In this qualitative research, we studied difficulties that undergraduate students face while learning the concept of inner product space. Participants were 35 first-year mathematics students from Yildiz Technical University in the 2011 and 2012 academic years. We asked participants to solve 5 inner product space questions. Data were jointly…

In partnership with both formal and informal learning institutions, researchers have been building a suite of online games, called choicelets, to serve as interactive assessments of learning skills, e.g. critical thinking or seeking feedback. Unlike more traditional assessments, which take a retrospective, knowledge-based view of learning,…

Intelligent behavior in everyday contexts may depend on both ability and an individual's disposition toward using that ability. Research into patterns of thinking has identified three logically distinct components necessary for dispositional behavior: ability, inclination, and sensitivity. Surprisingly, sensitivity appears to be the most common…

Design involves solving complex, ill-structured problems. Design tasks are consequently, appropriate contexts for children to exercise higher-order thinking and problem-solving skills. Although creating engaging and authentic design contexts for young children is difficult within the confines of traditional schooling, recently, game-design has…

You read in the paper this morning that people who take multivitamins have fewer heart attacks and are less likely to get cancer than people who don't. Does this information make you more likely to want to take multivitamins? To truly prepare students for life, schools need to teach them the critical thinking skills they need to answer questions…

Teaching leadership skills is an important goal for many schools, both within the curriculum and beyond it. The traditional definition of a leader has been based on a hierarchy, with levels, a chain of command, and a "top dog." Yet other definitions exist, and for girls and women a redefined view incorporates an alternative concept of…

Computational thinking (CT) parallels the core practices of science, technology, engineering, and mathematics (STEM) education and is believed to effectively support students' learning of science and math concepts. However, despite the synergies between CT and STEM education, integrating the two to support synergistic learning remains an important…

This study was aimed to analyze the ability of mathematical representations in the eighth-grade junior high school students by using the REACT strategy on the learning of Realistic Mathematics Education (RME). The REACT strategies represent Relating, Experiencing, Applying, Cooperating, and Transferring. This study was a quasi-experimental…

Today's shop floor, the area of a factory where operatives assemble products, is a complex and demanding work environment. The employed and produced technology becomes ever more complex, and employees are responsible for an increasing amount of tasks. As a consequence, the employee is under constant pressure to solve problems occurring on the shop…

In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…

Medical students master an enormous body of knowledge, but lack systematic problem solving ability and effective clinical decision making. High profile reports have called for reforms in medical education to create a better generation of doctors who can cope with the system based problems they would encounter in an interdisciplinary and…

The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with autism spectrum disorder and moderate intellectual disability (ASD/ID). Participants learned to solve two types of group word problems: missing-whole and missing-part. The themes of the word…

In 2009, we reported on a new Intelligent Tutoring Systems (ITS) technology, example-tracing tutors, that can be built without programming using the Cognitive Tutor Authoring Tools (CTAT). Creating example-tracing tutors was shown to be 4-8 times as cost-effective as estimates for ITS development from the literature. Since 2009, CTAT and its…

Design education exists to prepare students for design practice. Yet the goal state, design expertise, remains poorly defined. This paper presents a critical cross disciplinary literature synthesizing literature across design, engineering, expertise, creativity, and new evidence from a cognitive task analysis of expert designers to explore…

The benefits of mentoring are well documented (Buddeberg-Fischer, 2006; Kasworm, 2010). Every industry has mentors and protégés who seek mentors who achieved their aspirations. But what training do our mentors have in effective mentorship? Recognizing that it is never too early to learn, yet often overlooked, the Weill…