Math Links

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. "

Published 2012

An overview of online course offerings with an emphasis on data and statistics

Paper by John Olive,The University of Georgia ,Keynote Paper for the first IDEAL conference held at Bayburt University, Bayburt, Turkey, July 4, 2012

"In previous posts, I have summed up my position on Khan Academy as follows: Khan Academy teaches only one part of mathematics-procedures-and that isn't the most important part. Writing about mathematics, developing a disposition for mathematical thinking, demonstrating a conceptual understanding of mathematical topics are all more important than procedures. That said, procedures are still important, and Khan Academy provides one venue where students can learn them. In the end, I think every young person should have an account there. Even if only one in a thousand or ten thousand benefit, that would be a terrific outcome. "

"This is a rather unusual structure for organizing mathematical content, but offers an exciting opportunity for teachers across the nation and abroad to exchange ideas and discuss what they teach. This Wiki will address the underlying central concepts and propose activities that also provide rich opportunity to engage students in the Mathematical Practices. "

Report from the National Academies. Summary: "The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term."

Abstract: "In spite of the efficacy of Operations Research (OR), its tools are still underused, due to the difficulties that people experience when describing a problem through a mathematical model. For this reason, teaching how to approach and model complex problems is still an open issue. A strong relation exists between (video) games and learning: for this reason we explore to which extent (real time) simulation video games could be envisaged to be an innovative, stimulating and compelling approach to teach OR techniques."

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."

Educational music videos, many featuring math topics (giving rise to a new entertainment class which EdSurge calls "MuVHEMs: Music Videos Helping Explain Mathematics"

A blog featuring math games puzzles, activities, teaching and instruction tips.

Survey questions from a study on why undergraduates don't persist with STEM majors

Abstract: "A simulated academic career was combined with inquiry-based learning in an upper-division undergraduate mathematics course. Concepts such as tenure, professional conferences and journals were simulated. Simulation procedures were combined with student-led, inquirybased classroom formats. A qualitative analysis (ethnography) describes the culture that emerged within the simulation during a pilot test. A discussion follows evaluating the potential for career simulations to invite students to consider graduate studies and academic careers in the STEM disciplines."

"Banks love math. It's how they do their thing. But banks very very much want you to HATE math. Why? Crap like this:"

"Last week Tim Gowers, Cambridge University mathematician and open access advocate who led the recent boycott of Elsevier, announced an exciting new open access initiative for mathematicians on his blog. The project, called the Episciences Project, will make it super quick and easy to set up open access journals called "epijournals"."

"To help teachers and students succeed on the Algebra 1 End-of-Course exam (EOC), the University of Florida and Study Edge have created Algebra Nation - a FREE, online, easy-to-use, EOC preparation resource aligned with the latest state standards."

"a century ago this week. Mathematician Andrey A. Markov delivered a lecture that day to the Imperial Academy of Sciences in St. Petersburg on a computational technique now called the Markov chain. Little noticed in its day, his idea for modeling probability is fundamental to all of present-day science, statistics, and scientific computing. Any attempt to simulate probable events based on vast amounts of data - the weather, a Google search, the behavior of liquids - relies on Markov's idea."

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."

"Measurement explains how math should be done. With plain English and pictures, [Lockhart] makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living."

"Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. ... The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus."