When analyzing instructional quality in mathematics, observational measures can consider domain-specific instructional approaches (e.g., effective teaching of mathematics) and content-focused practices (e.g., effective teaching of a specific mathematical topic). In this study, we analyze lesson videos from secondary algebra classrooms using two…

In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that instantly checks the correctness of every step and provides immediate feedback. Teaching with Lean might present a challenge, in that students must write their proofs in a formal way using a specific syntax.…

Effective feedback improves grades, quality of work, and student perceptions regarding the quality of the feedback they receive. Recent feedback scholarship indicates that despite students' appreciation of quality feedback, they seldom use it. A shift in focus toward feedback engagement has resulted in several narrative reviews on the topic, each…

This study explores variations in prospective teachers' (PTs') noticing of students' mathematical thinking based on narrative writing within the context of a practicum course. The research involved eight PTs, each of whom produced ten weekly narratives throughout the course duration. Most PTs displayed noticing abilities within the average range,…

The goal of this paper is to explore aspects of the work of mathematics teachers that students consider problematic and in need of improvement. By using an inductive thematic analysis, we present three themes generated from interviews conducted with 15 students in Alberta, Canada who were participating in high school mathematics upgrading courses.…

Several major themes related to rethinking assessment emerged from a search of the papers published in "PRIMUS." Authors explored ways to change the stakes of assessments, often with outcomes-based grading and testing structures. They explored changing the "structure" of assessments by considering media beyond written exams and…

Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…

Background: The growing necessity of providing better education, notably through the development of Adaptive Learning Systems (ALSs), leveraged the study of several psychological constructs to accurately characterize learners. A concept extensively studied in education is engagement, a multidimensional construct encompassing behavioral expression…

Teaching observation protocols serve purposes beyond research, such as providing formative feedback for teachers' growth in their practice. Such observation tool usage requires different approaches for validation. For this reason, we developed the formative teaching evaluation framework adapted from the student-assessment literature. We used this…

Empirical studies on effects of formative assessment (FA) on motivational outcomes and underlying mechanisms are scarce. The core elements of FA, feedback and adaptive teaching behavior, might be helpful in promoting the experience of competence, which in turn is a prerequisite for promoting intrinsic motivation. However, instructional impact also…

Mathematical achievement and the factors that influence students' skills to apply their knowledge and reasoning to solving real-world problems are considered a critical area of study within the PISA framework. This study presents a systematic review of the impact of teaching strategies and practices on students' mathematical achievements in PISA.…

For fans of the bestselling book "The Formative 5: Everyday Assessment Techniques for Every Math Classroom" comes this updated and expanded edition for understanding and implementing highly effective, research-backed formative assessment techniques into seamless, daily practice with students in grades K-12. "The Formative 5 in…

We examined the suggestions mathematics coaches provided to teachers as part of one-on-one coaching cycles. The purpose was to understand the object (content) of the suggestions, the lesson phase in which the suggestion would occur, and the clarity of the suggestion (how actionable the suggestion would be if the teacher followed the suggestion).…

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and…

In this paper, we describe an idea for mathematics lectures that involves using digital tools for first-year university students. Materials in the Moodle course include live broadcasts, lecture recordings, Moodle tests, sample solutions and videos. The aim of the paper is to find out from students' feedback which digital tools help them understand…