Problem solving and Working Mathematically: an Australian perspective

Abstract

This article reviews ''problem solving'' in mathematics in Australia and how it has evolved in recent years. In particular, problem solving is examined from the perspectives of research, curricula and instructional practice, and assessment. We identify three key themes underlying observed changes in the research agenda in Australia in relation to problem solving: Obliteration, Maturation and Generalisation. Within state mathematics curricula in Australia, changes in the language and construction of the curriculum and in related policy documents have subsumed problem solving within the broader category of Working Mathematically. In relation to assessment, research in Australia has demonstrated the need for alignment of curriculum, instruction and assessment, particularly in the case of complex performances such as mathematical problem solving. Within the category of Working Mathematically, recent Australian curriculum documents appear to accept an obligation to provide both standards for mathematical problem solving and student work samples that illustrate such complex performances and how they might be assessed.

Relations between scientific reasoning, culture of problem solving and pupil's school performance

“…The phrase 'culture of problem solving' can be found in several pieces of work (e.g. Clarke, Goos and Morony;2007;Reiss and Törner, 2007), where the word culture is not strictly defined and can be understood as a more cultivated approach to the studied phenomenon. Such authors as Clarke, Goos and Morony (2007) link the word culture to the word inquiry -culture of inquiry.…”

“…Clarke, Goos and Morony;2007;Reiss and Törner, 2007), where the word culture is not strictly defined and can be understood as a more cultivated approach to the studied phenomenon. Such authors as Clarke, Goos and Morony (2007) link the word culture to the word inquiry -culture of inquiry. When forming the phrase CPS, the word culture was understood from us as a system of various meanings, activities and patterns of behaviour that can be met with in problem solving at schools.…”

Defining mathematical problems and problem solving: prospective primary teachers’ beliefs in Cyprus and England

“…Arcavi and Friendlander (2007) interviewed the managers of different curriculum development projects in Israel and concluded significant differences among the various theoretical and practical approaches to problem solving, even within the same community (curriculum developers), focusing on the same target population (elementary schools) within a centralised system (in Israel) with a uniform syllabus. From the Australian perspective, Clarke, Goos, and Morony (2007) discuss the evolution of the problem-solving research and describe the shift of the research interest from theory development (early 90s) to the investigation of classroom practices. The fact that there is no homogeneity, in so far as perceptions of and research on problem solving within single countries are concerned, has provoked our interest, from a comparative perspective, in the field.…”

Teaching Area Measurement and Subgoals through Problem Solving

“…Table 1.1 summarises these types. Teaching about problem solving (Type D) is the traditional, or default, pedagogical approach widely used in practice (Clarke, Goos, & Morony, 2007;Lester, 2013). In this pedagogical approach, students learn and practise a mathematical procedure, usually divorced from any real-world context.…”

“…Paradoxically, specific problem-solving strategies have remained a component of problem-solving curricula and pedagogy around the world (ACARA, 2017a; Anderson, 2014;Brodie, 2009;Clarke et al, 2007;Ministry of Education Singapore, 2012;OECD, 2013b;Reys, 2014). The appearance of specific problem-solving strategies in curricula and pedagogy brings the dominant position in the literature into question on several fronts.…”