We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Florida's Senate Bill 1720 allowed many students to bypass developmental education and enroll directly in introductory college-level courses. We use an interrupted time series design to introductory college-level courses enrollment and passing rates in English and math for three cohorts of college students prereform and three cohorts postreform.…

This study explored the relationships between Chinese college students' perceptions of the classroom environment and some affective aspects in the study of mathematics. A total of 2529 students responded to three measures that were specifically designed to assess college students' perceptions of the mathematics classroom environment, their…

Considerable past classroom learning environment research has focused on the primary and secondary levels of education and the subject areas of science and mathematics. The current study is distinctive in its focus on university business statistics learning environments. For the first time, we validated and applied the widely-used What Is…

This paper describes a method for using instructional analytics to support changes in teaching practice. The study took place in a discourse-focused undergraduate mathematics classroom taught by an experienced instructor. Using the classroom observation tool EQUIP and social network surveys, we generated quantitative data on patterns of student…

This study investigated whether strategy accuracy and flexibility on various types of complex multiplication problems could predict college GPA concurrently and longitudinally in 164 college engineering students. Additionally, it sought to answer whether low- and high-achieving students would show unique patterns of strategy flexibility, accuracy,…

This case study examined the current assessment practices in the math school of a large research university in the United States. After reviewing a sample of course syllabi offered in the spring 2021 semester, we descriptively summarized the use of 19 assessment methods in the school and examined the assessment patterns by subjects, class…

This study investigated personalization as an innovation that can be used to impact college mathematics achievement. In the reported study, similar tasks using personalized data and teacher-selected data were implemented in courses in both 4-year and 2-year colleges. Pre- and posttests and student work were analyzed to examine the impact of…

The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea…

Many education institutions in Uganda and the world at large were closed in March, 2020 in order to slow down the spread of the Corona Virus. More than fifteen million students and teachers in Uganda were affected, all education activities such as teaching, and assessing of learners were prematurely stopped. Different approaches have been adopted…

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

Our students experience difficulties in working on non-routine mathematical problems. They cannot see the general through special things or instead see things that are special through common things when dealing with mathematical concepts and examples. They cannot see the essential features of the way or recognize it when presented in various…

The study aimed at describing university students' ability in constructing mathematical proofs using logical arguments and constructing an effective teaching-learning map. The study adopted a correlational research design. An open-ended mathematics assessment involving questions on mathematical logic and construction of mathematical proofs was…

The problem was that testing instructions were normally presented as gains were more advantageous for promotion-oriented individuals, while testing instructions presented as losses were more advantageous for prevention-oriented. The purpose of this quantitative comparative study was to compare the performance on a measure of achievement for black…