Designing an optimal Norman window is a standard calculus exercise. How much more difficult (or interesting) is its generalization to deploying multiple semicircles along the head (or along head and sill, or head and jambs)? What if we use shapes beside semi-circles? As the number of copies of the shape increases and the optimal Norman windows…

This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…

The aim was to determine elementary mathematics teacher candidates' problem solving skills and analyze problem solving skills according to various variables. The data were obtained from total 306 different grade teacher candidates receiving education in Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylul…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

This article overviews the theoretical and applied works of the psychologist and pedagogue Leonid Zankov. Zankov's model of teaching is based on Vygotsky's theory that appropriate teaching methods stimulate cognitive development, whose core notion is the Zone of Proximal Development. This educational psychology research was verified by large scale…

This exploratory study reports on how students activated learner-controlled scaffolding and navigated through sequences of connected problems in a digital learning environment. A design experiment was completed to (re)design, iteratively develop, test, and evaluate a digital version of an instructional unit focusing on binomial distributions and…

We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams complemented with several oral interviews, which were held with first-year engineering and science university students. Their responses allowed us to…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

This study compared the effects of three different feedback formats provided to sixth grade mathematics students within a web-based online learning platform, ASSISTments. A sample of 196 students were randomly assigned to one of three conditions: (1) text-based feedback; (2) image-based feedback; and (3) correctness only feedback. Regardless of…

Teaching persistence and problem solving must begin with selecting a problem that can be solved mathematically, that allows for multiple methods of solving, and that generally captures the attention and curiosity of the student (Marcus and Fey 2003; NCTM 1991; Van de Walle 2003). This article shows how a STEM three-dimensional (3D) printing…

The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction…

Many educators face the challenge of engaging students in science and mathematics, often struggling to bridge the gap between theoretical concepts taught in classrooms and their real-world applications. This disconnect can lead to disinterest and disengagement among students, hindering their learning outcomes. "Cases on Informal Learning for…

In response to a desire to strengthen the economy, educational settings are emphasizing science, technology, engineering, and mathematics (STEM) curriculum and programs. Yet, because of the narrow approach to STEM, educational leaders continue to call for a more balanced approach to teaching and learning, which includes the arts, design, and…

Today's engineers, designers, and technologists are often thrust into the role of problem solver, from the initial design phase of a product or process all the way to final development. Many engineers in manufacturing environments are tasked with solving problems and continuously improving processes to enhance company profitability, efficiency,…