ArgumentIn this paper, I argue that studying school textbooks is a fruitful way to investigate mathematical conceptions in different national contexts. These sources give access to the written production of an extended mathematical milieu whose members write for various audiences. By studying the case of late 1950s French and English textbooks issued for a growing audience of 11- to 15-year-old pupils, I show that a plurality of conceptions was projected at the time onto pupils and their teachers in both (...) national contexts. I link this diversity to contemporaneous debates regarding mathematics teaching and argue that textbooks themselves have to be considered as active agents of such debates. (shrink)

What is argumentation? -- Building a classroom culture of argumentation -- Structuring classroom discussions to focus on argumentation -- Infusing all instruction with argumentation -- Argumentation for all students -- Argumentation and the mathematical practices -- Technology in teaching and learning argumentation -- Assessing argumentation and proof -- Conclusion.

The study aims to help primary and secondary school students develop a good habit of physical exercise by exploring the current situation of physical exercise of primary and secondary school students and analyzing the factors affecting their physical exercise. Then, intervention strategies are figured out for different groups of students and help them develop a good habit of physical exercise. From the perspective of educational psychology and parents’ entrepreneurship education, the research on the physical exercise of primary (...) and secondary school students is conducted by a questionnaire survey, mathematical statistics and literature review. A total of 280 students from five schools in Tianjin are selected as the research subjects, and the current situation of students’ physical exercise in these five schools is investigated. The results show that 40.5% of boys and 39.4% of girls can take physical exercise more than three times a week; 48.9% of the students do physical exercise for more than 30 mins each time; the students who usually take regular exercise at school account for 82.1%. The physical exercise that students always do is running, badminton and table tennis, which rank the top three among the sports they do. The students usually play basketball, volleyball, and football, and they rarely do the sports like swimming, Wushu, and aerobics. This result is closely related to the characteristics and places of primary and middle school students. The survey shows that the physical exercise awareness of most primary and secondary school students is correct; most students can participate in physical exercise, but few students can do it regularly; parents’ support, parents’ habits of doing exercise, and family’s spending on physical exercise have a significant impact on developing students’ habits of doing physical exercise. Based on the above, it is concluded that the primary and secondary stage is very important for students. Physical education teachers should follow the principle of teaching different students with different methods, enrich teaching materials, and improve teaching quality. The study provides a reference for the reform of PE to guide primary and middle school students to participate in sports activities, improving students’ physical quality. (shrink)

In this paper we present the relations between mathematics and mathematics education in Italy between the 12th and the 16th century. Since the subject is extremely wide, we will focus on two case-studies to point out some relevant aspects of this phenomenon: 1) Fibonacci’s studies (12th-13th century); 2) Abacus schools. More particularly, Fibonacci, probably the greatest European mathematician of the Middle Ages, made the calculations with Hindu-Arabic digits widely spread in Europe; Abacus schools were also based on (...) the teaching of the calculation with Hindu-Arabic digits. These case-studies are significant for understanding the connections between science, science education and the development of science within Western civilization. We think that the knowledge of such significant relations can be useful for the scholars who are nowadays engaged in mathematics education and in the research field of science-society relations. Finally, we attempt to outline the interaction between mathematics education and advanced mathematics in that period, focusing on the figure of Leonardo Pisano (c. 1170-c.1250), called Fibonacci, who played an influential role both in mathematics education and in advanced mathematics. (shrink)

Several years ago, while teaching middle and high school mathematics at a small progressive school in upstate New York, I was asked to evaluate and reconceptualize the school’s approach to teaching mathematics. From its inception in the early 1960s, the school had prided itself on its progressive ideals. It was child-centered, committed to both project-based learning and to the social and emotional development of children, and a place where independent and critical (...) thinking was highly valued. Yet, it was clear that our mathematics program was not delivering results in line with our expectations. Academically, our students were not low achievers. Yet, to our dismay, very few of our middle and high school students actually liked their mathematics studies. (shrink)

