In this article, we focus on pairing instructional approaches with a strong evidence base in math with evidence-based practices for students with extensive support needs. To do so we draw on two sources. We use the 2021 Practice Guide from the Institution for Education Sciences (Fuchs et al., 2021). In addition, we use identified evidence-based…

While the development of creativity, or creative thinking, in mathematics is considered important by many researchers, there are several difficulties in implementing creative tasks, especially before secondary school. Within the original context of a mathematical escape game, this paper reports two episodes exemplifying the difficulties met by…

Research shows primary teachers report negative dispositions towards teaching mathematics, impacting their confidence and student outcomes. One approach to improve teacher and student enthusiasm is using picturebooks. While research supports the use of picturebooks in mathematics learning, specific guidance for teachers to implement this practice…

According to the World Economic Forum (2016), "more than one third (36%) of all jobs across all industries" (p.21) need problem-solving as a key skill. Trilling and Fadel (2009) noted the shift from industrial to knowledge-based economies, requiring students not only to possess content knowledge but also have skills that enable them to…

Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the…

Membrane separation processes, from reverse osmosis to ultrafiltration to microfiltration, are gradually receiving more and more emphasis in undergraduate chemical engineering curricula. Of these processes, ultrafiltration tends to be the most amenable to the standard chemical engineering approach of theory development, mass and/or energy…

The "big bad wolf" chased the squealing children around the playground as they looked for a place to hide. Because Mr. Lòpez and Ms. Kim had introduced the work of engineers and the engineering design process into their unit on The Three Little Pigs, they knew their preschool students would choose a structure that could withstand any…

Problem-based learning (PBL) is an innovative educational approach that dates back to the 1960s. However, the twenty-first century goal of sustainable education poses a challenge to PBL, especially as it relates to isolation. Here we discuss the underlying issue of isolation in three respects. First, the information-processing model of PBL depends…

With problem-solving as the focus and wisdom as the goal, the concept of giftedness is reconceptualized in the 21st century context. The two most prominent constructs in the field of education for the gifted, creativity and intelligence, are integrated into a view of exceptional talent as consisting of the ability and willingness to solve complex…

When organic students are asked to design a total synthesis of a molecule, they are often overwhelmed by the multitude of possible transformations. A decision tree is a useful tool to break complex problems up into simpler steps and scaffold the thinking process that many seasoned chemists take for granted. While many comprehensive resources…

As consultants who infuse the "Habits of Mind" into schools, the authors explain how spreading these habits through school can increase the whole school's well-being and feed teacher efficacy. They list seven factors that can create a "culture of efficacy" that draws on these 16 habits (thinking dispositions at the core of…

The Pearson correlation coefficient can be recovered from the two least squares regression lines y[with circumflex] = b[subscript 0] + b[subscript 1]x and x[with circumflex] = a[subscript 0] + a[subscript 1]y without any data. This can be done both algebraically and geometrically. This can be done without data even when the scales of the variables…

The simple vehicle routing problem (VRP) is a common topic of discussion in introductory operations research/management science courses. The VRP can be framed in a variety of ways, and it can be difficult to solve to optimality. For solution purposes, introductory textbooks demonstrate how Excel's Evolutionary Solver (ES) add-in produces a…

This paper reports on a project that sought to enhance problem-solving practices within a cluster of primary schools. In-service teachers' description of their approach to problem-solving suggested it was treated as an isolated practice that occurred after concepts had been taught; often focusing on teaching particular problem-solving strategies…

In this work three examples of textbook circuits (resistor-capacitor, resistor-inductor and resistor-inductor-capacitor) have been modeled by employing the Euler method for the approximate solution of differential equations using algorithms implemented in the "Python" programming language. The aim of this work was to demonstrate how…