Influence of socio-economic background and cultural practices on mathematics education in India: a contemporary overview in historical perspective

The nature, extent and quality of mathematics learning among young children in India cannot be adequately understood without looking at the larger context of education and the social background of the children. Society, including schools, characterized by large inequalities impacts mathematics learning. Beginning with a brief overview of (mathematics) education in India, in historical and sociological perspectives, an appraisal is presented of the need and nature of mathematics learning revealed by field studies in two communities in a deprived rural setting and a low-income urban setting, respectively. While the latter was economically active, the former was much poorer in work and education opportunities, though had richer cultural practices that involved engagement with mathematical riddles, puzzles, folklores and mnemonic tables. The paper discusses the enabling potential of the knowledge resources, including work-context knowledge, which exist in both the communities despite the prevalent deprivations due to disadvantaged conditions. Yet in both situations mathematics learning remains disconnected from formal school mathematics. Factors within SES that possibly have strong bearings on mathematics learning are highlighted which can scaffold stronger integration with curricular and pedagogic practices. Both the groups presented potentially rich contexts for drawing upon everyday mathematical knowledge that can inform effective mathematics learning, which has been inadequately explored in curriculum and instructional design thus far.     

Mathematics textbooks and their use in English, French and German classrooms:

After a through review of the relevant literature in terms of textbook analysis and mathematics teachers' user of textbooks in school contexts, this paper reports on selected and early findings from a study of mathematics textbooks and their use in English, French and German mathematics classrooms at lower secondary level. The research reviewed in the literature section raises important questions about textbooks as representations of the curriculum and about their role as a link between curriculum and pedagogy. Teachers, in tunr, appear to exercise control over the curriculum as it is enacted by using texts in the service of their own perceptions of teaching and learning. The second and main part of the paper analyses the ways in which textbooks vary and are used by teachers in classroom contexts and how this influences the culture of the mathematics classroom. The findings of the research demonstrate that classroom cultures are shaped by at least two factors: teachers' pedagogic principles in their immediate school and classroom context; and a system's educational and cultural traditions as they develop over time. It is argued that mathematics classroom cultures need to be understood in terms of a wider cultural and systemic context, in order for shared understandings, principles and meanings to be established, whether for promotion of classroom reform or simply for developing a better understanding of this vital component of the mathematics education 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.     

Gender justice,human rights and measurement in the mathematics classroom

In line with international trends, the new South African mathematics curriculum implores mathematics educators to realize a pedagogy in their classrooms that is more practical, activity-oriented, and connected to their learners' lives. Drawing on data from a larger study that explores theory–practice relations in mathematics education, this paper shows how such progressive practices, when interpreted with respect to the teaching of measurement which required learners to use different measuring instruments for measuring the school grounds in learning about length and perimeter, were found to be deeply gendered. In two different contexts of an ‘African' township school and a predominantly ‘Indian' suburban school, girls in a grade 6 mathematics classroom faced direct sexism as they struggled to take the opportunity to participate in the activity and learn how to measure – an important mathematical competence and everyday knowledge and skill. The article analyses the data with reference to the human rights imperatives of the new national curricula and approaches to addressing disadvantage and discrimination for girls in mathematics classrooms.     

The relationship between students' mathematical thinking types and representation preferences in definite integral problems

ABSTRACT

Given that curriculum materials serve as cultural artefacts, this study addresses the need for more research on curriculum materials in different contexts. Most studies concerning curriculum materials have been conducted in US and, therefore little is known about the nature of materials in other cultural-educational contexts. The aim of this paper is to identify the underlying cultural norms of potentially constructed classrooms, by analysing recurrent activities in the most commonly used Finnish teacher guides at primary-school level. We identified three norms embedded in them: (1) creating opportunities for learning through a variety of activities and communication; (2) keeping the class gathered around a specific mathematical topic; and (3) concurrent active involvement of teachers and students. The results add to knowledge about both teacher guides and the Finnish educational context. Moreover, it adds to the growing body of methodologies, as our analytical approach is novel in the context of textual analysis.     

