The standby wooden blocks that are prevalent in most high-quality early childhood classrooms are missing from most primary and elementary grades. The goal for block play in early childhood is to support learning in mathematics, science, art, literacy and language arts, physical development, social studies, and social and emotional growth. This…

Even before the release of the National Council of Teachers of Mathematics (NCTM)'s Principles to Actions (2014), teachers paid significant attention to mathematics tasks based on their positive influence on student learning (Doyle, 1988; Kazemi, 1998; NCTM, 1989, 2000). Over the last almost quarter century, we have learned a lot about high-level…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

The instructional rationale behind critical pedagogy is to provide students the opportunity to voice their personal stories and opinions, and to reflect and act upon social concerns relevant to their daily lives. Students can then practice being agents of transformation in their own lives, starting in the classroom. This paper is based on the…

Research suggests that most college and beginning graduate students lack the cognitive complexity required to engage in effective practical and ethical reasoning. Studies on cognitive development support the view that how people approach complex problems varies significantly depending on the underlying epistemic assumptions they use to guide their…

Encouraging students' ability to reason can be looked at through the lens of both oral and written representations. In 2022, the author participated in the first intake of the Teacher Excellence Program run by the Victorian Teaching Academy. Being part of an in-depth professional learning program challenged the author's teaching practices to focus…

Problem-solving frameworks have the potential to promote objective data-based decisions that increase the likelihood students are matched to appropriate evidence-based interventions. Unfortunately, cognitive biases, heuristics, and fallacies can lead to erroneous conclusions within problem-solving frameworks. Some of these effects have been…

For years, researchers have recognized the expectation within the business community that business school graduates possess a working knowledge of spreadsheet applications. Academics continue to seek effective ways to teach these skills in an academic setting. This exercise uses Wordle, a five-letter word guessing game, to teach students…

Nuclear magnetic resonance (NMR) spectroscopy is a very powerful analytical method that has found many applications in physics, chemistry, biology, and medicine. It is an indispensable tool particularly for synthetic chemists because it can be used for a rapid elucidation of the structures of organic compounds. For this reason, NMR spectral…

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.

Students often struggle with the concept of dependence of events or random variables. We present a simple coin flipping game that yields surprising results due to the dependencies within the game. The game is simple enough for young children to understand and play, yet complex enough to yield results that are counterintuitive to even most graduate…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

When thinking of early childhood STEM, images of active, play-based design challenges, experiences with robotics/coding, or hands-on experiences with open-ended materials (e.g., balls, ramps, loose parts) often come to mind. While these are certainly images that align with developmentally appropriate early childhood STEM practices, some of the…

Since the content of the Theory of Interest course in an actuarial science program is tied to an external exam, instructors may be hesitant to attempt to use inquiry-based learning. In this paper, I outline how and why I did so, including descriptions of the materials that I wrote. I found that student performance on the final exam improved…

Historically, math education at the high school and introductory college levels has focused on computational skills. With the advancement of computational technologies, problemsolving and other higher-order thinking skills should become the focal point. This article discusses ways in which the University of Minnesota has integrated problem-solving…