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Descriptors:
Learning Disabilities; State Standards; Mathematics Skills; Mathematics Instruction; Elementary Secondary Education; Academic Standards; Mathematics Tests; Outcomes of Education; Mathematics Teachers; Evidence; Intervention; Basic Skills; Elementary School Teachers; Secondary School Teachers; Elementary School Students; Secondary School Students

Abstract:
The Common Core State Standards provide teachers with a framework of necessary mathematics skills across grades K-12, which vary considerably from previous mathematics standards. In this article, we discuss concerns about the implications of the Common Core for students with mathematics difficulties (MD), given that students with MD, by definition, struggle with mathematical skills. We suggest that instruction centered on the Common Core will be challenging and may lead to problematic outcomes for this population. We propose that working on foundational skills related to the Common Core standards is a necessary component of mathematics instruction for students with MD, and we provide teachers with a framework for working on foundational skills concurrent with the Common Core standards. We caution, however, that implementation of the Common Core is in its infancy, and the implications of the Common Core for students with MD need to be monitored carefully. (Contains 1 table and 3 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Student Characteristics; Racial Factors; Ethnicity; Stereotypes; White Students; Racial Differences; Grade 10; African American Students; Hispanic American Students; High School Students; Asian American Students; Surveys; Teacher Attitudes; Student Attitudes; Parent Attitudes; Student Behavior; English Teachers; Mathematics Teachers

Abstract:
Previous research demonstrates that students taught by teachers of the same race and ethnicity receive more positive behavioral evaluations than students taught by teachers of a different race/ethnicity. Many researchers view these findings as evidence that teachers, mainly white teachers, are racially biased due to preferences stemming from racial stereotypes that depict some groups as more academically oriented than others. Most of this research has been based on comparisons of only black and white students and teachers and does not directly test if other nonwhite students fare better when taught by nonwhite teachers. Analyses of Asian, black, Hispanic, and white 10th graders in the 2002 Education Longitudinal Study confirm that the effects of mismatch often depend on the racial/ethnic statuses of both the teacher and the student, controlling for a variety of school and student characteristics. Among students with white teachers, Asian students are usually viewed more positively than white students, while black students are perceived more negatively. White teachers' perceptions of Hispanic students do not typically differ from those of white students. Postestimation comparisons of slopes indicate that Asian students benefit (perceptionwise) from having white teachers, but they reveal surprisingly few instances when black students would benefit (again, perceptionwise) from having more nonwhite teachers. (Contains 4 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:
Standard Setting (Scoring); Cognitive Processes; Mathematics Tests; Language Tests; English (Second Language); Second Language Learning; English Teachers; Mathematics Teachers; Grade 5; Cutting Scores; Influences; Feedback (Response); Developing Nations; Foreign Countries

Abstract:
Considerable research about standard setting has revolved around a U.S.-centric policy context. That is, over the past decade, conclusions about thought processes and the interaction of education policy and panelists' judgments have been based on assumptions of comparable policy settings. However, whether these assumptions generalize to other education contexts is to some extent unknown. This study addresses what standard setting panelists in a developing nation think about when making item performance estimates for students in various performance categories. Panelists were asked to respond to a set of questions at various stages of the standard setting workshop. The results suggested that panelists gained experience about standard setting procedure, understanding descriptions of the performance level categories, and making more consistent decisions on the test items. Most of the panelists were not influenced by the item p-value and impact data while making Round 2 ratings. However, the panelists did mention that the feedback data helped them to understand better the four performance level categories and provided a reality check of their Round 1 item performance estimates. Salient factors for panelists in this study are compared with findings from other research in the area. (Contains 8 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:
Foreign Countries; Elementary School Mathematics; Grade 1; Grade 4; Grade 7; Capacity Building; Program Descriptions; Culturally Relevant Education; Units of Study; Teacher Education; Graduate Study; Curriculum Development; Teacher Role; Elementary School Teachers; Mathematics Curriculum; Mathematics Instruction; Mathematics Teachers; Pacific Islanders

Abstract:
The first goal of this Project is the development of elementary school mathematics curricula sensitive to indigenous mathematical thought and experience. A necessary prerequisite for the achievement of this goal is to recapture and honor the mathematics developed and practiced in the Micronesian communities. This is the Project's second goal. The third goal of the project is to build local capacity by offering advanced degree opportunities to the indigenous mathematics educators who transform what they find in their local cultural practices into grades 1, 4, and 7 mathematics curriculum units. 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:
Epistemology; Mathematics Education; Dialects; Mathematics Teachers; Culturally Relevant Education; Foreign Countries; Ideology; Knowledge Level; Philosophy

Abstract:
The problem of culturally decontextualised mathematics education faced by Nepali students, teachers and teacher educators has often been oriented by the view of the nature of "mathematics as a body of pure knowledge," which gives rise to an exclusive emphasis on an ideology of singularity, epistemology of objectivism, language of universality and logic of certainty whilst developing curriculum, conceiving pedagogies and implementing assessment strategies in school mathematics education and mathematics teacher education programmes. With epistemic referents of dialectical logics and performative imagination, an alternative view of the nature of "mathematics as an impure knowledge" is discussed with its possible disempowering features, such as essentialism, hegemony and dualisms. Finally, an inclusive view of the nature of "mathematics as im/pure knowledge system" is articulated with the help of various forms of dialectics. 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:
Individualized Instruction; Private Schools; Grade 11; Mathematics Instruction; Secondary School Mathematics; Mathematical Concepts; Mathematical Aptitude; Equations (Mathematics); Mathematics Teachers; Instructional Materials; Teaching Methods; Peer Teaching

