Making sense of and with mathematics: the interface between academic mathematics and mathematics in practice

This article summarises what we can learn from research into workplace practice and vocational preparation to inform the design of mathematics education curricula for learners in general education undertaking compulsory schooling. Key findings about workplace practices are identified and explicated through the report of a case study from research in which researchers, students, teachers and workers explored workplace and mathematical practices together. Further to this, issues of learning and personal development are considered and explored from a point of view that sees learning as practice (doing) and identity development (becoming). This leads to a proposal for principles that provide a strategic vision for curriculum design. A potential approach to tactical design that facilitates curriculum structuring is illustrated in the particular instance of understanding developing measures as a modelling activity. Overall, the exercise, whilst providing some insight into possible ways forward in curriculum development, also suggests areas that require further research and development.     

Pedagogical Practices and Support Systems of Inclusion: Empirical Evidence from Chinese Societies

China has a massive population of children with disabilities. To address the special needs of these children, special/inclusive education in China has developed dramatically since the early 1980s onwards. This Special Issue puts together seven empirical studies emerging from the Chinese societies. These studies analyse inclusive discourses embedded in the education policy documents; scrutinise professional competence of inclusive education teachers; evaluate inclusive education practices in physical education, mathematics education, and job-related social skills education provided to students with disabilities; debate the required in-class support for inclusive education teachers; and discuss the social attitudes towards people with disabilities. The foci, methods and theories vary across the seven studies, while their aims converge. These studies are seeking best possible approaches and best available resources that facilitate inclusion. Knowledge built and lessons learned from these studies will provide implications for future inclusive education practices in China and beyond.     

对大学数学与高中数学课程内容的衔接问题的思考

首先分析当前大学数学与高中数学缺乏衔接所造成的问题,然后回顾我国在基础教育领域开始了由应试教育向素质教育转变的新一轮的课程改革,对《高中数学新课程标准》要求的教学内容和大学数学的教学内容两者作了比较分析,最后提出了大学数学教学改革的几方面的建议。     

Policies for inclusive education practices in teacher education in the United Kingdom and France

Implementation of any inclusive policy is dependent on longstanding conceptions, beliefs, and public discourses on schooling, learning, and including children in mainstream schooling. The adoption of inclusive education in education policies in France and the United Kingdom requires discursive support to reshape the meaning and content of teachers' work, duties and practices. Although inclusive education is widely debated, analyses of the variations in policy narratives promoting inclusive teaching in Europe are lacking. This article reports on comparative and international analysis of discourses and policies for empowering teachers for continuous professional development and inclusive school practices. The analysis focuses on an exploration of varieties of articulations, resources, and conceptual dynamics in the UK and France. These elements are discussed within the broader scheme of the teaching profession, with reference to the inclusive education paradigm.     

School mathematics in the era of globalization

This essay reviews the principles motivating contemporarycritical mathematics discourses. Drawing from varied critical discourses including ethno-mathematics, critical theory, post-structural theory, and situated and ecological cognition, the essay examines the pragmatics of critiques to the privileged role of school mathematics in the era of globalization. Critiques of modern school curricula argue that globalization practices linking education to technological and economic development are increasing, and the curriculum is being re-defined through discourses of privatization, national standards, and global competitiveness. Globalization has reinforced the utilitarian approach to school mathematics and the Western bias in the prevailing mathematics curricula, as well as helped to globalize pervasive mathematical ideologies. In most instances, a newfound status that mathematics is enjoying in this era of globalization is not well deserved, as school mathematics can no longer be considered culturally, socially, politically, nor economically neutral. In particular, school mathematics is increasingly critiqued as a cultural homogenizing force, a critical filter for status, a perpetuator of mistaken illusions of certainty, and an instrument of power. With such concerns it is becoming more evident that mathematics learning and education have implications for building just and democratic societies. As an African female scholar who is now living in Canada, I reflect on what the critical stance might mean for contexts with which I am familiar. I discuss the challenges of school mathematics with a view to improving curriculum and pedagogy so as to raise the awareness of teachers and learners to the questionable assumptions from which mathematics derives its prestige. The mathematics curriculum is central to cultivating values as well as fostering the conscientization of learners.     

