For essentially anything about mathematics, you can find a precise, concise node about it, a node enhanced by hyperlinks to related equally crisp and accurate nodes, at WolframMathWorld. With justifiable pride, this marvelous mathematical network calls itself the web’s most extensive mathematics resource.
The Connected Graph detail image enters the WolframMathWorld through a cluster of Small World Network subjects, which are part of graph theory, in discrete mathematics. The Small World cluster provides the math behind six degrees of separation, the Kevin Bacon Game, and hyperlinking patterns in the internet.
The image with this post is from a MathExpression.com video explaining how to deal with brackets in an equation. Frankly, not having had a course involving algebra since 1957 (yes, that’s 51 years) I really loved the video’s explanation, and will be coming back for more explanations. Recently I have been watching physics DVDs about string theory; though the lecturer refers to only a few equations for me to cope with, I am grateful for MathExpression.com. It is an ideal tool for me to check what I don’t understand in the equations.
The example of the video’s usefulness to me illustrates a key power of online learn nodes: the level of learning difficulty of the tutorial does not restrict the video’s availability to learners of any particular age, grade, or geographical location. I doubt many string theory students in their seventies have used the MathExpression.com tutorial on removing brackets in algebraic expression. Most visitors to MathExpression.com are probably high school and college students, with a few precocious grade schoolers and forgetful graduate students mixed in.
If I were teaching algebra, I would find MathExpression.com a fine source for its lessons, tips, and practice. The delightful voice on the videos is also worth the visit: she sounds like the voice of algebraic AI.
Just about every American kid we see these days has a mobile phone in his or her pocket. Nothing could be simpler technically than seeing to it that each of those phones has interesting reading practice, the simple rules of grammar and basic math tutorials available for the youngster to use whenever the mood might strike — bored on the bus or in the car backseat, extra time in class at school or whenever.
Mobile learning would be trying something new. This very serious prediction from ETS researchers tells us why new really do have to try something new:
There is little chance that economic opportunities will improve among key segments of our population if we follow our current path. To date, educational reform has not been sufficient to solve the problem. National test results show no evidence of improvement over the last 20 years. Scores are flat and achievement gaps persist. Hope for a better life — with decent jobs and livable wages — will vanish unless we act now.
We must raise our learning levels, increase our reading and math skills and narrow the existing achievement gaps, or these forces will turn the American Dream into an American Tragedy — putting our nation at risk.
The interactive practice here for counting money would give mobile phone users exercise for their brains along with their thumbs. Math
Information Aesthetics pointed to this page as and example of visuospatial illustrations demonstrating some interesting properties of numbers. Whatever we call them, these are great images for grasping some mathematical concepts. Math
The Coin Paradox is one of dozens of animations of mathematical ideas on this page of Mathworld. WolframResearch creates and hosts MathWorld as open learning content that is a model of grand scope and excellence for 21st century education.
The paradox? After a half rotation of the coin on the left around the central coin (of the same radius), the coin undergoes a complete rotation. In other words, a coin makes two complete rotations when rolled around the boundary of an identical coin. Hummmm….?