In parallel with mathematical modeling studies that have gradually drawn interest in recent years, the aim of this study is to investigate the thought processes of fourth-grade students in the Butter Beans Problem and to identify possible challenges in this process. For this purpose, a qualitative study was conducted at a university-foundation…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

Our work is inspired by the book "Imagining Numbers (particularly the square root of minus fifteen)," by Harvard University mathematics professor Barry Mazur ("Imagining numbers (particularly the square root of minus fifteen)," Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of…

Mathematical models and their construction are discussed. Successful mathematical model building is suggested as requiring a combination of deductive thinking and an understanding of the external world. (MP)

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…

Based on a synthesis of the literature, a model for problem posing cognitive processes was formulated, and validated. The major constructs incorporated in this framework were the situations in which problem posing occurs. For each situation, four cognitive processes were established: the editing of problems based on iconic or symbolic stimuli, the…

Identified difficulties encountered in spontaneous modeling, as well as strategies, approaches, and language used in this activity. Graduate mathematics students (N=223) were asked to create a mathematical model of a biological process. Their solutions and strategies are analyzed and results described. Significant conclusions for teaching applied…

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

A cognitive/metacognitive framework is presented for analysing applications tasks and responses to these. Conditions facilitating or impeding access to such tasks at the upper secondary level were identified using qualitative data analysis techniques within this framework. Strategies employed in exploiting, or overcoming these conditions were…

Described is the use of story telling as a context to introduce mathematical concepts by providing a model, offering problem-posing situations, stimulating investigation, and illustrating concepts. Examples of appropriate stories are given for the primary and low secondary levels. (MDH)

This collection of nine papers, prepared for a conference held at Northwestern University in 1978, presents varied perspectives on applied problem solving. Assessing applied problem solving, planning for interest and motivation, developing a theory, reviewing research findings, considering learning disabilities, analyzing through information…

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…