This study examined proposed teacher responses to students' work to investigate how they respond, what characteristics of a good response are more difficult than others to achieve, and whether particular student error types are more difficult to respond to appropriately. Sixteen preservice secondary mathematics teachers' proposed responses to five…

Problem solving strategies of eight pre-service secondary school mathematics teachers (PSSMTs) were examined in this study. A case study research design was employed and clinical interview technique was used to collect the data. Materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subjects' notes and…

This paper suggests that complex practice dilemmas call for thick stories of masterful practice that don't ignore the tensions and ambiguities involved. The paper draws on an Australian study of policing as a fruitful example. Academic commentary suggests policing is beset with practice dilemmas unique in their complexity. However, empirical…

This paper describes the outcomes of a qualitative investigation into the range of different approaches that students use to solve open-ended, context rich problems. The study involved a small cohort of students individually solving open-ended, context-rich problems using a think aloud protocol. The problems required the students to develop a…

In order to address concerns with the underrepresentation of spatial thinking in K-12 curricula, (National Research Council, 2006), Valentine and Kopcha (in press) designed and implemented a learning environment integrating cases as alternative perspective (Jonassen, 2011) in the context of eighth-grade mathematics. The design aimed to provide…

While there has been worldwide interest in Japanese Lesson Study as a model for teacher professional learning, there has been less research into authentic implementation of the problem-solving lesson structure that underpins mathematics research lessons in Japan. Findings from a Lesson Study project involving teachers from three Victorian primary…

The study's goal was to examine the metacognitive practices and problem solving by preservice secondary mathematics teachers within secondary core content areas. The effort to analyze and describe the processes led to qualitative methods, a multiple case study. Transcripts of problem solving sessions and interviews were coded for the presence of…

The existing literature on indicators of an optimal learning environment for high-ability students frequently discusses the concept of challenge. It is, however, not clear what, precisely, constitutes appropriate challenge for these students. In this study, the authors examined an undergraduate honours course, Advanced Cell Biology, which has…

Previous research shows that speed is one of the most difficult in the upper grades of primary school. It is because students must take into consideration two variables; distance and time. Nevertheless, Indonesian students usually learn this concept as a transmission subject and teacher more emphasizes on formal mathematics in which the concept of…

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…