Mathematics Teacher Education and Development

Appreciating Productive Struggle: Educators’ Experience of "Confusion to Clarity" During Professional Learning

James Anthony Russo — 2024-07-31

Productive struggle is a vital aspect of mathematics learning; consequently, how teacher educators can effectively communicate the power of this idea to classroom teachers should in itself be an important consideration. We argue that providing teachers with firsthand experience of learning mathematics through structured inquiry approaches (e.g., launch-explore-summarise/review) is vital for supporting their appreciation of productive struggle. To facilitate this, during professional learning workshops with primary school teachers and education support workers, we have introduced a reflective template (the "confuse-o-meter") to enhance educator awareness of their own journey from "confusion to clarity" as work on a task unfolds. In this Illustration of Practice, we draw on data collected from several workshops we recently facilitated, which focussed on introducing challenging tasks and the launch-explore-summarise/review lesson structure. Our purpose is to both demonstrate the importance of providing educators with first-hand experience of productive struggle, and to illustrate how the reflective template designed supports this process.

Facilities for Mathematics Teachers’ Learning from Professional Development Programmes: A Qualitative Systematic Review

Daniel Brehmer — 2024-06-28

It is indicated that research on professional development programmes (PDPs) for mathematics teachers mostly concerns whether a programme affects the teachers’ practice or student learning, while the teachers’ learning is treated as a black box. Calls have been made for a shared body of knowledge on teachers’ professional learning and what supports such learning. In this article, 84 articles from mathematics education journals are examined with respect to facilities and catalysts for teacher learning from PDPs for mathematics teachers. Two main types of PDPs were identified—those that target teacher knowledge growth and those that target changed instruction—and it was determined that the types of facilities for catalysing learning linked to them differ. Typical of PDPs targeting teacher knowledge growth is that they emphasise knowledge of content and teaching, knowledge of content and students and specialised content knowledge; following insight and/or body of knowledge as facilities for catalysing the learning. Typical of PDPs targeting changed instruction is that they use more time and have a larger time span than PDPs targeting teacher knowledge growth, emphasise knowledge of content and teaching; and follow strategies by doing/experimenting when establishing them in the classroom as facilities for catalysing the learning.

Prospective Mathematics Teachers’ Epistemological Obstacles in Developing Project-based Numeracy Tasks

Vivi Suwanti — 2024-06-28

This study aims to describe the epistemological obstacles of prospective Indonesian secondary mathematics teachers’ in designing project-based numeracy tasks (PbNTs). Three case studies focused on qualitative analyses of prospective Indonesian secondary mathematics teachers’ PbNTs from responses to a semi-structured interview based on indicators of epistemological obstacles. It was found that epistemological knowledge was not the main cause of the obstacles they experienced, which is inconsistent with findings described in previous studies. It was revealed the prospective secondary mathematics teachers were too focused on the mathematical aspects and did not pay attention to the role of contextual knowledge in the process of PbNT design.

Pre-service Mathematics Teachers' Views on an Inquiry-based Learning Environment Emphasising Mathematical Communication

Mahir Biber — 2024-08-03

This study examined pre-service mathematics teachers' views on a communicative learning environment based on an inquiry-based learning approach. In the research, the phenomenological research model was used. The research was carried out with 24 pre-service teachers studying in the Primary Education Mathematics Teaching program of a state university located in Istanbul. The data were collected using a semi-structured interview protocol comprised of eight items prepared by the researcher. In the analysis of the data, content analysis was conducted using a qualitative data analysis computer software package. Within the scope of the research, pre-service teachers were asked to evaluate the inquiry-based learning abased on mathematical communication, and their level of readiness for the process. The results showed that pre-service teachers had difficulties in adapting to the inquiry-based learning approach and the mathematical communication environment, but they found the course process useful and efficient. It was determined that pre-service teachers attribute the difficulties they experience during the process to some factors, such as teachers, past learning experiences, and the education system.pproach, the course they took with this approach, the learning environment

Developing Statistical Thinking While Learning to Teach Statistics with Experiential Learning

