This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual…

The technological developments of the twenty-first century have enabled the emergence of alternative teaching-learning models and instructional tools. One of the concepts brought about by such developments is mobile learning. The aim of this study was to test the effect of mobile learning on students' mathematics achievement. A systematic database…

In the age of artificial intelligence where standard problems are increasingly processed by computers, creative problem solving, the ability to think outside the box is in high demand. Collaboration is also increasingly significant, which makes creative collaboration an important twenty-first-century skill. In the research described in this paper,…

In three experiments, we sought to understand when and why people use an algorithm decision aid. Distinct from recent approaches, we explicitly enumerate the algorithm's accuracy while also providing summary feedback and training that allowed participants to assess their own skills. Our results highlight that such direct performance comparisons…

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they…

Designers in out-of-school spaces often negotiate the meaning of mathematics as part of the design process, determining what to include in classes and exhibits both implicitly and explicitly. This analysis suggests that instead of keeping these conversations behind the scenes, we should foreground them for participants. In doing so, we may…

Mathematics education researchers (MERs) engage in interdisciplinary collaborations that contribute to the mathematics education discipline. MERs' learned forms of work and discourse, i.e., practices, are particular to their mathematics education discipline and might not align with practices needed to conduct interdisciplinary work. We interviewed…

Early childhood educators play a central role in fostering children's mathematics learning; however, few studies have focused on educators' beliefs about very young children's capabilities in mathematics. Understanding these beliefs is critical for gaining insight into the mathematics education provided in birth to three settings. In light of this…

In order to investigate pre-service teachers (PSTs') understandings of the terms mathematics and numeracy, the authors conducted a study at one Australian university. The PSTs were enrolled in a mandatory unit about numeracy across the curriculum, in which both teachers' and students' numeracy capabilities were considered. The study took place…

Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to conceptualize cognitive differences as natural forms of human diversity with unique sets of challenges and strengths. Using neurodiversity as our theoretical framework, we analyze the…

The Young-Laplace (Y-L) equation relates the pressure difference across the interface of two fluids (such as air and water) to the curvature of the interface. The pressure rises on crossing a convex interface such as a rain drop and falls on crossing a concave interface such as the meniscus of water in a glass capillary. The relation between…

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

We propose an original machine that traces conics and some transcendental curves (oblique trajectories of confocal conics) by the solution of inverse tangent problems. For such a machine, we also provide the 3D-printable model to be used as an intriguing supplement for geometry, calculus, or ordinary differential equations classes.

The natural exponential and logarithm are typically introduced to undergraduate engineering students in a calculus course using the notion of limits. We here present an approach to introduce the natural exponential/logarithm through a novel interpretation of derivatives. This approach does not rely on limits, allowing an early and intuitive…

Since Personalized Instruction increases the motivation, interest, performance and attitude of the student, it is aimed to develop an instructional management system that can be adapted to the individual, taking into account the prior knowledge level of the person who provides the personalization of all instructional materials. The project is…