Paul Ernest’s name is synonymous with social constructivism as a philosophy of mathematics. His contributions to mathematics education have occurred at a very fundamental level and to a extent shaped theory development in this field. His research addresses fundamental questions about the nature of mathematics and how it relates to teaching, learning and society. For the last three decades Paul has been a prolific scholar who has published in a wide array of topics such as the relationship between the philosophy of mathematics and mathematics education, and more generally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy of research methodology. The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certainty that Paul argued for in developing his philosophy, and also a play on words for the fact that absolute “earnestness” may perhaps be a Platonic construct, and not possible in the realm of language and human discourse! Paul Ernest’s scholarly evolution and life can best be summarized in the words of Walt Whitman “Do I contradict myself? Very well then I contradict myself” (I am large, I contain multitudes). Indeed his presence has been large and multitudinous and this Festschrift celebrates his 65th Birthday with numerous contributions coming from the mathematics, philosophy and mathematics education communities around the world.

This seventh edition of A History of Psychology: The Emergence of Science and Applications traces the history of psychology from antiquity through the early twenty-first century, giving students a thorough look into psychology’s origins and key developments in basic and applied psychology. It presents internal, disciplinary history as well as external contextual history, emphasizing the interactions between psychological ideas and the larger cultural and historical contexts in which psychologists and other thinkers conduct research, teach, and live. It also has a strong scholarly foundation and more than 400 new references. This new edition retains and expands the strengths of previous editions and introduces several important changes. The text features more women, people of color, and others who are historically marginalized as well as new sections about early Black psychology and barriers faced by people who are diverse. It also includes expanded discussions of eugenics and racism in early psychology. There is new content on the history of the biological basis of psychology; the emergence of qualitative methods; and ecopsychology, ecotherapy, and environmental psychology. Recent historical findings about social psychology, including new historical findings about the Stanford Prison Experiment, Milgram’s obedience research, and Sherif’s conformity studies, have also been incorporated. Continuing the tradition of past editions, the text focuses on engaging students and inspiring them to recognize the power of history in their own lives, to connect history to the present and the future, and to think critically and historically.

The picture on the front of this book is an illustration for Totakahini: The tale of the parrot, by Rabindranath Tagore, in which he satirized education as a magnificent golden cage. Opening the cage addresses mathematics education as a complex socio-political phenomenon, exploring the vast terrain that spans critique and politics. Opening the cage includes contributions from educators writing critically about mathematics education in diverse contexts. They demonstrate that mathematics education is politics, they investigate borderland positions, they address the nexus of mathematics, education, and power, and they explore educational possibilities. Mathematics education is not a free enterprise. It is carried on behind bars created by economic, political, and social demands. This cage might not be as magnificent as that in Tagore’s fable. But it is strong. Opening the cage is a critical and political challenge, and we may be surprised to see what emerges.

An Invitation to Critical Mathematics Education deals with a range of crucial topics. Among these are students’ foreground, landscapes of investigation, and mathematics in action. The book is intended for a broad audience: educators, students, teachers, policy makers, anybody interested in the further development of mathematics education. The book discusses concerns and preoccupation. This way it provides an invitation into critical mathematics education.

The title of the book is Critique as Uncertainty. Thus Ole Skovsmose sees uncertainty as an important feature of any critical approach. He does not assume the existence of any blue prints for social and political improvements, nor that certain theoretical structures can provide solid foundations for a critical activities. For him critique is an open and uncertain activity. This also applies to critical mathematics education. Critique as Uncertainty includes papers Ole Skovsmose already has published as well as some newly written chapters. The book addresses issues about: landscapes of investigations, students’ foregrounds, mathematics education and democracy, mathematics and power. Finally it expresses concerns of a critical mathematics education.

The teaching and learning of mathematics in British Columbia has a long and storied history. An integral part of the past 50 years (1962-2012) of this history has been Vector: Journal of the British Columbia Association of Mathematics Teachers. This volume, which presents ten memorable articles from each of the past five decades, that is, 50 articles from the past 50 years of the journal, provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a commentary from a prominent member of the British Columbia mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues in the teaching and learning of mathematics. This volume is meant to serve as a resource for a variety of individuals including: teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students. Most importantly, this volume is a celebratory retrospective on the work of the British Columbia Association of Mathematics Teachers.

