Vacuum Cleaners, Cannons, and the Quantum Mechanics of Empty Space

The force exerted by air molecules is something that we take for granted every day, but it is a surprisingly powerful force with equally surprising applications. For example, a vacuum cleaner “sucks” dirt in by creating a partial vacuum that allows the air outside the vacuum cleaner to push dirt into it. Similar reasoning can be used to create a vacuum cannon that relies on air pressure to eject a projectile at great (even supersonic) velocity. The following video from the Sixty Symbols Youtube channel illustrates this and provides further technical details.

If you’re interested in learning more about vacuums, Sixty Symbols has a follow up video that reveals their surprising quantum mechanical nature. You may be surprised to learn that a complete vacuum cannot really exist and that empty space actually contains energy. The conversational nature of the video doesn’t allow for a rigorous treatment of the subject, but instead offers an enticing glimpse into the exciting world that research scientists get to explore.

Wolfram Alpha: A Computational Knowledge Engine with Educational Applications

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Sometimes one discovers a tool that is incredibly useful, yet surprisingly not as widely known as it should be. Wolfram Alpha, an intelligent search engine that responds to queries with answers as opposed to a list of links, has been around since 2009, but many teachers and students still haven’t heard of it.

This is surprising because there might not be another online tool that is as applicable in as many academic subjects as Wolfram Alpha. Because it is based on Mathematica, one of the top computational software packages used by scientists, mathematicians, and engineers all over the world, it is clearly extremely good at answering math questions. Beyond complex numeric computations, it can do symbolic computation (like factoring polynomials) that is much harder than simply crunching numbers. This computational power applies to mathematics and all of the sciences (is math a science?) but Wolfram Alpha is more than just a fancy online graphing calculator.

It is actually an intelligent system that taps into a myriad of online data sources that enable it to answer questions in almost any field. For example, suppose you wanted to know the identities of the characters in Shakespeare’s A Midsummer Night’s Dream. A simple query would yield the answer and provide additional details. To give a sense of the scope of it’s knowledge engine, Wolfram has conveniently created a page of sample uses that covers a wide range of human activities. If you have never heard of Wolfram Alpha, you will be surprised when you first use it.

Is Mathematics Real? A Thought-Provoking Discussion for Any Math Class

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.

NRICH: An Organized Collection of Math Enrichment Problems and Activities

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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.

Two Minutes of Thermodynamics: Heat Versus Temperature

Sometimes a simple drawing or animation is all that it takes to understand a previously confusing idea. A good illustration of this principle is the following video by Henry Reich which does a good job of explaining the difference between heat and temperature. These two concepts are clearly related but students often erroneously equate them, especially when they first start thinking about them in science class.

A similar, but much older animation from the Eureka! Science series also addresses this thermodynamics issue, but from a slightly different perspective. If you have five minutes to spare, you won’t regret getting a better grasp of this fundamental area of physics.

A Book on Modern Mathematics for Elementary School Students

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Sadly, professional mathematicians play a mostly decorative role in shaping mathematics education. Research is simply a much more attractive activity than the politics of education reform and curriculum development. There are not enough incentives to lure most mathematicians away from their academic responsibilities and to push them into improving the quality of mathematics instruction, unless of course, those mathematicians are parents concerned with the quality of their children’s education. That is the story of Oleg Gleizer, a mathematician and parent who could not find a suitable mathematics program for his five year old son and decided to take matters into his own hands.

The result of his effort is the book Modern Math for Elementary Schoolers [PDF], which bridges the gap between the requirements of school mathematics and a deeper conceptual understanding of the subject. This is not a replacement for a good textbook because it does not cover all of the standard topics, but it is a vital supplement that opens the doors of high level mathematical thinking to elementary school students. For example, the first chapter introduces number partitions, parity, and other basic properties of numbers using Young diagrams, which are important objects in advanced mathematics. This approach actually makes the topic more visual and easier to understand even though advanced ideas lurk in the background. Other topics that are deeply yet playfully explored in the book include straight line geometry (and its connection to physics), straight edge and compass constructions, modular arithmetic, and algorithms.

In effect, Modern Math for Elementary Schoolers [PDF] is a lively guide and collection of problems for parents and teachers who want to weave a non-superficial mathematics, computer science, and physics narrative into their teaching. Contrary to the title of the book, a significant part of the material in the book will be relevant to students of any age. If you’re looking for something similar to Math from Three to Seven, this book fits the bill perfectly.

Photo Credit: faungg

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

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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.

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

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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.