Seeking big ideas in algebra: the evolution of a task

In this paper we describe a strand of activities for teachers of mathematics that we used with two cohorts of participants in a professional development program called Revitalizing Algebra (REAL). We first discuss our goals and describe the participants, and then we describe the construction and selection of the tasks followed by teacher responses. Finally, we reflect on different iterations of the tasks, their impact on the teachers’ thinking and practice, and the role of school and department culture in the process of change.     

Conceptions of teaching held by academic teachers

This study examines conceptions of teaching held by academic teachers in the fields of science and social science, in two universities: a distance university in the UK and a traditional one in Australia. A five level classification of conceptions of teaching is proposed. A process of arriving at this scheme is discussed and a formalised coding system is presented which helps to delimit, with greater confidence, the boundaries of each conception, and helps to order conceptions, to compare conceptions proposed by other researchers, and to place individuals within conceptions. The same coding system is then used to define the concepts of student-centered and teacher-centered approaches to teaching. There is a strong suggestion that teaching conceptions are context-dependent.     

Improving the Measurement of Cognitive Skills Through Automated Conversations

Open-ended, short-answer questions, referred to as constructed responses (CR), allow students to express knowledge and skills through their own words. While CRs can reduce the likelihood of guessing correct answers, they also enable students to provide errant responses due to a lack of knowledge or a misunderstanding of the question. Conversation-based assessments (CBAs) require constructing responses to open-ended prompts (similar to CRs), but also leverage natural-language processing to provide adaptive follow-up prompts that target particular information. This work describes an investigation into potential benefits of CBAs as they are compared to a CR approach. Results from 632 middle schoolers indicate that, when compared to CRs, the CBA items allowed 41% of students to provide a more complete response and improve their score.     

Secondary science students’ beliefs about class discussions: a case study comparing and contrasting academic tracks

The dialogue that occurs in science classrooms has been the subject of research for many decades. Most studies have focused on the actual discourse that occurs and the role of the teacher in guiding the discourse. This case study explored the neglected perspective of secondary science students and their beliefs about their role in class discussions. The study participants (N?=?45) were students in one of the three differentially tracked chemistry classes taught by the same teacher. Findings about the differences that exist among students from different academic tracks are reported. While it seems that epistemological beliefs focusing on content are common for the students in this study, the students' social framing in the different tracks is important to consider when teachers attempt to transition to more dialogic forms of discourse. Some key findings of this study are (a) students’ beliefs that science is a body of facts to be learned influenced the factors they deemed important for whole-class discussion, (b) students from the lower-level track who typically were associated with lower socioeconomic status were more likely to view their role as passive, and (c) students’ comfort level with the members of the class seemed to influence their decisions to participate in class discussions.     

Teachers’ enactments of curriculum: Fidelity to Procedure versus Fidelity to Goal for scientific argumentation

Fidelity of implementation (FOI) has received attention in calls for funding and research; however, there are numerous ways of conceptualising and measuring this construct. We argue that this conceptualisation is important for recent reform efforts focused on science practices. Consequently, we explored FOI in the context of the enactment of a middle-school curriculum focused on one particular science practice, argumentation. We coded videos of five teachers’ enactments of argumentation lessons using two different fidelity coding schemes. First, Fidelity to Procedure targeted teachers’ adherence to the order and types of procedures. Second, Fidelity to Goal examined teachers’ adherence to the overarching argumentation goals. This analysis resulted in case studies that illustrate distinct patterns in the teachers’ curriculum enactments. One case in particular, Ms Newbury, received a low score for Fidelity to Procedure, but a high score for Fidelity to Goal. She altered procedures to provide her students, all of whom were English Language Learners, with different linguistic supports, but maintained the overarching argumentation goals. Consequently, we argue that FOI for goals may better capture whether teachers’ enactments are supporting students in the science practices. Furthermore, the results suggest the importance of educative curriculum including rationales for the curricular goals.     

The role of IQ, expertise, and motivation in the recall of familiar information

High- and low-IQ children in the first, third, and fifth grades performed two free-recall tasks: a sort-recall task with sets of categorically related pictures, and a class-recall task, with children recalling the current members of their school class. All children were deemed to be experts concerning the composition of their school class, but, unlike experts in other domains, had no special motivation associated with their expertise. Recall and clustering on both tasks were high. The high-IQ children performed better than low-IQ children only on the sort-recall task. IQ was significantly correlated with measures of performance on the sort-recall task but not on the class-recall task. The results reflect the fact that the memory benefits associated with being an expert (here, elimination of IQ effects) are related to the greater knowledge the expert possesses and not to factors of motivation.     

Feasibility of the MTAI as a Selection Instrument for Pre-Service Teacher Education — A Pilot Project

The Institute of Education is the only institution in Singapore that trains and prepares individuals for the task of teaching. In order to ensure that its products, the teachers, are of a respectable calibre, not only should the training programme be reviewed regularly, but also the method of selecting trainees.