training programs over the last decade. This change raises concerns about the pressures placed on dogs. We look at the potential incommensurability of ‘loving’ a dog as a companion animal and making the dog engage in competitive sports. We evaluate texts, photographs and videos from successful agility coaches and identify four types of loving relationships through which the coaches express their commitment to the sport. While an affinity for dogs appears important for building the coaches’ reputation and provides the justification for engaging the dog in physically and mentally demanding sports, the question remains whether this dogmanship can be straightforwardly turned into action.     

Coherent Knowledge Structures of Physics Represented as Concept Networks in Teacher Education

A characteristic feature of scientific knowledge is the high degree of coherence and connectedness of its conceptual structure. This notion is also behind the widely accepted instructional method of representing the concepts as networks. We suggest here that notions of explanatory coherence and deductive coherence naturally connect the structure of knowledge to the processes which are important in constructing the concept networks. Of these processes, experimental method and modelling are shown to be closely connected with explanatory and deductive coherence, respectively. From this viewpoint, we compare here how experts and novices represent their physics knowledge in the form of concept networks, and show that significant differences between experts’ and novices’ quality of knowledge become directly reflected in the structure of the networks. The results also show how concept networks make visible both the structure of knowledge and the methodological procedures, which support its formation.     

Gender Neutralities, Dichotomies and Hidden Inequalities: Analysis of Vocational Teachers’ Reflections on Gender in the Profession

This article analyses how Finnish vocational teachers make sense of the meanings of gender in their work. The context of the study consists of the two most gender segregated environments of vocational education: the female-dominated Sector of Health and Social Services and the male-dominated Sector of Technology and Transport. Our analysis draws on 23 teacher interviews conducted in two vocational institutions, offering vocational upper secondary education and training to both young and adult students. The data is analysed from post structural and material feminist theoretical positions, using various conceptualizations of gender. Our findings suggest that both male and female teachers have adopted the idea of gender neutrality, whilst they simultaneously provide dichotomical and hierarchical perceptions of men and women as vocational teachers. Consequences of minority position in the staff room are different for females and males. In the field of technology and transport, women in the minority, on the other hand, need to struggle continuously with masculine vocational hierarchies to gain professional respect.     

PAIR: a cooperative effort to meet informational needs

St. Joseph Mercy Hospital organized a cooperative association of area institutions (the Pontiac Area Instructional Resources group: PAIR) in order to (1) promote a forum in which to exchange ideas and information on software used for learning materials and hardware for using such materials, (2) provide a resource library system to lend such learning materials, and (3) cooperatively produce such learning materials for use in member institutions. In less than one year of cooperation, a union list of serials and a union list of software for the area have been produced. A forum has been created in which ideas and information can be shared, and a sound/slide program has been produced.     

Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used

In this paper, we focus on Finnish pre-service elementary teachers’ (N?=?269) and upper secondary students’ (N?=?1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: “We know that 498:6?=?83. How could you conclude from this relationship (without using long-division algorithm) what 491:6?=?? is?” This problem especially measures conceptual understanding, adaptive reasoning, and procedural fluency. Based on the results, we can conclude that division seems not to be fully understood: 45% of the pre-service teachers and 37% of upper secondary students were able to produce complete or mainly correct solutions. The reasoning strategies used by these two groups did not differ very much. We identified four main reasons for problems in understanding this task: (1) staying on the integer level, (2) an inability to handle the remainder, (3) difficulties in understanding the relationships between different operations, and (4) insufficient reasoning strategies. It seems that learners’ reasoning strategies in particular play a central role when teachers try to improve learners’ proficiency.     

Vocational teachers' gendered reflections on education,teaching and care

In this article, we discuss teachers' reflections on the relation between teaching and care in the two most gender-segregated sectors of vocational upper secondary education in Finland, namely Health and Social services and Transport and Technology. We first discuss the concepts around education, teaching, taking care for and caring about students, using theoretisations of care and feminist pedagogies. Using teacher interviews and field notes, we then analyse teachers' ambivalence about care work in the context of teaching, placing special emphasis on care as a gendered task, and then discuss the ‘moral panic’ or ‘worry speech’ about young people in vocational education from the perspective of caring about. The findings are reflected through earlier studies in lower secondary schools. We argue that even if teachers in vocational education, especially male teachers, tend to feel awkward about caring work, they cannot avoid it, and they do care about their students and regard care as a general responsibility.     

Socio-emotional orientations and teacher change

In this article we consider how elementary education students’ views of mathematics changed during their mathematics methods course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation, two with negative views of the subject and an ego-defensive orientation. The biggest change observed was that the trainees’ views of teaching and learning mathematics became more positive. Moreover, what had been an ego-defensive orientation changed towards a social-dependence orientation. The crucial facilitators of change seemed to be (1) handling of and reflection on one’s experiences of learning and teaching mathematics, (2) exploring content with concrete materials, and (3) collaboration with a partner or working as a tutor of mathematics.