This interpretive cross-case study investigates complexity in the ways teachers frame mistakes and the reasons behind their framing, challenging the assumption in the literature that productive beliefs about errors generate productive error-handling practices, while unproductive beliefs result in unproductive practices. The study draws on…

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

The aim of this research is to determine the students' misconceptions of using concept cartoons and to evaluate the lessons taught with concept cartoons according to the students' opinions. The model of the research is the case study, which is one of the qualitative research methods. Participants are a total of 82 students, attending the 3rd grade…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics,…

Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…