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The article analyzes the conversations of four middle school students in the U.S. It states that the conversation of these students will allow mathematics teachers to analyze common conceptions and misconceptions about students' algebraic thinking to provide insight into instructional decisions. It will also help teachers think on how small groups of students collectively discuss, debate, and apply strategies as they attempt to formulate generalizations and solutions for a given algebra problem.

Research on modelprocedure selection has focused on selecting a single model globally. In many applications, especially for high-dimensional or complex data, however, the relative performance of the candidate procedures typically depends on the location, and the globally best procedure can often be improved when selection of a model is allowed to depend on location. We consider localized model selection methods and derive their theoretical properties.This research was supported by U.S. National Science Foundation CAREER Grant DMS0094323. We thank three referees and the editors for helpful comments on improving the paper. [ABSTRACT FROM AUTHOR]

The article presents ten problems that are characteristic of the type of problems that are commonly encountered in experimental mathematics in the United States. Each of the ten problems presents the challenge of obtaining a high precision numeric evaluation of the quantity and if possible, to obtain a symbolic answer that is ideally with proof. The authors provides the solutions to these mathematical problems and presents a concise account of the use of hybrid computation, which combines numeric and symbolic computation, in the mathematical discovery process.

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]

The article presents a solution from the middle school students in the U.S. to the mathematical problem on how to divide an 8x8 inches cake into four pieces with different shapes equally. The students had successfully determined that the top area of each piece of cake had to be 16 inches and that using regular polygons would not be helpful to the task at hand. This problem gave them an opportunity to think about what it meant for a shape to be hexagon or a pentagon.

The article offers information on the gathering of the Department of Education discussing the most important topics on how to teach student become proficient in algebra in the U.S. According to the report, the meeting centers recommendations on how to increase a pupil's achievement in mathematics, which also discuss rigorous algebra courses. Moreover, the event also recommend in providing teachers more confidence in selecting the best educational and practices for the students. Furthermore, the board also bring the heavy political baggage within the math residential area.

Reports that the Clay Mathematics Institute in Cambridge, Massachusetts has offered $1 million for proof of each of the seven classical mathematical problems. Establishment of the importance of mathematics to the general public; Competition to solve these problems, and the strict guidelines that have been derived to determine if the problem is actually solved correctly; List of the mathematical problems, including the Riemann hypothesis, which concerns the distribution of prime numbers.

The article offers information about the results of a study that clearly points to the desirability of a study of relative achievements attained in arithmetic in schools in the U.S. The study took the methodology of using a questionnaire which were sent to city schools superintendents as well as to county superintendents in the country. The study revealed that 50 percent of the responding superintendents were in favor of eliminating their attention to certain subjects in arithmetic such as alligation, cube root, unreal fractions, progression, and certain obsolete tables. Furthermore, results of the educational survey reveals an overwhelming attitude in favor of increased emphasis on the fundamental subjects of addition, multiplication, subtraction, and division.