Blog Archives

NRICH: An Organized Collection of Math Enrichment Problems and Activities


If you liked the expository writing in Plus Magazine, you may enjoy Nrich, a sister project from Cambridge University. The site features hundreds of math problems and activities organized by grade and ability level, as well as by topic. Although Nrich has a section for students, teachers who need to prepare lesson plans may find it more useful. The site content is closely aligned with US and British math curriculum standards, which should make it particularly appealing to educators.

An outstanding feature of the site is it’s emphasis on math enrichment topics that are usually outside a standard school curriculum, yet close enough to it to be relevant in a regular math class that needs to follow strict education guidelines. Another welcome aspect of Nrich is that professional mathematicians, not just math educators oversee the project, making sure that it is both mathematically sound and relevant. There is even a forum for those who need math help. Nrich may not be the easiest site to navigate, but it does contain a convenient topic directory that organizes all of the content. This project is worth exploring and should contain something useful for anyone teaching or learning math.

Moebius Noodles: A Mathematical Playground for Young and Old

Moebius Noodles book

Contrary to popular belief, mathematics is not an activity that requires textbooks, calculators, and years of training. Because it consists of such fundamental notions as symmetry, classification, counting, and geometric transformations — all concepts that come naturally to even the youngest children — mathematics can truly be studied at any age. If you have picked up a copy of Math From Three to Seven and are wondering whether there is something similar for kids that are younger still, you should take a look at Moebius Noodles.

This book, the work of Yelena McManaman, Maria Droujkova, and Ever Salazar, is a beautifully illustrated collection of activities that engages young kids (even toddlers) in discovering fundamental mathematical principles and abstractions. For example, why wait until middle school or high school to learn about functions when you can think about them in any almost any context? For instance, Moebius Noodles proposes an activity where a child is given the name of a baby animal (like “kitten”) and must identify the corresponding adult animal name (in this case “cat”). The child has just created a baby-to-mother function and there are endless other possible activities that reinforce this idea of mappings between sets. The book covers basic ideas involving numbers, symmetry, functions, and even a little bit of calculus. If you’re a parent or preschool teacher interested in fun activities that involve both playing with and internalizing fundamental mathematical concepts, then Moebius Noodles is worth your time.

Plus Magazine: A Collaboration Between Mathematicians and Educators

plus magazine

Unfortunately, too many of the English language math textbooks that students see on a daily basis are written exclusively by professional educators without any serious input from mathematicians. As a result, these books are too much about teaching procedures and not enough about inspiring future mathematicians and scientists. At the other extreme, textbooks (usually at the college level) written by mathematicians tend to be dry and extremely dense. They may present all of the necessary definitions, lemmas, and theorems, but there is not enough room left for applications.

Plus Magazine, a University of Cambridge project is an attempt to correct this situation. It is an online publication that features articles, podcasts, book reviews, and news stories that makes mathematics relevant to those who are don’t grasp its importance and it is a collaboration between full-time educators and full-time researchers and practitioners of mathematics. You can find an article on why the violin is so hard to play and learn about the research of a recent Abel Prize winner (one of the top awards for mathematical research). The site also includes a collection of interesting nonstandard math problems and quite a bit of the content is related to physics. This should be a useful resource both for teachers and high school students.

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

cut the knot logo

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.

How to Start Your Own Math Circle or Enrichment Program

math circle session

Traditionally, math enrichment programs are run by professional mathematicians with an interest in education or by teachers with an interest in math competitions, but for most other people the idea of starting their own program seems like a daunting task. Fortunately, a few years ago, Sam Vandervelde and the Mathematical Sciences Research Institute put together Circle in a Box, a definitive guide on starting your own math enrichment program. It includes almost two hundred pages of advice on everything from the logistics of setting up an enrichment program to a fairly large set of suggested math topics and problems. There is even a section on how to apply for funding. Circle in a Box focuses primarily on setting up a math circle as opposed to any other type of enrichment program. Math circles are informal problem solving and discussion groups that were extremely popular for decades in Eastern Europe and which have played a crucial role in the development of several generations of mathematicians. Unlike school math clubs which usually focus on preparing students for specific math competitions, math circles are more flexible and their aim is to introduce a greater range of mathematical ideas (not simply problem solving tricks) and to explore even nontraditional topics in depth.

In our experience, the approach outlined in the book is similar to the one used by The Math Circle, one of the oldest math circles in the United States and by the Gentle Knowledge Math Circle, one of the first free out of school math enrichment programs. The author is the founder of the Stanford Math Circle and is well-known in the world of math outreach. If you’re a teacher, a parent, or simply a math enthusiast who is interested in starting your own program, this book along with Mathematical Circles (Russian Experience) will be an invaluable guide.

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 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.