This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…

Using learning objectives to guide course design is often considered an educational best practice, but little research exists that explores how students use them over time and across courses. We surveyed students on their use and perceived value of learning objectives as the semester progressed across four science, technology, engineering, and…

Preparing secondary students for college entrance requirements and the expectations of the job market, a market which is actively seeking the employees who are most qualified to take on jobs that require data analysis skills, is becoming increasingly important. Federal, state, and local education administrators and personnel must rewrite many of…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

Realistic mathematics education (RME) has proven to be an effective model for mathematics elsewhere. However, students and teachers still grapple to confront the circle equation to learn and teachers to teach. This study explored students' didactical phenomenological discourses in the circle equation as an alternative. The mixed methods research…

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral…

With the shift to next generation digital assessments, increased attention has focused on Technology-Enhanced Assessments and Items (TEIs). This study evaluated the feasibility of a high-fidelity digital assessment item response format, which allows students to solve mathematics questions on a tablet using a digital pen. This digital ink approach…

Students at Century High School (CHS), a Catholic all-boys high school on Long Island, New York, who started ninth grade with Algebra 1 instead of Geometry demonstrated less obvious career interest in science, technology, engineering, and mathematics (STEM) and lower mathematics achievement, as typically evidenced by Iowa Tests of Educational…

Mathematics as a discipline requires abstract operations under many sub-learning areas is considered hard by students to learn. In this respect, it has become indispensable to make mathematics teaching processes fun and to structure teaching procedures by using different teaching methods, techniques or materials. In this context, the purpose of…

This article describes a carefully structured exploration of formative assessment, conducted in the form of a classroom research experiment. The authors are an instructor and a student in a graduate course that assigned teachers to research formative assessment strategies, implement one or more strategies for several weeks, collect data from…

The aim of this study is to develop a valid and reliable measurement tool that measures mathematical visualization perceptions for mathematics teacher candidates. Therefore, the type of study is a survey research. Research was carried out with 462 (336 Female, 125 Male) mathematics teacher candidates from a university located in the Eastern…

The purpose of this study was to examine the effects of using GeoGebra software in a computer-supported collaborative learning (CSCL) environment on seventh grade students' geometry achievement, retention of learning, and attitudes toward geometry. The study was designed using a quasi-experimental research method with pretest, post-test and…

We developed generalizable affect detectors using 133,966 instances of 18 affective states collected from 69,174 students who interacted with an online math learning platform called Algebra Nation over the entire school year. To enable scalability and generalizability, we used generic interaction features (e.g., viewing a video, taking a quiz),…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

In this article, we present the results of a classroom action study that was done in the course of advanced algebra and analytic geometry at Huaiyin Institute of Technology. Specifically, we identify and analyze the students' difficulties in learning the course of advanced algebra and analytic geometry, put forward three visual strategies to…