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Ability grouping is a common practice in elementary mathematics instruction, but some research suggests that grouping by ability can exacerbate existing inequities, and there is evidence that alternatives to grouping can improve learning experiences for all students. In this paper, we describe an effort to support teachers in using equitable teaching practices that was part of an Elementary Mathematics Specialist (EMS) certification program at a public university in the United States. We employ multiple perspectives in our collaborative action research approach: the first author was the director of the EMS program, the second author was a graduate researcher working to support the program, and the third, fourth, fifth, and sixth authors were all teachers in the program. We start by introducing efforts to address equity from the perspective of program designers, including specific activities used during a Summer Institute to prompt consideration of alternatives to ability grouping. Then we share several experiences of reducing ability grouping from the perspectives of four teachers who were participants in the program, noting successes and challenges. We conclude with implications for research and practice. [ABSTRACT FROM AUTHOR]

Within-class ability grouping (WCAG) is widely used in elementary mathematics instruction in the United States, yet it has drawn criticism on the grounds that it can inequitably limit the learning opportunities of some students, not least because of its connection to between-class ability grouping (BCAG) that is more common in middle or secondary schooling. Meanwhile, some high achieving countries use relatively little ability grouping in elementary school in comparison to the United States. In this paper, we draw on qualitative data from a series of assignments in four sections of an elementary mathematics methods course in the beginning teacher education programme at a United States university. These assignments were designed to explore the potential of using preservice teachers' (PSTs') memories of and experiences with ability grouping in their own schooling to support critical reflection about the possible negative consequences of within-class ability grouping practices. We found that while many PSTs reported negative personal experiences with ability grouping in mathematics, they often remained uncritical when reflecting on the use of ability grouping in the elementary classes they visited as part of their teacher education programme. [ABSTRACT FROM AUTHOR]

This paper presents a Takagi-Sugeno fuzzy model-based approach to modeling, controlling, and stabilizing an aircraft in both normal and damaged conditions. The major contributions of this paper are as follows. First, it introduces the Takagi-Sugeno modeling and the parallel distributed compensation control approach. Then, it demonstrates how the approach can be applied to aircraft in a systematic manner. Finally, the approach is applied to the modified NASA F-15 number 837 nonlinear model, and preliminary simulation results are presented. The benefits of using a Takagi-Sugeno model-based parallel distributed compensation control approach include a systematic controller design procedure, mathematical proof of stability for classes of failures, and intuitive insight into damage effects on an aircraft. This work is the first to present this control approach as applied to aircraft. [ABSTRACT FROM AUTHOR]

Problem Statement: The acquisition of certain mathematical skills is part of many curricula around the world. These skills involve problem-solving, effective use of mathematics in daily life, thinking logically and systematically, taking risks and making decisions. The US National Council of Teachers of Mathematics ([NCTM], 1991) relates these skills to mathematical power. Knowledge construction and abstraction might have an impact on mathematical power. In this paper, the primary concern is with the construction of new knowledge structures rather than with consolidation or abstraction for that matter. Recognizing, Building-with, and Constructing (RBC hereafter) theory of abstraction provides a particularly useful framework in achieving a detailed examination of the new mathematical constructions through epistemic actions. Therefore, this paper, with reference to the RBC epistemic actions, examines the knowledge construction process of students with different mathematical power. Purpose of Study: The purpose of the study is to explain the similarities and differences between the knowledge construction processes of 6th grade students with different mathematical power. Methods: A case study was used as the main research approach. The mathematical power scale was applied to 282 students. The case study was conducted with four students who were chosen purposefully among them. The RBC theory of abstraction was used as an analytical tool. The patterns noticed in the case study were determined and interpreted. Findings and Results: According to findings, it was seen that the students with low mathematical power, whose knowledge constructing processes were examined, could recognize structures while they could not building with and constructing. When observing that the students with low mathematical power have low communication, connection and reasoning skills, in general, it can be said that for building-with and constructing, it is important to have these three skills. The students who reflected themselves and used the feedback to continue had high mathematical power. They also were able to construct mathematical knowledge more quickly. Conclusions and Recommendations: The RBC theory of abstraction can be useful in explaining the relationship between the components of mathematical power and other mental activities. For this purpose, the usage of the RBC theory of abstraction in the mathematical knowledge construction process in the classroom can be proposed as a new study. [ABSTRACT FROM AUTHOR]

