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In this paper we argue that the academic fields of critical mathematics education and post-normal science are complementary and can provide mutual benefits for the future. Post-normal science promotes the idea of extended peer communities, through which citizens participate with knowledge and insights in urgent and complex societal issues with conflicting stakes. Meanwhile, critical mathematics education is a philosophy of mathematics education that includes attention to the central role of mathematics in a technological society, the effects of this role, and the need for epistemic dialogue in learning and teaching mathematics. We argue that a mathematics education based on these ideas can prepare students to participate in extended peer communities. We focus particularly on the uncertainty that characterises post-normal situations. Post-normal science distinguishes various characteristics of uncertainty and highlights its centrality to post-normal situations. A critical mathematics education should prepare citizens who are able to deal with the different ways in which uncertainty matters in such situations. We illustrate these ideas through brief descriptions of three classroom studies in which students discuss issues of uncertainty and risk. [ABSTRACT FROM AUTHOR]

The article describes the social nature of mathematical reasoning.

Copyright of Contrapontos is the property of Universidade do Vale do Itajai and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article reports on the self-perceptions of primary and secondary teachers and their mathematical content knowledge.

Despite increases in the representation of African American and Hispanic youth in advanced math courses in high school over the past two decades, recent national reports indicate that substantial inequality in achievement remains. These inequalities can temper one's optimism about the degree to which the United States has made real progress toward educational equity. Using data from the Education Longitudinal Study of 2002 (ELS), the authors find that the math achievement gap is most pronounced among those students who take the most demanding high school math classes, such as precalculus and calculus. The authors explore the roles of family socioeconomic status and school composition in explaining this pattern. Findings suggest that among those students reaching the advanced math high school stratum, Hispanic youth from low-income families and African American youth from segregated schools fare the worst in terms of closing the achievement gap with their white peers. The authors discuss potential explanations for the achievement differences observed and stress the need for more research that focuses explicitly on the factors that inhibit minority/majority parity at the top of the secondary curricular structure. Keywords math, course-taking, race-ethnicity, segregation, social class DOI: 10.1177/0038040710375689

Teachers and families are encouraged to work together to ensure that mathematical experiences are relevant and meaningful, while encouraging strong connections between home and school. Good relationships between teachers and families also empower children to explore and build a mathematical understanding of the world.

A longitudinal approach was used to examine the effects of parental task-intrinsic and task-extrinsic motivational practices on academic intrinsic motivation in the subject areas of math and science. Parental task-intrinsic practices comprise encouragement of children's pleasure and engagement in the learning process, whereas task-extrinsic practices comprise parents' provision of external rewards and consequences contingent on children's task performance. A conditional latent curve model was fit to data from the Fullerton Longitudinal Study (A. W. Gottfried, A. E. Gottfried, & D. W. Guerin, 2006), with academic intrinsic motivation in math and science assessed from ages 9 to 17 and parental motivational practices measured when children were age 9. The results indicated that task-intrinsic practices were beneficial with regard to children's initial levels of motivation at age 9 as well as with regard to motivational decline through age 17. Conversely, parents' use of task-extrinsic practices was adverse with regard to children's motivation both at age 9 and across the 8-year interval. Theoretical implications of the findings with regard to academic intrinsic motivation are discussed. Keywords: parental motivational practices, latent curve modeling, developmental motivational decline, math intrinsic motivation, science intrinsic motivation

Recent mathematics assessment findings indicate that Native American students tend to score below students of the ethnic majority. Findings suggest that students' beliefs about mathematics are significantly related to achievement outcomes. This study examined relations between self-beliefs and mathematics achievement for a national sample of 130 Grade 8 Native American students from the Trends in International Mathematics and Science Study (TIMSS) 2003 United States sample of (M age=14.2 yr., SD=0.5). Multiple regression indicated several significant relations of mathematics beliefs with achievement and accounted for 26.7% of the variance in test scores. Students who earned high test scores tended to hold more positive beliefs about their ability to learn mathematics quickly, while students who earned low scores expressed negative beliefs about their ability to learn new mathematics topics.

