We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence…

In the spirit of the networking of didactical theories, it is advocated in this presentation in favor of a mixed networking of philosophical theories, namely Husserlian phenomenology and hermeneutics, and didactical theories to produce a fertile interplay between philosophy and mathematics education. The cross-analysis of students' work on a…

This study aims to understand the instructional interactions that foster students' generalizing. By analysing video-recorded lessons from 13 different Grade 3 classrooms in which an early algebra intervention was implemented, activities related to generalizing and students' generalizing activities were identified, and the nature of the…

This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview…

Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing…

This study explored the impact of homogeneity of answer choices on item difficulty and discrimination. Twenty-two matched pairs of elementary and secondary mathematics items were administered to randomly equivalent samples of students. Each item pair comparison was treated as a separate study with the set of effect sizes analyzed using…

This article summarises activities that happened during the first three weeks of a fictitious high-school-level linear algebra section that used magic squares as a teaching tool to inspire students to further investigate the topics. The author has been working with students from high school and college levels for years, and although this situation…

In 1936, Albert Einstein wrote a brief article where he suggested the possibility that a massive object acted as a lens, amplifying the brightness of a star. As time went by, this phenomenon--known as gravitational lensing--has become a powerful research tool in astrophysics. The simplest and symmetrical expression of a gravitational lens is known…

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

Research reported in this article has been conducted from the theoretical perspective of the Anthropological Theory of the Didactic developed by Y. Chevallard and his collaborators, and from the institutional perspective of university mathematics education in France. It focuses on the teaching and learning of algebraic structures. The article…

In this exploratory case study, the researchers conducted a descriptive, qualitative microanalysis of the tutoring of two eighth grade students with learning disabilities while solving algebra problems. The researchers analyzed the participants' problem solving tendencies and interventions that helped the students succeed. One of the students,…

In this work, students' thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students' thinking modes and representation types of linear algebra. The participants were 74 undergraduate…

For 500 years, dream catchers have been cultural symbols of intrigue worldwide. The most common folkloric design is a 12-point dream catcher. According to Native American legend, the first dream catcher was woven by a "spider woman" to catch the bad dreams of a chief's sick child. Once the bad dreams were caught, the chief's child was…

It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult…

This study focuses on the undergraduate mathematics students' perceptions and applied techniques for the preparation for their final examination in Abstract Algebra. The results of this study suggest that the revision for the final examination involves, firstly, the review of the lecture notes, followed by the solution of the coursework together…