This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.

A completely updated edition of the definitive guide for researchers in international management

A volume that concentrates on the substantive gaps in the IB/IM field and addresses whether these gaps are resolvable with the theoretical and methodological toolkit.

Semiotics as a Tool for Learning Mathematics is a collection of ten theoretical and empirical chapters, from researchers all over the world, who are interested in semiotic notions and their practical uses in mathematics classrooms. Collectively, they present a semiotic contribution to enhance pedagogical aspects both for the teaching of school mathematics and for the preparation of pre-service teachers. This enhancement involves the use of diagrams to visualize implicit or explicit mathematical relations and the use of mathematical discourse to facilitate the emergence of inferential reasoning in the process of argumentation. It will also facilitate the construction of proofs and solutions of mathematical problems as well as the progressive construction of mathematical conceptions that, eventually, will approximate the concept(s) encoded in mathematical symbols. These symbols hinge not only of mental operations but also on indexical and iconic aspects; aspects which often are not taken into account when working on the meaning of mathematical symbols. For such an enhancement to happen, it is necessary to transform basic notions of semiotic theories to make them usable for mathematics education. In addition, it is also necessary to back theoretical claims with empirical data. This anthology attempts to deal with such a conjunction. Overall, this book can be used as a theoretical basis for further semiotic considerations as well as for the design of different ways of teaching mathematical concepts.

This volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in the life world of people whether these range from the everyday individual numeracy level to sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for multi-disciplinary work that involves knowledge from a variety of communities of practice such as those in different workplaces (e.g., those of educators, designers, construction engineers, museum curators) and in different fields of academic endeavour (e.g., history, archaeology, mathematics, economics). From an educational perspective, researching the development of competency in real world modelling involves research situated in crossing the boundaries between being a student engaged in modelling or mathematical application to real word tasks in the classroom, being a teacher of mathematical modelling (in or outside the classroom or bridging both), and being a modeller of the world outside the classroom. This is the focus of many of the authors of the chapters in this book. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.

Over the past years a substantial amount of research has been undertaken relating to the development of powerful learning environments for the acquisition in students of worthwhile educational objectives focussing on conceptual understanding, higher-order cognitive and metacognitive skills, and self-regulated learning. This research has been mainly undertaken from three distinct, but related perspectives in the study of learning and instruction, namely instructional psychology, instructional technology, and instructional design. Against this background a "research community" involving 14 European research teams has recently been initiated with the aim of interactively contributing to the advancement of theory and methodology relating to the design, implementation, and evaluation of powerful learning environments.This volume, based on the plenary lectures and working sessions during the community's third workshop, constitutes a collective output of this research community, focussing on the identification and analysis of major components and dimensions of powerful learning environments aimed at the promotion of deep conceptual and strategic learning in major domains of school curricula, like mathematics, physics, history, and social sciences.In Part I of the volume three chapters present general perspectives on the central theme of the third workshop. In Part II six studies are reported wherein novel learning environments for elementary and secondary mathematics education have been designed, implemented and evaluated. In Part III of the volume another set of five investigations is presented relating to the design, implementation and evaluation of powerful learning environments in other subject-matter domains (physics, history, social sciences) and in teacher training.

The Cycle of Emanations - From the Source to the Return "Emanations" is a spiritual and philosophical journey that invites us to explore the essence of the universe and the self. Through a narrative that weaves together ancient esoteric traditions, such as Gnosticism, Neoplatonism, and Kabbalah, the book reveals the deep interconnectedness between the cosmos and the primordial source of all existence. The text guides us through the stages of creation, where everything that exists, from the stars to the human soul, is an emanation of a singular absolute force. This energy, which flows incessantly from the cosmic center, gives rise to what we know as reality, while simultaneously concealing a greater truth, hidden beneath layers of light and shadow. Every fragment of matter, every being, carries a spark of this primordial light, even when immersed in the density of material existence. As the narrative unfolds, we are led to understand that nothing in the universe is truly separate. The multiplicity we perceive is merely the expression of divine unity, and the path back to the original source is inevitable. The fall of light that forms the material world is simultaneously a fall into ignorance, but also an opportunity to return to wisdom. With its mystical and enigmatic tone, the book challenges the reader to look beyond appearances and seek the lost link that connects the material world with the spiritual. Here, the apparent chaos dissolves into an ordered cosmic dance, where every action and thought is part of an eternal cycle of emanation and return. Immersed in this work, the reader not only discovers a new paradigm of reality but also an invitation to actively participate in this flow, aligning with higher energies and rediscovering the unity behind the diversity.