This study is based on the stance that Polya's "Look Back," though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project,…

College students' epistemological belief in their academic performance of mathematics has been documented and is receiving increased attention. However, to what extent and in what ways problem solvers' beliefs about the nature of mathematical knowledge and thinking impact their performances and behavior is not clear and deserves further…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

Describes a study in which Australian children aged 5-8 years old (N=70) were presented with a range of measurement tasks to determine the strategies and devices that they would choose to use to measure length. Results are in conflict with the normal curriculum sequence. Contains 30 references. (DDR)

In this paper, some aspects of French mathematical education theory concerning "problem situations" are taken into account. In this theoretical framework, the choice of problem situations is fundamental in order to allow pupils to make hypotheses, to mobilize their knowledge, to argue, and finally, to construct new knowledge. Certain…

Presents the experiences of a Russian mathematician teaching in Russian and American Universities. Topics discussed include what was taught, the importance of grades, cultural and parental factors, mathematicians' attitudes toward teaching, and some problems in elementary mathematics. (MDH)

This paper examines the classroom practices of three teachers teaching mathematics at the 5th grade level in three Singapore schools. Using a video-coding scheme, a series of lessons was coded into relevant phases comprising problem solving, teaching concepts/skills, going over assigned work, and student activities. It explores the teachers'…

Shows fragility of knowledge in connection with a false application of mathematical induction, as observed in a problem-solving course for prospective teachers. The attempt to explain the observations is based upon an analysis of the logic underlying proof by mathematical induction and a concept formation theory. (MKR)

An exploratory study assessed the degree to which 13- and 14-year olds (n=100) adjusted assumptions of direct proportionality suggested by surface structure of word problems. Virtually no errors were made on "straightforward" items, but many students showed no adjustment for realistic constraints on complex items. (Contains 21…

This longitudinal study investigated the ways in which two groups of eight students used spreadsheets to represent and solve algebra problems and related this to their previous arithmetical experiences and evolving use of symbolic language. The spreadsheet environment supported students to move from specific to general thinking. Includes story…