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Abstract:"This paper discusses the results of a pilot st udy that explored how prospective secondary school teachers are shaped by learni ng experiences during their undergraduate mathematics education. The collabora tive study, which was conducted by a mathematician and a mathematics educator, dr ew from the experiences of prospective teachers in a non-traditional undergraduate ma thematics program that makes extensive use of technology. Analysis of data collect ed from detailed questionnaires, journals, and focus group discussions strongly suggests that designing, implementing, and testing Learning Objects promotes prospective teache rs' learning of the mathematics needed for teaching. Furthermore, the analysis shows t hat prospective teachers' experiences of ownership, engagement, and pride are key to positive learning experiences. "

My name is Patrick Honner. I teach mathematics at Brooklyn Technical High School, a large, public, specialized high school in Brooklyn, New York. As a NYC public school teacher I have taught everything from Introductory Algebra to Multivariable Calculus.  I mentor student research in mathematics, and I am actively involved in extracurricular mathematics programs both in my school and around New York City. Math research is an instructional focus of mine. Independent, investigative, mathematical research projects can be crafted by and for students at all levels of knowledge, in all areas of interest. A primary objective of MrHonner.com is to exhibit the math all around us in order to stimulate question-posing and hypothesizing, the first steps in structuring a good research project. I am a two-time recipient of Math For America's Master Teacher Fellowship, and I am active in MfA's professional community.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here. On our website you will find thousands of our free mathematics enrichment materials (problems, articles and games) for teachers and learners from ages 5 to 19 years. All the resources are designed to develop subject knowledge, problem-solving and mathematical thinking skills. The website is updated with new material on the first day of every month. For guidance on how to find the right resources for you, go to the Help section of the site.

Northwestern University scientists created a model to explore food web dynamics towards species conservation. "The goal of this project, funded by the National Science Foundation's Division of Mathematical Sciences, is to develop mathematical methods to study dynamical processes in complex networks. Although the specific application mentioned here may be useful in management of ecosystems, the mathematical foundation underlying the analysis is much more universal. The broad concept is innovative in the area of complex networks because it concludes that large-scale failures can be avoided by focusing on preventing the waves of failure that follow the initial event."

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/

abstract: "In this paper I address the use of digital tools (GeoGebra) in open ended design activities, with primary school children. I present results from the research and development project "Creative Digital Mathematics", which aims to use the pupil's development of mathematical board games as a vehicle for teaching skills with GeoGebra, as well as an entrepreneurial attitude towards Mathematics. Using the instrumental approach I discuss how open ended transdisciplinary design activities can support instrumental genesis, by considering the extent to which the pupils address mathematical knowledge in their work with GeoGebra and how they relate their work with GeoGebra and Mathematics to fellow pupils and real life situations. The results show that pupils' consider development of board games as meaningful mathematical activity, and that they develop skills with GeoGebra, furthermore the pupils considers potential use of their board game by classmates in their design activities."

"Beautiful Mathematics is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared." (MAA, 2011)

Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early Mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of Mathematics experiences for young children.

"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."

Mathematics has a reading protocol all its own, and just as we learn to read literature, we should learn to read Mathematics. Students need to learn how to read Mathematics, in the same way they learn how to read a novel or a poem, listen to music, or view a painting.

"Calls are frequently heard for improving schooling by closing the gap between children's life out-of-school and traditional learning styles, and by broadening the space and span for life-long learning opportunities. The Math4Mobile development endeavors to engage all students with mathematical ideas. It provides a collection of tools that could be included in a variety of activities to support students' mathematical skills, conceptual understanding, and creative mathematical thinking. "

by dr. sarah-marie belcastro, "You might wonder why one would want to knit mathematical objects. One reason is that the finished objects make good teaching aids; a knitted object is flexible and can be physically manipulated, unlike beautiful and mathematically perfect computer graphics. And the process itself offers insights: In creating an object anew, not following someone else's pattern, there is deep understanding to be gained. To craft a physical instantiation of an abstraction, one must understand the abstraction's structure well enough to decide which properties to highlight. Such decisions are a crucial part of the design process, but for the specifics to make sense, we must first consider knitting geometrically."

From the abstract: "ew innovations by math- ematicians themselves are starting to harness the power of social computation to create new modes of mathematical production. We study the effectiveness of one such system, and make proposals for enhancement, drawing on AI and computer based mathematics. We analyse the content of a sample of questions and responses in the community ques- tion answering system for research mathematicians, math- overflow . We find that mathoverflow is very effective, with 90% of our sample of questions answered completely or in part. A typical response is an informal dialogue, allowing error and speculation, rather than rigorous mathematical argument: 37% of our sample discussions acknowledged er- ror. Responses typically present information known to the respondent, and readily checked by other users: thus the effectiveness of mathoverflow comes from information shar- ing. We conclude that extending and the power and reach of mathoverflow through a combination of people and machines raises new challenges for artificial intelligence and compu ta- tional mathematics, in particular how to handle error, anal - ogy and informal reasoning."

Published November 2012. "The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. "

From the abstract: "Studies on creative mathematics conducted in the past decades revealed that the importance of creation of learning and teaching environment favourable to the identification and nurturing creativity in mathematics. Based on psychological, methodological and didactical models created by Krutetskii (2006), Shchedrovtiskii (2008), Brousseau (2007) and Sierpinska (2004), we have developed our challenging situation approach. During 5 years of field study in the elementary grade VII classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical creativity in very young children, keeping and increasing their interest towards more advanced mathematics curriculum. This article is an humble attempt to present our model and illustrate how it works in the mixedability classroom. We will also discuss different roles that teachers and students might play in this kind of environment and how each side could benefit from it."

In defense of mathematics and mathematical literacy

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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."

The Math Forum: Philadelphia Engineering / Math Challenge |#stem #mathematics http://t.co/YqJJnAKSt6

The Math Forum: Philadelphia Engineering / Math Challenge |#stem #mathematics http://t.co/YqJJnAKSt6

Brief musing on mathematical physics with links to a variety of perspectives on the influence of math on physics.

"Complicated mathematics presented in a generally understandable way Examples from everyday life are mathematized Many examples presented with a good sense of humor Small riddles and conjuring tricks garantee an entertaining reading Imagine that you've finally found a parking space after a long and harrowing search, but are now encountering some difficulty in trying to enter this space."