独立学院大学数学课程体系改革与实践

以华中科技大学文华学院为例,介绍了通过开设选修课、改革大学数学教学内容、改革大学数学教学方法等方式,对大学数学课程进行教学改革的一些做法和体会.通过这些改革,提高了学生学习大学数学的积极性,取得了一定的成效.     

大学复变函数课程与高中数学的衔接

分析近二十年来高中数学经历的三次重要改革中复数部分教学内容、要求的变化和大学数学与应用数学专业复变函数教材处理复数部分的状况.在此基础上,给出大学复变函数课程关于复数部分的一些教学建议.     

Mathematics teaching in French écoles normales primaires, 1830–1848: social and cultural challenges to the training of primary school teachers

In the nineteenth century, the French education system, and teaching itself, was organized according to the social class the pupils came from: primary education was for the working classes, and secondary education was for the wealthier classes. In relation to this ??educational duality?? this paper looks at the mathematics teaching provided in the écoles normales primaires (primary teacher training colleges), which developed in France in the 1830s to train future (male) primary school teachers. What, precisely, was the content of this teaching? How was it organized? In what spirit and for what purpose was it provided? The aim of the paper is to show how these schools participated in the construction of a specifically primary mathematics culture for the education of the children from the lower classes, as distinct from the scholarly culture of secondary education.     

Mathematics teaching development as a human practice: identifying and drawing the threads

The didactic triangle links mathematics, teachers and students in a consideration of teaching?Clearning interactions in mathematics classrooms. This paper focuses on teachers and teaching in the development of fruitful learning experiences for students with mathematics. It recognises primarily that teachers are humans with personal characteristics, subject to a range of influences through the communities of which they are a part, and considers aspects of teachers?? personhood, identity and agency in designing teaching for the benefit of their students. Teaching is seen as a developmental process in which inquiry plays a central role, both in doing mathematics in the classroom and in exploring teaching practice. The teacher-as-inquirer in collaboration with outsider researchers leads to growth of knowledge in teaching through development of identity and agency for both groups. The inclusion of the outsider researcher brings an additional node into the didactic triangle.     

Neoliberal and nationalist discourses in Turkish elementary mathematics education

Within the last three decades, critical educators have highlighted that all components of education are under great pressure from neoliberal ideologies. These educators underline the close relation between neoliberal projects in education and inequality in educational opportunities and outcomes. Turkey is no exception to this trend. The view that education is simply another market commodity has become normalized in policy and public discourses, and business discourse that relies on only profit-making has a growing place in curriculum and newly defined education goals. Emphasizing that mathematics education is one of the main targets of this neoliberal attack, this paper focuses on how neoliberal and neo-conservative tendencies have affected mathematics education in Turkey. These effects are examined through revealing profit-driven business discourse and nationalist discourse in elementary mathematics education texts. Bourdieu’s cultural capital is instrumentalized to clarify neoliberal policies’ impacts on the reproduction of social and educational inequalities. The discourse analyses of elementary mathematics curriculum, textbooks, workbooks, and teacher’s guide books imply that elementary mathematics discourse (a) orients students to use their mathematical abilities and skills for the benefit of private corporations instead of public welfare and (b) fosters nationalism via ignoring ethnic minority and non-Muslim groups living in Turkey.     

What students value in effective mathematics learning: a ‘Third Wave Project’ research study

Considerations of how mathematics can be effectively taught and learnt may be cognitive, affective or sociocultural in approach. ??What students value in effective mathematics learning?? is a research study of the Third Wave Project, an international consortium of research teams adopting a sociocultural approach to investigate the harnessing of relevant values to optimise school mathematics teaching and learning. This paper seeks to contextualise the study, as part of the study examines what the high-achieving East Asian mathematics students value. The study is framed by knowledge relating to the relative cultural influence on effectiveness in mathematics learning, Alan Bishop??s values in mathematics education and the role of interactions in education, in particular David Tripp??s idea of critical incidents as reflecting professional judgement (and, thus, underlying values). Features of the innovative qualitative research design are also presented, which include the facilitation of photo-voice, the argument for an international collaborative team and focus group interviews for all values research, and a two-stage data analysis process aimed at clarifying both etic and emic perspectives.     

