This paper aims to tell how the Russian national examination in mathematics (the Uniform State Examination or USE) has been conducted most recently. The author must say at once that the history of the system of secondary school graduation examinations or even the history of the USE will be covered only to the small degree that is necessary for…

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

In this article, the authors explore framing, a non-multiplicative technique commonly employed by students as they construct similar shapes. When students frame, they add (or subtract) a "border" of fixed width about a geometric object. Although the approach does not yield similar shapes in general, the mathematical underpinnings of…

A history is given of the Educational Museum of Teachers College, which began in 1886, and David Eugene Smith's extensive collection of mathematical tools used in the Museum's exhibits is discussed. Historic mathematical instruments including, the astrolabe, abacus and counting rods, and the slide rule are examined. The author uses digitized…

The U.S. school mathematics curriculum changed slowly during the last century, and only in the past few decades have there been serious efforts to establish it nationally rather than having it be, at least in principle, locally determined. Waves of change have periodically swept the curricular ocean, but on the seabed, in the classrooms where…

This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…

Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

As part of promoting and improving pattern discovery skills among school children, a Sudoku puzzle can be used as example of a problem solving task. A simplified version of the puzzle will be used first to explain the aim and reinforce the rules of solving the puzzle. Three strategies--"Strategy of Obvious Missing Number, Strategy of…

Developing curriculum and instruction for mathematics education and designing technologically enhanced learning environments are often pursued separately, but may need to be addressed together to effectively link the strengths of technology to performance in mathematics and conceptual understanding. This paper addresses current challenges with…

Last year the United States unveiled the Common Core State Standards (CCSS) in English and Mathematics for grades K-12. In particular, the authors included two possible sequences of 8-12 mathematics courses that would fulfill the standards. Most notably, the courses titled "3a" and "3b" in these two sequences have become…

This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are…

This article analyzes the findings from an 18-section experiment studying the effect of homework-completion tutoring on community college students' remedial mathematics performance. The experiment involved 529 students registered for two remedial math courses: math skills and algebra. For each course, the experiment studied nine sections: three…

The project reported here is conducting repeated randomized control trials of an approach to high school geometry that utilizes Dynamic Geometry (DG) software to supplement ordinary instructional practices. It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploration tools. The basic…

This exploratory study compared a computer-based mathematics education intervention with two more traditional approaches with the purpose of improving instruction in perimeter and area. Kidspiration software, tile/stick manipulatives and pencil/paper-based copying/drawing of shapes were implemented in a 3rd Grade New York City public school…

The National Curriculum Framework 2005 envisions a reformed curriculum that connects knowledge and learning to the child's context. While concerns of equity, accessibility, and social transformation have been aimed through education, the crucial link of "teacher"--instrumental in realizing these aims--seems missing. This study explores…