An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond…

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

Research has shown that students have difficulties with understanding the process of determining whether an object is speeding up or slowing down, especially when it is applied to the analysis of motion in the negative direction. As inductively organized learning through its scaffolding sequencing supports the process of knowledge acquisition…

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

A common textbook problem asks students to calculate the total distance traveled by a bouncing ball, from its initial release until it comes to rest, under the assumption that the height of each bounce is some fixed proportion "r" of the height of the previous bounce. The solution is found by inserting information about "r" and the height from…

Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999,…

"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…

These proceedings contain the papers of the 18th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2021), held virtually, due to an exceptional situation caused by the COVID-19 pandemic, from October 13-15, 2021, and organized by the International Association for Development of the Information Society…

This note considers a family of piece-wise linear functions that can be used in the classroom to illustrate various concepts involved in iteration theory such as periodicity. These functions require minimal background on the part of the student. (Contains 2 figures.)

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

As part of the discussion about Newton's work in a history of mathematics course, one of the presentations calculated the amount of energy necessary to send a projectile into deep space. Afterwards, the students asked for a recalculation with two changes: First the launch under study consisted of a single stage, but the students desired to…