The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

Design thinking and virtual reality continue to infiltrate the K-12 landscape, with incredible promise for fostering deeper engagement with content. Design thinking in particular embodies maker education's beliefs in learning through building, but with the added caveat of solving real-world problems with the consideration of others' perspectives.…

Background: College students often do not retain what they learn in Statistics in order to apply it in Experimental Psychology. Self-explanation, that is, elaborating on what one is trying to learn by asking questions, making inferences, etc., improves learning and may improve retention. Objective: The purpose of this study was to determine…

In the first part, we investigate Birman, Ko, and Lee's left canonical form of a braid and give a new diagrammatic approach. We use the left canonical form to characterize almost strongly quasipositive braids. In the second part, we investigate students' confidence in mathematics and problem solving skills. Every math instructor has heard students…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

The increasingly neoliberal course of Higher Education is linked to rises in student anxiety around assessment and increased fear of the consequences of failure. Making mistakes is an inevitable part of any learning process (and of life generally) and managing failure in a productive and positive way is crucial for success and wellbeing beyond…

Modern online education has the capacity to provide intelligent educational services by automatically analyzing substantial amounts of student behavioral data. Knowledge tracing (KT) is one of the fundamental tasks for student behavioral data analysis, aiming to monitor students' evolving knowledge state during their problem-solving process. In…

The lecture technique still dominates in biology education, and there are not enough hands-on, interactive, creative, and problem-solving learning activities to encourage students to apply their problem-solving skills. The purpose of this study is to examine how the problem-based learning (PBL) model and students' metacognition skills affect their…

This study investigates the affective and performative effects of ludicization, i.e., the process of transforming the original contexts into immersive ludic experiences based on metaphorized desired behaviors and reflexive space, on language learning. The effects of ludicization are based on an integrated model involving multidimensional…

AHP and Conjoint analysis methods are used to determine the priorities and preferences of groups or individuals in the decision-making process. These methods provide predictive results in many fields such as economics, politics, and environmental sciences. Multi-criteria decision-making methods have the potential to produce effective results in…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

Emergency situations are generally described as combining both threat and time pressure. Creative solutions to deal with such situations are important. The present studies (N[subscript total] = 1190) investigated how people are able to produce creative solutions in an emergency. Our first study was correlational, and assessed individual creativity…

This paper proposes a three-step approach to develop knowledge graphs that integrate textbook-based target knowledge graph with student dialogue-based knowledge graphs. The study was conducted in seventh-grade STEM classes, following a collaborative problem solving process. First, the proposed approach generates a comprehensive target knowledge…

A pedagogical dilemma occurs when an in-class event or external factor challenges a teacher's principles or instructional practices and compels the teacher to resolve the dilemma. This article focuses on how resolving dilemmas can enhance the conceptual understanding of both student teachers and their supervisors. The supervisory setting this…

Background: A defining characteristic of expertise is the use of intuition to navigate tasks. The construct of intuition and its importance is well-studied in other disciplines, but little is known about how it translates to engineering. Existing literature on intuition does not clearly define the construct and its relationship to problem solving,…