The purpose of this paper is the influence of Science- Technology- Engineering- Art- Mathematics education on the Olympic education of primary and middle school students. The research object is the Beijing Olympic model school. The frame structure and educational concept of STEAM education are studied, and a questionnaire survey on the current situation of Olympic education is conducted. Finally, improvement measures based on the survey results are provided combined with STEAM education, and the teaching effect (...) is analyzed. The results show that after the improvement of the educational model, the student’s mastery of the Olympic knowledge has been greatly improved. The proportion of students who can master all knowledge increases from 5.78 to 8.45%, by 2.67%. The proportion of students with knowledge of most Olympic sports increases from 48.6 to 55.67%, by 7.07%. The proportion of students with little or no knowledge drops to 1.54%. Meanwhile, students are increasingly interested in Olympic events, especially after being inspired by the STEAM education model. The proportion of students who are very concerned about Olympic events has increased by 6.45%. The proportion of students who are more concerned about Olympic events has increased by 5.11%. Thus, the Olympic education work has achieved some results. Students gradually become interested in the Olympic events. They begin to actively pay attention to the Olympic events and learn the Olympic spirit. Then, their physical literacy is improved. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy in the School Music ProgramBennett ReimerWho is philosophy of music education for? Several groups of people immediately spring to mind. First, it is for those of us in music education who produce it and consume it as a major or important responsibility in our work—people like members of our Special Research Interest Group at MENC. Second, teachers of music education courses at the undergraduate and graduate levels (...) who deal with it either in a full course or series of courses or seminars devoted to philosophy, or as one part of courses devoted to other topics (as I believe is most often the case.) Third, school music teachers, many of whom have taken or are taking such courses (and many who have not) who are expected to have some level of acquaintance, however rudimentary, with philosophical issues so as to be able to cope with them, as when writing curriculum guides, or explaining to other teachers, administrators, school boards, and parents why music education is valuable and deserves support. If we stretch it, we might include among those who need to be involved with philosophy of music and music education all educational professionals, since all, in one way or another, exert some sort of influence on the fortunes of music education. But that begins to strain a bit at the edges.No doubt there are other constituencies that can be identified. But one that has not been conceived as requiring substantive encounters with philosophical issues of music is that of students in schools, K-12. We all assume that philosophy can and should play a major role in determining what is most valuable for students to learn in their study of music. But seldom has it been argued, to my [End Page 132] knowledge, that philosophical issues should be addressed in all programs of music education intended to produce people who are, in any convincing sense, musically educated.My premise is that philosophical reflection relating to music and to the teaching and learning of music should be foundational in school music programs. Further, philosophy needs to be present in our programs in three distinctive ways, reflecting common practices of education in America and all over the world. That is, as integral in the general music education of all students, as a component of all elective offerings, and as one particular, focused offering among the electives available to all students.My position is that what we call "general music" (which, as we know, goes by a variety of names around the world including just "music") is not complete; in fact is invalid, if it does not provide philosophical challenges of the same level of complexity, and the same degree of authenticity, as everything else we believe all students should know and be able to do in music. What we call the "music elective program," or the "music specialization program," is incomplete, in fact is invalid, if philosophical matters are not addressed as they relate to the particularities of each elective offered. And, in addition, philosophy needs to be a standard elective offering, taught with the same level of expertise by specialist teachers as we now routinely make available in performance and in the meager smattering of other electives we manage to offer.What? Philosophical thinking for all children, even in the primary grades, and as electives starting perhaps at the middle school or high school level? Electives taught by music educators whose specialization is the teaching of philosophy of music to youngsters? Am I serious? After all, even those of us who are devoted to it as a major aspect of our professionalism are constantly at the edges of our competence given the deep challenges philosophy presents to our intellect. And I expect children—all children—to be able to deal with it authentically?Well, we could ask precisely the same questions about, say, mathematics, and science, and history, and social studies, all the ways of thinking which constitute the basic learnings in all grades of our schools. As educators we know better than to conceive the nature of those subjects as only apparent at the level of professional work in them. We recognize the obvious: while at... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Spatializing Culture: The Ethnography of Space and Place by Setha LowCarlos J. L. BalsasSpatializing Culture: The Ethnography of Space and Placeby setha low London: Routledge, 2017Spatializing Culture: The Ethnography of Space and Place adds clarity to our understanding of the value of ethnographic scholarship in the study of socio-economic, cultural, and developmental transformations. The book is a thorough review of two established conceptual frames of analysis—the social (...) production of space and the social construction of space—coupled with an in-depth discussion of four newer ways to make sense of the world around us: embodied space, language and discourse, emotion and affect, and translocal space. As the world is transformed by a myriad of forces and events occurring simultaneously, its complexity intensifies insurmountably and we require clear and robust concepts, theories, methods, and tools to not only interpret it, but above all to attempt to change it in ways that are more beneficial to our collective co-existence while enabling the flourishing of those most at risk.Readers of Spatializing Culture will find plentiful theoretical constructs, lineages, diverse viewpoints, examples, and overall opportunities for reflecting on how the (built) environment, spaces, and places have been changing mostly due to our behavior. Inspired by Foucault’s take on genealogy, in chapter 2, Setha Low traces the history of space and place according to distinct interpretative schools of thought ranging from philosophical and mathematical, French social theory, geographical, architectural, environmental psychology, to anthropological, and even archeological. Five Venn diagrams are utilized to illustrate the main conceptual relationships between space and place. Most of the book’s in-depth case studies were researched by the author with only a small number investigated and written up by fellow scholars, which Low utilizes in the book with gratitude. The interrelated thematic and distinct geographical scope of the cases is one of the book’s hallmarks. The illustrative case studies come from such faraway places as Latin America (San José, Costa Rica), Asia (Taipei, Taiwan), North America (New York City; Washington, D.C.; Philadelphia, Pennsylvania; and San [End Page 151] Antonio, Texas), Southern Europe (Smederevska Palanka, Serbia), and the Middle East (Beirut, Lebanon; Cairo, Egypt; and Tel Aviv, Israel).Spatializing Culture was first mentioned to me years ago by a former colleague at the University at Albany, SUNY. His ongoing work in Latin America, coupled with his ethnographic training and prior work in a region of the world also extensively examined by Low in other scholarly works, was likely the reason for bringing it up in a conversation about the latest developments in the field and potential research opportunities. I acquired the book when I was teaching Global Urbanism and Culture and International Urban Planning. I was pleasantly surprised with the book’s thorough conceptual lineage, historic characterizations, attention to detail, comprehensive ethnographic investigations, and implications for transforming reality as well as institutional processes. Spatializing Culture is a welcome addition to urban planning textbooks, which tend to be relatively less critical, are often covered with normative constructs and statistics, and are more institutional in their characterization of problems and recommendations for further action.For the most part, the ethnographic method is qualitative, participa-tory, detailed, and quite comprehensive in characterizing key variables as the researcher found them on the ground. This differs slightly from urban planning’s preoccupation with public policy, policy analysis, rules and regulations, institutionalized procedures, the public good, and overall positivist and rationalist concerns with documenting reality and helping to lead transformative planning processes, whether in the realm of land use, transportation, housing, economic development, infrastructure, or the environment. Although International Urban Planning was to be taught in a rather orthodox manner with recourse to understanding planning cultures, best practices, lessons learned, and implications for similar situations, the Global Urbanism and Culture course was slightly more aligned with the discussions put forward by Low. These included attention to postmodern ideals, the use of creativity in community planning, distinctions between popular and highbrow culture, and the building of iconic structures in contexts of urban regeneration and mega-event planning. As such, my students were somewhat already exposed to issues of embodied spaces and to ideas of... (shrink)

