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Descriptors:
Foreign Countries; Indigenous Populations; Educational Change; Rural Areas; Geographic Isolation; Culturally Relevant Education; Program Implementation; Program Effectiveness; Scaffolding (Teaching Technique); Educational Strategies; Mathematics Instruction

Abstract:
This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Foreign Countries; Gender Discrimination; Gender Bias; Gender Differences; Social Class; Social Differences; Ethnicity; Ideology; Differences; Barriers; Mathematics Achievement; Science Achievement; Student Participation; Pattern Recognition

Abstract:
An examination of gender, social class and ethnicity performance and participation patterns in different UK countries shows that inequities occur in relation to gender, class and ethnicity but that the patterns of inequity look quite different in the three domains. Achievement is equal for different genders but many more males take mathematics forward to advanced levels; social class differences persist in both achievement and participation; and ethnicity shows a varied pattern with some groups performing and participating at particularly high levels and some particularly low. This paper identifies some critical issues that we face in making mathematics and science equitable and begins to analyse some of the barriers that stand in the way of students who are female, and from some ethnic and social groups. (Contains 1 note, 7 figures and 7 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
High Schools; Heterogeneous Grouping; Educational Change; Teaching Methods; Track System (Education); Mathematics Instruction; Longitudinal Studies; Achievement Gains; Achievement Gap; Urban Schools; Case Studies; Educational Innovation; Instructional Effectiveness; Student Attitudes; Outcomes of Education; Rural Schools; Mathematics Achievement

Abstract:
Background/Context: School tracking practices have been documented repeatedly as having negative effects on students' identity development and attainment, particularly for those students placed in lower tracks. Despite this documentation, tracking persists as a normative practice in American high schools, perhaps in part because we have few models of how departments and teachers can successfully organize instruction in heterogeneous, high school mathematics classes. This paper offers one such model through a qualitative and quantitative analysis. Focus of Study: In an effort to better the field's understanding of equitable and successful teaching, we conducted a longitudinal study of three high schools. At one school, Railside, students demonstrated greater gains in achievement than students at the other two schools and higher overall achievement on a number of measures. Furthermore, achievement gaps among various ethnic groups at Railside that were present on incoming assessments disappeared in nearly all cases by the end of the second year. This paper provides an analysis of Railside's success and identifies factors that contributed to this success. Participants: Participants included approximately 700 students as they progressed through three California high schools. Railside was an urban high school with an ethnically, linguistically, and economically diverse student body. Greendale was situated in a coastal community with a more homogeneous, primarily White student body. Hilltop was a rural high school with primarily White and Latino/a students. Research Design: This longitudinal, multiple case study employed mixed methods. Three schools were chosen to offer a range of curricular programs and varied student populations. Student achievement and attitudinal data were evaluated using statistical techniques, whereas teacher and student practices were documented using qualitative analytic techniques such as coding. Findings/Results: One of the findings of the study was the success of Railside school, where the mathematics department taught heterogeneous classes using a reform-oriented approach. Compared with the other two schools in the study, Railside students learned more, enjoyed mathematics more and progressed to higher mathematics levels. This paper presents large-scale evidence of these important achievements and provides detailed analyses of the ways that the Railside teachers brought them about, with a focus on the teaching and learning interactions within the classrooms. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
High Schools; Mathematics Achievement; High Achievement; Teaching Methods; Equal Education; Urban Schools; Cultural Awareness; Cultural Differences; Student Behavior; Social Class; Academic Ability; Gender Differences; High School Students

Abstract:
Equity is a concept that is often measured in terms of test scores, with educators looking for equal test scores among students of different cultural groups, social classes or sexes. In this article the term "relational equity" is proposed to describe equitable relations in classrooms; relations that include students treating each other with respect and responsibility. This concept will be illustrated through the results of a four-year study of different mathematics teaching approaches, conducted in three Californian high schools. In one of the schools--a diverse, urban high school--students achieved at higher levels, learned good behaviour, and learned to respect students from different cultural groups, social classes, ability levels and sexes. In addition, differences in attainment between different cultural groups were eliminated in some cases and reduced in all others. Importantly, the goals of high achievement and equity were achieved in tandem through a mixed-ability mathematics approach that is not used or well known in the UK. (Contains 2 tables.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Global Approach; Teaching Methods; Urban Schools; Suburban Schools; Graduate Students; Mathematics Instruction; Advanced Courses; Classroom Observation Techniques; Questionnaires; Interviews; Block Scheduling; Heterogeneous Grouping; Student Responsibility; Departments; Educational Cooperation

