Engineering design is a core component of technology and engineering education, and although not every student will become an engineer following high school, all students can profit from having engineering design experiences in high school (Apedoe, Reynolds, Ellefson, & Schunn, 2008; Denson & Lammi, 2014; Grubbs & Strimel, 2015;…

When teachers make the effort to build a solid relationship with each student, built on trust, they often engender a life-long connection, one that's life-changing for the student. But how can teachers grow such long-lasting relationships with all students, especially disenfranchised learners and those who make it hard to connect? Crowley, a…

We conducted two AB experiments (treatment vs. control) in a massive open online course. The first experiment evaluates deliberate practice activities (DPAs) for developing problem solving expertise as measured by traditional physics problems. We find that a more interactive drag-and-drop format of DPA generates quicker learning than a multiple…

This paper discusses the complementarity of human and cyber physical production systems (CPPS). The discourse of complementarity is elaborated by defining five criteria for comparing the characteristics of human and CPPS. Finally, a management portfolio matrix is proposed for examining the feasibility of optimal collaboration between them. The…

This research brief discusses the benefits of teachers using mathematical discourse--allowing students to explain, justify, and debate their individual techniques for solving math problems--to enhance learning. Using this strategy requires educators to discard traditional teacher-centered modes of instruction and adopt new student-centered modes…

In this article, John Larmer paints the picture of the ideal high-school graduate--one who is ready for college, career, and life in general. Among other qualities, this student is a problem solver, manages time effectively, works well with others, is open to feedback, and is innovative and creative. How do K-12 schools go about building this…

Large foundational courses delivered in lecture halls are disadvantaged in eliciting participation from all students and maintaining engagement throughout the class session. We introduced a question-driven method facilitated by an audience response system, namely TopHat™, that allows the instructor to engage students in solving Calculus problems…

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Have you ever considered how technology could facilitate reasoning and sense making of systems of linear inequalities? In this article, the authors share how to use Google® Maps® and Desmos to achieve this and provide students with opportunities to access mathematics as they build a more formalized understanding. Using an inquiry-based approach,…

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

With innovations in technology, adult educators can begin to create learning opportunities in very expansive terms. But, innovative, technologically advanced learning environments still benefit from a solid foundation in adult learning theory, instrumental theories like John B. Watson's Behaviorism, Lev Vygotsky's Social Development Theory, Jack…

In recent years, accreditation standards for international engineering education have led to a dramatic rise in the use of outcome-based education at universities. In this system, enticing new undergraduate students to science and engineering, although challenging, is the first important step toward building students' career competencies. An…

The Common Core State Standards (CCSS) began to take form when dozens of educators from across the country were led by governors and chief state school officers in gathering and reviewing the academic standards of states that had the best outcomes. Their goal was to determine what the current best academic standards were in the country and then…

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…