Cyberinfrastructure has become a major defining force for America, because of its economic, social, and national importance. Over the last two decades, scientists within all sectors of Science, Technology, Engineering and Mathematics (STEM) have witnessed an explosive rise of cyberinfrastructure as a research tool; universities are utilizing this infrastructure and its applications as an integral part of scientific education. The Arkansas Minority Cyberinfrastructure Training, Education Consortium (AMCTEC), is a unique interdisciplinary cyberinfrastructure (CI) educational community within Arkansas to educate a majority minority student population, and faculty in cyberinfrastructure- oriented concepts, theories, practices, and principles within STEM at teaching-oriented Historically Black Colleges and Universities (HBCUs). The project focuses on developing the capacity of these institutions within three core areas as they relate to cyberinfrastructure elearning resources, (1) institutional faculty development (2) tangible cyber-based student activities (3) CI curriculum enhancement. This paper presents some of the strategies that have been successfully deployed by the universities involved in the project to institutionalize a renaissance in STEM education, e-learning at student-focused universities, through the sharing of resources and expertise to transform STEM education and research by injecting in cyberinfrastructure resources. [ABSTRACT FROM AUTHOR]

After two decades of work, many in the SoTL community are pondering the future of the SoTL movement. Will it sustain its influence? Will it continue to attract new participants? What role should the disciplines play? From the perspective of mathematics, this paper examines efforts by the Carnegie Academy and individuals within the mathematical community to build disciplinary support for the scholarship of teaching and learning. The authors, both mathematicians and Carnegie scholars, restrict their observations to the efforts undertaken in the United States during the last decade and examine the situation in mathematics in greater depth than has heretofore appeared. They shed light on particular complications they have observed for SoTL in their discipline and offer suggestions for improving the situation within mathematics. Practitioners in other disciplines, or those involved with SoTL at a "meta-level" may find their observations applicable in other venues. [ABSTRACT FROM AUTHOR]

This study presents the findings of a qualitative investigation about four elementary preservice teachers' experiences learning to teach social studies in the No Child Left Behind era. The participants' internship took place in an elementary school which devoted the majority of the day to literacy and mathematics instruction. Because previous interns in the school had limited or no opportunity to teach social studies, the four participants were required to complete an Interdisciplinary Teaching Assignment to ensure that they were able to teach and reflect upon teaching social studies at least one time during the semester. Findings indicated the interns found the experience meaningful and rewarding because of their students' enthusiasm toward the content and instructional approaches. After meeting the requirements of the assignment, the participants found ways to borrow time from the hours dedicated to literacy and mathematics instruction in order to address social studies topics and themes. The paper concludes with a discussion of teacher educators' roles in preserving social studies education in American. [ABSTRACT FROM AUTHOR]

The article focuses on the Flatland project of geometry students in the U.S. Accordingly, Flatland is a mathematical novel written in the 1800s by Edwin A. Abbott. It offers a story of a two dimensional world where women are straight lines, and men are polygons with various numbers of sides depending on their social status. In the novel women are really line segments, not lines. However, this mathematical precision was ignored on the novel. Moreover, the paper quoted some of the initial paragraphs of the novel, and examines the ideas that the student groups develop as they share their ideas about the novel.

The ability to integrate technology into instruction is among the characteristics of a competent mathematics teacher. Research indicates that the vast majority of teachers in Turkey believe the use of computers in education is important, but have limited knowledge and experience on how to use technology in their instruction. This paper describes the T-Math project (http://www.t-math.org), which adapted the InterMath (http://intermath.coe.uga.edu) knowledge base for mathematics teachers in the United States and developed relevant resources for professional development of Turkish mathematics teachers to guide them in constructing useful strategies for their students while developing as expert mathematics teachers. Examples of mathematical investigations adopted and developed in the T-Math project arc presented as well as the anticipated challenges and subsequent strategies for integration. [ABSTRACT FROM AUTHOR]

A survey of centers in the United States that are engaged in engineering, science or mathematics education was conducted to help understand current practices. The survey addressed sources of funding, types of pre-college outreach activities, activities related to improvement of teaching in higher education, and methods of promoting collaboration between faculty. Also collected were recommendations, based on the experience of the survey respondent, which would help others develop a successful center. Response to the study was high, with 173 of 271 returned. This paper discusses the results and suggests a set of best practices for engineering education centers. [ABSTRACT FROM AUTHOR]

A critical issue related to the use of simulation environments in school-based learning is the relationship between the use of these environments and the structure of traditional curricula. Teachers are often caught in the bind of attempting to address significantly raised standards for what all students should know, yet receiving very little support to innovate in their use of simulations in their approaches to teaching. Particularly challenging for practitioners and school-based re- searchers alike is the expectation that students should first master "the basics" before engaging innovation related to learning advanced content such as calculus. This paper summarizes years of work related to the early learning of the mathematics of change. The goal is to resolve this tension by suggesting that advanced mathematics, embodied in an accessible simulation environment, helps situate and deepen students' understanding of the basics as they typically are encountered in the traditional mathematics curriculum. Selected episodes transcribed from work in economically challenged schools in the United States are used to illustrate the practical potential of this reconsideration of the relationships between basic and advanced topics. The delta-blocks approach to the mathematics of change, making use of widely available forms of technology and the Math Worlds simulation software, is introduced and illustrated. [ABSTRACT FROM AUTHOR]