Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

Anaerobic respiration reactions are of fundamental importance to global biogeochemical cycling of elements. Yet, the idea that cellular respiration can occur not only in the absence of oxygen but also involve the oxidation of inorganic substrates (e.g., AsO[subscript 3 superscript 3-], Fe[superscript 2+], H[subscript 2], H[subscript 2]S,…

By some estimates, over 1.2 billion tons of soil was blown across the Great Plains during the height of the Dust Bowl. The so-called "black blizzards" these massive dust storms caused suffocated cattle, sickened children, and destroyed thousands of family farms. Formerly prosperous farmers, unsure why they had such bad luck, wondered if…

In response to the adoption of Agile practices and processes by businesses, IT/IS educators are working to add Agile content to their courses. Teaching students about Agile involves teaching them about the history, mindset, and values of Agile, along with an introduction to the practices and processes used in an Agile product. Along with this, it…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

The comprehensive practical activity curriculum can be said to be created to cater to children's curiosity and nature of exploration. Through the creation of problem situations, children are guided not only to explore what the world is, but also to pay close attention to what the world will be and cultivate children's key competencies in the real…

In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

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.

This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to…

In this paper, we present an overview of a series of 1-credit applied problem solving courses. The goal of these courses was to help students develop their oral and written communication skills, ability to work as a team, and general problem solving skills through preparation and participation in the Mathematical Contest in Modeling (MCM) and…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

This generation of students enters a workforce that increasingly demands interdisciplinary thinking to solve complex problems and create sustainable value. The global pandemic, climate crisis, and state of social inequality call for future business leaders to practice a broader intellectual vision to "see" across domains and apply…

The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its…

Research confirms that critical thinking plays a fundamental role in decision making and problem solving, skills that are essential to function as successful adults in a complex world. Consequently, it has been a focus of educational research for decades. Faculty meetings and teacher training sessions repeatedly run sessions on ways that teachers…

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…