Contradictions,dialectical oppositions and shifts in teaching mathematics

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is οn the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging contradictions and we elaborate on the construct of dialectical opposition to understand the nature of these contradictions and their potential for teacher learning. We provide evidence that discussions about contradictions and their dialectical character in the two groups support teachers to engage differently in mathematics teaching and learning and carry potentials for shifts in the practices that evolve in their classrooms. Our study addresses empirically in the context of mathematics teaching the philosophical claim about the role of contradictions as a driving force for any dynamic system.     

Whose ‘voice’ is it anyway? The paradoxes of the participatory narrative

This study discusses some of the paradoxes found in the rhetoric of participatory research. Research-with-children views them as competent and agentic and as social actors, as citizens with opinions that must be listened to and given due weight. This image of the child as a social actor fails to acknowledge the structural, contextual and relational conditions that can afford or restrict opportunities for children’s agentic action. It conceals the multi-faceted, multi-dimensional properties of power that shape children’s (and adults’) contributions and ‘voices’. Our research took place in a primary school and aimed at training Year 6 children to carry out their own research on their chosen topic of interest. The participatory research ‘space’ was informed by the participants’ different intentionalities and agendas. The children were invited to take initiatives and make decisions, to be agentic. However, their agency, or what counts as ‘proper’ agency, was framed and defined in our adult terms. Tensions arose when the children’s agendas conflicted with and threatened ours. As we argue here, this participatory space should rather be seen as a political arena, where different and often competing agendas are at play, where the roles and relationships between children and adults are far from fixed, and where the capacity for agentic action is always socially mediated and shaped by social structure.     

Promoting teachers’ awareness about mathematics,its teaching and learning

Journal of Mathematics Teacher Education -     

Mathematics teacher professional learning and teacher education practices

Journal of Mathematics Teacher Education -     

Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development

This paper is methodologically based, addressing the study of mathematics teaching by linking micro- and macro-perspectives. Considering teaching as activity, it uses Activity Theory and, in particular, the Expanded Mediational Triangle (EMT) to consider the role of the broader social frame in which classroom teaching is situated. Theoretical and methodological approaches are illustrated through episodes from a study of the mathematics teaching and learning in a Year-10 class in a UK secondary school where students were considered as “lower achievers” in their year group. We show how a number of questions about mathematics teaching and learning emerging from microanalysis were investigated by the use of the EMT. This framework provided a way to address complexity in the activity of teaching and its development based on recognition of central social factors in mathematics teaching–learning.     

Teachers’ and researchers’ collaboration in analysing mathematics teaching: A context for professional reflection and development

The study reported here concerns 4 years of collaboration between secondary school teachers and academic researchers, constituting an emerging community of inquiry into mathematics teaching. In the article, the process of the forming of this community is discussed, focusing on the reflective activity developed by its members as well as the tensions and conflicts that emerged in the shaping of an inquiry identity by them. Furthermore, shifts in the mode of participation in the community and thus learning gains of all members are identified, with the teachers gradually developing an awareness of teaching practice in general, and the researchers becoming progressively acquainted with the reflexive relationship between inquiring into teaching practice and teachers’ professional development.     

Mathematical practices in a technological workplace: the role of tools

This paper investigates the role of tools in the formation of mathematical practices and the construction of mathematical meanings in the setting of a telecommunication organization through the actions undertaken by a group of technicians in their working activity. The theoretical and analytical framework is guided by the first-generation activity theory model and Leont’ev’s work on the three-tiered explanation of activity. Having conducted a 1-year ethnographic research study, we identified, classified, and correlated the tools that mediated the technicians’ activity, and we studied the mathematical meanings that emerged. A systemic network was generated, presenting the categories of tools such as mathematical (communicative, processes, and concepts) and non-mathematical (physical and written texts). This classification was grounded on data from three central actions of the technicians’ activity, while the constant interrelation and association of these tools during the working process addressed the mathematical practices and supported the construction of mathematical meanings that this group developed from the researchers’ perspective. Technicians’ emerging mathematical meanings referred to place value, spatial, and algebraic relations and were expressed through personal algorithms and metaphorical and metonymic reasoning. Finally, the educational implications of the findings are discussed.     

Inspiratory muscle training effects on oxygen saturation and performance in hypoxemic rowers: Effect of sex

ABSTRACT

Exercise-induced arterial hypoxemia (EIAH) has been consistently reported in elite endurance athletes. This study examined the effects of an inspiratory muscle training protocol (IMT) on resting pulmonary function, end-exercise arterial oxygen saturation and performance in hypoxemic rowers. Twenty male and sixteen female well-trained hypoxemic rowers were divided into four groups: IMT-male, control-male, IMT-female and control-female. The IMT groups, additionally to the regular training, performed IMT (30 min/day, 5 times/week, 6 weeks). Before and after training, groups underwent an incremental rowing test, a 2000-m time trial and a 5-min “all-out” race. IMT increased respiratory strength in the IMT-male (135 ± 31 vs. 180 ± 22 cmH₂O) and IMT-female (93 ± 19 vs. 142 ± 22 cmH₂O) (P < 0.05). The IMT-female group exhibited lower EIAH and improved rowing performance in the 2000-m time trial (487 ± 32 vs. 461 ± 34 sec) and in the 5-min “all-out” test (1,285 ± 28 vs. 1,310 ± 36m) (P < 0.05). IMT protocol improved performance in IMT-male only in the 5-min test (1,651 ± 31 vs. 1,746 ± 37m) (P < 0.05). IMT may be a useful tool for increasing respiratory strength and enhancing performance in hypoxemic rowers, especially for women.

Abbreviations: EIAH: Exercise-induced arterial hypoxemia; IMT: inspiratory muscle training protocol; PaO2: partial pressure of arterial oxygen; SaO2: arterial oxyhemoglobin saturation; VO2max: maximal oxygen consumption; [(A-a)DO2]: alveolar-to-arterial oxygen difference; VA/Q: ventilation-perfusion inequality/mismatching; PImax: maximal inspiratory pressure; BMI: body mass index; BSA: body surface area; FVC: vital capacity; FEV1: forced expiratory volume in 1 sec; VCin: vital capacity; MVV12: maximal voluntary ventilation in 12 sec     

The ecology of role play: Intentionality and cultural evolution

This study examines the evolutionary function of children's pretence. The everyday, cultural environment that children engage with is of a highly complex structure. Human adaptation, thus, becomes, by analogy, an equally complex process that requires the development of life skills. Whilst in role play children engage in ‘mimesis’ and recreate the ecology of their world in order to gradually appropriate its structures. Role play enables them to create their group cultures, through which they communally explore and assign meaning to their worlds and themselves in it. The research took place in a Greek state school and employed participant and non‐participant observation of the children's role play sessions. The findings, grouped under four thematic categories, may reflect the players’ adaptation and evolutionary processes but also the expression of their deeply rooted, existential concerns at that particular stage of their development.