Conception of expert mathematics teacher: a comparative study between Hong Kong and Chongqing

This paper reports the similarities and differences in how “expert mathematics teacher” is conceptualized by mathematics educators in Hong Kong and Chongqing, two cities in China which share similar but different cultural and social backgrounds. Thirty-seven mathematics education researchers, school principals with mathematics education background, and mathematics teachers were interviewed on their perceptions of expert mathematics teacher. It is found that in both cities an expert mathematics teacher should have a profound knowledge base in mathematics, teaching, and students; strong ability in teaching; and a noble personality and a spirit of life-long learning. As for differences, an expert mathematics teacher should have the ability to conduct research, mentor other teachers, and have profound knowledge of examination and educational theories in Chongqing. These attributes were not found in Hong Kong. These similarities and differences are discussed, and relevant social and cultural factors in the two contexts are examined.     

Investigations and explorations in the mathematics classroom

In Portugal, since the beginning of the 1990s, problem solving became increasingly identified with mathematical explorations and investigations. A number of research studies have been conducted, focusing on students’ learning, teachers’ classroom practices and teacher education. Currently, this line of work involves studies from primary school to university mathematics. This perspective impacted the mathematics curriculum documents that explicitly recommend teachers to propose mathematics investigations in their classrooms. On national meetings, many teachers report experiences involving students’ doing investigations and indicate to use regularly such tasks in their practice. However, this still appears to be a marginal activity in most mathematics classes, especially when there is pressure for preparation for external examinations (at grades 9 and 12). International assessments such as PISA and national assessments (at grades 4 and 6) emphasize tasks with realistic contexts. They reinforce the view that mathematics tasks must be varied beyond simple computational exercises or intricate abstract problems but they do not support the notion of extended explorations. Future developments will show what paths will emerge from these contradictions between promising research and classroom reports, curriculum orientations, professional experience, and assessment frameworks and instruments.     

The quality of non-textual elements in mathematics textbooks: an exploratory comparison between South Korea and the United States

As an exploratory investigation, this study aims to analyze non-textual elements in some Korean and US mathematics textbooks using a conceptual framework whose components include accuracy, connectivity, contextuality, and conciseness. By analyzing three US textbooks and three Korean ones, the study not only shows patterns in the use of non-textual elements in mathematics textbooks in different contexts but also provides insights into how to assess the quality of non-textual elements in mathematics textbooks, which I hope will contribute to the provision of more meaningful and productive learning opportunities to school children. Overall, the results from this study show that there is significant difference across topics and textbooks, which implies different opportunities to learn through non-textual elements. This study makes a unique contribution to the conceptualization of non-textual elements in mathematics education and has implications for textbook analysis and curriculum development.     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

Antiracist Education: A Special Role for the History of Science and Technology

In recent years, emphasis in multicultural education has shifted from an approach in which the primary concern is coping with the learning problems thrown up by cultural diversity (thereby assisting children to be assimilated into the dominant culture) to an approach that accepts and actively promotes cultural diversity. However, some have argued that celebration of diversity is no more than patronizing tokenism unless it is accompanied by a vigorous antiracist approach. Antiracism is concerned to reveal and combat racist attitudes and practices which disadvantage and discriminate against some minority groups, and which result in an unequal distribution of opportunity, wealth and power. This paper claims that the history of science and technology has a special role within a curriculum that seeks to celebrate diversity and to combat racism.     

School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States

This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbooks to which the teachers were accustomed. However, variation emerged when considering the ways in which the teachers interacted with the materials for their learning of mathematics. Whereas some teachers accepted and even embraced changes to the teaching–learning process that accompanied use of the curriculum materials, other teachers experienced discomfort and frustration at times. Nonetheless, each teacher considered that use of the curriculum materials improved her mathematical understandings in significant ways. Implications of these results for mathematics teacher education are discussed.     