Margaret Marshman — 2024-11-22

Secondary preservice teachers’ experiences in their discipline studies may lead to preconceived ideas about appropriate pedagogies without understanding how to implement them. In our experience, many students claimed to be using an experiential learning pedagogy in their lesson planning when they were teaching directly from the textbook. Experiential learning is the underlying pedagogy used in Outdoor and Environmental Studies. It occurs through active engagement in an experience and subsequent reflection on the experience. In this article we present two teaching activities—Random and non-random sampling, and An appropriate measure of centre (mean or median)—to illustrate how the experiential learning cycle could be used to develop statistical thinking as part of a course learning how to teach secondary mathematics. In interviews, secondary mathematics preservice teachers described how they planned to address students’ misconceptions and develop students' statistical thinking in the future. The findings suggest that engaging in contextually specific abstract conceptualisation can develop statistical thinking.

Co-teaching Strategies in Action: Selection and Implementation in a Mathematics Course for Pre-service Teachers

Bridget Druken — 2024-12-02

Increasingly, teacher preparation programs are transitioning to a co-teaching model to better prepare future teachers for the co-teaching experiences they will likely encounter in their PK–12 careers when they share a classroom with another teacher. Despite this transition, co-teaching remains rare in undergraduate university courses. To address this issue, two mathematics teacher educators explored on a co-teaching model in an undergraduate mathematics content course for future elementary teachers. An interpretive qualitative analysis was conducted on primary data sources of instructor journal entries and observation protocol forms, with videos of instruction and lesson materials as secondary sources. Episodes of each co-teaching strategy employed was coded for rationale in selection, reflection on implementation, affordances, and limitations. University classroom examples are provided for each strategy. Findings indicate that co-teaching strategies have numerous impacts on the classroom, such as opportunities for students to learn, opportunities for teachers to learn, opportunities for teacher-student interaction, opportunities for teacher-teacher interaction, power dynamics among instructors, and logistics (such as classroom space and available manipulatives). Implications of this research include an increased understanding of a co-teaching model for instructors interested in implementing the model in university courses.

Learner-generated Examples Within a System for Computer-aided Assessment as a Tool for Engaging In-service Teachers with Linear Functions

Siri Ovedal-Hakestad — 2024-12-20

This paper examines how learner-generated examples (LGE) tasks within a system for computer-aided assessment (CAA) facilitate in-service teachers' (ISTs') engagement with and explorations of the features of linear functions. Employing the concept of example spaces, the study explores how ISTs approach and engage with linear functions through these tasks. Seven ISTs participated in a series of LGE tasks in a CAA system, and their digital responses were collected. Semi-structured interviews were conducted with four participants following task completion. The results reveal common procedures adopted by the ISTs, such as using the "one-unit-right-a-up/down" procedure, as well as varying approaches to generation points and plotting them into a coordinate system. ISTs, however, faced challenges in effectively communicating their mathematical explanations. This study highlights the potential of LGE tasks in a CAA system to enhance ISTs' example spaces and improve their understanding of mathematical concepts.

Motivational and Fun! Preservice Teachers’ Recontextualizing of Discourses on ICT Integration in Mathematics for Their Practicum Assignments

Diana Paola Piedra Moreno — 2024-12-20

Even though it is advocated in educational policies worldwide to integrate digital tools as a way of transforming teaching, this has not occurred, even with teachers who have grown up surrounded by digital technologies. To expand understandings about why this might be the case, the study reported here investigated preservice teachers' collective meaning-making about ICT integration. The preservice teachers' mandatory group assignments for their first mathematical course, in a Norwegian teacher education institution, were analysed. Bernstein's description of recontextualising is employed to gain insights into preservice teachers' meaning-making through the discourses that they produced from the resources made available to them in their teacher education. The recontextualising of discourses shows, for example, how mathematics curriculum references to playing games with digital tools were recontextualised by the preservice teachers into discourses about fun and motivation. This allowed the preservice teachers to focus on general pedagogical positive aspects of ICT beyond perceptions of students being bored but hindered them in attending to other mathematics classroom issues.