Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

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…

This paper presents the design, features and pilot evaluation study of a web-based environment--the SORTING environment--for the learning of sorting algorithms by secondary level education students. The design of this environment is based on modeling methodology, taking into account modern constructivist and social theories of learning while at…

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…