Curriculum traditions in Berlin and Hong Kong: a comparative case study of the implemented mathematics curriculum

Many studies (such as Pepin in Learners and pedagogy, Sage Publications, London, 1999; Kaiser in ZDM 34(6):241–257, 2002; Park and Leung in Mathematics education in different cultural traditions: a comparative study of East Asia and the West. The 13th ICMI Study, pp. 227–238, Springer, New York, 2006) have revealed that there is a strong dependence on cultural traditions in mathematics teaching in different countries. Education in Germany is influenced by the Central and North European Didaktik tradition (Westbury in Teaching as a reflective practice: the German Didaktik tradition, L. Erlbaum Associates, Mahwah, pp. 15–39, 2000), while that in East Asia is influenced by Confucian heritage culture. However, there have not been studies investigating the relationships between these two cultural traditions and their influences on teaching and learning. This study aims at filling this gap in knowledge. Some commonalities in the aims and beliefs in the underlying philosophies in education in traditional China and Germany were found and are presented in this paper. Specifically, the relationship between cultural traditions and the implemented mathematics curriculum was investigated, using Berlin and Hong Kong as examples. It was found that culture affects the implemented curriculum in a complicated way and that other factors such as the intended curriculum and textbooks may also influence the implemented curriculum.     

Toward Understanding the Role of Technological Tools in Statistical Learning

This article begins with some context setting on new views of statistics and statistical education. These views are reflected, in particular, in the introduction of exploratory data analysis (EDA) into the statistics curriculum. Then, a detailed example of EDA learning activity in the middle school is introduced, which makes use of the power of the spreadsheet to mediate students' construction of meanings for statistical conceptions. Through this example, I endeavor to illustrate how an attempt at serious integration of computers in teaching and learning statistics brings about a cascade of changes in curriculum materials, classroom praxis, and students' ways of learning. A theoretical discussion follows that underpins the impact of technological tools on teaching and learning statistics by emphasizing how the computer lends itself to supporting cognitive and sociocultural processes. Subsequently, I present a sample of educational technologies, which represents the sorts of software that have typically been used in statistics instruction: statistical packages (tools), microworlds, tutorials, resources (including Internet resources), and teachers' metatools. Finally, certain implications and recommendations for the use of computers in the statistical educational milieu are suggested.     

Identity,Goals, and Learning: Mathematics in Cultural Practice

In this article, I explore and elaborate the relation between goals, identities, and learning and argue for their utility as a model by which to understand the nature of learning in general and to better understand the way in which race, culture, and learning become intertwined for minority students in American schools. Drawing on sociocultural perspectives on learning and development, including Wenger (1998) and Saxe (1999), I describe findings from 2 studies of learning among African American students outside of school, in the cultural practices of dominoes and basketball. This research shows that indeed, as players come to learn these practices, they both shift in regard to the goals they seek to accomplish within the practice and change as they come to define themselves vis-à-vis the practice. The implications for understanding the relation between race, culture, and learning are discussed.     

Rhetoric,Reality, and Possibilities: Interdisciplinary Teaching and Secondary Mathematics

The National Council of Teachers of Mathematics has proposed a broad core mathematics curriculum for all high school students. One emphasis in that core is on “mathematical connections” both among mathematical topics and between mathematics and other disciplines of study. It is suggested that mathematics should become a more integrated part of all students' high school education. In this article, working definitions for the terms curriculum, interdisciplinary, and integrated and a model of three categories of curriculum design based on the work of Harold Alberty are developed. This article then examines how a “connected” mathematics core curriculum might be situated within the different categories of curriculum organization. Examples from research on interdisciplinary education in high schools are presented. Issues arising from this study suggest the need for a greater emphasis on building and using models of curriculum integration both to frame and to give impetus to the work being done by teachers and administrators.     

Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories

In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. Our “visits” to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This journey through history and schooling represents a good occasion to address some questions: Are there “good” contexts in which to develop mathematical instruments? Are there “good” teaching practices which assist students’ instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed.     

