Research has identified several students' misinterpretations of the principles of the photoelectric effect (PE). Students cannot interpret the formula using the graph's context despite the linear dependence inherited in it. Many studies pointed out that the graphical representation of kinetic energy of the ejected electrons versus frequency of…

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…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

The aim of this study is to characterise students' understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

Amazon, Walmart, and other large-scale retailers owe their success partly to efficient inventory management. For such firms, holding too little inventory risks losing sales, whereas holding idle inventory wastes money. Therefore profits hinge on the inventory level chosen. In this activity, students investigate a simplified inventory-control…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)