The paper that follows is a report written in 1988 describing a city-wide program that was in effect in New York City from 1985 until 1988. It was intended for publication in a journal, The New York Supervisor, which unfortunately ceased to exist during that year. The program described included twelve school districts at its initiation and resulted in a variety of projects which included: A Philosophy for Children project in three districts; a three year effort to intregrate critical (...) thinking in the reading, social studies, and bilingual curricula in one district; a two year program to integrate thinking skills into a gifted and talented program in yet another; infusion of thinking skills into the reading program in two other districts; a mathematics curriculum for gifted middle school students, a science curriculum for junior high school students, a curriculum based on local history; a program for drop-out prevention; and a prgram to enhance critical thinking through a media center in five other districts. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance (...) in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

This article provides a basic general introduction to Ramus, and evaluates his role in the history of logic and rhetoric, especially with relation to the study of argumentation. The author agrees with Ong and other historians of logic that Ramus is not to be taken seriously as a logician, and that his undoubted importance in the history of ideas is to be found elsewhere.Ramus advocates a belief in nature, experience and reason, and rejects the reliance on the authority of (...) ancient philosophers, above all Aristotle, though ‘experience’ does not mean scientific experiment and, paradoxically, includes the example of great philosophers and writers. In the end Ramus is seen as responsible for substituting for ancient classical rhetoric an entirely ornamental rhetoric of figures which was to take over education (with the exception of the Jesuit schools) almost until our own day. This curtailing and diminishing of rhetoric is seen as a degeneration. Ancient five-part rhetoric had been concerned with convincing and persuading: Aristotle distinguished the analytic, scientific reasoning of logic, from dialectic which was based on opinion and probability and had close links with rhetoric; by the time of Cicero and Quintilian, who addressed themselves to jurists and politicians, logic has given way to dialectic. In the Middle Ages and the Renaissance the two become assimilated; the evolution of this is traced here through the thirteenth-century Summulae logicales of Peter of Spain to the fifteenth-century German humanist logician Rudolph Agricola, who influenced Ramus partly through the intermediary of Johann Sturm. Ramus took over their topical theories but restricted them to logic/dialectic, and left rhetoric with little more than tropes and figures. He believed that there was only one method for teaching all the arts, and one dialectic common to them all. The distinction between analytical and dialectical has disappeared, with far-reaching consequences for the study of argumentation. Over the centuries logic has lost its connection with controversy and persuasion. With the development of the post-Cartesian, post-Baconian emphasis on the clarity of scientific discourse, and the mid-nineteenth-century interest in mathematical and formal logic, the process was complete. Argumentation, or the ‘new rhetoric’, aims to fill the gap thus created. (shrink)