This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

This work presents experiments to teach fundamentals of automation through a sequence of laboratory practices that naturally guide to development of an on/off control system. It focuses on the integration of technological and scientific concepts, based on an educational approach associated with a problem-solving technique.

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…

This article describes two heuristic strategies for problem solving: the "use of false assumption" strategy and the "use of double false assumption" strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances…

Finding intersections, unions, and complements of sets is an essential issue in elementary mathematics. It builds the foundation for set theory, probability, logic, and other topics. It is commonly recognized that drawing a Venn diagram, which was first introduced by the British philosopher and mathematician John Venn in 1881, is a classic and…

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

In this article, the author shares the Menu Writing project, designed to promote a meaningful, real-world connection to mathematics with the lives of students. The rationale for developing this project was two-fold: (1) to connect school mathematics to students' lived experiences to encourage and sustain students' interest, motivation, and…

A sense of disillusionment grips many doctoral students as they face financial distress, lack of adequate mentorship, concern about job prospects, and other challenges. The Old Testament book of Malachi is a little-recognized resource for students struggling with feelings of disillusionment. Malachi's audience faced disappointment after joyfully…

This brief provides considerations for conducting and implementing functional behavior assessments (FBA) and behavior intervention plans (BIPs) using virtual technology. There are many situations in which virtual FBA/BIP implementation may be necessary or desired. For example, virtual FBA/BIPs can support students attending schools in areas that…

A detailed characteristic of teaching and learning approaches used within the new concept of Learning by Being (LBB) is given. The evolution of educational paradigms from Learning by Doing (LBD) and Learning by Understanding (LBU) toward LBB is analyzed. The basic idea of LBB is students' ownership on cognitive goals, or the assumption of learning…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

This practice report describes how escape rooms have been used by one Australian university to successfully engage with high-school students who reside in areas of relative socio-educational disadvantage. We discuss how the escape room approach aligns with Lizzio's "Five Senses of Success" and offer recommendations for further use and…

NP-complete problems such as the traveling salesman problem (TSP) play a prominent role in most advanced undergrad/graduate courses in discrete optimization modeling. Teaching such an important topic from a purely mathematical perspective without discussing specific applications may result in reduced student interest and motivation. The DeLand…