Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’.     

Rhetoric and poetry

To win in 1972 the Democrats needed a unified rhetoric. Their strategy was to emphasize persona. The breaking news of Senator Eagleton's mental health, coming at a strategic time, created a fantasy that chained through the electorate and presented the McGovern persona as inconsistent, inept, and untrustworthy.     

What are we trying to understand and improve? Educational research as Leerlaufreaktion. 1

The problems that educational research are supposed to solve have been poorly analyzed and the basic phenomena that we are trying to understand have not been clearly described. Educational experimenters often resemble Leerlaufreaktionen in lower animals, i.e., complex, highly integrated activities that take place despite the absence of an appropriate environmental occasion.

We have tended to forget the practical origins of science and have allowed ourselves to be dominated by overly abstract ideas that betray our goals. Experimenters require tangible events to think and wonder about in order to improve their intuitions and in order to generate and test ideas that will deepen our understanding of nature and make a real difference in the practical world. Better observations of what actually goes on in instructional situations are therefore needed and more detailed records of teaching and learning must be kept. An instructional record‐keeping system called a course memory is described.     

Letters to the editor

This study examines editorial photography in nine major erotica magazines to determine how pictures vary as a function of the social class, gender and sexual preference of the intended readership. The analysis reveals that upwardly‐mobile, heterosexual men are treated to idealized images, whereas working‐class, heterosexual men are presented with more mundane yet highly‐sexualized images. Heterosexual women are provided with photographs of nude males in a low‐sexual context. Magazines for homosexual men present images, except for gender, very similar to those created for upwardly‐mobile, heterosexual men. These patterns are discussed from a functionalist perspective to show how erotica magazines contribute to social‐order maintenance.     

Primary school children's health-enhancing physical activity patterns: the school as a significant environment?

The moderate-to-vigorous physical activity (MVPA) of 70 children (age 8.6 years; 40 boys) was measured and gender and age differences were compared. Boys spent 28 minutes per day more than girls in MVPA (p=0.02, d=0.54), and younger children accumulated 24 minutes more MVPA than older peers (p=0.0001, d=0.91). Similar gender and age-related trends were apparent during segmented periods of the day. The majority of daily MVPA was accrued during school-related time (56.4±9.1%; p=0.0001, d=1.57). The findings reinforce the significance of schools as key environments for MVPA participation and promotion.     

The mathematical education of engineers

Mathematics has always played an important role in the education of engineers and production managers. At the present time, the importance of mathematics has increased significantly and it is quite natural that in universities around the world engineering students are taking courses in mathematics which constitute, as a rule, a significant portion of their programme. At the same time, however, the mathematical education of the engineer is far from ideal and its improvement deserves the closest scrutiny. The present article deals with several general aspects of this problem.