A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

Using parent report to assess bilingual vocabulary acquisition: a model from Irish

This chapter describes the adaptation of a parent report instrument on early language development to a bilingual context. Beginning with general issues of adapting tests to any language, particular attention is placed on the issue of using parents as evaluators of child language acquisition of a minority language in a bilingual context. In Ireland, Irish is the first official language and is spoken by about 65,000 people on a daily basis. However all Irish speakers are bilingual, and children are exposed to the dominant English language at an early age. Using an adaptation of a parent report instrument, 21 typically developing children between 16 and 40 months were assessed repeatedly over two years to monitor their language development. The form allowed parents to document their children’s vocabulary development in both languages. Results showed that when knowledge of both languages was accounted for, the children acquired vocabulary at rates similar to those of monolingual speakers and used translational equivalents relatively early in language development. The study also showed that parents of bilingual children could accurately identify and differentiate language development in both of the child’s languages. Recommendations for adapting and using parent report instruments in bilingual language acquisition contexts are outlined.