Generalization has been a major focus of curriculum standards and research efforts in mathematics education. While researchers have documented many productive contexts for generalizing and the generalizations students make, less attention has been given to the processes of generalizing. Moreover, there has been less work done with high school…

"Emoticons" are simple face icons expressing common feelings such as happiness, interest and boredom and are popularly used in electronic communication. Emoticons were utilised in this study as experience sampling devices. Year 10 students selected emoticons to indicate their emotional states at set intervals during classroom tasks.…

In this paper we analyze and discuss students' performance in a CAS environment related to the simplification of rational expressions. Results indicate that if students have more initial paper-and-pencil techniques, the CAS environment spurs them to deeper theoretical reflections than for students who have fewer techniques. [For the complete…

Rate is an important, but difficult mathematical concept. More than twenty years of research, especially with calculus students, report difficulties with this concept. This paper reports on an alternative analysis, from the perspective of multiple representations and context, of interviews probing twenty Victorian Year 10 students' conceptions of…

This study uses the Mathematical Tasks Framework (Stein & Smith, 1998) to assess the cognitive demand of mathematical tasks implemented in four mathematics classrooms, and to investigate the role of technology in both low- and high-level cognitive demand tasks. The metaphor of using technology as an amplifier or reorganizer (Pea, 1987) is used…

The purpose of this investigation was to explore the ideas and beliefs of high school science students (n=37) about the processes of observation in their learning of science, and how these students approached the task of observing during their science experiments. Findings include: many students saw observation as a teacher-directed process;…

The importance accorded mathematical connections in the professional literature is not properly reflected in the relatively small number of empirical investigations of students' mathematical connections. The purpose of this study was to investigate the mathematical connections that students form and use in solving nonroutine problems. Two main…

The usefulness of achievement goal theory in explaining motivation in writing classrooms was studied with 14 students interviewed in fifth, sixth, and tenth grades. In the tenth-grade interview, students were asked about their writing experiences and processes. Interview statements were analyzed by three judges regarding mastery and performance…

This qualitative assessment of tenth-grade students' (n=17) problem solving focused on the nature of students' thinking, their problem-solving strategies and heuristics, the mathematical approaches they selected, and the ways they monitored their own progress. The problem, presented orally and with photographs in a task-based interview, involved a…

Despite enormous political, social, and psychological forces working against them, some inner city black youths defy the odds and succeed academically. This study focuses on a group of successful at-risk minority students in an urban secondary school, and in particular on their student experience, including interactions with school culture,…