In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

In the mathematical community, two notions of "function" are used: the set-theoretic definition as a univalent set of ordered pairs, and the Bourbaki triple. These definitions entail different interpretations and answers to mathematical questions that even a secondary student might be prompted to answer. However, mathematicians and…

Mathematics preparatory workshops were offered to college students at a diverse urban undergraduate institution. The goal was to prepare students for their mathematics course, by offering non-credit bearing and free preparatory workshops. The lack of adequate preparation for mathematics courses is a barrier for student engagement in future STEM…

The purpose of this concurrent mixed methods action research study was to investigate the impact of new technology-enhanced Dual Enrollment (DE) math courses on students' perception of college courses, the influence the technology-enhanced DE had on students' intention of going to college, and the students' perception of the technology-enhanced DE…

This quantitative study investigated the academic outcomes of high school students from one community college district in Illinois who took a high school transitional math course designed to give them direct placement into a college-level math course. The goal of successful completion of a transitional math course is to allow students direct…

Investigating the transition between educational levels is one of the main themes for the future of mathematics education. In particular, the transition from secondary school to STEM degrees is problematic for the widespread students' difficulties and significant for the implications that it has on students' futures. Knowing and understanding the…

Annually, 40% to 60% of students who graduate high school and enroll in higher education do not exhibit the skills necessary to succeed in college-level work and will need remediation in mathematics or English (Jimenez et al., 2016). Successfully graduating from high school does not guarantee academic preparedness for college. To understand why a…

Research has identified several aspects that influence students' transition to mathematics studies at university, but these aspects have often been studied separately. Our study contributes to the field's understanding of the transition between upper secondary and university mathematics by taking a multifaceted perspective not previously explored.…

The tutor-web is an open-source learning environment designed to be used for teaching mathematics and statistics. The system offers thousands of exercises at high school and university level, and has been used for a decade to teach introductory statistics courses with good results. A new component has recently been added to the tutor-web so that…

In this article, the author presents a Desmos activity where students adjust the measures of angles in radians to reposition a laser and a mirror so the beam passes through three stationary targets. This Radian Lasers activity can be extended to simulate project-based learning (PBL), a pedagogical approach for applying concepts and skills from…

Secondary mathematics pre-service teachers (PSTs) are required to take university-level mathematics content courses to develop their mathematical content knowledge. Although PSTs' experiences as students play a major role in the types of teachers they become, there is limited research investigating the experiences of PSTs engaging in these…

In Tunisia, calculus is a fundamental component of mathematics curriculum in high school and a major requirement at the advanced level in the mathematics bachelor's degree and in engineering. Yet, paving the way for a passage between high school calculus and university calculus remains a challenge for both mathematics education researchers and…

Assembly Bill 1705 (AB 1705) seeks to strengthen students' completion of the first STEM Calculus course for Science, Technology, Engineering, and Math (STEM) programs across the California Community Colleges. The law sets new standards for students' placement and first math enrollment to ensure STEM students begin in transfer-level coursework that…

A theoretical-didactic proposal based on variational ideas and the use of GeoGebra is described as a response to a local problem on the understanding of the concept of function and quadratic equation in pre-university students. The theoretical elements of this work are based on the understanding of concepts and the theory of semiotic registers and…

The objective of this article is to determine which are the international standards and norms of usability that are used in educational technology applied to the teaching of mathematics at secondary and higher education levels, focused on two scenarios: (1) digital educational resources and virtual learning environments (VLEs), and (2) game-based…