This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The current research trend of metacognitive regulation has shifted from an individual to a social context. One such social context is collaborative problem-solving. Interaction between group members is an essential factor in completing collaborative problems. Metacognitive regulation is divided into four forms based on the interaction in…

This study investigates the embodied, symbolic, and formal reasoning of two fourth-year university students while exploring geometric reasoning about the Cauchy-Riemann equations with the aid of "Geometer's Sketchpad (GSP)." These students participated in a teaching activity designed to encourage shifts between embodied, symbolic, and…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

For several decades, literature on the history and pedagogy of mathematics has described how history of mathematics is beneficial for the teaching and learning of mathematics. We investigated the influence of a history and philosophy of mathematics (HPhM) course on students' progress through the lens of various competencies in mathematics (e.g.,…

Purpose: This study presents the competence level of education students in College Geometry and the development of a Computer Generated Instructional Materials (CGIM). Method: This research used the model for research and development by Borg and Gall (2003) with revision. The researchers developed a CGIM, specifically, the worktext paired with…

This research is aimed at analyzing the solutions of Euclidean Geometry problems using the Polya method. This present study was made through qualitative and quantitative approaches with 85 respondents of the second semester students at the Department of Mathematics Education, University of Muhammadiyah Malang Indonesia, in the 2012/2013 academic…

The goal of this study was to examine the pathways to being college ready in mathematics. Students who enter high school already having demonstrated mathematics proficiency on a standardized test in the 8th grade have already taken a significant step towards being college ready. The best scenario is to enter high school proficient in mathematics…

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in…

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate…

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…

Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

Developed is a condition, expressed in terms of an index, that ensures that a quasinormal subgroup is normal. The arguments suggest a variety of exercises for a course in group theory or Galois theory. Included are the definitions, lemmas, and proofs. (KR)