Trust and Discipline: Adolescents’ Institutional and Teacher Trust Predict Classroom Behavioral Engagement following Teacher Discipline

This daily diary study examined how adolescents’ institutional and teacher-specific trust predicted classroom behavioral engagement the day after being disciplined by that teacher. Within mathematics classrooms, adolescents (N = 190; M_age = 14 years) reported institutional and teacher-specific trust and then completed a 15-day diary assessing teacher discipline and behavioral engagement. The results indicated that, among adolescents with low teacher trust, discipline was unrelated to next-day behavior. Contrastingly, adolescents with high teacher but low institutional trust became less engaged following discipline, whereas those with high teacher and institutional trust became more engaged. These findings suggest that adolescents interpret discipline within the social context of trust, and adolescents’ trust in the institution and teacher are important for discipline to improve behavior.     

Differentially positioned language games: ethnomathematics from a philosophical perspective

This paper discusses a new philosophical perspective for ethnomathematics which articulates Ludwig Wittgenstein’s and Michel Foucault’s theoretical notions. It is conceived as a theoretical toolbox which allows the analysis of, on the one hand, the mathematical language games of different forms of life and their family resemblances and, on the other hand, the Eurocentric discourses of academic and school mathematics and their effects of truth. Based on fieldwork done in rural forms of life in the south of Brazil, examples of the use of this perspective are presented. The paper analyzes language games of those different forms of life and the school mathematics discipline, highlighting the complex network of learning and powers that makes other mathematics than that known as the mathematics be positioned “in a void” in school curricula.     

Reflections on the Dilemmas and Tensions in Mathematics Education Courses for Student Teachers

The paper outlines the dilemmas and paradoxes faced by lecturers and student teachers as they interact in a mathematics education subject that deals with both mathematics as a discipline and as a language, and with appropriate pedagogies for the teaching and learning of mathematics in primary schools. For the lecturer there is a tension between comforting and challenging the students. Are they to be wooed into a more positive attitude to mathematics, at the cost of avoiding the complexity of the discipline; or are they to be challenged by the unique character of mathematics, at the risk of alienation and exclusion? The latter often returns students to their original perception of maths as a harsh and unforgiving subject which is beyond their capabilities as they struggle with unfamiliar concepts and the discomfort of ‘not knowing’. For student teachers there is, paradoxically, a desire to ‘instil understanding’ when they themselves may not fully understand. They often idealise what is good practice but deny it in their own learning.     

Presidential Address: The academic discipline of education. Reciprocal relationships between practical knowledge and academic knowledge

This article explores the nature of education as a vital part of human knowledge. The argument that is presented addresses the critique of education as having epistemological weaknesses as an academic discipline. The argument is framed by scholarship that has categorised the discipline of education as derived from three main traditions of knowledge. In order to explore the coherence of education as a discipline, contrasts are made with other disciplines such as mathematics and sciences. The article also reviews scholarship in relation to the concept of education research that is close-to-practice, and the relevance of this to understanding education as an academic discipline. The article concludes by suggesting a new model that shows the relationships between practical knowledge and academic knowledge that are an intrinsic part of education. A more confident portrayal of education as an academic discipline is also advocated.     

Mathematics Instruction in Safe Space: Prospective Elementary Teachers' Views of Mathematics Education

This article discusses findings from an investigation into 42 prospective elementary teachers' views of mathematics teaching and learning. The focus is on how the participants saw the roles of teachers, pupils,and mathematics in mathematics classes as they communicated their views in journals written during the study. I argue that some prospective teachers express a tendency to protect and relieve their future pupils from mathematics. I show how this tendency affects a shift from school being the place where teachers teach pupils toward a conception of a safe space where the teachers predominantly care for the children. This revised version was published online in September 2006 with corrections to the Cover Date.     

Globalized curriculum or global approach to curriculum reform in mathematics education

The mathematics education community has shown considerable awareness of the international status of their discipline. While internationalization of the discipline is not a new phenomenon, globalization is a relatively recent term in educational discourse. This paper presents a theoretical model towards the study of globalization and internationalization in mathematics education based on previous publication by the authors. Secondly, it identifies some key issues that have been discussed in the literature and that may require further discussion and research in the field. In particular it discusses the issue of similarity of mathematics education curricula around the world. The concept of a global curriculum is rejected in favor for more internationalized approach to curriculum reform based on collaboration between mathematics educators.     

