Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive…

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for…

360°(degree-)-videos inherit interesting potentials for teaching competence development. Reflecting on personal teaching performance from multiple perspectives potentially increases the depth in situated reflection and provides new learning insights for pre-service teachers. In this light, this paper describes a case study conducted at the…

Our qualitative case study explored the nature of pre-service teacher (PST) reflections when analysing video-based lessons aimed at developing their reflective practice. 14 PSTs participated in the study. Data were collected through lesson observation and individual PSTs' written reflections. The initial data show that PSTs find lesson reflection…

Incorporating video case study of mathematics teaching into professional development (PD) can provide opportunities for teachers to develop new ways of seeing teaching and learning and inform efforts to enact new instructional practices. However, more research is needed to understand how such PD can foster sustained teacher learning about…

We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…

New technologies are changing the way of learning foreign languages. However, one of the main challenges for software developers and mobile assisted language learning designers remains the creation of learning environments for students' language immersion in and outside the classroom. This paper describes the design and evaluation of a VR-based…

This case study is excerpted from a larger study where we explore collaborative encounters, i.e. practices and discourses, within a blended learning project where vlogging, i.e. video blogging, is used in Finnish language learning. The data has been collected in 2017-2018 during an intermediate Finnish course at the University of Toronto. In this…

Students' opportunities to struggle with mathematical ideas have long been considered paramount to learning. However, there's little research on how teachers; (1) draw on and make sense of the discourses of perseverance; (2) enact it in classroom; and (3) develop an expansive view of perseverance. To contribute to these lines of research, we build…

Research has yet to make measurable progress toward understanding how to help students with math learning disabilities (MLDs) overcome their persistent difficulties. Prior research has traditionally framed MLDs as cognitive deficits and studied these deficits by analyzing failing students' errors. In this paper, we provide an alternative. We…

Senior secondary mathematics in Australia is generally characterised by a challenging prescribed curriculum, textbook usage, high homework expectations and externally imposed assessment tasks. An increasing number of senior secondary mathematics teachers are incorporating a flipped classroom approach into their teaching as a means of addressing…

In this paper, we present findings from the third year of a multi-year research investigation into the mentoring and coaching practices of cooperating teachers and university facilitators working together with preservice teachers. In this third year, our focus was collaborative coaching--coaching that intentionally involves both the university…

Blended learning, structured as a combination of traditional course instruction and additional supporting multimedia course content, can be used in higher education for a variety of reasons. In the case study that we examine, the introduction of blended learning was initiated three years ago with the purpose of creating more resources for…

We report on the development and evaluation of MathVision, a mobile-application designed to develop Virtual Professional Learning Communities through asynchronous discussion about 2nd, 3rd, 4th, and 5th grade students' mathematical thinking. MathVision allows teachers to upload videos of problems solving sessions using Cognition Based Assessment…

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…