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"Italian psychologist Geatano Kanizsa first described this optical illusion in 1955 as a subjective or illusory contour illusion. The study of such optical illusions has led to an understanding of how the brain and eyes perceive optical information and has been used considerably by artists and designers alike. They show the power of human imagination in filling in the gaps to make implied constructions in our own minds. Kanizsa figures and similar illusions are a really useful way to encourage learners to 'say what they see' and to explain how they see it. It offers a chance for others to become aware of the different views available in a diagram and share their own thoughts without the 'danger' of being wrong; many people see different things."

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.

from the National Council of Mathematics Teachers

Get as much money in your piggy bank as possible, by figuring out the correct change.

See real-time data on a host of topics important to daily life around the world!! * world population (e.g., births this year, deaths today, net population growth for today) * government and economics (daily government spending by category; computers sold) * society and media (new book titles published, money spent on video games, Google searches) * environment (forest loss, carbon dioxide emissions, current average temperature) * food (tons of food produced; people who died of hunger) * water (water consumed, people with no access to safe drinking water) * energy (solar energy striking Earth; oil pumped; oil, gas, and coal left) * health (deaths caused by alcohol, suicides, road traffic accident fatalities) Worldometers' algorithm takes the latest statistical data available from the United Nations (UN), the World Health Organization (WHO), the Food and Agriculture Organization (FAO), and other institutions, and then processes them together with its estimated progression to compute figures current up to the millisecond. Available in dozens of languages, this site is part of the Real Time Statistics Project. Read more about that here: http://www.realtimestatistics.org/

This Math Resource Directory will link you to resources on the web for Math Directories, Math Tutorials, Calculators and Converters, Money and Financial Literacy, Formulas and Symbols, Data, Facts and Figures, History of Math and Math Tools

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."

"a man who figured out how to have his pi and recite it, too - beyond 60,000 decimals. All it took was intensive practice and a knack for storytelling, a new study finds."

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. "

Discusses inferior textbook publishing practices and offers advice for evaluation of materials by parents

"There may be a reason you can't figure out some of those math problems in your son or daughter's math text and it might have nothing at all to do with you. That math homework you're trying to help your child muddle through might include problems with no possible solution." Lack of quality control in text publishing described and evaluation suggestions for parents offered.

An article examines the use of drawing in science learning, starting from the history of drawing in experimental science. Unfortunately the full text requires a subscription. Thinking of implications for math learning.

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Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "

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