Educating the Young Mathematician: The Twentieth Century and Beyond

Educational programs for young children emerged reasonably early in the history of the United States of America. The movements of Child-Centered Education, the Nursery School, the Project Method, Curriculum Reform, and contemporary research have all influenced mathematics in early childhood education. The Froebelian kindergarten and the Montessori Casa die Bambini (Children’s House) included approaches to teaching mathematics. This article reviews the history of mathematics education in relation to the history of early childhood education from the turn of the twentieth century. It also discusses how research in mathematics education attempted to gain its own identity. Throughout history, researchers have identified mathematics issues and addressed them, defining the field, and generating a cadre of mathematics researchers.     

Mathematics and Mathematicians at Sapienza University in Rome (XVII–XVIII Century)

This article introduces some data regarding the teaching of mathematics in La Sapienza in the 17th century, with particular reference to the discipline’s role in the statutes, the lecturers, the courses’ programmes, the interest that Popes took in it. Specifically, it will focus on the changes that occured at the end of the 17th century, with regards to the development of the discipline and the improvement of a “scientific culture” in the city of the Pope.     

The Notion of Proof in the Context of Elementary School Mathematics

Despite increased appreciation of the role of proof in students’ mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major features of any given argument – foundation, formulation, representation, and social dimension – so that the argument could count as proof at the elementary school level. My examination is situated in an episode from a third-grade class, which presents a student’s argument that could potentially count as proof. In order to examine the extent to which this argument could count as proof (given its four major elements), I develop and use a theoretical framework that is comprised of two principles for conceptualizing the notion of proof in school mathematics: (1) The intellectual-honesty principle, which states that the notion of proof in school mathematics should be conceptualized so that it is, at once, honest to mathematics as a discipline and honoring of students as mathematical learners; and (2) The continuum principle, which states that there should be continuity in how the notion of proof is conceptualized in different grade levels so that students’ experiences with proof in school have coherence. The two principles offer the basis for certain judgments about whether the particular argument in the episode could count as proof. Also, they support more broadly ideas for a possible conceptualization of the notion of proof in the elementary grades.     

Prospective primary teachers’ perceptions about the use of mathematics homework

The benefit of homework (HW) has been the subject of ongoing debate among various stakeholders. Within this debate, and in relation to teacher development, prospective teachers’ views of HW have received limited attention. In this study, we survey primary pre-service teachers’ (‘PSTs’) views of HW use (n = 45 teaching grades 2–5; n = 39 teaching grades 6 and 7) in a single discipline (mathematics) at one large Australian university.

The literature suggests students in upper primary and secondary grades will benefit from the use of mathematics HW. Results of the study, in contrast, suggest our PSTs teaching early primary grades planned to give proportionally (but not significantly) more mathematics HW than those teaching later grades. Reasons for this disparity are discussed. We argue there is a need in teacher development to equip PSTs with a better understanding of how classroom and home-based learning work together in the development of mathematical understanding.     

Future Directions in Research on Mathematics-Related Teacher Identity

Mathematics education research has placed great emphasis on teacher identity, examining both pre- and in-service teachers, and within these cohorts, specialised mathematics teachers and non-specialists such as elementary teachers. Extensive research has already been done; hence, this paper discusses possible future directions for research on teacher identity in mathematics education. Among other issues, we highlight that general education research on identity has infrequently informed research on mathematics-related teacher identity. This not only limits the transfer of knowledge but also isolates mathematics education from general education research. We suggest that connecting these lines of research and their findings may not only strengthen mathematics education research and mathematics teaching and learning but also contribute to less isolation within the discipline as a whole.     

Learning Through Computational Modeling

Summary

When thinking of reasoning, problem solving, communication, and connecting related ideas, the tool of choice in nearly every discipline is the microcomputer. Furthermore, unlike the traditional calculator, the modern classroom computer has an unparalleled ability to implement both graphical and procedural components of mathematics understanding in a single unified object. By students' creation and utilization of mathematically relevant computer-based objects, this dual encapsulation provides them with a unique opportunity to see both the form of representation and their actions utilizing this representation simultaneously.

This paper suggests that the object-oriented environments that modern technology enables are ideally suited to parallel and facilitate the ability of students to take a broader variety of action upon objectsof a nature and kind hitherto unknown. These student-controlled actionsupon these mathematically powerful and computer-enabled objectshave the potential for creating classroom environments that both surpass the pale hopes of the integrated learning system and surprise those wedded to a conservative view of Piagetian developmental levels.     

