Noticing is an essential skill for all teachers of mathematics. Mathematics teacher educators have utilized a variety of tools to practice and develop preservice teachers' (PSTs') ability to notice, which we extend to include photographs and learning trajectories. This article explores PSTs' noticing skills by analyzing work samples from a methods…

Preservice teachers often find it difficult to apply professional knowledge to their teaching practice. The ability to connect professional knowledge with one aspect of practice -- lesson planning -- was assessed with the Lesson Analysis and Plan Template in (N = 18) preservice teachers after one year of teacher preparation. Lesson plans were…

Although the effects of professional development programs on teachers' noticing skills have attracted considerable interest among mathematics education researchers, little is known about the developmental process of prospective teachers' noticing skills within initial teacher education. This paper examines the extent to which prospective teachers'…

Background: Artificial Intelligence (AI) technologies offer unique capabilities for preservice teachers (PSTs) to engage in authentic and real-time interactions using natural language. However, the impact of AI technology on PSTs' responsive teaching skills remains uncertain. Objectives: The primary objective of this study is to examine whether…

This paper presents Big Ideas of Measurement as a framework of students' thinking about measurement. Drawing from research-based evidence, the framework is a collection of key concepts that students must develop for a robust understanding of measurement and, as such, are key aspects of students' thinking teachers should learn to notice. In a case…

Student engagement is a complex measurement that can be viewed through behavioral, emotional, and cognitive constructs. Authentic intellectual engagement requires more than task compliance and requires teachers to make decisions and moves to promote engagement. Pre-service teachers need to have these teacher decisions deconstructed and explicitly…

Teacher noticing, a situation-specific part of teachers' professional competence, has gained much importance in the past two decades. The construct is believed to play a crucial role in the transfer of knowledge and skills into professional teaching performance. However, there is little empirical evidence on how the length of teachers' teaching…

This study investigated how pre-service middle school mathematics teachers attend, interpret, and respond to the students' thinking about statistical concepts in a case-based teacher training environment. 25 pre-service middle school mathematics teachers participated in the study, and they were asked to make evaluations on the cases given. Based…

This study investigates the development of prospective secondary mathematics teachers' (PSMTs') noticing skills in a course conducted at the last year of their teacher education program. PSMTs watched and analysed different instructional videos, including an unknown teacher's, their mentor teacher's, and their own teaching videos. The data were…

Higher education instructors are inundated with options to engage their students in virtual observation to improve the learning experience, yet more research is needed to identify effective practices to establish a virtual field experience. The purpose of this case study is to evaluate a virtual field experience utilizing video playback that…

Graduate teaching assistants (GTAs) hold a unique positionality as instructors and research mentors to undergraduate students, research mentees to faculty members, and employees to an institution. With limited pedagogical training and teaching resources, the enactment of planned teaching activities and learning resources may be influenced by how…

The purpose of this paper is to describe secondary mathematics student teachers' types of noticing while teaching. We discuss the importance of focusing on the interrelatedness of the noticing skills rather than reporting on individual skills separately. We apply the types of noticing to videos of student teachers to identify their ability to…

The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those…

Learning to teach students with disabilities is challenging. Preservice special educators must develop critical knowledge of content as well as skill for enacting evidence-based practices effectively. Preservice special educators need increased opportunities to learn core knowledge coupled with a mechanism to support them in situating their newly…

To support pupils' learning, teachers must understand what and how their pupils have learned, and teacher education should teach candidates how to do this. This article reports on survey data (n = 270) from three programmes and observation data (N = 104 h) from six programmes, located in Norway, Finland and the US. It examines the candidates'…