Metaphors of hierarchy in mathematics education discourse: the narrow path

This paper adopts a rhetorical perspective in order to examine language about children in the discourse of mathematics education through a study of metaphor. Previous research has tended to emphasize the notion of ‘beliefs’, which locates responsibility for problematic conceptions of children within the heads of individuals, particularly practising and preservice teachers. Using the notion of metaphor, this paper examines several texts in US mathematics education, including conversations in an elementary classroom, a university mathematics methods classroom, mathematics textbooks, and standards documents. All of these texts draw on the metaphor of children’s learning as travel along a physical path, which supports talking and thinking about children in hierarchical ways. The dominance of this metaphor presents a new challenge for teacher educators concerned with equity: that of examining their own language and practices for hierarchical language.     

The modern mathematics reform movement in Brazil and its consequences for Brazilian mathematics education

This paper reports on the conclusions drawn from an investigation of the modern mathematics reform movement in Brazil. The focus of the study was an analysis of the mechanisms of transfer of knowledge from developed to developing countries, through a case study of Brazil and its adoption of the modern mathematics curriculum.The report presented here focuses on the dynamics of the reform movement and on the consequences of the movement for Brazilian mathematics education. The movement is studied as to how ideas about modern mathematics reform were disseminated to the Brazilian mathematics education community and the consequences due to misinterpretations of the intended curriculum in the implementation process. The intent of the study is that future initiatives in curriculum change proceed more efficiently in light of previous experiences, without repeating the mistakes committed in the past.     

An inclusive pedagogy in mathematics education

In this article, the author discusses characteristics in feminist pedagogy literature and situates them with respect to four dialectical aspects. These characteristics are then combined with non-discriminatory classroom practices to develop a frame of reference for an inclusive pedagogy in mathematics education.     

Teaching mathematics with a holistic approach

Many mathematics teachers opt for a strictly teacher‐centred curriculum and/or instructional strategy. Given the well‐documented evidence noting the benefits of student‐centred instruction, it is easy to see that teacher‐centred learning on its own cannot best meet the needs of students. On the other hand, some teachers, aware of the importance of a student‐centred mathematics curriculum, adopt an exclusively student‐centred approach to curriculum and instruction. What is less obvious is that this approach can put some students who belong to certain ethnic groups at a disadvantage. Hence, to be more inclusive, mathematics educators need to take a balanced instructional approach. This paper outlines an inclusive instructional strategy that resembles the structure of and exemplifies the values promoted by the Aboriginal model of the Medicine Wheel.     

Preparing teachers for inclusive education in Cyprus

In this study, we explore the following questions: (a) How do Cyprus universities that educate teachers respond to the challenge of inclusive education? Are the programmes of these institutions designed on the basis of the principles of inclusive education? What are the barriers that prevent student teachers to develop inclusive practices? How universities could help their student teachers to develop inclusive practices? These questions were investigated through qualitative data. In particular, the case study of a higher education institution in Cyprus was developed. The analysis of these data indicates certain factors that act as barriers in the development of inclusive practices by student teachers. These factors are related to the curricula, the notion of inclusion and to the different levels of culture. Developing these factors, we present at the same time particular suggestions for overcoming these barriers.     

Discrete mathematics in deaf education: a survey of teachers' knowledge and use

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.     

基于应用视角的高等数学教学模式研究

在高等数学教育教学过程中,基于应用视角的高等数学模式研究,大胆借鉴和吸收国内外一些先进的教学成果,运用现代教育理念进行课程设计,不断改革高等数学课程教学内容、方法和手段是必要的。     

Teaching mathematics after hours

The quantum of instruction time allocated to curriculum subjects such as mathematics facilitates greater exposure to knowledge and skill development, leading to higher levels of achievement. There are a number of manifestations of time to consider when investigating the quantum of time in mathematics education. The OECD have investigated the time allocated to mathematics by schools internationally, while also reporting on the prevalence of private tuition and time spent on homework. However, to date, no attention has been afforded to the provision of ‘hidden curriculum time’ for mathematics. This study seeks to advance the work of the OECD and describes a case study that sought to ascertain if teachers in Ireland provide additional mathematics lessons outside of school hours. The authors examined how prevalent this practice is, how many additional minutes some students receive as a result of this practice and ascertained teachers’ reasons for providing/not providing these additional mathematics classes. The results from this case study show that the majority of teachers at Senior Cycle provide these classes while a large proportion of Junior Cycle teachers also do. In extreme cases, these additional classes expose students to an additional 88.3 h of mathematics over the two-year Senior Cycle programme.     