Boundary-Work and Discipline Construction: Boundary Strategies to Institutionalize Guoxue as a Discipline and Its Failure

Abstract

The construction of knowledge boundaries is an important mechanism in the formation of disciplines. This article examines and analyzes boundary strategies and difficulties in the institutionalization of guoxue (“national studies” or “Chinese classics”) as a discipline in recent years from the perspective of boundary-work. To establish guoxue as a discipline, proponents of the discipline have proposed the knowledge strategies of “new guoxue” and “broad guoxue,” so as to dispel potential conflict between guoxue and the external political environment. In addition, in the construction of the discipline, proponents have emphasized the differences between Chinese and Western scholarship, and also made analogy to Western Sinology, to highlight the necessity of constructing a holistic “discipline of guoxue.” However, these strategies and efforts have not achieved the objective of building guoxue as a discipline. One important reason is that guoxue studies are, to a very great extent, embedded in Chinese literature, Chinese history, Chinese philosophy and other related disciplines. The knowledge boundaries between guoxue and these disciplines are fuzzy, and the construction of the discipline lacks driving force from daily research practices. The process of to build a guoxue discipline can contribute to reflect on the existing discipline governance system in mainland China.     

Computer Science in Liberal Arts Colleges

When a liberal arts college decides to include computer science as one of its academic disciplines, a number of questions arise. What is an appropriate curriculum? What sort of laboratory support does this new discipline need? How does a small liberal arts school attract, retain, and evaluate faculty in this area? Do computer science faculty become a separate department or remain joined with mathematics or some other discipline? In short, what must be done to put computer science on equal footing with mathematics and other scientific disciplines? This paper addresses these questions.     

Reconsidering the Study of Mathematics Instructional Practices: The Importance of Curricular Context in Understanding Local and Global Teacher Change

This paper discusses the case of one teacher, Jackie, whose instructional practices illuminate the importance of textbooks and student/parent expectations in shaping pedagogy. Jackie teaches in the Plainview district, which offers parents and students a choice between a reform-oriented, integrated curriculum (Core Plus) and a more conventional algebra sequence (the University of Chicago series). Each day, Jackie teaches two very different sections of accelerated eighth-grade mathematics using each of these curricular materials. Drawing from students’ survey responses, classroom observations, and teacher interview data, we show ways in which Jackie’s pedagogy differs considerably between the two courses and we shed light on reasons underlying this variation.By examining one teacher who enacts different practices in each of the two curricular contexts, this paper highlights factors that contribute to teachers’ enacted curricula – factors that have been understated in previous mathematics education research on teacher development. The study establishes the importance of distinguishing between global and local teacher change, and suggests implications for future studies of teaching and reform.     

Interconnecting Content and Community: A Qualitative Study of Secondary Mathematics Teachers

The publication of the National Council ofTeachers of Mathematics initial Standards(1989) has acted as a catalyst to beginreforming the way mathematics is taught in theUSA. However, the literature regarding reformmovements suggests that changing oureducational systems requires overcoming manybarriers and is thus difficult to achieve.Reform in mathematics education, like reformmovements in other areas of education, has thusbeen slow to take hold. One structure that hasbeen shown to support educational reform,particularly instructional reform, has beenteacher community. This paper discusses aprofessional development intervention thatattempted to start a professional communityamong a group of secondary mathematics teachersthrough in-service work on mathematical problemsolving and technology. The results of thisstudy suggest that the use of mathematicalcontent explorations in professionaldevelopment settings provides a means to helpmathematics teachers build professionalcommunities. Together, these two components –mathematical content explorations and teachercommunity – provided these secondarymathematics teachers with a strong foundationfor engaging in the reform of their mathematicsclasses.     

“几何画板”作分段函数图像

几何画板是一个优秀的专业学科平台软件,它以数学为根本,以"动态几何"为特色来动态表现设计者的思想,为探索几何奥秘提供一个新的工具.本文研究了使用"几何画板"画分段函数图像,给出详细的制作步骤.     

高等代数教学对学生学科素质的培养及相关的教学策略

基于高等代数的学科特点与师范类数学专业学生的培养目标,作者对高等代数教学所具的意义与应采取的教学策略作了相关探究,重点从高等代数对学生知识结构的统一、数学思想的形成、数学能力的培养以及数学修养的提升四个方面论述了高等代数教学的重要作用及意义。     

Comparative analyses of discourse in specialized STEM school classes

ABSTRACT

The authors detail the discourse patterns observed within mathematics and science classes at specialized STEM (science, technology, engineering, and mathematics) high schools. Analyses reveal that teachers in mathematics classes tended to engage their students in authoritative discourse while teachers in science classes tended to engage students in dialogic discourse. The authors examined variations in the type of discourse in relationship to the discipline being taught, the educational level of the teacher, and course requirements were also explored.