Implementing Coteaching and Cogenerative Dialoguing in Urban Science Education

Over the past 7 years the authors have been involved in the development of a new model for the education of science teachers that has the potential to address teacher education in challenging urban settings characterized by problems such as teacher turnover and retention, low job satisfaction, and contradictions arising from cultural and ethnic diversity. An intensive research program accompanied the development effort; the research results were used as resources in redesigning the evolving model to make it more appropriate for the situations at hand. The science teacher education program at an urban university was built around a yearlong field experience, during which all prospective teachers learned to teach in an urban high school while coteaching, that is, while teaching at the elbow of a mentor teacher or one or more peers. Over this period, a number of different configurations of coteaching and the associated cogenerative dialoguing were tried, tested, and investigated. The paper describes the historical development of the different configurations of the model and the emergent contradictions that led the researchers to enact changes to their approach. The central idea in the development effort was the creation of an environment that (a) best affords the learning of how to teach in urban high schools, (b) decreases teacher isolation, (c) mitigates turnover and retention, and (d) addresses contradictions arising from the cultural and ethnic diversity of students and teachers. Most importantly, this model of teacher education and enhancement simultaneously multiplies the resources and opportunities to support the learning of students.     

Toward Understanding the Role of Technological Tools in Statistical Learning

This article begins with some context setting on new views of statistics and statistical education. These views are reflected, in particular, in the introduction of exploratory data analysis (EDA) into the statistics curriculum. Then, a detailed example of EDA learning activity in the middle school is introduced, which makes use of the power of the spreadsheet to mediate students' construction of meanings for statistical conceptions. Through this example, I endeavor to illustrate how an attempt at serious integration of computers in teaching and learning statistics brings about a cascade of changes in curriculum materials, classroom praxis, and students' ways of learning. A theoretical discussion follows that underpins the impact of technological tools on teaching and learning statistics by emphasizing how the computer lends itself to supporting cognitive and sociocultural processes. Subsequently, I present a sample of educational technologies, which represents the sorts of software that have typically been used in statistics instruction: statistical packages (tools), microworlds, tutorials, resources (including Internet resources), and teachers' metatools. Finally, certain implications and recommendations for the use of computers in the statistical educational milieu are suggested.     

A Brief Comparison of the U.S. and Chinese Middle School Mathematics Programs

The U.S. generally has a less intense mathematics curriculum in the middle school grades than China. Some factors contributing to the lower intensity in the U.S. mathematics curriculum are textbooks with extensive drill, repetition of content, lack of challenging problem solving, lower curricular and cultural expectations, and ability grouping. In comparison, China utilizes challenging problem solving, sequential development of content without repetition, expectations of hard work, high values for mathematics by the curriculum and culture, and a common curriculum for all as aspects of mathematics instruction. The U.S. is taking a positive direction in its mathematics curriculum with the use of technology and reform while compulsory education is mandating that the theoretical depth of middle school curriculums in China be lowered for all of its students in grades 1–9.     

Research, practice, uncertainty and responsibility

Three issues concerning the relationship between research and practice are addressed. (1) A certain ‘prototype mathematics classroom’ seems to dominate the research field, which in many cases seems selective with respect to what practices to address. I suggest challenging the dominance of the discourse created around the prototype mathematics classroom. (2) I find it important to broaden the school-centred discourse on mathematics education and to address the very different out-of-school practices that include mathematics. Many of these practices are relevant for interpreting what is taking place in a school context. That brings us to (3) socio-political issues of mathematics education. When the different school-sites for learning mathematics as well as the many different practices that include mathematics are related, we enter the socio-political dimension of mathematics education.On the one hand we must consider questions like: Could socio-political discrimination be acted out through mathematics education? Could mathematics education exercise a regimentation and disciplining of students? Could it include discrimination in terms of language? Could it include sexism and racism? On the other hand: Could mathematics education bring about competencies which can be described as empowering, and as supporting the development of mathematical literary or a ‘mathemacy’, important for the development of critical citizenship?However, there is no hope for identifying a one-way route to mathemacy. More generally: There is no simple way of identifying the socio-political functions of mathematics education. Mathematics education has to face uncertainty, and this challenge brings us to the notion of responsibility.