Jaguthsing Dindyal

Making mathematics practical : an approach to problem solving

Mathematical Problem Solving Scheme of Work and Assessment of the Mathematics Practical Detailed Lesson Plans Scaffolding Suggestions, Solutions to the Problems and Assessment Notes.

Relooking ‘Look Back’: a student's attempt at problem solving using Polya's model

Against the backdrop of half a century of research in mathematics problem solving, Pólyas last stage is especially conspicuous – by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, Conditions for promoting reasoning in problem solving: Insights from a longitudinal study, J. Math. Behav. 24 (2005), pp. 361–372; J.A. Taylor and C. Mcdonald, Writing in groups as a tool for non-routine problem solving in first year university mathematics, Int. J. Math. Educ. Sci. Technol. 38(5) (2007), pp. 639–655.), with little or no successful attempts at following through with the subjects. In this article, we describe a case study of how the innovation of a ‘Practical Worksheet’ within a new paradigm of a ‘Mathematics Practical’ enabled a high-achieving student to push beyond getting a solution for a problem to extending, adapting and generalizing his solution. The findings from this study indicate promise in achieving the learning of Polyas model with notable success in the fourth stage, Look Back.

The problem-solving approach in the teaching of number theory

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to adopt a Pólya-style approach in learning mathematics. The Practical Worksheet is an instructional scaffold we adopted to help our pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. The Worksheet was initially used in a design experiment aimed at teaching problem solving in a secondary school. In this paper, we describe an application and adaptation of the MProSE (Mathematical Problem Solving for Everyone) design experiment to a university level number theory course for pre-service mathematics teachers. The goal of the enterprise was to help the pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. Our analysis of the pre-service mathematics teachers’ work shows that the MProSE design holds promise for mathematics courses at the tertiary level.

Infusing Mathematical Problem Solving in the Mathematics Curriculum: Replacement Units

There are many reports on how problem solving is successfully carried out in specialised settings; relatively few studies report similar successes in regular mathematics teaching in a sustainable way. The problem is, in part, one of boundary crossings for teachers: the boundary that separates occasional (fun-type) problem solving lessons from lessons that cover substantial mathematics content. This chapter is about an attempt to cross this boundary. We do so by designing “replacement units” that infuse significant problem solving opportunities into the teaching of standard mathematics topics.

Boundary Objects Within a Replacement Unit Strategy for Mathematics Teacher Development

We recognise that, for instructional innovations to take root in mathematics classrooms, curriculum redesign and teachers’ professional development are two necessary and mutually-reinforcing processes: a redesigned curriculum needs to be seen as an improvement in order to facilitate teachers’ buy-in—an ingredient for effective professional development; on the other hand, teachers’ professional development content needs to be directed towards actual useable classroom implements through the enterprise of collaborative curriculum redesign. In this chapter, we examine the interaction between researchers and teachers in this collaborative enterprise through the metaphor of boundary crossing. In particular, we study a basic model of how “boundary objects” located within a “Replacement Unit” strategy interact to advance the goals of professional development.

Mathematics Teacher Noticing: Expanding the Terrains of This Hidden Skill of Teaching

This paper was published in the Proceedings of the 13th International Congress on Mathematical Education held at Hamburg, Germany from 24 - 31 July 2016

Mathematics education in Singapore

Mathematics education in Singapore is a shared responsibility of the Ministry of Education (MOE) and the National Institute of Education (NIE). The MOE overseas the intended, implemented and attained curriculum in all schools while the NIE is involved in teacher preparation and development and also research in mathematics education. Therefore this report has two sections respectively, the first describes the education system and school mathematics curricula while the second briefly provides relevant information on teacher preparation and development and mathematics education research in Singapore.

Commentary on the Chapter by Wolfgang Schlöglmann, “Mathematics Education for Adults: Can It Reduce Inequality in Society?”

The four “new societal goals” promulgated by the National Council of Teachers of Mathematics in 1989 provide a lens to look at Wolfgang Schloglmann’s chapter “Mathematical Education for Adults: Can It Reduce Inequality in Society?”.