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…

Covariational reasoning, essential for understanding functions and modeling dynamic situations, is traditionally introduced in secondary education. This paper proposes introducing covariational reasoning in primary school settings through an artifact, the Tracer. Previous studies investigate a covariational approach to functions with younger…

Mathematics learning in higher education today focuses on the need to enhance students' diverse creativity through learning process. To address this challenge, this study introduces the Differentiated Instruction based on Lateral Thinking Techniques (D-LTT) framework. It provides an overview of D-LTT, demonstrates its application in a numerical…

Mathematical modeling is crucial in the field of education, particularly in mathematics, as it enhances students' mathematical skills and prepares them for solving real-world problems. The study focuses on the challenges of teaching mathematical modeling, specifically in the Malaysian education system. We utilized a case study approach, involving…

This study compares the effects of student-centred teaching methods, teacher-centred methods, and teacher-student interactive methods on students' mathematics academic achievement. For this purpose, calculus, compound interest, annuities, and depreciation topics were taught to first-year college students in three different groups: traditional…

This study explores the use of Large Language Models (LLMs), specifically GPT-4, in analysing classroom dialogue--a key task for teaching diagnosis and quality improvement. Traditional qualitative methods are both knowledge- and labour-intensive. This research investigates the potential of LLMs to streamline and enhance this process. Using…

Supporting students' problem-solving skills, solution planning and sequencing of different stages that are involved in successfully developing a meaningful solution to a problem has been a challenge for teachers. This case study was informed by reflective investigation methodology which explored how procedural flowcharts can support student…

We propose the 'flow of a proof' as a construct that relates to the balance lecturers achieve in their presentation between the proof as a whole and its different parts, taking into account various aspects (informal, contextual) of proof classroom presentation. We conducted expert interviews in which we presented two different proofs of the same…

Purposeful questioning is one of the most important elements to promote successful mathematics understanding (National Council of Teachers of Mathematics, 2014; Ontario Ministry of Education, 2011). Questioning helps teachers to elicit, interpret, and respond to student thinking (Stein et al., 2008) and supports students' understanding,…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics…

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

This research examined the impact of the Cognitive-Communicative (C-C) model as a pedagogical strategy for teaching algebraic word problems (AWPs). The C-C model integrates structured dialogue, concept clarification, and systematic problem-solving steps to enhance students' comprehension and reasoning. Employing a mixed-methods framework, the…

Background and Aims: Students with intellectual disability benefit from high-quality instruction in reading and mathematics. Methods: This Theoretical Paper outlines the need for effective, evidence-based instructional practices for this population and the potential for observation research to inform such advancements. We report our systematic…

This study contributes to the literature on linear algebra instruction by designing and researching a teaching sequence based on APOS Theory to introduce engineering students to vector spaces. The sequence offers students multiple opportunities to understand the concept. Another contribution is the evidence that introducing prerequisite…