Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

This paper explored the following: (1) teachers' ways of attending to students' written responses in pattern generalization tasks and (2) differences in the ways of attending to students' responses associated with different factors. A questionnaire was developed to classify teachers' ways of attending to students' written responses. The…

This study investigated the longitudinal trends of e-learning research using text mining techniques. Six hundred and eighty-nine (689) refereed journal articles and proceedings were retrieved from the Science Citation Index/Social Science Citation Index database in the period from 2000 to 2008. All e-learning publications were grouped into two…

Context is identified as an important factor when considering the learning of informal statistical inferential reasoning, but research in this area is very limited. This small exploratory study in one grade 10 (14 year olds) classroom seeks to learn more about the role context plays in learners' inferential reasoning, where both teacher and…

Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in…

Firstly, the many characteristics of expertise are examined: they include aspects of pattern recognition, knowledge, skill, flexibility, metacognitive monitoring, available cognitive space and teaching abilities. Secondly, three educational models from different domains(Nursing, Surgical Education, Education) are analysed, compared and contrasted,…

Educational design for networked learning is becoming more complex but also more inclusive, with teachers and learners playing more active roles in the design of tasks and of the learning environment. This paper connects emerging research on the use of design patterns and pattern languages with a conception of educational design as a conversation…

Electronic language corpora, and their attendant computer software, are proving increasingly influential in language teaching as sources of language descriptions and pedagogical materials. However, few teachers are clear about their nature or their relevance to language teaching. This paper defines corpora and their types, discusses their…

A computerized symbol processor system using an Apple IIe computer and a Power Pad graphics tablet was tested with 22 nonspeaking, multiply disabled students. The students were taught to express themselves independently in writing, and they did significantly better than control students on measures of language comprehension and symbol recognition.…