Learning analytics research has used both knowledge engineering and machine learning methods to model student behaviors within the context of digital learning environments. In this paper, we compare these two approaches, as well as a hybrid approach combining the two types of methods. We illustrate the strengths of each approach in the context of…

STEM instruction often uses visual representations. To benefit from these, students need to understand how representations show domain-relevant concepts. Yet, this is difficult for students. Prior research shows that physical representations (objects that students manipulate by hand) and virtual representations (objects on a computer screen that…

Abstract electronics concepts are difficult to develop because the phenomena of interest cannot be readily observed. Visualisation skills support learning about electronics and can be applied at different levels of representation and understanding (observable, symbolic and abstract). Providing learners with opportunities to make transitions…

Knowledge of the appropriate technologies for sustainable development projects has encouraged grass roots development, which has in turn promoted sustainable and successful community development, which a requirement is to share and reuse this knowledge effectively. This research aims to propose a tutorial ontology effectiveness modeling on organic…

The most common tools individuals use to articulate complex and abstract concepts are writing and spoken language, long privileged as primary forms of communication. However, our, explanations of these concepts may be more aptly communicated through visual means, such as drawings. Interpreting and analyzing abstract graphic representations is…

Parametric systems have been proposed as models of how humans represent knowledge about language, motivated in part as a way to explain children's rapid acquisition of linguistic knowledge. Given this, it seems reasonable to examine if children with knowledge of parameters could in fact acquire the adult system from the data available to them.…

This case study describes an "out of field" teacher's use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects, effective "virtual" pedagogy, and technical support…

The effectiveness of serious games is often measured with verbal assessment. As an alternative we propose Pathfinder structural assessment (defined as measuring the learners' knowledge organization and compare this with a referent structure) which comprises three steps: knowledge elicitation, knowledge representation and knowledge evaluation. We…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

The purpose of this thesis is to improve our understanding of sensemaking process as a basis for building better systems to assist sensemaking. Sensemaking is the task of creating an understanding of a problem or task so that further actions may be taken in an informed manner. Sensemaking is a pre-requisite for many other tasks such as decision…

Purpose: The development of adaptable and intelligent educational systems is widely considered one of the great challenges in scientific research. Among key elements for building advanced training systems, an important role is played by methodologies chosen for knowledge representation. In this scenario, the introduction of ontology formalism can…

It is generally believed that students should use multiple representations in solving certain physics problems, and earlier work in PER has begun to outline how experts and novices differ in their use of multiple representations. In this study, we build on this foundation by interviewing expert and novice physicists as they solve two types of…

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…

Using a symbolic object such as a model as a source of information about something else requires some appreciation of the relation between the symbol and what it represents. Representational insight has been proposed as essential to success in a symbolic retrieval task in which children must use information from a hiding event in a scale model to…