Research in cognitive neuroscience suggests that the brains of mathematically gifted children are quantitatively and qualitatively different from those of average math ability. Math-gifted children exhibit signs of enhanced right-hemisphere development, and when engaged in the thinking process, tend to rely on mental imagery. They further manifest heightened inter-hemispheric exchange of information between the left and right sides of the brain, reflecting an unusual degree of neural connectivity. Consequently, educators should develop instructional techniques that capitalize on the special learning styles of math-gifted children. Such methods may include multimodal lecture presentations and other classroom activities that highlight the use of visual images. Creating specialized outreach programs in math/science to provide supplemental learning experiences not often supplied by understaffed and underresourced school systems may prove particularly valuable to the development of math-gifted children. Until such measures are commonplace, society's best young thinkers risk underachievement. Policy changes are needed to address the needs of math-gifted children and to enhance their developmental well-being., A selective review of the cognitive neuroscience literature (Butterworth, 1999; Dehaene, 1997) yields support for a neurobiological foundation to exceptional mathematical ability. One proposed brain characteristic of math giftedness is [...]

The high school boys' and girls' academic effort in the form of mathematics coursetaking is influenced by the cluster of students with whom they take courses or social contexts or local positions is examined. Findings indicate that girls are highly responsive to the social norms in their local positions.

This study examines the effect of a small-scale service-learning experience on college undergraduates. The example in this paper illustrates how shortterm service-learning can be implemented in an introductory-level nonmajor mathematics course for students who may have little or no previous mathematics education. [ABSTRACT FROM AUTHOR]

Abstract Teachers can draw on their care for students to promote more positive attitudes toward mathematics. Persistence in simultaneously caring for students and ideas holds generative possibility for challenging negative [...]

Ethnomathematics is the study of mathematical ideas and practices situated in their cultural context. Culturally Situated Design Tools (CSDTs) are web-based software applications that allow students to create simulations of cultural arts--Native American beadwork, African American cornrow hairstyles, urban graffiti, and so forth--using these underlying mathematical principles. This article is a review of the anthropological issues raised in the CSDT project: negotiating the representations of cultural knowledge during the design process with community members, negotiating pedagogical features with math teachers and their students, and reflecting on the software development itself as a cultural construction. The move from ethnomathematics to ethnocomputing results in an expressive computational medium that affords new opportunities to explore the relationships between youth identity and culture, the cultural construction of mathematics and computing, and the formation of cultural and technological hybridity. [Keywords: mathematics, computing, youth subculture, indigenous knowledge, identity]

In this study, we explored the possibility that when parents endorse particular academic gender stereotypes (e.g., boys are better at math, girls are better at English) they are more likely to engage in uninvited intrusions with homework, intrusions which then undermine children's confidence in these domains. Participants included 38 fifth to eighth grade students (mean age = 12.16 years, 60% girls, 87% White) and their mothers and fathers. The findings indicated that even though boys received more parental intrusive support with homework, girls were more sensitive to these intrusions, specifically when they involved math. Parents' intrusive support mediated the relationship between parents' math-related gender stereotypes and girls' math ability perceptions, which suggests that these behaviors communicate to girls their parents' math stereotype beliefs. KEY WORDS: gender stereotypes; parental intrusive support; math ability perceptions.

This longitudinal study tracked 1,110 adolescents identified as mathematically precocious at Age 13 (top 1%) with plans for a math-science undergraduate major. Participants' high school educational experiences, abilities, and interests predicted whether their attained undergraduate degrees were within math-science or nonmath-nonscience areas. More women than men eventually completed undergraduate degrees outside math-science, but many individuals who completed nonmath-nonscience degrees ultimately chose math-science occupations (and vice versa). At Age 33, the 2 degree groups reported commensurate and uniformly high levels of career satisfaction, success, and life satisfaction. Assessing individual differences is critical for modeling talent development and life satisfaction; it reveals that equal male-female representation across disciplines may not be as simple to accomplish as many policy discussions imply.

Copyright of Zona Próxima is the property of Fundacion Universidad del Norte and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Significant mathematical developments throughout history have often been linked with social, economic or political developments. Mathematics teachers can play a part in making students aware of the way in which mathematics has been a product of cultural influences.

