What Constitutes Good Mathematics Teaching and How it Develops: Nine High School Teachers’ Perspectives

Scholars of decades past, current researchers, and various reform documents all deal, directly or indirectly, with the question of what constitutes good mathematics teaching. Often good teaching is situated in the context of broader educational goals, such as preparing literate citizenry. Researchers generally define good teaching implicitly with attention to various processes such as reasoning and problem solving. In a series of three interviews, we examined nine experienced and professionally active teachers’ views of good mathematics teaching and how it develops. The interviews were couched in the context of the teachers mentoring student teachers. In general, these teachers thought good teaching requires a sound knowledge of mathematics, promotes mathematical understanding, engages and motivates students, and requires effective management skills. Furthermore, the teachers felt that good teaching is developed from experience, education, personal reading and reflection, and interaction with colleagues. Experience was considered the primary contributor. The article compares and contrasts the teachers’ notions of good teaching with those of various scholars and researchers and positions stated in various reform documents.     

What makes for effective feedback: staff and student perspectives

Since the early 2010s the literature has shifted to view feedback as a process that students do where they make sense of information about work they have done, and use it to improve the quality of their subsequent work. In this view, effective feedback needs to demonstrate effects. However, it is unclear if educators and students share this understanding of feedback. This paper reports a qualitative investigation of what educators and students think the purpose of feedback is, and what they think makes feedback effective. We administered a survey on feedback that was completed by 406 staff and 4514 students from two Australian universities. Inductive thematic analysis was conducted on data from a sample of 323 staff with assessment responsibilities and 400 students. Staff and students largely thought the purpose of feedback was improvement. With respect to what makes feedback effective, staff mostly discussed feedback design matters like timing, modalities and connected tasks. In contrast, students mostly wrote that high-quality feedback comments make feedback effective – especially comments that are usable, detailed, considerate of affect and personalised to the student’s own work. This study may assist researchers, educators and academic developers in refocusing their efforts in improving feedback.     

Bumble Boosters: Students Doing Real Science

Bumble Boosters was a lottery grant funded cooperative project between the University of Nebraska – Lincoln Department of Entomology, the Lincoln Public Schools Science Focus Program, and the Lincoln Folsom Children's Zoo. The primary education goal of the project was to create a community of learners to conduct authentic research on bumble bees in Nebraska. Participants were actively engaged in collecting bumble bees and placing nesting domiciles. Internet technology was employed to facilitate networking between project participants. Systematic evaluation was conducted during and after the project.     

Conditions that enable effective feedback

ABSTRACT

Despite an increasing focus on assessment feedback, educators continue to find that simply replicating an effective feedback practice from one context does not guarantee success in the next. There is a growing recognition that the contextual factors surrounding successful practices need to be considered. This article reports on a large-scale mixed methods project and proposes 12 conditions that enable successful feedback in higher education. The conditions were distilled from seven rich case studies through multiple stages of thematic analysis, case comparison and reliability checking. The conditions were also evaluated by surveying senior leaders of Australian universities. These conditions highlight the importance of carefully designing feedback processes, along with the need for addressing capacity and culture for feedback. This helps to explain why there are such variances in effective feedback across contexts, and offers insight into how it may be achieved.     

Facilitating Learning Events Through Example Generation

This study deals with the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of instances of the concept. Data were collected in spring of 1995 through interviews with 11 third and fourth year undergraduate mathematics students. We discuss the data from the perspective of the student's concept image and introduce the notion of learning event to indicate when a student communicates and applies a new understanding of a concept. We infer that the students in our study who employed an example generation learning strategy were more effective in attaining an initial understanding of the new concept than those who primarily employed other learning strategies such as definition reformulation or memorization.This revised version was published online in September 2005 with corrections to the Cover Date.