Blog Archives

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

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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.

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.

Plus Magazine: A Collaboration Between Mathematicians and Educators

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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.

How Much Money Is There on Earth? An Entertaining Introduction to the Monetary System

How much money exists on Earth may sound like a silly question, but answering it leads to several important concepts underlying the modern economy. Michael Stevens, in his usual engaging style, answers the question and turns a normally dry subject into an exciting one. His video discusses the creation of money, how it acquires it’s value, and even touches upon some esoteric topics like the dirtiness of physical currency. If you’re an expert on the topic, there may not be many revelations here, but if you’re new to the subject of economics, this is a fun place to start.

Google Science Fair 2013: Pre-College Research Recognized

Google Science Fair

Winning science competitions is clearly not a requirement for future successful scientific careers, and the winners of these competitions are not necessarily geniuses, although they are definitely bright. That said, an event like the Google Science Fair can be a good motivator for students. This annual event lets students from all over the world submit their research projects online, which are then evaluated by a panel of experts that includes Nobel laureates. The winners receive various awards and there are several age categories with their own prizes, but of course the future opportunities that come with winning are the greatest reward. Perhaps, the most important lesson from such a competition is that learning should not be limited by school textbooks and that sufficiently motivated students can go far if they follow their intellectual curiosity. If you have a science fair project ready you still have a week to submit it. Even if you don’t take part this year, following the work of the winners is an educational experience in itself. Good luck!

Street-Fighting Mathematics: Inexact Reasoning Leading to Deeper Understanding

All too often school teaches us to “guess and check” when a simple exact calculation would lead to the right answer. Guessing the answer to a one variable equation may not further our mathematical knowledge, but is it possible that guessing can lead to deep insights? According to Sanjoy Mahajan, physicist and author of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving [PDF], the answer is yes. He makes the case that by using certain basic problem solving strategies one can avoid rigorous and complicated calculations while the result will be the same. Moreover, these strategies and the solutions that they yield lead to a deep understanding of the subject matter. The book is full of examples from mathematics, engineering, and physics and although some parts require knowledge of calculus, it should be accessible to motivated high school students. As a bonus, it is freely available from MIT Press. Here is a TEDx talk that the author gave illustrating the street-fighting techniques in his book.

A Search Engine for Massive Open Online Courses

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The number of Massive Open Online Courses (MOOCs) is growing rapidly and it is becoming increasingly difficult to keep track of available courses as well as their starting dates. Class Central is a site that attempts to alleviate this problem by cataloging available courses and offering a search engine to help you find what you’re looking for. You can filter courses by those that have just been announced, those starting soon, those in progress, those that are already completed, as well as by whether they are self paced; the latter being especially convenient for those who don’t have a lot of spare time. Obviously, keeping track of every possible online class is a complicated task as more individuals start creating their own courses through online learning platforms like Udemy, but Class Central does a good job of tracking the largest online course providers most of which offer courses taught by faculty members at top universities. We will continue to highlight individual courses that we think merit special attention, but this is a good place to start your online education search.

(Photo credit: opensourceway)

Trigonometry the Nonboring Way

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Few subjects have such a reputation for being boring as trigonometry. Most students who study it miss both the historical context and the interesting applications because most textbooks are too dry and skip the story that gives the subject meaning. Eli Maor’s book, Trigonometric Delights, addresses these shortcomings by a offering a historical development of trigonometry that will be eye-opening even to professional mathematicians. It’s not a textbook or a tutorial but an in-depth guide to some of the most important and beautiful theorems and applications of the subject. Having past exposure to trigonometry helps as Trigonometric Delights is not popular mathematics literature intended for casual browsing. The book is ideal for teachers who want to spice up their trigonometry classes with exciting material, and as an added bonus it is completely free online.