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Computer Science Unplugged: A Computational Thinking Curriculum Without the Computer

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The chorus calling for teaching computer science to all children seems to be getting louder by the day. Even the White House seems to think that programming is the new literacy. Programming is clearly an important skill, but the rush to teach programming languages and popular web technologies seems to have eclipsed a much more fundamental aspect of computer science: computational thinking. Billions of lines of code may run today’s infrastructure, helping land airliners and processing billions of dollars in commerce, but behind that code are algorithms and deep mathematical ideas. Unfortunately, most of the theory of computer science is left to either AP or college-level courses, which is too late. Computer Science Unplugged, a free computer science curriculum that features activities, games, and problems, seeks to address that problem. The curriculum comes with a free book that contains engaging activities, some of which are kinesthetic, but which cover topics like binary numbers, information theory, and searching algorithms. Computer Science Unplugged is appropriate for children as young as seven and is a good way to incorporate computer science concepts into regular math classes or enrichment programs. In some ways, the best part of the curriculum is that it does not require a computer and lets students move around.

The Fascinating World of Preschool Mathematics Education and Enrichment

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Teaching math to young kids who don’t know how to read, write, or count is a complicated task. Providing these kids with mathematical enrichment seems like an even more daunting task. Unfortunately, the vast majority of math materials for young kids involve colorful pictures, games, and activities without real mathematical substance. Sure, knowing the names of shapes is important and receiving prizes for this knowledge is fun, but it doesn’t require too much thinking. A more sophisticated but still age appropriate activity would require giving a child three pencils and asking her to place them on a table so that none of the erasers touch the table (the pencils cannot be made to stand vertically). Solving this problem requires the application of three dimensional spatial reasoning, an important long-term skill.

This type of activity has been the cornerstone of elite Eastern European preschool math programs, and until recently was not widely available in the English-speaking world. The recent translation and publication of Alexander Zvonkin’s unique book, Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers, changes that. This memoir gives an in-depth view of a two year math circle that Zvonkin, a professional research mathematician, ran for a group of kids ages three to seven. It meticulously describes every session and reveals a world of problems and activities far beyond the confines of the regular preschool curriculum. Perhaps as valuable as the mathematical content of the book, are the observations and insights that Zvonkin shares with the reader. Anyone interested in math education, not just at the preschool level, will learn a great deal from this one-of-a-kind work. Once you read this, you will be prepared to start your own enrichment program.

Cut-the-Knot: A Hidden Treasure Trove of Mathematical Miscellany

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The Web may contain almost every possible problem, puzzle, and article imaginable, but it’s decentralized nature makes it’s hard to locate good content in a sea of endless tutorials, amusing pictures, and commercial promotions. If you’re trying to find extracurricular mathematical materials you need to know where to look, but more importantly, what to look for. Knowing an erudite guide makes life much easier. Alexander Bogomolny, a professional mathematician and curator of mathematical recreations and other topics, is that guide. His site Cut-the-Knot is an enormous collection of fascinating articles, illustrations, and animations covering a wide range of mostly non-advanced mathematics. One of the defining features of his articles are the interactive Java applets that illustrate a problem or principle. The site has been continuously updated since 1997, which makes it among the most comprehensive such repositories online. Unfortunately, because it was created more than fifteen years ago, its age shows in the design and technology used (Java applets are no longer the preferred delivery mechanism for interactive media). Although Cut-the-Knot has garnered over twenty awards, including one from Scientific American, it is not as well known as it should be. If you’re looking for a source of enrichment for regular math classes this is one of the best places to start.

A Miniature Introduction To Infinity

Infinity is a topic that has for ages caused a great deal of both fascination and confusion among students. It is a mathematical abstraction that unlike other abstractions seems hard to make concrete. The fact there is more than one type of infinity and that infinity is often treated like a number but is not an element of what we know as the real numbers adds to the confusion. The charming little video below from the Open University takes a sixty second look at Hilbert’s paradox of the Grand Hotel, a comic, yet mathematically serious example of how to think about infinity. The name is a bit of a misnomer as it’s not really a paradox, but simply a question with a somewhat counterintuitive answer. The animation does not explore all aspects of Hilbert’s thought experiment, but it is a good start that will pique anyone’s curiosity.

The Scale of the Universe and How We Measure It

Students often ask about the existence of the largest, smallest, or most distance objects that exist. These questions undeniably provide intellectual entertainment, especially when we can visualize the answers with ease. Take a look at this beautiful interactive animation created by Cary and Michael Huang to get a sense of the the kinds of distances and sizes that exist in the universe, and then look at the Royal Museums Greenwich animation that introduces the physics of measuring distances to macroscopic objects in the Universe. The video skips the details of how some of the distances are calculated but is a good starting point for further geometrical explorations that are not beyond the school curriculum.

2013 Cambridge (MA) Science Festival April 12 – April 21

If you’re anywhere near the Boston area in the second half of April don’t miss the 7th annual Cambridge Science Festival featuring lectures from some of the world’s top researchers, hands on activities, theatrical performances, a robot zoo, and much more. One of the outstanding features of the Cambridge Science Festival, unlike other science events, is that everyone from elementary school kids to adults with science backgrounds will find something interesting to see or do there. If you haven’t been to Cambridge Science Festival before you can see videos of some past activities on their Youtube channel.

The Story of Martin Gardner and Mathematics as Magic

Martin Gardner, one of the greatest recreational mathematicians of all time, is responsible not only for helping popularize mathematics as an art form and as a form of recreation but for inspiring a generation of future mathematicians to pursue it as a profession. He wrote the Mathematical Games column for Scientific American for a quarter of a century, and his mathematical and scientific gems have found their way into dozens of foreign publications as well as numerous research papers. The Nature of Things documentary gives the viewer an up close look at Martin Gardner’s work and the work of other people with whom he collaborated. If you’re looking for some mathematical entertainment with serious mathematical substance, or simply want a glimpse into the playful nature of mathematics and mathematicians, this is a highly recommended film.