Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

In response to the criticism that theory-driven researcher-developed learning tools lack scalability and sustainability in the real world, the design-based implementation research (DBIR) approach was proposed. However, few empirical studies actually describe what a DBIR study looks like and how it can inform readers about learning tool design. We…

Engineering is developing extensive leadership education, supporting future professional engineers to engage with others in solving complex sociotechnical problems. A contemporary challenge is to integrate leadership learning into foundational coursework requirements.

The intention of this article is to provide Technology and Engineering Educators (T&EEs) with a more thorough understanding of implementing the product realization process (PRP) to help manage the design and development processes in their classrooms. The product realization process (PRP) innately involves a practical combination of knowledge,…

Engineering design has been central to technology education. Currently, online collaborative platforms for designers are widely used as digital forms of an engineer's notebook. However, traditional forms are still valued as the medium of engineering design during the conceptual phase of design since a paper notebook and pen or pencil allow…

As the importance of non-technical skills in the software engineering industry increases, the skill sets of graduates match less and less with industry expectations. A growing body of research exists that attempts to identify this skill gap. However, only few so far explicitly compare opinions of the industry with what is currently being taught in…

This introduction presents Active Learning Methodology, surveying its history, main existing tools and supporting evidence, with an emphasis on mathematics and higher education, in particular engineering studies. This work is part of the DrIVE-Math project, developing innovative mathematical teaching strategies in engineering studies.

A central problem in undergraduate mathematics education for future engineers consists in the perceived and actual relevance of the mathematical content. One strategy to strengthen both is to let students experience how that content appears in posing and solving authentic problems from the field of engineering which the students have signed up to…

In this note, some variants of Cauchy's mean value theorem are proved. The main tools to prove these results are some elementary auxiliary functions.

Design thinking--a human-centered approach to problem solving--is a process by which K-12 teachers engage students in solving relevant issues that occur in their schools. In this article, the authors describe a project in which fourth-graders used design thinking to solve an unexpected issue related to a much-anticipated class project. The project…

Visual literacy is essential for engineers. Technological professions have important visual characterization, both in the transmission of information and problem-solving. This means that future engineers must be proficient at communicating, thinking, and learning visually. However, engineering curricula takes partially the need to have visually…

It is well accepted that many mechanical engineering (ME) design processes are complex. We believe that many ME design approaches include unnecessary complexity, intended to assist the teaching of engineering knowledge. This technical complexity has contributed to many critical issues in ME education, including decreased enrolments in many…

Engineering has led the way in responding to the COVID-19 pandemic, including developing masks that reduce transmission, digital tools that allow contact tracing, and vaccines that show promise to put an end to the pandemic and allow a more normal way of life. Society is not only "following the science," but is also applying principles…