Brian Griffiths (1927–2008) – his pioneering contributions to mathematics and education

Brian Griffiths (1927–2008) was a British mathematician and educator who served as a member of the founding editorial board of Educational Studies in Mathematics. As a mathematician, Griffiths is remembered through his work on what continue to be known as ‘Griffiths-type’ topological spaces. As a mathematics educator, his most profound contribution was, with Geoffrey Howson, in offering a conceptualisation of the relationship between mathematics, society and curricula.     

Individual differences in achievement goals: A longitudinal study of cognitive, emotional, and achievement outcomes

Within achievement goal theory debate remains regarding the adaptiveness of certain combinations of goals. Assuming a multiple-goals perspective, we used cluster analysis to classify 1002 undergraduate students according to their mastery and performance-approach goals. Four clusters emerged, representing different goal combinations: high mastery/performance (i.e., multiple goals), dominant mastery, dominant performance, and low mastery/performance (i.e., low motivation). In a longitudinal analysis over one academic year, the clusters were compared on cognitive appraisals (expected achievement, perceived success), achievement-related emotions (enjoyment, boredom, anxiety), and objective measures of academic achievement (final grade in Introductory Psychology, GPA). The low-motivation cluster demonstrated the least adaptive profile across all outcomes. The multiple-goals, mastery, and performance clusters showed equivalent levels of achievement; however, students in the performance cluster were more psychologically and emotionally vulnerable than the multiple-goals and mastery clusters. Our discussion focuses on the immediate and potentially long-term implications of specific goal combinations for students and educators, with particular attention to understanding the cognitive and emotional vulnerabilities of students in the performance cluster which appear despite satisfactory achievement levels.     

Mentoring Undergraduate Interdisciplinary Mathematics Research Students: Junior Faculty Experiences

Abstract

To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student) can be undertaken as a full-time summer experience, or as a part-time academic year commitment. With many potential undergraduate research formats, and with different types of students, junior faculty may find challenges in forming their research group, establishing a structure that promotes student productivity, picking an appropriate project, or in effectively mentoring their students. This article draws from the authors’ experiences to help junior faculty navigate these complexities so that all parties reap the benefits of undergraduate research in interdisciplinary mathematical disciplines.     

Video Production Technology in Australian Higher Education

The paper describes the present state of the art of video programme production in Australian tertiary education, discusses the identity of the decision‐makers in the production sequence, and assesses the importance of video aesthetics. Against the background of some Australian media departments' production and hardware philosophy, the author describes four series of programmes produced at the ACUE.     

The role of relationships and emotions in student perceptions of learning and assessment

The paper addresses the way in which participants in a qualitative study drew upon accounts of relationships and emotions in sharing their perceptions of assessment. By first exploring ideas about emotions and relationships in learning and assessment through the literature and subsequently discussing an interpretation of participant narratives, the author suggests that emotions and relationships surrounding past learning and assessment contexts can influence current perceptions of assessment and learning in powerful ways. The study also reveals how students value opportunities to express their beliefs, feelings and emotions during the assessment process. They also expect teachers to balance objectivity in assessment with empathy for those parts of themselves shared in the process. The conclusion is drawn that there are important implications for learning in the emotional response of students to assessment and in the nature of teaching and learning relationships that are worthy of further investigation.     

Putting Making into High School Computer Science Classrooms: Promoting Equity in Teaching and Learning with Electronic Textiles in Exploring Computer Science

Recent discussions of making have focused on developing out-of-school makerspaces and activities to provide more equitable and enriching learning opportunities for youth. Yet school classrooms present a unique opportunity to help broaden access, diversify representation, and deepen participation in making. In turning to classrooms, we want to understand the crucial practices that teachers employ in broadening and deepening access to making. In this article, we investigate two high school teachers' approaches in implementing a novel eight-week, electronic textiles unit within the Exploring Computer Science curriculum, where students designed wearable electronic textile projects with microcontrollers, sensors, and LEDs. We share teachers' emergent practices in transforming their classrooms into makerspaces, including valuing student expertise and promoting connections in personalized work. We discuss the ways these practices succeeded in broadening access to making while deepening participation in computing and establishing home-school connections.     

Realization of Techniques in Problem Solving: The Construction of Bijections for Enumeration Tasks

This paper deals with a teaching approach aimed to help students become aware of targeted techniques of significance in problem solving. The teaching approach is to present a series of tasks that all can be solved by applying the same technique. Two levels of prompting are used; first for the students to realize solutions without necessarily being cognizant of the technique, second for them to perform further mathematical modeling that should highlight the similarities in solution shared by all the tasks. In the fieldwork, a teaching sequence based on this approach is implemented for a technique involving enumeration via constructing a bijection. Certain factors in the students' behavior suggested that their realization of the technique at the end was not as secure as desired. Some modifications of the teaching sequence are proposed to counter these factors.     

The Right “Fit”: Exploring Science Teacher Candidates’ Approaches to Natural Selection Within a Clinical Simulation

Teachers and students struggle with the complexities surrounding the evolution of species and the process of natural selection. This article examines how science teacher candidates (STCs) engage in a clinical simulation that foregrounds two common challenges associated with natural selection—students’ understanding of “survival of the fittest” and the variation of species over time. We outline the medical education pedagogy of clinical simulations and its recent diffusion to teacher education. Then, we outline the study that situates each STC in a one-to-one interaction with a standardized student who is struggling to accurately interpret natural selection concepts. In simulation with the standardized student, each STC is challenged to recognize content misconceptions and respond with appropriate instructional strategies and accurate explanations. Findings and implications center on the STCs’ instructional practices in the simulation and the use of clinical learning environments to foster science teacher learning.