The "object lesson" is a particular teaching method that was widespread in Europe and the westernised world during the nineteenth century, which was variously adapted according to national contexts under the name of "Anschauungsunterricht, leçon de choses, lezione di cose, and lección de cosas." Based on the intuitive…

Although complex analysis is part of the study programs of many mathematics undergraduates, little research has been done on how individuals interpret basic concepts from complex analysis. To address this gap, this paper investigates how experts individually think about complex path integrals. For this purpose, the commognitive framework is used…

We discuss how research on student difficulties was used as a guide to develop, validate, and evaluate a Quantum Interactive Learning Tutorial (QuILT) to help students learn how to determine the completely symmetric bosonic or completely antisymmetric fermionic wave function and be able to compare and contrast them from the case when the particles…

Taking the "practice turn" in K-12 science classrooms requires students to engage in processes of knowledge building, constructing explanatory accounts of natural phenomena. To support students in these sensemaking opportunities, a significant departure is needed from how science is typically taught in many classrooms. Teachers will need…

This study examines the behavior of individuals when two intuitive rules in their minds lead to two different outcomes concerning a problem. In the absence of the formal knowledge, intuitive rules can affect the mathematical thinking. Hence, studies have usually compared the correct answer of the related formal knowledge with the incorrect one…

This article describes how a secularized version of Lectio Divina is used within the classroom as a model for engaging in anti-racism and social justice discussions. Lectio Divina is an ancient tool for understanding texts. From its religious beginnings, it has been adapted to its secular forms for critical contemplative practice in twenty…

The authors present a Web application they designed in the R programming language as an experiential learning tool for teaching production theory. The app simulates production decisions where a manager is tasked to find the optimal mixture of inputs through experimentation. Users of the application are instructed to use calculations and intuitions…

This work is the result of a pre-experiment carried out as part of a master's course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology…

The purpose of this study was twofold. First, to explore middle and high school students' intuitively-based (mis)conceptions in probability, particularly availability and representativeness heuristics. Second, to investigate teachers' awareness of these intuitively-based (mis)conceptions and the effectiveness of their instructional practices to…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

Meta-analysis results are usually presented in forest plots, which show the individual study results and the summary effect along with their confidence intervals. In this paper, we propose a system of linear springs as a mechanical analogue of meta-analysis that enables visualization and enhances intuition. The length of a spring corresponds to a…

To a student in introductory physics, using vectors is at best an exercise in bookkeeping. A two-dimensional kinematics problem effectively doubles the number of equations that a student must know, and invites the student to memorize factoids: "The horizontal motion is constant," "Gravity is only in the y-direction," etc. Force…

Computational thinking (CT) has the potential to enhance learning when integrated into mathematical classroom activities. Teachers are being asked to include CT concepts in their core disciplines; however, there is an open question as to how best to equip teachers to integrate CT into their practice. Oftentimes teacher candidates enter math and…

The aim of this paper is to show how an innovative technique can be used to introduce a method for uncovering intrinsic mechanisms that motivate changes in students' mental models. The theoretical framework used to develop the method is based on the ONEPSY (ONtology, EPistemology and PSYchology) model. The ONEPSY model is rooted in the theoretical…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…