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…

Unified Modeling Language (UML) Class Diagramming is the commonly accepted mechanism used to describe relationships between software components. In addition, it is an essential educational tool that is used to convey the structure of software and the patterns of software design to students. Unfortunately, UML is a visual-only mechanism and…

Virtual reality (VR) has the potential to revolutionize the way we learn and educate, enhancing and supplementing the traditional learning experience by providing new ways to interact with information and people. However, its full potential in education has yet to be fully realized, as work in this space requires resolving cutting-edge technical…

The purpose of this content analysis study was to identify the affordances embedded in core reading program (CRP) teacher's manuals that facilitate graphical literacy skills as a component of literacy instruction. In the informational text selections of selected CRPs, graphic category, type, function, and connection to text were assessed to…

The learning of basic facts, or the sums and products of numbers 0-10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts.…

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional…

Laboratory activities are a prevalent and essential part of chemistry learning because of their potential to help students develop problem solving abilities, visualize chemistry concepts learned in lecture, and gain practical skills. However, learning in the laboratory environment is not without its challenges. For example, cookbook-style…

Flashcards are with us from our very earliest learning experiences. As infants, we learn to speak words from flashcard pictures. As toddlers, we are introduced to vocabulary concepts and thinking skills with flashcards. In early learning experiences we learn facts, languages, associations, and even social skills. Flashcards remain highly prevalent…

Infographics are part of daily life because of the rise of digital media and technology, as learners now encounter a barrage of images carefully designed to convey data and information through social media. But what happens in the classroom when young learners first encounter this expressive genre? This case study examined a unit of instruction on…

Algebra I encompasses several topics that serve as a basis for students' subsequent mathematics courses as they progress in school. Some of the key topics that students struggle with is solving linear equations and algebraic word problems. There are several factors that may contribute to this ongoing struggle for students such as the structure of…

Background: With around 200,000 autistic students set to enter universities and the workforce in the next decade, inclusive programs are receiving increased attention to helping educational systems carefully integrate these students' needs. Moreover, educational programs recognize that problem-solving is critical for school success and optimal…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

There has been an increase of both neurodivergent students and enrollment in Computer Science programs in higher education. These increases have brought attention to two separate challenges: neurodivergent college students struggle more compared to their neurotypical peers and many students struggle in introductory computer science courses. This…

Purpose. Researchers have recommended using comprehensive visual materials in engineering courses, as visuals instill more information in students than auditory information and they have the ability to engage students more effectively than other types of content and to convey the nuances of non-verbal communication. The purpose of this study was…

The effectiveness of video modeling (VM) has been well documented in research studies completed in the Western world. VM has been used to establish skills in several areas, such as language, imitation, social behavior, play, academics, and other adaptive skills. VM has been shown to be particularly effective with children with autism. However,…