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This theoretical article explores an issue of developing education research competencies in mathematics teachers through their involvement in mathematics education research. We first argue that the development of education research competencies is beneficial for the teachers’ professional growth. We then identify opportunities for mathematics teachers to develop education research competencies through different modes of research-practice partnerships. In the main part of the paper, we present a particular theoretical-organizational framework for large-scope teacher-researcher collaborations in educational research. The framework is called Teacher-Researcher Alliance for Investigating Learning (TRAIL), and consists of a set of theoretically laden premises, design heuristics, and provisional partnerships.

Undergraduate mathematics students are expected to spend a substantial amount of time outside class studying proofs independently. Yet, little is known about how such expectations shape instruction in proof-oriented courses. This paper investigates this issue in a case study of an experimental teaching strategy, designed by a mathematics professor, for scaffolding student independent proof reading. On the basis of interviews and classroom observations we scrutinize the instructor’s course image – his envisioning of the teaching and learning activities, inside and outside class, throughout the course. We examine a representative case of proof presentation through the lens of the instructor’s course image. Our analysis reveals complex relationships between various teaching and learning activities in the course, and demonstrates that unpacking these relationships can provide valuable insights into specific teaching practices. Findings suggest that the concept of course image can be useful in enhancing our understanding of mechanisms underlying collegiate mathematics instruction.

In this paper we investigate task design in an unusual professional development course for elementary school teachers, conceived and taught by research mathematicians. Prior analysis singled out relevance for teaching as a critical design issue for engaging teachers in effective learning. The aim of the current research is to uncover how relevance for teaching was achieved without compromising mathematical rigor and depth. Findings are based on an analysis of three representative cases of task designing in which the authors where involved – one as instructor and task designer, the other as participant observer. Our analysis reveals a designing model that first addresses purely mathematical concerns and then refines tasks, taking into consideration a series of constraints imposed by the requirement of relevance for teaching. Using Schoenfeld’s Resources-Orientations-Goals framework for decision-making, we show how the mathematicians drew on their special knowledge of mathematical content to achieve such relevance in ingenious ways. We find that tasks were best aligned with Knowles’s principles of Adult Learning in cases where the designers appropriated the teachers’ point of view, no longer seeing the need for relevance as a constraining imposition, but rather as an opportunity to combine and merge knowledge specific for teaching and purely mathematical knowledge.

This paper investigates the variability in the content of lectures by different university mathematics instructors teaching concurrently in the same course. The instructors enacted a shared lesson-plan and coordinated their teaching to ensure students in different sections of the course will receive equivalent academic preparation. However, classroom observations and interviews with the instructors indicate that while explicitly discussing the same definitions and theorems and working out similar examples, the instructors were implicitly trying to convey different informal content. An analysis of the instructors’ mathematical discourse during the lectures and the interviews reveals that the instructors coordinated with each other content corresponding with object-level learning, while implicitly orienting their lectures towards fostering meta-level learning. This found gap highlights miscommunication between the instructors and points to the need of a shared and explicit discourse on meta-level learning at the collegiate level.