The teaching and learning of mathematics in Saskatchewan—one of three Canadian provinces sharing a border with Montana—has a long and storied history. An integral part of the past 50 years (1961-2011) of history has been vinculum: Journal of the Saskatchewan Mathematics Teachers' Society (in its many different renditions). This monograph, which presents ten memorable articles from each of the past five decades (i.e., 50 articles from the past 50 years of the journal), provides an opportunity to share this rich history with a wide range of individuals interested in the teaching and learning of mathematics and mathematics education. Each decade begins with an introduction, providing a historical context, and concludes with a decade-specific commentary by a prominent member of the Saskatchewan mathematics education community. As a result, this monograph provides a historical account as well as a contemporary view of many of the trends and issues (e.g., curriculum, technology) in the teaching and learning of mathematics. This book is meant to serve as a resource for a variety of individuals, including teachers of mathematics, mathematics teacher educators, mathematics education researchers, historians, and undergraduate and graduate students and, further, as a celebratory retrospective on the work of the Saskatchewan Mathematics Teachers' Society.

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at undergraduate mathematics education, particularly in the teaching and learning of the history of mathematics and other undergraduate topics. In this monograph, the chapters cover topics such as the development of Calculus through the actuarial sciences and map making, logarithms, the people and practices behind real world mathematics, and fruitful ways in which the history of mathematics informs mathematics education. The book is meant to serve as a source of enrichment for undergraduate mathematics majors and for mathematics education courses aimed at teachers.

This book provides an insightful view of effective teaching practices in China from an international perspective by examining the grades 7-12 mathematics teacher preparation in the Shandong province of China. It is an excellent reference book for teacher educators, researchers, reformers, and teaching practitioners. A qualitative research approach, involving in-depth interviews with purposive sampling of ten grades 7-12 award-winning mathematics teachers, was chosen to conduct the study. The participants are from the Shandong province and have been awarded recognition for his/her achievements in teaching grades 7-12 mathematics by the different levels: school, district, city, province, or nation; and his/her students have achieved high average scores in college entrance exams or in high school entrance exams among the classes at the same grade level. Data analysis revealed the following findings: first, grades 7-12 mathematics teachers from the Shandong province of China were prepared to teach through pre-service training, in-service training, and informal learning. The pre-service training can be characterized as emphasizing formal mathematics training at advanced level. The in-service training is integrated with teacher collaboration and teaching research, and has the characteristics of diversity, continuity, and orientation toward teaching practice. The in-service training also stimulates teachers to conduct self-directed learning. Second, the award-winning grades 7-12 mathematics teachers are identified by the following characteristics: they are passionate about mathematics and share their passion through teaching; they actively take part in teaching research through application of teaching research in the classroom, collaboration with peers, and systematic lesson preparation; they apply technology into teaching; and they take an active role in teaching research in order to expand their professional opportunities. Based on the findings of this study, the following conclusions were reached: pre-service training and in-service training are both necessary processes for mathematics teachers to build up their knowledge base for effective teaching. Pre-service training is just a starting point for the teaching profession. In-service training, integrated with teacher collaboration and teaching research should be a continuous activity that is a part of a teacher’s everyday life.

The intent of this monograph is to showcase successful implementation of mathematical discourse in the classroom. Some questions that might be addressed are: * How does a teacher begin to learn about using discourse purposefully to improve mathematics teaching and learning? * How is discourse interwoven into professional development content courses to provide teachers with the tools necessary to begin using discourse in their own classrooms? * What does a discourse-rich classroom look like and how is it different from other classrooms, from both the teacher's and the students' perspectives? * How can teachers of pre-service teachers integrate discourse into their content and methods courses? * How can we use discourse research to inform work with teachers, both pre- and in-service, for example, to help them know how to respond to elicited knowledge from students in their classrooms? * What are the discourse challenges in on-line mathematics courses offered for professional development? Can on-line classrooms also be discourse-rich? What would that look like? * In what ways does mathematical discourse differ from discourse in general?