The number of e-learning platforms and blended learning environments is continuously increasing and has sparked a lot of research around improvements of educational processes. Here, the ability to accurately predict student performance plays a vital role. Previous studies commonly focused on the construction of predictors tailored to a formal…

This study presents part of a research project that aims to develop prospective mathematics teachers' Technological Pedagogical Content Knowledge (TPCK). The project considers various TPCK components. This report focuses on a particular component, namely the "knowledge of using multiple representations (MRs) with technology". A course…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

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…

Analyzes students' representations of fractions as they work on fraction comparison tasks and justify their solutions in a collective classroom activity. Emphasizes the importance of setting a problematic situation and encouraging students to make various representations for their learning. Suggests some implications for teacher activities and…

As biological and socio-cultural beings, humans are encouraged and aspire to "see" not only what comes "within sight," but also what is not possible to see. Visualization is described as offering a method of seeing the unseen. These ideas are organized into sections that focus on seeing the unseen in data, seeing the unseen in…

This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is…

This paper addresses dilemmas in the practices of six teachers from the perspective of alternate paradigms of knowledge growth, particularly constructivism. The dilemmas focus on the relationships between theory and practice in the growth of knowledge in learning and teaching mathematics. The data for this study are drawn from a four-year…

This paper presents a new model for simulating procedural knowledge in the problem solving process with our ontological system, InfoMap. The method divides procedural knowledge into two parts: process control and action performer. By adopting InfoMap, we hope to help teachers construct curricula (declarative knowledge) and teaching strategies by…