Monthly Archives: May 2013

A Collection of Natural Science Demonstrations from Harvard

Science often feels like a magic show and that aspect makes it particularly appealing to science education. Great communicators of science like Walter Lewin can enchant any audience by turning ordinary physical phenomena into captivating demonstrations that violate intuition and tickle imaginations. In this tradition, Harvard University has created a collection of science demonstrations and simulations covering chemistry, physics, and astronomy. Some of these demonstrations are hard to replicate at home or even in a regular school classroom because of the complex equipment requirements, which is why putting them online is so beneficial. Below is an example of one of the demonstrations that features Chladni plates. More videos are available on the Harvard Natural Sciences Demonstrations Youtube channel.

Mechanical MOOC: A New Type of Online Course That Teaches Basic Programming

mechanical mooc picture

Most massive open online courses (MOOCs) seem to follow a familiar pattern. Thousands of students sign up for free structured courses that require first watching videos of university professors lecturing and then doing homework and taking exams following a strict schedule. These MOOCs tempt students looking for convenient and free access to top universities, but unfortunately most of those who sign up drop out without completing the courses. One of the problems maybe that not everyone learns at the same pace and some students may simply not have enough time outside of work and school to put in the required hours every week. The Mechanical MOOC, a collaboration between MIT OpenCourseware, OpenStudy, Peer to Peer University, and Codecademy, is taking a stab at addressing some of the underlying problems plaguing most MOOCs. In their course A Gentle Introduction to Python, they are eliminating an instructor and a strict schedule and instead encouraging students to work in groups to learn at whatever pace works for them. There will be a mailing list that will coordinate all learning activities and direct students to the the appropriate resources, but beyond that there will be complete freedom for groups of students to work together and help each other while following their own schedule. Most of the material will come from MIT OpenCourseWare and OpenStudy will provide a question and answer forum to facilitate group discussions. The course begins in June and given it’s flexible nature is worth a try for those who have had a hard time committing to any of the other MOOCs. You can sign up here.

The Seasons Simply Explained

The fact that certain months are hot and others are cold is so deeply ingrained in our brains that we take it for granted. Fortunately, it doesn’t take advanced science to explain the basics behind this phenomenon. In the “Reasons for Seasons” animation below, Rebecca Kaplan talks about the science of seasons as if she is reading a fairy tale, not giving a serious lecture. This makes for wonderful bedtime learning even if you’re already a serious adult.

K-12 Science and Engineering Workshops at MIT

Edgerton outreach logo

One problem that online learning, with all of its obvious advantages, cannot currently solve is how to bring hands-on learning to students. Luckily, quite a few colleges and universities offer out of school STEM programs that complement videos and textbooks, and MIT is no exception. If you’re anywhere near the Greater Boston area you can schedule a free group workshop at the Edgerton Center at MIT, which runs a variety of science and engineering programs for kids of all ages. The activities, which are run by MIT undergraduate and graduate students, include working with electrical circuitry and exploring chemical reactions. For those who want more time to learn and build, longer summer programs are available, but you need to sign up early as they are quite popular. Below is a video that captures some of the spirit of the Edgerton Center.

Stop Mindlessly Memorizing the Order of Operations

Breaking news: the order of operations that elementary schools teach students is not a fundamental law of nature but a convention to make our lives easier. Unfortunately, many students add PEMDAS (as the order of operations is commonly called in the US) to the list of mystical yet unquestionable truths to be memorized and feared. Everyone’s life might be a bit easier if we realized that mathematical expressions are written in a special mathematical language, and that like any language it has its own rules. The English language, for example, has spelling rules that dictate how to spell the word “bite” in the sense of eating and the word “byte” in the sense of data stored in a computer. If it wasn’t for those rules, there would be a great deal more confusion, and different people would read the same sentence in multiple ways. The same is true in mathematics. The notation and rules that we learn in school have developed over centuries to make reading and writing mathematical expressions an unambiguous activity. In the short video below, Henry Reich explores the conventions we use today and reminds us that thinking deeply about even the most basic ideas is more important than memorizing them. If you’re interested in the history of modern mathematical notation Ask Dr. Math has a bit more information.