Adult Education and Ethnomathematics: appropriating results, methods, and principles

This article aims at discussing the ways that Youth and Adult Education have been taking on the production, methods and principles of Ethnomathematics in the last decades, especially in Brazil. First, it focuses on how Youth and Adult educators found Ethnomathematics to be a resource to know their students and the mathematics they use and produce better. The second part discusses how intercultural studies undertaken by Ethnomathematics research offered a new perspective under which mathematics knowledge and educational practices of Youth and Adult Education are conceived. Finally, the interlocutive and interdiscursive dimensions of teaching and learning practices are approached to present a reflection about the relations among Youth and Adult Education, Ethnomathematics and the search for the meanings of teaching and learning mathematics at school into an Inclusion project.     

在军事院校大一新学员高等数学的教学中融入数学文化的思考与体会

军事院校的高等数学的教学有其固有的特点,大学数学的部分内容进入中学课堂,对高等数学的教学产生了一定的积极影响,在此过渡基础上军校的高等数学的教学中融入数学文化,不仅增强了趣味性有利于克服脱节现象,而且在教学内容、教学理念、教学方法上也得到衔接与提升,有助于培养军事院校大学生的综合素质与创新能力.     

Educational philosophies and their influence on mathematics education— An ethnographic study in English and German mathematics classrooms

In the first part of the paper different educational philosophies, developed in, England and Germany in the last centuries, are described. In the second part results of an ethnographical study in English and German mathematics classrooms are presented. The study indicates the influence of this different educational philosophies on the educational systems of both countries and on the understanding of mathematics teaching and the teaching practice developed there     

Incorporating the dynamic mathematics software GeoGebra into a history of mathematics course

The purpose of this study was to investigate pre-service teachers’ views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. An open-ended questionnaire was used as a data collection tool. Qualitative data obtained from the pre-service teachers were analyzed by means of content analysis. As a result, it was determined that GeoGebra software was an effective tool in the learning and teaching of the history of mathematics.     

Online paths in mathematics teacher training: new resources and new skills for teacher educators

This paper considers the work carried out by online teacher educators and their professional development. We use the theoretical perspective of the documentational approach that focuses, in this case, on the interaction between teacher educators and the resources they use for their online training work. We thus study the following issues: (1) What kinds of resources do online teacher educators need, and how are such resources modified according to the educators?? specific skills and needs? (2) What specific skills are needed for setting up online training for mathematics teachers and how do these skills evolve as teacher education resources are used? We consider both questions simultaneously, while presenting results from a study within a specific teacher training programme in France that proposes ??training paths?? on a national platform. These ??paths?? are resources designed for teacher educators. We follow the appropriation of two training paths by two educator teams. The ways in which these educator teams were able to appropriate the paths give insights into the teacher educators?? skills and, as well, into the resources they need. By looking at their use of resources (as online mathematics teacher educators), we observe and analyse professional geneses, leading to the development of new skills.     

Can't do maths--understanding students' maths anxiety

The number of students continuing with their mathematics educationpost GCSE level has declined in recent years and hence studentsentering Engineering degrees are reducing. The University ofBirmingham recognized this problem and introduced the Suiteof Technology programme (STP) which no longer requires studentsto have A-level mathematics. Therefore lecturers at universityare now faced with teaching A-level mathematics in order togive the students the mathematical skills for their technologydegree. With little experience of teaching at this level, lecturersfrequently face the challenge of choosing the most appropriatelevel for a lecture that encourages students to engage withand learn a subject that they are novices in. It turned outthat some students have a mathematics anxiety and hence thebiggest challenge for a lecturer is supporting the studentsovercoming this fear of mathematics. Choosing the appropriatestarting level for any lecture and the fear of mathematics wasacknowledged during a peer learning group meeting as part ofthe Post Graduate Certificate in Learning and Teaching in HigherEducation (PGCLTHE) at the University of Birmingham. In orderto explore this further, a session of mathematics was taughtby a Civil Engineering lecturer to fellow peers who do not havean engineering background. This article describes the mathematicsteaching session, reflections from the lecturer and the learners,and the impact that this had on teaching mathematics to undergraduates.Further, the article explores the difficulties and challengesexperienced by lecturers when teaching mathematics as a servicesubject.     

