Biased Weak Polyform Achievement Games

In a biased weak $(a,b)$ polyform achievement game, the maker and the breaker alternately mark $a,b$ previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the $(a,b)$ game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all $(a,b)$ pairs for polyiamonds and polyominoes up to size four

Virtual Versus Tangible Math Manipulatives: A Quasi-Experimental Study Comparing the Impact of Different Types on Mathematical Understanding

The purpose of this quantitative, quasi-experimental nonequivalent control group design study was to measure the effects of both types of manipulatives on student mathematical understanding of 1st and 4th grade, Title I students. This data is needed for teachers to make informed decisions regarding their instructional choices. 270 participants were separated into three groups based on which type of manipulative their classroom teacher used during instruction: physical, virtual, or both. After 10 weeks of instruction with these manipulatives, student achievement was calculated for each student utilizing the Universal Screeners for Number Sense, and the groups within each grade level band were compared using an analysis of covariance test while controlling for pre-test scores. Both grade levels resulted in statistically significant differences between treatment groups. Physical manipulatives were found to be most impactful for both grade levels, followed by mixed manipulatives, with students using virtual manipulative performing at the lowest levels in both grade levels. It is recommended that future studies consider researching the impact of physical manipulatives first and then virtual manipulatives, repeating this study with a different instrument and/or a longer study period, providing coaching support as part of the study, or researching the impact of an innovative technological tool, such as augmented reality

Polyominoes with minimum site-perimeter and full set achievement games

AbstractThe site-perimeter of a polyomino is the number of empty cells connected to the polyomino by an edge. A formula for the minimum site-perimeter with a given cell size is found. This formula is used to show the effectiveness of a simple random strategy in polyomino set achievement games

Proceedings of the tenth international conference Models in developing mathematics education: September 11 - 17, 2009, Dresden, Saxony, Germany

This volume contains the papers presented at the International Conference on “Models in Developing Mathematics Education” held from September 11-17, 2009 at The University of Applied Sciences, Dresden, Germany. The Conference was organized jointly by The University of Applied Sciences and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on Our Project Home Page http://math.unipa.it/~grim/21project.htm It has been our pleasure to edit all of the papers for these Proceedings. Not all papers are about research in mathematics education, a number of them report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators. These Proceedings begin with a Plenary Paper and then the contributions of the Principal Authors in alphabetical name order. We sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future

Errata and Addenda to Mathematical Constants

We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.Comment: 162 page