Sometimes it takes decades for works that have had an immense impact to become easily and cheaply available, and this is especially true in the sciences. The difficulty of making a science or math text, with all of its special symbols and diagrams, browser-friendly poses a serious technical challenge. Since 1964, the “Feynman Lectures on Physics” have been a physics education classic, but now, the first volume is finally available online.
Richard Feynman is known not only as one of the great physicists of the twentieth century, but also as one of its great communicators who could explain the most complicated topic with rare clarity. His physics lectures, however, have traditionally been an expensive financial investment and used mainly at the undergraduate level. Now, ambitious high school students can try them out for free. We’ll be looking forward to the rest of the volumes becoming available in the near future.
Suppose you learned that transistors are a fundamental building block of modern electronics, and you decided to learn about how they function. If you looked at the first result in a google search you would see this Wikipedia article filled with technical details, but not that much beginner-friendly clarity. As with many such important concepts, explaining it at just the right level of detail to be both technical and accessible is a serious challenge.
To the rescue comes Derek Muller, creator of the Veritasium Youtube channel, who demystifies the idea behind transistors. His video features just the right type of animations and visual props to make a point without getting lost in technical details that would only be relevant to graduate students or scientists. If you’re interested in electronics, this six minute video is as good a starting point as any textbook or lecture.
Most math classes try to teach computation skills and not much more. This is true not only in school where students memorize mechanical procedures and how to plug numbers into formulas, but also in university courses targeting scientists and engineers. Computational fluency is important but it is only a stepping stone to mathematical maturity.
Higher level mathematics requires the ability to prove mathematical statements, which in turn, requires the ability to think logically and create convincing and rigorous arguments. If this sounds more like something taught in law school, it’s because much of math education has been divorced from actual math. We’ve addressed the topic of mathematical thinking before, but now there is an online course that teaches the most foundational concepts in non-computational math.
That course, Introduction to Mathematical Thinking is offered by Stanford University via Coursera and is taught by Keith Devlin, who is a well known and charismatic math popularizer, educator, and researcher. The main purpose of this course is to serve as a transition between computation-fixated school math classes and undergraduate math major courses. In some ways, this is a traditional course that many university math departments require, but as a MOOC it is now accessible to anyone from high school students to math teachers. As Professor Devlin says in the introductory video (below), the course does not teach students new mathematics; instead it teaches them how to think mathematically and work with the standard mathematical language that involves notions like equivalence relations and logical quantifiers.
The course has been offered before with tens of thousands of students and has received excellent reviews. If you have never been exposed to anything beyond plug and chug math, this course is for you. Once you acquaint yourself with the basics of mathematical thinking, you will gain a deeper appreciation of some important topics that are usually left out of the regular school math curriculum.
The desire to create their own video games is one of the top reasons why kids give programming a try. As a result, teaching programming through computer game creation has become increasingly popular. One can now easily find books and after school programs that follow this trend, but as tempting as this approach may be, it suffers from false expectations. A student who wants to learn how to make video games doesn’t realize that computer science educators are more interested in teaching him how to program than in helping him create something that resembles the slick professionally-produced games that he plays at home. Of course, the initial excitement of creating your own computer program may compensate for unmet expectations, but it’s not clear that this is a good trend.
What if, on the other hand, students could create real modern video games alongside industry professionals? That is the idea behind Pipeline, an outreach effort by Valve, a major video game company. They have recruited a group of high school students who are working alongside their much older colleagues on video game titles that will be sold to millions of players around the world. These students are not only exposed to the video game industry, but are sharing their experience with their peers through the Pipeline website. This may be the easiest way to learn about what it actually takes to make a professional video game. Learning to code is important no matter what your goals are, but if you’re interested in joining the video game industry, signing up for Pipeline will give you a realistic view of the work and knowledge required to do so.
Euclidean geometry is one of the most beautiful math topics that is part of the standard school curriculum, yet it is consistently butchered by standard teaching practices. Even more surprising is that straight edge and compass constructions are usually excluded from geometry classes instead of being used as a way to lure students in. Using a compass and straightedge to construct a geometric figure feels like playing a game and has the added benefit of being a hands-on activity.
