Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open…

The aim of this study is to understand how students' mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The…

A short series of practical classroom mathematics activities employing the use of a large and publicly accessible scientific data set are presented for use by students in years 9 and 10. The activities introduce and build understanding of integral calculus and trigonometric functions through the presentation of practical problem solving that…

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…

This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. The model is designed for a measurement context in which categories of response to an item cannot be completely ordered. (SLD)

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a…