This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers' mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two…

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006; Fuson & Murata, 2007), the process of mediation is explicated. The tape diagram, a central visual…

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)

This study illustrates a process for selecting a preferred model in the validation of hierarchical learning scales. The test performance of 100 8-to 11-year-old children on subtraction tasks involving variations in borrowing are examined. Goodman's response scaling technique is illustrated. (Author/GDC)

An analysis of methods of teaching children to solve verbal arithmetic problems is presented together with transcriptions of interviews in which children solve problems by reference to problem types. (SD)

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Suggestions for teaching problem solving which include the use of general models, variation of illustrations and terminology, and diagrams are illustrated for comparison multiplication word problems. (MN)

This paper describes a models and modeling framework that has been applied to various areas in teaching, learning and problem solving. It examines the implications of that framework on metacognition and higher order thinking during everyday problem-solving situations that required teams of students to produce complex solutions in approximately 1-2…

A model that can be effectively used to develop the notion of function and provide varied practice by using "real world" examples and concrete objects is covered. The use of Popsicle-sticks is featured, with some suggestions for tasks involving functions with one operation, two operations, and inverse operations covered. (MP)

Described is the development of a simulation, or model of an existing congested pedestrian crossing situation by elementary school students in order to conduct trials of their solutions. (MN)

An alternative explanation is presented for the pattern of relative difficulty of arithmetical word problems to that suggested in a 1983 article. It is argued, that for many problems, much of the symbolic manipulation is accomplished externally, not internally. (MNS)

Outlines a possible framework for allowing teachers to explore how children learn mathematics. A mathematical modelling process and three domains, including content, process and pragmatic domain, are described. Twelve strategies for encouraging children to translate between the domains are suggested. (YP)