Abstract:
Teachers of mathematics recognize the difficulty of reaching every student when the range of student abilities puts a considerable strain on the classroom discussion and time. In a response to the problem, students are grouped so that those with greater mathematical aptitude help those who have difficulties. While this approach is to be appreciated, it tends to mean that the more able students have less opportunity to explore further their own initiatives in mathematics, while those who have more difficulties find themselves on the receiving end with little opportunity to be in the role of enriching the mathematics experience for everyone, including themselves. A "multiple-centres" approach is designed to overcome these problems. In this variation of differentiated instruction, all students get the chance to engage the material from a vantage point and at a level they find interesting and challenging as a consequence of their selecting extensions of the teacher's initial focus problem. This article will present some findings of 11th year (roughly Fifth Form) average mathematics students at a US Independent School in transforming the standard quadratic equation to represent fountain parabolic trajectories, which was the teacher's focus problem, along with some multiple-centre investigations they chose. A further set of opportunities with commentaries providing additional centres for student inquiry are included. 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:
Foreign Countries; Mathematics Curriculum; Online Surveys; Teacher Surveys; Questionnaires; Interviews; Mathematics Instruction; Mathematics Teachers; Curriculum Design; Curriculum Development; Teacher Attitudes; Secondary School Mathematics

Abstract:
One-third of the current A-level mathematics curriculum is determined by choice, constructed out of "applied mathematics" modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant impact on students' post-compulsory study of mathematics, it is not well understood how this choice is navigated. This article explores how mathematics teachers perceive each of these three areas of applied mathematics, how widely each of the modules is offered and in what ways perception might be connected to provision. Data from an online questionnaire and follow-up interviews demonstrate that teachers are influenced by a wide range of factors, including strategic concerns and views on the relative worth of each strand. The results also highlight the presence of inertia in centres' provision. In this way, this article offers some insight into current perception and provision of applied mathematics in England, and speaks to contemporary debates about curriculum content and reform. It argues that students' exposure to the powerful utility of mathematics is often unhelpfully steered or limited at a critical point in their education. 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:
Problem Solving; Mathematics Instruction; Teacher Characteristics; Preservice Teacher Education; Preservice Teachers; Mathematics Teachers; Teacher Attitudes; Difficulty Level; Reflection; Discussion (Teaching Technique); Interviews; Professional Development; Instructional Effectiveness

Abstract:
The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions associated with systematic employment of multiple-solution tasks (MSTs) in a "problem-solving" course for prospective mathematics teachers (PMTs). Our attention to teachers' mathematical conceptions focused on the development of PMTs' problem-solving competences. Our attention to teachers' meta-mathematical and pedagogical conceptions focused on changes in teachers' views concerning the level of interest and level of difficulty of the mathematical tasks. We differentiated between the systematic and craft modes of professional development integrated in the course. Systematic mode involved problem-solving sessions and reflective discussions on collective solution spaces. Craft mode involved interviewing school students. The study demonstrates the effectiveness of MSTs for PMTs' professional development. 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:
Secondary School Teachers; Mathematics Teachers; Teacher Characteristics; Learning; Change; Mathematics Instruction; Teacher Workshops; Faculty Development; Pretests Posttests; Mixed Methods Research

Abstract:
This investigation describes secondary mathematics teachers' learning and instructional change following their participation in a professional development workshop, the Enhancing Secondary Mathematics Teacher Preparation Project (ESP) (2004-2005), specifically focused on the selection and implementation of cognitively challenging mathematical tasks. Data consist of a pre/post-assessment of teachers' knowledge of the cognitive demands of mathematical tasks and videotaped discussions and written artifacts from the professional development sessions. A mixed methods approach was used to identify connections between teachers' learning and their experiences in the ESP workshop. Results indicate that ESP teachers developed new ideas about the influence of mathematical tasks on students' learning. Increases in teachers' knowledge of the cognitive demands of mathematical tasks were closely linked to ideas represented in frameworks and discussions from the ESP workshop and to teachers' experiences in solving challenging mathematical tasks as learners. 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:
Video Technology; Probability; Mathematics Instruction; Statistics; Mathematics; Mathematics Education; Elementary Education; Mathematics Teachers; Middle School Teachers; Elementary School Mathematics; Elementary School Teachers

Abstract:
The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses within a collaborative course design were used to support a teaching experiment about teachers' conceptions of random processes. In particular, teachers were asked whether the outcomes of "Rock-Paper-Scissors" (RPS) are generated randomly or not, were presented with a definition for random selection, and were asked to come to a conclusion about RPS. Teachers struggled to reconcile the equality of winning outcomes for each player with the potential for human interference in the process of generating outcomes. Ultimately, teachers concluded the outcomes were not generated randomly, but encountered a variety of unexpected obstacles along the way. (Contains 2 figures and 3 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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