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…

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…

The creative dancing body is an ideal exemplar of the embodied mind. However, creativity research has ceased to develop due to a lack of study of the embodied mind in cognitive science. Thus, much can be gained through exploring ways in which we maximize students' creative potential by engaging 4E cognition through rich dance experiences. In my…

Reading mathematics problems can frustrate students to the point of shutting down. Although Pólya's four-step plan is a well-known problem-solving framework, the author's students benefited from a more concrete and detailed approach: chunking the reading. In this article, the author describes an approach to problem solving used with eighth-grade…

The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17-18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems…

The looking-back stage is rarely observed in students' problem solving in spite of its recognized importance. The importance of this stage is attributed to practices of engagement with queries on verification of the obtained solution(s), comparative consideration of alternative solutions, and formulation of implications for future problem solving.…

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with…