Optimization is a vital mathematical concept widely applied in various engineering fields. However, teaching this subject to engineering students often involves abstract materials, making it challenging for them to grasp. To address this issue, a group of five mathematics lecturers collaborated on designing a practical lesson on optimization for…

Implementing an equity agenda in the classroom is both necessary and challenging for classes containing pre-service teachers. For this intervention, we chose to begin our History of Mathematics course for preservice middle school teachers with a cultural simulation training exercise: Bafa Bafa. After participating in the exercise, pre-service…

Gravitational lensing is an interesting phenomenon in astronomy and is most typically given rise to by galaxies. The majority of the matter in a galaxy is thought to be dark matter, and the galactic gravitational lensing effect is mainly caused by dark matter halos. In gravitational lensing-related demonstrations in physics education, the feet of…

The virtual-representational-abstract (VRA) framework adapts an evidence-based practice, the concrete-representational-abstract (CRA) framework, while trying to meet students and teachers where they are in terms of technology interest and use in education. This article discusses the VRA framework and the advantages of virtual manipulatives, and…

The aim of this paper is to describe the innovative teaching approach used in the Southern Federal University, Russia, to teach accounting via a form of matrix mathematics. It thereby contributes to disseminating the technique of teaching to solve accounting cases using mutual calculations to a worldwide audience. The approach taken in this course…

Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of…

Interactive Mathematica simulations with graphical displays of system behavior are an excellent addition to chemical engineering courses. The Manipulate command in Mathematica creates on-screen controls that allow users to change system variables and see the graphical output almost instantaneously. They can be used both in and outside class. More…

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

We present an approach to Intelligent Tutoring Systems which adaptively personalizes sequences of learning activities to maximize skills acquired by students, taking into account the limited time and motivational resources. At a given point in time, the system proposes to the students the activity which makes them progress faster. We introduce two…

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

Although problem-based learning (PBL) has many advantages, it often fails to connect to the real world outside the classroom. The integration with the laboratory setting and the use of information and communication technologies (ICTs) have been proposed to address this deficiency. Multi-user virtual environments (MUVEs) like Second Life (SL) are…

This paper provides a description and rationale for a performance assessment of a teaching practice--leading a classroom discussion (LCD)--included in the ETS® National Observational Teaching Examination (NOTE) assessment series. In this assessment, candidates interact with a small class of virtual students represented by avatars in a…

This report describes and provides research and scholarly support for a core practice of teaching--eliciting student thinking (EST)--that is the target for a performance assessment contributing one component of the "ETS"® National Observational Teaching Examination (NOTE) assessment series. The purpose of this report is to review the…

This report reviews the scholarly and research evidence supporting the construct labeled modeling and explaining content (MEC), which is measured via a performance assessment in the "ETS"® National Observational Teaching Examination (NOTE) assessment series. This construct involves practices at the heart of teaching that deal with how…