One and One is Sometimes Three in Small Group Mathematics Learning

In recent years, Mathematics teaching has been confronted by demands for higher standards and better pupil achievement in several parts of the world. Researchers have suggested the shift from teacher‐centred instruction towards more active participatory learning methods as one way to improve the quality of the teaching and learning process. The tension between whole‐class teaching versus small group learning in Mathematics has been particularly apparent in many education systems. This article analyses the development of Mathematics teaching by asking whether small group learning is an effective arrangement in teaching school Mathematics. We conclude that although there is no unanimity about the affects of small group learning on student achievement in school Mathematics, it seems that it produces at least equal academic outcomes among all students compared to more traditional methods of instruction. Working in pairs is a particularly effective form of learning Mathematics and that small groups are beneficial for developing mathematical problem‐solving skills. We also conclude that the present educational policies and increased quality assurance structures in many countries conflict, or are not consistent with scientific‐professional thinking and research on the teaching of Mathematics.     

An Objectivist Critique of Relativism in Mathematics Education

Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.     

Qualitative data analysis in cross‐cultural projects

Large‐scale research projects, conducted in a cross‐European context, are increasingly attractive to educational researchers and policy‐makers. However, this form of comparative research across cultures brings problems concerning the standardization of data collection and analysis, particularly where ethnographic research is concerned, as it prioritizes a full range of qualitative research strategies. This paper outlines the use of a universal model and the approaches recently taken by two research teams and contrasts these with another recent nine‐partner comparative European study that used ethnographic methods. We then describe the analytical procedures used in the project, which encouraged participant observation and individual researcher interpretation in order to generate grounded accounts and outline how they were culturally sensitive and meaningful to research teams who used varied analytical approaches. However, this raised difficult issues for the ‘final’ analysis and the production of a loosely coupled research report. Our pragmatic solution was a process of ‘qualitative synthesis’ whereby individual partner reports were collated by the Project Director and treated as data and a grounded theory approach was applied to generate tentative theory in respect of creative learning. The paper concludes by arguing that data generated by a loosely coupled approach to qualitative comparative research which uses a wide range of data collection methods can be effectively analysed with a qualitative synthesis.     

Coping Collectively: The formation of a teacher self-help group

Some social movements theorists argue that contemporary social movements such as pressure groups and support groups are increasingly fulfilling the protest function of political parties and trades unions in post-industrial societies. Furthermore, these social, cultural, emotional and economic developments are occurring on a global scale. This article is an ethnographic account of teachers in an English local education authority who formed a self-help group for what they perceived to be 'bullied' (i.e. abused in the workplace) local authority and private sector employees. This was a mode of collective rather than individual coping. The identity work involved in self-renewal for these workers was a collective, social and political process, involving networking with other similar individuals and groups nationally. I argue that, given the decline in trades union powers, the teachers can be considered to be reinventing collectivity and collective protest. And the self-help group studied is not fundamentally different in character to labour movements of the past.     

Education in England – a testbed for network governance?

Abstract

Since devolution in the late 1990s, education policy in England has diverged further from that in Scotland and also from policy in Wales and Northern Ireland. In this paper we review the roots and trajectory of the English education reforms over the past two decades. Our focus is the schools sector, though we also touch on adjoining reforms to early years and further and higher education. In so doing, we engage with various themes, including marketisation, institutional autonomy and accountability. Changes in governance arrangements for schools have been a defining feature of education reforms since devolution. This has been set against an evolution in national performance indicators that has put government priorities into ever sharper relief. In theorising the changes, we pay particular attention to the suggestion that the English education system now epitomises the concept of ‘network governance’, which has also been applied to education in a global context. We question the extent to which policies have in practice moved beyond the well-established mechanisms of ‘steering at a distance’ and undermined the very notion of an education system in England. We conclude by considering possible futures for education policy and how they may position England in relation to other parts of the UK and the wider world.     

Why lecturers still matter: the impact of lecturer-student exchange on student engagement and intention to leave university prematurely

This research examines the impact of lecturer-student exchange (student-LMX) on engagement, course satisfaction, achievement, and intention to leave university prematurely for 363 students in one Australian university. Survey and grade point average (GPA) data were collected from domestic undergraduate first- and second-year students and analysed using structural equation modelling. The results indicated that student’s levels of engagement and course satisfaction fully mediated the relationship between student-LMX and intention to leave university, when demographic and socio-economic factors were controlled for. In an era when low student engagement and attrition is often attributed to individual demographic factors, and lecturers are under increasing threat of being replaced by technology, this research offers compelling evidence regarding the role of lecturer-student relationships in enhancing tertiary student outcomes.     

Methods of analysis and overall mathematics teaching quality in at-risk prekindergarten classrooms

Research Findings: This study analyzed the quality of teacher–child interactions across 10 videotaped observations drawn from 5 different prekindergarten classrooms delivering the same mathematics curriculum: MyTeachingPartner–Math. Interactions were coded using 2 observational measures: (a) a general measure, the Classroom Assessment Scoring System (CLASS); and (b) a math-specific measure, the Classroom Observation of Early Mathematics–Environment and Teaching (COEMET). Practice or Policy: High correlations were found between the 2 measures, suggesting that the CLASS may serve as a sufficient metric to determine the quality of mathematics instruction in prekindergarten, though the COEMET may provide finer grained detail about teachers’ practice. Results indicate that the quality of mathematics instruction provided by teachers generally fell in the low- to medium-quality range and did not differ significantly across curriculum-related contextual factors.