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(Abstract only online, full text requires subscription) "The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem. "

Maria Chudnovsky, mathematician, is one of 23 MacArthur Fellowship recipients in 2012. She is an associate professor in the department of industrial engineering and operations research at Columbia University and specializes in graph theory. With colleagues she successfully solved the "Srong Perfect Graph Theorem" which was proposed in the 1960s, and her research is potentially "deepening the connections between graph theory and other major branches of mathematics, such as linear programming, geometry, and complexity theory." A video featuring the awardee can be viewed on the web site.

I'm no slouch at maths, but this site has taught me lots. See videos of maths theories at the forefront of research presented in an understandable way. http://ictmagic.wikispaces.com/Maths

" The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks designed to observe what students do as they construct meaning. APOS Theory was used as a framework for analysis of growth. APOS Theory is a useful theoretical framework for studying and explaining conceptual development. Closely linked to Piaget's notions of reflective abstraction, it begins with the hypothesis that mathematical activity develops as students perform actions that become interiorized to form a process understanding of the concept, which eventually leads students to a heightened awareness or object understanding of the concept. Prior to any investigation, the researcher must provide an analysis of the concept development in terms of the essential components of this theory: actions, process, objects, and schemas. This is referred to as the genetic decomposition. The results of this study suggest a framework that a learner may use to construct meaning for logarithmic concepts. Using tasks aligned with the initial genetic decomposition, the researcher made revisions to the proposed genetic decomposition in the process of analyzing the data. The results indicated that historical accounts of the development of this concept might be useful to promote insightful learning. Based on this new set of data, iterations should continue to produce a better understanding of the student's constructions. " (from the abstract)

description of the Adjusted Winner Procedure (used for Mathematical models of social choice theory)

"This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics."

2010 book considering "implications of infinity ... for mathematics," also mathematical logic and set theory

Joel David Hamkins, a professor of Mathematics at CUNY, describes his day teaching graph theory to his daughter's third grade class starting with the Euler characteristic and connected planar graphs tested on a variety of combinations and shapes.

Subtitled "A Place for Elegant Solutions." From the author's description: "This blog is a presentation of the interesting solutions I come across, and an exploration of the deeper mathematical ideas therein. Most often this means exploring the mathematical structure of a problem to lubricate the cogs of algorithm design. In seldom cases, this involves using programs to reason about mathematical theory."

Discusses theory of motivational learning in educational games and presents a research study involving 115 elementary school students in math class using digital game-based learning

16-year old solves particle dynamics theories which eluded traditional computational problem solving

From the abstract: :The first aim of this discussion is to suggest a framework for designing serious games based on game features in commercial games, opinions of fourth graders and their teachers, literary studies, contemporary learning theories, as well as successful and unsuccessful similar endeavours. The second part of this paper describes a concrete example of a maths game based on the proposed framework that implicitly tests math and collaboration skills. The game is made of three components: the game itself, a social network, and a teacher reporting tool. Despite a growing interest in GBL, some teachers are reluctant to use serious games in school. To increase usage of serious games as resource, it is important to equip teachers with information and address their concerns. The paper concludes with the idea that serious games need to be designed well in order to provide the immersion and collaborative active learning that most learning theories recommend."

"This book is designed to provide mathematics undergraduates with some historical background to the material that is now taught universally to students in their final years at school and the first years at college or university: the core subjects of calculus, analysis, and abstract algebra, along with others such as mechanics, probability, and number theory. All of these evolved into their present form in a relatively limited area of western Europe from the mid sixteenth century onwards, and it is there that we find the major writings that relate in a recognizable way to contemporary mathematics."

Book to be published in November 2011

Published in 2011, "reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. ... Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem." Read more about one of the authors here: http://chronicle.com/article/The-Magical-Mind-of-Persi/129404/

"The cookbook contains a succinct representation of various topics in probability theory and statistics. It provides a comprehensive reference reduced to the mathematical essence, rather than aiming for elaborate explanations."

"As Markov chains have become commonplace tools, the story of their origin has largely faded from memory. The story is worth retelling. It features an unusual conjunction of mathematics and literature, as well as a bit of politics and even theology."

abstract: "A large number of studies carried out on pupils aged 8-14 have shown that teachable agent (TA) based games are beneficial for learning. The present pi- oneering study aimed to initiate research looking at whether TA based games can be used as far down as preschool age. Around the age of four, theory of mind (ToM) is under development and it is not unlikely that a fully developed ToM is necessary to benefit from a TA's socially engaging characteristics. 10 preschool children participated in an experiment of playing a mathematics game. The partic- ipants playing a TA-version of the game engaged socially with the TA and were not disturbed by his presence. Thus, this study unveil exciting possibilities for further research of the hypothesised educational benefits in store for preschoolers with regard to play-and-learn games employing TAs."

Abstract: "Together, brain science and learning design inform Adaptive Interaction Design (AID), a technique for curriculum planning and development. Mathematics is a particular case in which AID can help. The Way of the Game is vital to learning design. There are many definitions of "game." Here, we mean game to be the means by which spontaneous play becomes responsible learning. That innovative games figure as the centerpiece of many 21st century curricula is no accident. Games are a critical element in modern theories of learning design especially when related to insights from neuroscience and online learning/teaching methods. But beyond simple gamification, can games provide the disruptive transformation to mathematics education that is required to effect substantive and sustainable improvement? Can we game the educational system to ensure students' success in mathematics? To find out, we will look at the AID process and two sample products for the development of mathematical thinking and practice based on the Way of the Game."