‘Excellent’ primary mathematics teachers’ espoused and enacted values of effective lessons

This paper reports a study that explored the characteristics of mathematics lessons that were espoused as effective by six ??excellent?? mathematics teachers and how they enacted their values in their classroom practice. In this study, we define espoused values as values that we want other people to believe we hold, and enacted values as values that we actually practice. Qualitative data were collected through video-recorded lesson observations (3 lessons for each teacher) and in-depth interviews with teachers after each observation. At the end of the project, stimulated-recall focus group interviews were used to allow teachers to define the meaning of an effective mathematics lesson as well as to recall and reflect on a 10-min edited video clip of one of their teaching lessons. The findings showed that these teachers shared five common characteristics of effective mathematics lessons: achieving teaching objectives; pupils?? cognitive development; affective achievement of pupils; focus on low-attaining pupils; and active participation of pupils in mathematics activities. These values were espoused explicitly as well as enacted in the lessons observed.     

Mathematik und “der Rest der Welt”

The necessity to re-connect the subject of mathematics closer to the other subjects taught at school is undisputed. We provide an overview over the state of discussion and of the realisation taking place in Germany, also taking into consideration the available literature on the topic During the last years, many concrete efforts have been made in almost all states of Germany in order to bring cross-curricular activities into everday teaching experience, with help of curricular and educational guidelines. In doing this, all 16 German states take different ways.     

Exploring the quality of the mathematical tasks in the new Turkish elementary school mathematics curriculum guidebook: the case of algebra

To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries and previous experiences with mathematics education in Turkey. This study attempts to provide a perspective on the nature of the instructional tasks in the new elementary school mathematics curriculum. In particular, our focus is to explore the level of cognitive demands (LCD) in the algebra tasks provided in the national elementary mathematics curriculum guidebook. This curriculum document is a major resource for administrators, stakeholders, textbook publishers and ultimately for teachers. For every learning objective, it provides sample tasks to be used in mathematics instructions. In this study, our purpose is to explore the LCD of each of these tasks by utilizing a framework developed by Smith and Stein (Math Teach Middle School 3:344–350, 1998). The framework classifies mathematical tasks according to the level of demands: lower-level and higher-level demands. While the lower-level demands are related to memorization and procedures without connections, the higher-level demands are related to procedures with connections and doing mathematics. The findings revealed that 60% of algebra tasks for each grade level required higher LCD and a great majority of the remaining tasks were at the level of procedures without connections. The findings of the study particularly inform curriculum developers about issues regarding the quality of the tasks given in the curriculum guide and provide possible suggestions to improve the implementation of the curriculum change process.     

Learning from similarities and differences: a reflection on the potentials and constraints of cross-national studies in mathematics

Research in mathematics education that crosses national boundaries provides new insights into the development and improvement of the teaching and learning of mathematics. In particular, cross-national comparisons lead researchers to more explicit understanding of their own implicit theories about how teachers teach and how children learn mathematics in their local contexts as well as what is going on in school mathematics in other countries. Further, when researchers from multiple countries and regions study collaboratively aspects of teaching and learning of mathematics, the taken-for-granted familiar practices in the classroom can be questioned. Such cross-national comparisons provide opportunities for researchers and educators to probe typical dichotomies such as “high-performing” versus “low performing”, “teacher-centred versus student-centred”, or even “East versus West”, in searching for similarities and differences in educational policies and practices in different cultural contexts.     

Curriculum research to improve teaching and learning: national and cross-national studies

Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learning activities in school education. Studies of curriculum and its changes are thus important to reveal the expectations, processes and outcomes of students’ school learning experiences that are situated in different cultural and system contexts. In this article, we aim to propose a framework that can help readers to develop a better understanding of curriculum practices and changes in China and/or the USA that have been reported and discussed in articles published in this themed issue. Going beyond the selected education systems, further studies of curriculum practices and changes are much needed to help ensure the success of educational reforms in the different cultural and system contexts.