Inclusive education in Latin America and the Caribbean: Exploratory analysis of the national reports presented at the 2008 International Conference on Education

This exploratory analysis of inclusive education issues in Latin America and the Caribbean is based on a series of documents produced in the framework of the organization of the 48th session of the International Conference on Education, in particular the National Reports presented at the Conference as well as country reports presented at preparatory meetings. The content analysis of the materials focused on the following topics: (a) the legal and normative framework; (b) the current educational policies; (c) the proposed or adopted approach in terms of inclusive education; (d) the main target groups; (e) inclusive education and the curriculum; (f) the kind of indicators most frequently mentioned; and (g) problems and challenges for inclusive education. One of the main challenges for the countries in the region is the appreciable gap between the stated principles and vision on one side, and the actual practices of inclusive education, on the other. Thus, there is an urgent need to ensure that policies and strategies translate into concrete actions aimed at changing the institutional practices and pedagogical approaches in the school and the classroom.     

高职计算机应用技术专业课程标准与实践标准的关系

高职计算机应用技术专业在过去的十几年中得到长足的进步。随着社会需求和高职教育的不断发展,高职计算机应用技术专业正在完成外延式扩张向内涵式发展的转变,计算机应用技术专业教学的规范化问题正日益成为高职教学改革的主要内容。如何实现产学无缝对接?如何制定专业课程标准?按照岗位的实践标准制定专业课程标准有着至关重要的作用,科学制定专业课程标准越来越重要。     

Japan’s educational practices for mathematically gifted students

This study documents the inclusive, deliberate, and unintended educational practices in Japan for mathematically gifted students. It also aims to identify various schools’ strengths and challenges in improving the mathematics education of these students. Case studies with multisite designs were undertaken in five middle schools selected using purposive sampling. Mathematics education practices – assessed in terms of assessment, mathematics instruction, support and interventions, and teachers’ collaboration – guided the data collection and analysis. The primary goal of this study was to describe current school practices and identify common strengths and challenges (including outlier practices across schools) which were valuable in generating conclusion regarding how certain practices might lead to different student and/or teacher outcomes.     

Policy-to-practice contexts for early childhood mathematics in England

This article considers the relationship between policy and practice in the early childhood mathematics curriculum for reception-class (RC) children of five years in England. It explores what the policy requires RC teachers to do in terms of curriculum implementation; what RC teachers’ views and understanding of the early childhood mathematics curriculum are; how RC teachers implement early years mathematics policy; and how RC children respond. A case study design included interviews with elite participants who influenced the policy-making process, survey of RC teachers and a detailed investigation of RC classes on three school sites. As elite interviews underlined, international comparison studies have had an important influence on early childhood mathematics policies by creating top-down pressure for standards. Elites and practitioners drew attention to a tension between a play-based pedagogy and a standards agenda. Tensions in policy text were reflected in mixed and ambivalent views and reported practices by elites and practitioners. RC teachers did not merely receive and implement policy expectations but brought their own values and understandings to practice. The study reveals interplay between local and global influences in a context of changing views of early childhood, early learning and early years pedagogy.     

融合教育课程:内涵、缘由及策略

随迁农民工子女的社会融合教育是一个热点话题。要使学校的融合教育更富有成效,应重视课程问题。学校应调查并根据随迁农民工子女的教育需求、社会生活需要来确定融合教育课程目标、构建融合教育内容,根据随迁农民工子女的特点在课程实施时贯彻渗透性、活动性、合作性原则,并根据随迁农民工子女社会融合的指标体系来评价融合教育的效果。     

The Erosion of FAPE for Students with LD

How schoolsfulfill Free and Appropriate Public Education (FAPE) requirements has evolved. Decades of general and special education reforms have led to dramatic increases in expectations for students in special education to be included in the general education classroom and curriculum and to achieve to the same high standards as their general education peers. Students with learning disabilities (LD) in particular are impacted by these reforms. The notion of their individually‐appropriate education has been slowly eroded as limitations in special education practices and the goals of education reform have been responded to. As special education intentions and practices advance, stakeholders have a responsibility to protect the FAPE of students with LD, to ensure meeting these students’ individualized learning needs.     

Tales from three countries: reflections during COVID-19 for mathematical education in the future

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries—Italy, the USA (California), and Germany—to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country’s standards for mathematics education. These three stories are framed by the authors’ backgrounds, experiences, interests, their country’s situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual.