This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well…

In science education, building models of dynamical systems is a promising method for understanding various natural phenomena and artifacts with scientific concepts. It is, however, difficult to learn skills and concepts necessary for modeling. Though several model-building learning environments (MBEs) have been developed with potentially useful…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…

Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires…

Synergistic learning combining computational thinking (CT) and STEM has proven to be an effective method for advancing learning and understanding in a number of STEM domains and simultaneously helping students develop important CT concepts and practices. We adopt a design-based approach to develop, evaluate, and refine our Collaborative,…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Fermi problems are problems which, due to their difficulty, can be satisfactorily solved by being broken down into smaller pieces that are solved separately. In this article, we present different sequences of activities involving Fermi problems that can be carried out in Secondary School classes. The aim of these activities is to discuss…

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…

Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

This article allows students to apply their knowledge and experience of area and volume to find the volume of Norris Lake, a large reservoir lake in Tennessee. Students have the opportunity to demonstrate their skills in using maps and scales as well as to incorporate the use of technology in developing the solution. This project satisfied the…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

The integration of History in the educational practice can lead to the development of a series of activities exploiting genetic "moments" of the history of Mathematics. Utilizing genetic ideas that developed during the 14th century (Merton College, N. Oresme), activities are developed and mathematical models for solving problems related to uniform…

The University of Maryland offers a physics course as part of the Maryland Collaborative for Teachers' Preparation (MCTP) project. One of the course aims is to promote the learning of the concept of a function through the learning of physics. Students learn in small groups through problem solving and with the aid of microcomputer-based…