African-American educator and civil rights leader Robert P. Moses discusses the need for minority and poor children to learn algebra. Because of low expectations, minority children have not been encouraged to take algebra and lack of algebra training keeps them from taking higher mathematics and entering high technology industries.

Issues discussed concern the life and work of mathematician Grace Chisholm Young in England at the beginning of the 20th century, focusing on the social aspects of women's education at that time. Topics addressed include women in higher education, gender roles, and how women achieved in mathematics because of the discipline's strict formality.

In mathematics education, there is a continuing debate about the nature of mathematics, which some claim to be an objective science, whereas others note its socially and individually constructed nature. From a strict cultural-historical perspective, the objective and subjective sides of mathematics are but manifestations of a higher-order phenomenon that may be summarized by the aphorism that mind is in society to the extent that society is in the mind. In this study, we show, drawing on exemplifying materials from a second-grade unit on three-dimensional geometry, how mathematics manifests itself both as objective science all the while being subjectively produced. A particular three-turn interactional sequence comes to play a central role. We conclude by re-assigning a positive role to a much-maligned sequentially ordered conversational routine. [ABSTRACT FROM AUTHOR]

This paper presents data on the mathematical content knowledge and attitudes of pre-service primary teacher education students. The assessment consisted of nine tasks, including 2-digit computations and proportional reasoning. Students rated their liking for mathematics at three time points: primary, secondary, .and when assessed. Fewer than half the students liked mathematics, currently. Those with positive attitudes tended to perform well on mathematics tasks, but some low scorers were positive and some high' scorers were negative about mathematics. Most students used algorithmic procedures to solve problems and several consistent misconceptions were identified. Performance was noticeably poor on adding common fractions and converting fractions to percentages using knowledge of common factors. The implications of these findings for Initial Teacher Education (ITE) providers are presented. [ABSTRACT FROM AUTHOR]

The limited mathematical knowledge of preservice primary teachers is an international concern. The areas of mathematical difficulties have been well documented, which has led to many universities instituting testing regimes to ensure that preservice teachers have appropriate knowledge of primary school mathematics. In our study, the preservice teachers identify some benefits for being tested, but these were often related to having sufficient knowledge so that they did not lose face in front of students. We suggest that this emphasis on performance could exacerbate preservice teachers' reliance on procedural rather than conceptual understanding. Thus, there needs to be consideration of the type of testing that is instituted so that it connects to preservice teachers' professional identities as teachers. [ABSTRACT FROM AUTHOR]

The article presents the principles on how to maximize mathematics moments with preschool children to deepen their mathematical understandings. It says that math naturally happens in early childhood classrooms, in which it is accessible to children's success level. It mentions the record sheets use by teachers which is constructed in formats such as the children's lists in the group and a separate sheet for each child. Moreover, the math-themed picture books which promote literacy are discussed.

Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These two aspects make mathematics a motivating activity. Unfortunately, the subject that students often encounter in school mathematics classes does not resemble authentic mathematical activity. School mathematics is characterized by the memorization and regurgitation of rote procedures in isolation from peers. It comes as no surprise that many students have little motivation to continue mathematics study because it lacks intellectual and social appeal. I suggest several practical changes in school mathematics instruction that are drawn from the literature. These changes will lead to instruction that more readily engages students with the subject because they are rooted in the intellectually and socially appealing aspects of mathematics. [ABSTRACT FROM AUTHOR]

By comparing the problems concerning area calculation among several mathematics book with each other and analyzing the land policies in the Mid-Ancient Period, this article points out that the Wucao Suanjing seeks extensiveness more than accuracy in the methods of area calculation, and this characteristic is closely related to the Equal Field System (Juntian System), which made the fields to be frequently measured and frequently divided into smaller ones as well. These methods became more exact and classified in such subsequent mathematical books as Dunhuang Suanjing and Xiahou Yang Suanjing. When the latter book was compiled, the Equal Field System had declined. The article indicates that social elements can influence not only the objects dealt with mathematics, but also influence the expression of the mathematical texts. [ABSTRACT FROM AUTHOR]