Using paper and pencil has been the traditional way to do constructions but software makes it a great deal easier, especially in the age of sloppy handwriting. Although a number of geometry software packages exist, none is as simple or as addictive as this web app. No download is required and you can immediately start constructing the shapes that are offered as challenges on the right side of the app page. The challenges are ordered by difficulty and you gain points when solving them. Although the app lacks instructions, it shouldn’t take more than a few minutes to get a hang of how it works. If you teach geometry, do your students and yourself a favor — let them try out a few challenges and they’re likely to get hooked not just on the game, but on geometry as well.
When learning mathematics, you need a concrete mental representation of the often extremely abstract ideas that you need to internalize. Unfortunately, most math books, even good ones, don’t provide the needed intuition. Fortunately, Kalid Azad has come to the rescue with Better Explained, a site dedicated to helping anyone learning a new subject develop a way to think about it in intuitive and concrete terms.
The math topics covered include basic arithmetic, probability and statistics, exponents, complex numbers, and even advanced topics like calculus and the Fourier Transform. Better Explained is not comprehensive, nor is it rigorous; its goal is to give its readers the kinds of insights that will enable them to jump start further in-depth learning on their own. Khalid’s tone is that of a student who at one point also struggled with the given concepts and is a welcome change from the often austere tone found in textbooks and lectures. The site features excellent articles on programming and a few other topics, but it certainly stands out for its clear and concise math articles.
As previously discussed, mathematics is not a science in the same way as physics, chemistry, and biology, yet because it is treated as a scientific discipline in school, students rarely understand it’s role. If you’re a math teacher, ask your students the following question: “Biology is the study of living organisms, physics is the study of matter, motion, energy, and forces, but what does math study?” You are certain to elicit a great deal of confusion.
In the following video, Richard Feynman, one of the great physicists of the twentieth century, attempts to answer the question by differentiating between the mental models of mathematicians and those of physicists (and by extension other scientists). Feynman, whose mathematical abilities stood out even among other elite physicists, was supremely qualified to compare the different approaches and to elucidate the peculiar nature of mathematical research. His lecture was recorded almost half a century ago, and lacks the polish of more modern science productions, but it more than makes up for it in both substance and Feynman’s impassioned lecture style. This is a must-see lecture for high school students who have an interest in a math or science career.
Successful startup founders seem to be starting their companies earlier than ever before. Whereas Bill Gates and Mark Zuckerburg dropped out of college to start their companies, David Karp whose company, Tumblr, was recently acquired by Yahoo, dropped out of high school to work on his own software projects. While leaving school is not a requirement for successful entrepreneurship, starting early can help.
High school students who have completed an AP computer science course, or who have had previous programming experience, and are interested in learning about the way software engineering is done at the top startups, can now take a startup engineering course that will not only expose them to the latest technology and methodologies, but will give them an opportunity to launch their own project. Stanford University is offering this free online course through Coursera, and although it is a massive open online course (MOOC) it will have a few unique features that set it apart from other MOOCs. First of all, students will be exposed not only to the technical tools of the trade, but also to the business side of starting a company. Secondly, and perhaps more importantly, students will complete a final project that will entail building their own web application, and the best projects will qualify for prizes from sponsoring startups. The course starts June 17 and should be an interesting learning experience for both students and their teachers.
Mathematics is so frequently put into the same category as the sciences that students often assume that it is one of the many scientific disciplines, just like physics, chemistry and biology. This can become a problem when students try to understand the reason for studying mathematics. Most students can immediately see that biology is the study of living organisms and the immediacy of that subject makes it both instantly appealing and comprehensible. In mathematics, however, as soon as the studied objects become sufficiently abstract and far removed from everyday experience, students fail to see their significance. As layers of abstraction are added, visualizing mathematics becomes even harder than picturing microscopic cells.
When confusion arises about the nature of mathematics, it can be helpful to introduce a few ideas from the philosophy of mathematics. That is exactly, what the following PBS Idea Channel video does. The question of whether mathematics is a science that studies objects that exist in this universe or is a mental construct that is aesthetically elegant and just happens to be the best language we know for describing nature, remains unanswered, but the discussion is important. Without it, students may never suspect that mathematics plays a unique role in human history and that it spans almost all disciplines. For those who want a deeper take on the nature of mathematics, Eugene Wigner’s classic paper on The Unreasonable Effectiveness of Mathematics in the Natural Sciences will provide much more food for thought.
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.