Math Links

The deficit is a key consideration for all parties as the federal government brings down its budget. Use the chart to explore Canada's budgetary surplus and deficit history, including revenue and expenditure figures for every fiscal year from 1963-1964 to 2010-2011. Select a prime minister's name on the left-hand side to highlight figures from his time in office.

"Mathematics is not a series of Statement-Reason proofs punctuated by the occasional "QED". Mathematics, as Paul Lockhart writes in A Mathematician's Lament, is "wondering, playing, amusing yourself with your imagination.""

A Kickstarter project for a children's math and science-oriented detective story: "This is the made up story about two very real girls - Ada, the world's first computer programmer, and Mary, the world's first science fiction author - caught up in a steampunk world of hot-air balloons and steam engines, jewel thieves and mechanical contraptions. For readers 8-12. "This is a pro-math, pro-science, pro-history and pro-literature adventure novel for and about girls, who use their education to solve problems and catch a jewel thief. Ada and Mary encounter real historical characters, such as Percy Shelley, Charles Babbage, Michael Faraday, and Charles Dickens - people whom the girls actually knew. If Jane Austen wrote about zeppelins and brass goggles, this would be the book."

"An interesting group participation project for the Manchester Science Fair: growing sunflowers" Includes video on Fibonacci sequences in nature with the example of sunflowers

"A physicist faced with a fine for running a stop sign has proved his innocence by publishing a mathematical paper, and has even won a prize for his efforts. Dmitri Krioukov is a physicist based at the University of California in San Diego."

"The purpose of this study is to determine the effect of supplemental instruction using technology on the attitude toward mathematics of fifth grade students with learning disabilities in a classroom."

From the abstract (full text requires subscription or purchase): "Though cooperative learning has been a topic of considerable interest in educational research, there has been little study specific to learning in the mathematics content area of geometry. This paper seeks to address that gap through a design experiment featuring a novel small-group computing environment for supporting student learning about quadrilaterals. In this design, each student controls a unique point in a shared geometric space, and those points are linked such that a group of four students collectively forms a quadrilateral. We first present results from pre- and post-measures to show how the students learned from the activities and developed in terms of geometric reasoning. We then present three episodes, elaborated with the notion of appropriation, to explain how students took up ways of using the technological tools and of talking about geometric concepts from one another in the interactive environment. Our study found that students achieved learning gains in this novel environment, that the environment provided rich opportunities for peer interaction around geometric objects, and that student learning opportunities and interactions were characterized by processes of appropriating ways of talking about and using software features."

"This book explores 20 geometric diagrams that play crucial roles in visualizing mathematical proofs."

"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)

Prometheus Books The Glorious Golden Ratio [978-1-61614-423-4] - "For centuries, mathematicians, scientists, artists, and architects have been fascinated by a ratio that is ubiquitous in nature and is commonly found across many cultures. It has been called the "Golden Ratio" because of its prevalence as a design element and its seemingly universal esthetic appeal. From the ratio of certain proportions of the human body and the heliacal structure of DNA to the design of ancient Greek statues and temples as well as modern masterpieces, the Golden Ratio is a key pattern that has wide-ranging and perhaps endless applications and manifestations. What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. With their talent for elucidating mathematical mysteries, veteran educators and prolific mathematics writers Alfred S. Posamentier and Ingmar Lehmann begin by tracing the appearance of the Golden Ratio throughout history. They demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. They also point out the intriguing relationship between the Golden Ratio and other famous numbers (such as the Fibonacci numbers, Pythagorean triples, and others). They then explore its prevalence in nature as well as in architecture, art, literature, and technology. "

"This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism -- both symbols appearing on flags of the nations having those distinct faiths. ... The approach taken here explores the possibility that the "pieces" only fit together on a three-dimensional surface, namely a sphere. It is the spherical geometry that then merits consideration, together with the challenge of how to get from any "mis-fitting" two-dimensional layout to a three-dimensional form. Of course, two-dimensional layouts are far more readily comprehensible. Hence the focus on them. However the three-dimensional layout has the potential of rendering comprehensible a far more elegant layout which may well exemplify intuitions characteristic of the faiths so dramatically opposed. The approach follows from various earlier explorations of the potential of mathematics to offer a new perspectives on these issues" ....

"The article reports the main insights gained from a study that implemented a game-enhanced learning environment for the training of pre-service elementary school teachers. Teachers taking an undergraduate mathematics methods course experienced some of the ways in which online educational games could help students internalize key mathematical concepts across the school curriculum while at the same time improving their attitudes towards the subject. The course also familiarized teachers with the design principles for constructivist gaming environments. Findings indicate a positive impact on teachers' competence in selecting, evaluating, and productively using online games as an instructional tool."

A pre-college bridge program using an assessment software is described, with some note of increased mentoring, tutoring availability and accommodations between first and second year implementation

From the abstract: "The problem addressed by this study is the need to identify practical predictors of success for community college developmental mathematics students in online, hybrid and seated course delivery formats. This study examined two possible predictors of success, mathematics self-efficacy and technology self-efficacy, in the three delivery formats and how they related to performance on a final assessment. The study used a quantitative research design employing binomial logistic regression to determine if the independent variables (math self-efficacy and technology self-efficacy) were significant in predicting the outcome category (score on the final assessment dichotomized about the mean). Next linear regression analysis was used to build a predictor equation for a particular score on the outcome variable. A previously developed survey and an adapted version of another survey were combined to measure the independent variables; demographic factors were also measured for descriptive purposes. Binomial logistic regression analysis showed that math self-efficacy was a valid predictor of success for the developmental math students in this study but technology self-efficacy was not. Regression analysis produced a valid equation to predict standard score from average math selfefficacy score. When separated into groups according to course format, math self-efficacy was only a valid predictor for students in hybrid courses. The implications of these results are discussed and recommendations are made for further research."

"Math tutorials for students in introductory geosciences"

"this essay will focus on the implications of the design and implementation of games for teaching and learning mathematics via mobile devices as one specific means to address the gap in achievement in mathematics, and even more specifically, how it might further address the equity gap among minorities. "

"Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers - a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat's Last Theorem, but in some ways it is more significant. "The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem," says Dorian Goldfeld, a mathematician at Columbia University in New York. "If Mochizuki's proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century." See additional commentary at: http://bit-player.org/2012/the-abc-game?utm_src=HN2

An online college math course under development including the following topics (so far): Sets Math Foundations Linear Equations Solving and Graphing Inequalities Graphing and Factoring Quadratic Equations Properties of Exponents Logarithms and Exponential Equations