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a 'web of authority' ever present in mathematics classrooms. In past work, it has been shown how those relations of authority may sometimes interfere with students' reflecting on mathematical ideas. However, "…by shifting the emphasis from domination and obedience to negotiation and consent…" (Amit & Fried, 2005, p.164) it has also been stressed that these relations are fluid and are, in fact, a sine qua non in the process of students' defining their place in a mathematical community. But can these fluid relations be operative also in the formation of specific mathematical ideas? It is my contention that they may at least coincide with students' thinking about one significant mathematical idea, namely, the idea of proof. In this talk, I shall discuss both the general question of authority in the mathematics classroom and its specific connection with students' thinking about proof in the context of work done in two 8th grade classrooms. [ABSTRACT FROM AUTHOR]

The article explores the content, social uses and functions of mathematical text from a semiotic perspective. The author also investigate the reading and listening as well as writing and speaking dimensions of written and spoken mathematical texts as well as texts presented multi-modally. He also explores one of the most important dimensions of written mathematical text in use, which is its social context.

Mathematical principles behind certain card tricks are described. Tricks include taking cards out of a deck, replacing them, and later identifying the replaced cards using such principles as invariant pairs.

Through an analysis of gains in mathematics achievement between the tenth and twelfth grades for respondents to the National Education Longitudinal Study of 1988, we examine Coleman's explanation for why Catholic schools apparently produce more learning than public schools. According to Coleman, Catholic schools benefit from larger endowments of social capital, generated in part through greater intergenerational social closure (i.e., dense network connections between the parents of students). Instead, we find that for public schools, social closure among parents is negatively associated with achievement gains in mathematics, net of friendship density among students. This evidence of a negative effect of parental social closure within the public school sector lends support to our alternative hypothesis that horizon-expanding schools foster more learning than do norm-enforcing schools. Moreover, this result renders social closure incapable of explaining any portion of the Catholic school effect on learning, even though within the Catholic school sector there is some evidence that social closure is positively associated with learning.

Copyright of Mathématiques & Sciences Humaines is the property of Editions du CNRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Mathématiques & Sciences Humaines is the property of Editions du CNRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Connecticut Valley comprises two mathematical communities, one being the research sector and the other being high-school and middle-school teachers. Research mathematics remains a Valley industry despite the fact that the University of Massachusetts is the only one of five colleges that grants doctoral degrees. The second community is also lively with its own professional association, MathWest.

The cultures here in question are those of mathematics and of physics that I shall interpret with the goal of exploring different modes of creativity. As case studies I will [...]

Mathematics is rarely discussed as a component of the rise of civilization. On the contrary, mathematics has a significant influence in the general human condition, a fact that can be gleaned from the philosophies of Plato, Leibnitz and Spinoza. One aspect of mathematics that has received little or no notice at all is its relation to the crucial concept of evolution. Mathematics is also the only secular human activity that involves an element of the infinite.

In this ethnographic account of mathematical activity among the Juruna, Kayabi, and Suya of central Brazil, I show how arithmetic practices are fashioned in a specific social setting. Values and symbolic properties of both the gift exchange and capitalist economics structure arithmetic dilemmas in the Xingu Indian Park. Within a broad social field that transcends the boundaries of the park to include prospecting sites and cattle ranches, economic calculations are extended to all kinds of goods, both material and symbolic. The distribution and circulation of these different forms of capital are discussed in view of the constitution of particular arenas of exchange. Practice theories highlight the ways in which mathematical knowledge is constituted in everyday activities, challenging functional assumptions about cognition and schooling. By articulating principles of the gift with those of capitalist exchange, mathematics is construed by the Juruna, Kayabi, and Suya as a product of social work and symbolic fashioning. [mathematics, gift exchange, practice theories, cognition and schooling, Kayabi, Juruna, Suya, Xingu Indian Park]

In the article, the author discusses the role of mathematics education researchers in helping the society to evolve by provoking their thinking ability and inspiring them to understand mathematics teaching and learning practices.

Game theory served as a leading force to develop mathematics in the social sciences of the 1950s. Intellectual trends or research fronts combined with the research front of game theory between 1945 and the 1960s. One front was Kurt Lewin's team research and social experimentation school. Another front was the latent structure school of Paul Lazarsfeld and also the Bureau of Applied Social Research.