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.

Quadratics Done Simply and Properly

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A common middle school algebra topic like quadratics is all too often spread across hundreds of confusing textbook pages and several years of tedious instruction. It’s as if the subject is a mix of rocket science and neurosurgery. In reality, if you set aside some of the more beautiful geometric examples, the basic algebra of quadratic equations should not pose much of a problem for a typical math student. James Tanton confirms this with his Guide to Everything Quadratic [PDF], a short 64 page booklet on the fundamentals of quadratic equations. The guide presents the algebra of quadratics in an intuitive and mathematically sound way with plenty of examples. In addition to the algebra section, there is a section on graphing quadratics, and a section on fitting quadratics to data. As an added bonus, Tanton demonstrates a quick way to graph parabolas and includes a set of exercises that walk the reader through the derivation of the cubic formula, something that almost never appears in the standard school curriculum. If you want a more geometric perspective we recommend the book Lines and Curves. For those approaching quadratics for the first time, Tanton’s guide can replace or at least supplement most of the coverage of quadratics in a standard algebra textbook.

Dimensions: A Beautiful Excursion Through Geography, Geometry, and Topology

Unfortunately, some of the most beautiful mathematics is hidden from most people because it is so difficult to visualize. A good explanation has limited reach when the discussion at hand is about geometry, especially when it spans more than two dimensions. We may have an abundance of technology to help illustrate the subject, but someone still needs to spend an enormous of time and energy creating the kind of visualizations that are mathematically accurate, yet breathtaking. Fortunately, a group of French engineers, mathematicians, and education enthusiasts have done some of this hard work and produced Dimensions, an incredible nine part animated film that is nothing short of a visual feast featuring some of the most important and beautiful ancient and modern mathematics

The first chapters of the film introduce geography and the geometry of the sphere. Later chapters extend our intuition about two and three dimensions to four dimensions. The final chapters are more advanced but present a fairly elementary treatment of complex numbers and some topology. Every new idea is presented by an important mathematical personality, putting the whole narrative into a historical context. Although you can watch all nine chapters in one sitting, they are not all connected and it might be easier to watch them separately. The film website has a useful guide to help you choose what to watch, and we can’t recommend watching it enough.

Lively Chemistry Crash Course for Those in a Hurry

Although chemical experiments can yield exciting results, the theoretical part of chemistry may appear overly dry to students who are not already interested in it. Those who are studying the subject and need to review it may be overwhelmed by the sheer volume of details that they need to memorize. In both of these cases, it is helpful to have a highly condensed and lively summary of the key concepts. That is exactly what Hank Green accomplishes in his video series, Chemistry Crash Course. The videos in this series are short and entertaining, but they still highlight fundamental concepts. You can think of the collection as an extended trailer for the much broader and deeper subject or as a fun way to review for a chemistry test. The videos do not replace a textbook or a good teacher but they pack enough content into a few minutes that we recommend pausing them to process all of the information. If you have encountered any chemistry at all, these videos will be a bit more useful than if you have never heard about the existence of atoms.

A Possible Mathematical Theory Behind The Coming Cicada Infestation

The eastern United States is about to be overrun by billions of cicadas who will crawl out of the ground and create a deafening commotion. The interesting thing about their emergence is that they only come out every 17 years. Some scientists think that this is a coincidence, but the late Stephen Jay Gould, one of the major figures of evolutionary biology, postulated that the fact that this number is prime might not be an accident. He reasoned that if these periodical cicadas were to come out every, say, 12 years they would coincide with the emergence of predators whose life cycles are 1, 2, 3, 4, 6, and 12 years. Because their life cycle is 17 years, only predators with life cycles of 1 and 17 years coincide with the cicadas and it is easier for them to survive. In other words, periodical cicadas evolved to minimize their exposure to predators. You can learn more about this possible connection between number theory and biology in this Nature article and in a more detailed math paper [PDF] from the Courant Institute at New York University. Even if questions remain about the validity of this particular theory, it is an important reminder that purely mathematical ideas can provide fertile ground for scientific theories in any discipline.