This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

Many organizations utilize some form of automation in the test assembly process; either fully algorithmic or heuristically constructed. However, one issue with heuristic models is that when the test assembly problem changes the entire model may need to be re-conceptualized and recoded. In contrast, mixed-integer programming (MIP) is a mathematical…

Researchers point at the need to study the creative processes of students in problem solving, as these may indicate how to encourage creative problem solving. The present research attempts to study, based on the heuristic framework of Polya, pre-service teachers' flexibility processes when they solve a mathematical problem with technology. The…

This paper presents a fine-grained process analysis of 22 students in a classroom-based learning setting. The students engaged (and failed) in problem-solving attempts prior to instruction (i.e., the Productive-Failure approach). We used the HeuristicsMiner algorithm to analyze the data of a quasi-experimental study. The applied algorithm allowed…

There is a large body of literature concerning the potential of dynamic geometry software (DGS) in the problem solving process. However, questions regarding how teaching should take place to prepare students to use DGS as a heuristic tool in non-routine problem situations seem to be overlooked. To address this gap in the literature, the current…

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources…

This article gives an example for using Dynamic Geometry Software to encourage making conjectures, reasoning, and experiencing mathematics as a process.

Design activities typically involve and culminate in the creation of models representative of new ideas and conceptions. The format is often dictated by the specific discipline, with ideas in design and technology education regularly being externalised through the use of computer aided design (CAD). This paper focusses on the realisation stage of…

This article reports and analyzes different types of problems that nine students in a Master's Program in Mathematics Education posed during a course on problem solving. What opportunities (affordances) can a dynamic geometry system (GeoGebra) offer to allow in-service and in-training teachers to formulate and solve problems, and what type of…

Swarm intelligence approaches, such as ant colony optimization (ACO), are used in adaptive e-learning systems and provide an effective method for finding optimal learning paths based on self-organization. The aim of this paper is to develop an improved modeling of adaptive tutoring systems using ACO. In this model, the learning object is…

In an attempt to specify in some canonical terms what many heuristic programs known as "expert systems" do, an analysis was made of ten rule-based systems. It was found that these programs proceed through easily identifiable phases of data abstraction, heuristic mapping onto a hierarchy of pre-enumerated solutions, and refinement within this…

As a demonstration of the application of heuristic devices to decision-theoretical techniques, an interactive computer program known as MAUD (Multiattribute Utility Decomposition) has been designed to support decision or choice problems that can be decomposed into component factors, or to act as a tool for investigating the microstructure of a…

This paper discusses the incorporation of heuristics in computerized decision aids that are used for structuring decision problems. Decision theory is described in terms of linked subsystems, and sites where it is necessary to employ heuristic rather than normative, algorithmic procedures are identified. Production systems are then used to…

Discusses geometry and Dynamical Geometry Software (DGS). Analyses the way DGS-use influences traditional geometry. Highlights changes in the interactions between geometry, computers, and DGS and human users, focusing on changes in the teaching and learning of geometry. Concludes that DGS deeply changes geometry if it is taken as a human activity…

Examines processes by which general but weak search methods are transformed into powerful, domain-specific search strategies by classifying types of heuristics learning that can occur and components that contribute to such learning. A learning system--SAGE.2--and its structure, behavior in different domains, and future directions are explored. (36…