-
I would like to propose a new introductory statistical inference textbook, which I believe takes a fresh look at a course that fits into nearly every quantitative major at universities.
Initial Motivation
My motivation for this project stems from my dissatisfaction with traditional approaches to the topic, and my belief that there is a better way. A first semester statistics course is generally divided into the following four parts:
I. Basic Statistical Concepts
• Basic statistical concepts including population, parameter, sample, and statistic
• Types of data (ordinal, time-series, etc...), and sampling methodology
• Organizing the data visually or graphically - including histograms, pie graphs, box plots, and stem-and-leaf plots
• Statistical computations including mean, median, mode, standard deviation, and percentiles
II. Probability
• Properties of unions, intersections, conditional probability, independence and mutual exclusivity
• Permutations and combinations
• Discrete distributions
• Continuous distributions
• Normal distribution
III. One-sample Statistics
• Confidence intervals
• Sampling distributions
• Computations involving the normal distribution, t-distribution, and binomial distribution (for proportions)
• Hypothesis testing
IV. Two-sample Statistics
• Two sample problems - expanding topics from Part III to two variables
-
In this introductory chapter I give a preview of the landscape of issues concerning mathematics education in the Netherlands and the role of Realistic Mathematics Education (RME) that one can come across in this volume, which contains the reflections of twenty-eight Dutch mathematics didacticians on teaching and learning mathematics in the Netherlands. Although all chapters have their own focus and mostly only discuss one particular aspect, together they provide a rich inside view into what is worth knowing of Dutch mathematics education and RME. The preview highlights some significant topics from these chapters, such as what tasks are preferred in RME to elicit students’ mathematical thinking, RME’s focus on the usefulness of mathematics, the role of common sense and informal knowledge, changes over time in the content of the mathematics curriculum, aspects of the Dutch educational system, including teacher education and assessment, the implementation of RME, and the context of developing RME.
-
-
This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved.
-
This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Dörfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands.
-
This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established.
-
This chapter provides a brief overview of the state of the art in research and curricula on mathematical modelling and applications of mathematics in education. Following a brief illustration of the nature of mathematical modelling in educational practice, research in real-world applications and mathematical modelling in mathematics curricula for schooling is overviewed. The theoretical and empirical lines of inquiry in mathematics education research related to teaching and learning of mathematical applications and mathematical modelling regularly in classrooms are then selectively highlighted. Finally, future directions are recommended.
-
This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education.
-
Although the ideas of values and valuing have been totemic notions in education for forever, when applied to mathematics they become quite problematic. Even today for many mathematic teachers and learners, mathematics is a value-free space. For them, school mathematics is learning the skills of manipulating numbers before moving to the more abstract ideas of algebra, and occasionally delving into geometry and measurement ideas. Likewise teaching mathematics in schools is ensuring students get good marks on the tests and examinations using whatever pedagogical techniques ensure this. Although in schools this is still the prevailing attitude to mathematics, nevertheless for some decades there has been a growing counter position in mathematics education research that problematizes and challenges this orthodoxy. It has argued that at a fundamental level there are mathematical values that underpin the doing of mathematics, and indeed the same is true for mathematics pedagogy. This chapter briefly explores a number of these notions as it introducesthe various chapters in this volume.
-
In German speaking countries, educational thinking and theorizing on mathematics teaching and learning originated with the establishment of compulsory education for all children and the creation of a school system. Though first efforts go back to the 18th century it does make sense to start this survey with the beginning of the 19th century, with the implication that educational research on mathematics has a history of about two hundred years in German speaking countries. During the 19th century a more and more sophisticated system of publication (journals and books) on mathematics education emerged, the education of mathematics teachers had become more professional and teacher training had developed into one of the main obligations of university teaching. However, didactics of mathematics as an academic discipline is a comparably new achievement. Its establishment began approximately fifty years ago, predominately by creating professorships and opportunities of graduation at universities. After a phase of broad discussion on the identity of the discipline (e.g., in a special issue of ZDM edited by Steiner, 1974), the community of didactics of mathematics steadily expanded, diversified and developed fruitful connections to other neighboring disciplines. This overview intends to outline this development with respect to intuitions, key ideas, research strategies and the connection between research and practice. Selected topics are presented in the following chapters in more detail.
-
The purpose of this chapter is to preface, and introduce, the content of this book, but also to help clarify concepts and terms addressed, set the stage by summarising our previous work, and issue some caveats about our limitations. We will close with a discussion of the mathematics in Interdisciplinary Mathematics Education (IdME), which we see as a lacuna in the literature, and even in this book.
-
This open access book is the first major publication on the topic of “Interdisciplinary Mathematics Education” and arose from the work of the first International Topic Study Group of the same name at the ICME-13 conference in Hamburg in 2016. It offers extensive theoretical insights, empirical research, and practitioner accounts of interdisciplinary mathematics work in STEM and beyond (e.g. in music and the arts).
Scholars and practitioners from four continents contributed to this comprehensive book, and present studies on: the conceptualizations of interdisciplinarity; implementation cases at schools and tertiary institutions; teacher education; and implications for policy and practice. Each chapter, and the book itself, closes with an assessment of the most significant aspects that those involved in policy and practice, as well as future researchers, should take into account.
-
This survey provides an overview of German meta-discourse on theories and mathematics education as a scientific discipline, from the 1970s to the 1990s. Two theory strands are offered: a semiotic view related to Peirce and Wittgenstein (presented by Willibald Dörfler), and the theory of learning activity by Joachim Lompscher (presented by Regina Bruder and Oliver Schmitt). By networking the two theoretical approaches in a case study of learning fractions, it clarifies the nature of the two theories, how they can be related to inform practice and renew TME-issues for mathematics education as a scientific discipline. Hans-Georg Steiner initiated the first of five international conferences on Theories of Mathematics Education (TME) to advance the founding of mathematics education as a scientific discipline, and subsequently German researchers have continued to focus on TME topics but within various theory strands.
-
This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community?
These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research.
Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country.
-
This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved.
The main topics you will find in “ICME-13 Topical Survey” include:
• Discussions of methodological issues in the history of mathematics education and of the relation between this field and other scholarly fields.
• The history of the formation and transformation of curricula and textbooks as a reflection of trends in social-economic, cultural and scientific-technological development.
• The influence of politics, ideology and economics on the development of mathematics education, from a historical perspective.
• The history of the preeminent mathematics education organizations and the work of leading figures in mathematics education.
• Mathematics education practices and tools and the preparation of mathematics teachers, from a historical perspective.
-
This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.
-
-
-
-
-
-
-
-
-
-
-
-