Abstract:
The poor performance of students in America's urban high schools, both in absolute terms and in comparison with their more economically secure counterparts in suburban schools, is a critical issue for the country, and the opportunity for all students to learn mathematics has been heralded as the new "civil right." In a recent study of mathematics teaching in different schools, the author and a group of graduate students at Stanford found that students at Railside High School (a pseudonym), an urban school in California nestled within a few feet of the train tracks, performed better in mathematics than students at other schools and that differences in achievement among Railside students of different cultural groups were reduced in all cases and eliminated in some. Railside was one of three schools in which they spent four years following cohorts of students from their freshman to their senior years as they experienced different approaches to mathematics instruction. As part of the study, they documented the teaching practices of the Railside mathematics department--practices focused upon equity. In this article, the author considers some of the most important aspects of Railside's reform-oriented approach to mathematics instruction--an approach that transformed students' lives by helping them to see mathematics as a part of their future and by providing them with the quantitative reasoning capabilities needed to function in an increasingly technological and global economy. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
High School Students; Student Diversity; Urban Schools; Mathematics Achievement; Mathematics Teachers; Peer Relationship; Academic Achievement; Curriculum Design; Teaching Methods; Longitudinal Studies; Mathematics Instruction; Suburban Schools; Comparative Analysis; Age Differences; Teacher Collaboration; Equal Education; Grouping (Instructional Purposes); Cooperative Learning; Problem Solving; Interpersonal Relationship; Heterogeneous Grouping

Abstract:
In a four-year, longitudinal study conducted between 2000 and 2004, the author followed 700 students as they progressed through three high schools: a diverse, urban school as well as two suburban schools. Although incoming freshmen at the urban school scored significantly lower in mathematics than incoming students at the two suburban schools, by senior year, 41 percent of the urban school's students were taking calculus, compared with approximately 27 percent of students in the other two schools. The urban school's approach encouraged both relational equity and high achievement. Important dimensions of the mathematics teachers' work included working collaboratively to design curriculums and teaching methods, a shared commitment to equity, heterogeneous classes, and a teaching approach in which students worked on complex conceptual problems in groups. These positive and respectful intellectual relations--which the author refers to as "relational equity"--depended on students' committing to the learning of others, respecting the ideas of others, and learning to communicate. (Contains 1 figure.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Urban Schools; Student Diversity; High Achievement; Mathematics Achievement; Mathematics Instruction; Heterogeneous Grouping; Equal Education; Responsibility; Teaching Methods; Track System (Education); Outcomes of Education

Abstract:
This article describes the ways in which the mathematics department of an urban, ethnically diverse school brought about high and equitable mathematics achievement. The teachers employed heterogeneous grouping and complex instruction, an approach designed to counter status differences in classrooms. As part of this approach teachers encouraged multidimensional classrooms, valued the perspectives of different students, and encouraged students to be responsible for each other. The work of students and teachers at Railside School was equitable partly because students achieved more equitable outcomes on tests, but also because students learned to act in more equitable ways in their classrooms. Students learned to appreciate the contributions of students from different cultural groups, genders, and attainment levels, a behavior termed relational equity. This article describes the teaching practices that enabled the department to bring about such important achievements. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Social Class; Ability Grouping; Educational Practices; Social Bias; High Achievement; Equal Education; Educational Practices

Abstract:
In stark contrast to the recommendations of the current White Paper, Jo Boaler's recent research suggests that the radical progressive state school commitment to mixed ability teaching has, in the case of this landmark study, led to better results and better life-chances than its more traditional counterpart whose ability grouping practices created, in the words of one ex-pupil, "psychological prisons" that "break ambition" and "almost formally label kids as stupid." If ability grouping reproduces social class inequalities, any political party that really cares about social justice must look again at the norms of ability segregation that blights so much of contemporary practice. In their stead, we need equitable and effective grouping polices that promote high achievement for all. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Mathematics Education; Mathematics Instruction; Teaching Methods; Intermode Differences; Educational Practices; Classroom Environment; Classroom Techniques; Educational Research; Theory Practice Relationship; Teaching Models; Instructional Effectiveness; Protocol Analysis

Abstract:
In this paper I will explore three contrasting teaching and learning environments, including one in which students engage in a "dance of agency". I will move from a consideration of classroom practices to a contention that our work as researchers of mathematics education should pay more attention to teaching practices. Further, that understanding and capturing teaching practices will help researchers to cross traditional and elusive divides between research and practice. (Contains 4 footnotes.) [For complete proceedings, see ED500857.] Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Low Income; Mathematics Achievement; Mathematics Instruction; Mathematics Tests; Secondary Education

Abstract:
Describes features of excellent mathematics department in California high school serving multiethnic, low-income students. Explores reasons why these low-income students outperform students from wealthier school districts on independently designed mathematics tests, but have significantly lower SAT-9 mathematics scores than students in other high schools. (PKP)

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