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Another possible reason may be that secondary mathematics teachers are resilient to change.

For example, Thompson , p. This was manifested through their emphasis on the development of basic social arithmetical fluency as a key practical life skill in order to prepare learners for a world beyond school, and a truncated provision for the employment of non-routine mathematical problems. Dominated throughout both sectors is an attainment perspective driven by external forces, that all children must be seen as progressing irrespective of ability.

This was typically accentuated during an interview with Cormac, an inexperienced secondary mathematics teacher who expressed:. I feel under intense pressure to teach not my subject [mathematics] but the exam techniques that the SQA are looking for What appears to be deep-rooted is a culture where the conceptualisation of mathematical problem solving is not fully understood and which, as an essential pedagogical requirement, does not resonate with both sectors. One possible factor presented to explain this result is mathematical self-efficacy, which may help to clarify why some primary teachers do not possess a working knowledge of problem solving strategies such as working backwards, finding a pattern, logical reasoning, etc.

This study found that among secondary mathematics teachers, there is a dominant viewpoint that as a curricula priority, all pupils should possess strong numeracy skills in order to survive in the real world. Misconceptions exist with the conceptualisation of mathematical problem solving, which has triggered a lack of engagement for teaching mathematics through problem solving.

Whilst it is acknowledged by many that this method can release the power of mathematics, such an approach appears to be rarely demonstrated in practice. Concurrently, in terms of a salient learning focus, little support exists for empowering learners to develop critical thinking skills at the expense of passing national examinations in my view it is important to deliberate why some teachers deem these themes to be mutually exclusive.

A recurrent theme in the interviews was a sense among participants that there is insufficient time to engage with problem solving due to excessive workload demands. It can thus be suggested that the vast majority of primary and secondary mathematics teachers are manipulated by a national assessment instrument which shapes their professional practice. It is of considerable interest that problem solving is not amalgamated within the current assessment model for mathematics in Scotland. In his review of Australian education, Clarke , p.

In general, the perpetual resonance between both sectors seems to posit that many of the influences in the formulation of mathematical beliefs that underpin their practice are implicit rather than explicit. In this respect, this finding is consistent with previous research Hudson, Henderson and Hudson, The results of this study show that gender, age and experience have no effect on both sectors. Regarding primary, it is suggested that Deputy Head Teachers hold significantly stronger mathematical beliefs compared with classroom teachers.

Regarding secondary, it was unanticipated that grade had no impact. This is a troubling finding given that senior management are expected to drive reform agendas and uphold professional standards. Pajares , p. Nevertheless, this finding is consistent with previous research. In general, both sectors exhibited a range of positive and negative mathematical beliefs towards the nature of mathematics, the learning of mathematics and the teaching of mathematics.

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In particular, the associated philosophy of mathematical beliefs regarding the nature of mathematics aligns with Ernest whose conceptualised views were designated as instrumentalist, Platonist and problem solving. The findings of this research suggest that limited support for teaching mathematics through problem solving exists and a widespread belief that problems can be solved if you know the right steps to follow. Teachers from both sectors appear to conceive problem solving as an irregular follow on step after learners have acquired the mastery of basic numerical and computational skills coupled with procedural understanding.

Modest encouragement is extant for the promotion of multiple solutions. Overall, it was found that, when judged against the mathematical philosophy as championed by CfE, primary teachers hold significantly stronger positive mathematical beliefs than secondary mathematics teachers.

Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving

Although the current study is based on a moderate sample of participants, the findings suggest that the conceptualisation and operationalisation of mathematical problem solving is restricted in practice. A number of variables impinge on the process including a lack of a shared understanding of what constitutes a mathematical problem. According to Raymond , p. Finally, from a personal perspective, this research experience has been enriched by the decision to engage in a cross-sector study.

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It furnished me with increased professional knowledge, coupled with a wider appreciation of the diversity that exists across classrooms and schools. Future studies should attempt to identify additional evidence that Curriculum for Excellence requires further conceptual clarity and detailed guidance on the effective mobilisation of problem solving.

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Qualitative Research in Psychology , 3 2 , pp. CAI, J. Evaluation of mathematics education programs.

Teaching and Learning Mathematical Problem Solving

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International Encyclopaedia of Education. Oxford: Elsevier, 3, pp. Solution representations and pedagogical representations in Chinese and U. Journal of Mathematical Behavior , 24 , pp. Problem solving in Chinese mathematics education: research and practice. ZDM Mathematics Education , 39, pp. A rational for assessment alternatives in mathematics. The Australian Mathematics Teacher , 46 3 , pp.

Research methods in education , 7 th edn, Oxon: Routledge. Fennema and B. Nelson Eds. Mathematics teachers in transmission, Mahwah: Lawrence Erlbaum, pp. Report of a review of teacher education in Scotland. The Scottish Government. Scottish survey of literacy and numeracy SSLN Professional Learning Resource. The Scottish context for the curriculum. Arthur and T. Cremin Eds. Learning to teach in the Primary school, 2 nd edn, London, Routledge, pp.

Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving | SpringerLink

Future directions and perspectives for problem solving and curriculum development. The impact of beliefs on the teaching of mathematics. Ernest Ed. Mathematics teaching: The state of the Art. London: Falmer Press, pp.

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The standard for career-long professional learning: supporting the development of teacher professional learning. Beliefs - No longer a hidden variable in mathematical teaching and learning processes. The heart of mathematics. The American Mathematical Monthly , 87 7 , pp. I want to be a mathematician. An automathography. New York, Springer-Verlag. Mathematics Education Research Journal , 15 1 , pp. Ruffling the calm of the ocean floor: merging practice, policy and researching assessment in Scotland. Oxford Review of Education , 30 3 , pp.