So, if we want to change the path that the country is on, then how ‘bout raising the public appreciation for how important mathematics is, realize that it is the queen of all sciences giving a great amount of credibility to the other sciences.

Although I didn’t have much of a problem compared to others in my early years learning math, I remember there were a lot of confusing things that didn’t make sense at the time. For instance, when they were teaching us the rules of algebra, the teacher would lead off the course with, “For all Real numbers, ...” At the time I was confused but afraid to say anything as others likely were, but I was thinking, duh, what do expect, fake numbers? We didn’t learn imaginary numbers until the end of the year. So I thought the teacher was being strangely awkward and redundant.

Once I finished school, I bought myself textbooks and retaught myself from scratch. When teachers teach, they tend to skip chapters and material and probably presume the students understand more than they really do. But if kids get confused (or people in general), they are not going to speak up if they think their thoughts are too stupid to ask. I surely didn’t want to be the one to ask, “Is there such thing as imaginary numbers in math?”, and be ridiculed for such stupidity for thinking I was serious.

Good points Scott Mayers. Imaginary numbers is one of those annoying problematic terms in Mathematics, it and “real” are misnomers.

Everyone else, in school the only bad question is the question that you don’t ask. I wish this thread to be the same way. Students need that sort of re-assurance that the classroom is the place for questions, that’s really the best place to ask them. Without an answer to your question, you’ll be confused about the rest of the semester and beyond. Reviewing and teaching yourself the math that you missed, for whatever reason you missed it, is a great idea. Why waste an education? Math texts have changed, you can find one written in a style that YOU like, now-a-days. When a student asks a question, they should expect that the teacher try to answer it for them in a way that the student understands.

Mathematically speaking, imaginary numbers become real when multiplied together, real becomes imaginary when multiplied by an imaginary.

Electrical voltage, amperage, and power are calculated with complex numbers. In physics, the complex numbers really exist, they are how the physical world behaves, they are measurable, that is their importance, their application, their practicality. The imaginary number seems like a mathematical impossibility, a number that can become real or imaginary (not real) in mathematics, but in physics they both really exist. Once again, reality is more fascinating than fiction! Some people think that if you know how to count, then you know all the numbers, but there is more to number theory than just counting the naturals.

This video is good, I like when the narrator Derek Owens says that “In that sense, I like to think of the complex numbers as the real numbers, unfortunately the term ‘real’ is already taken. But these are real in the sense that, ‘they are the numbers that really do the job’.” [9:18] That Derek Owens shows some good insight, which makes his a pretty good math video.

The Cassiopeia Project has got some videos on quantum mechanics that are very accessible and a bit mathematical, pleasantly so. Other videos too. Click if you’d like.

This video series was good because they included the math. They include it as animations, which really makes the math clear. I originally saw this on PBS TV in high school, at a time when I was struggling with math and loosing my enthusiasm for school. This show really picked up my spirits. It’s as compelling as it is instructive. The math should be included, not left out, for the sake of popularity.

They introduce calculus in the second episode.

“Mechanical Universe” was done well by Caltech Professor David Goodstein and Dr. James F. Blinn did the computer animations.

NOVA did a good job exploring the history and potential of fractals. I loved how they stressed the connection fractals have to natural complex shapes such as branching trees/blood vessels, the dynamic shapes of clouds, the patterns of noise in telephone lines, the flow of water. Shapes with amazing properties of being complex, but stemming from simple rules.

The complex fractal shapes having strange properties like an infinite perimeter but within a finite area, a property that prevented mathematicians of the past from plotting them by hand. Computers overcoming that limitation. Or the property of self-similarity, where zooming in closer to the shape the fractal looks the same as you get closer to it. The property of roughness too.

And then there is the artistic connection where artists, using some math tools, found new abilities that they never had thought possible before. When generating virtual landscapes with drama, grandeur, and detail in Hollywood movies, fractals do it, and more artistry.

Fractals are opening up biological, artistic, and other fields, fields that used to be considered off-limits, now open to a new possibility… mathematics.

A member of our monthly evening CFI discussion group often brought his ten year old daughter there, and she was working on a simple mathematical puzzle. I dug out one of my earliest math puzzle books and brought it for her at the next meeting. However, it got me to thinking. I saw my first math puzzle book when I was about ten and in the youth section of the local library, and I got hooked. I must have gone through every puzzle book they had there, then got my parents to buy me others. While I couldn’t do quite a few of them, I read the well spelled out solutions in the back of the books. It had never occurred to me, but that was probably the reason that I loved algebra from the first moment, and it made complete sense to me. Little did I know that those books were teaching me the concepts necessary while I thought I was just playing.

Good story Occam, and yes I think that playing and discovery are the natural ways to learn and school should have more of that, bring out the natural scientist in everyone.

That’s why Good Math Videos are merely good and not excellent. Television is an old technology that shows videos, but videos are one-way there is no interaction its just the obsolete couch potato idea again. Instead, now-a-days, we have computers, these are the modern technology that allows interactive discovery and play, even if that potential has not been well utilized by commercial software. I do see some who agree with me who are offering to step forward with some good interactive “physics java applet” (just Google search that phrase to see many examples). Here’s some examples:

That’s shows that the free software movement can do some things that the commercial software won’t really do. Java is just the language of choice in achedemia and science it seems, rather than Flash. So you’ll need the proper java plugins to use those.

Once the video becomes interactive then it could be called many things, like interactive animation, simulation, video game, virtual laboratory, etc. Video games are made with good physics simulations, the math really is in there, and if they’d show the audience some of the math then they could become educational, but no that hasn’t happened.

And to step from excellent interactive discovery up to great, one needs a customizable, self documenting, programmable interface to the interactive video. They need to offer a good interpreter so that the audience can recreate, customize, experiment, and expand the interactive video that they’re using. Books are good, as you said, but they just aren’t as dynamic and exciting as a computer can be, one can play a video game not just read it.

Interactive tests where the test tells you when your answer is wrong, giving you some constructive or encouraging feedback immediately, and then giving you a chance to look-up and double-check your answers, this may sound like a very simple idea, but I’ve tried it and it is a very good learning technique. It can be scored as 95% or higher is passing. Astropitch is close to what I’m talking about, but has no feedback and unlimited retrys.

If Kahn has Gates’ money behind him, I hope he learns that video is the old has-been technology, and dynamic interaction that is customizable is the modern way. With Gates’ money, there is no reason that modern learning tools can’t be made into a Flash, Java Applet, Javascript, widget for a web browser, desktop application, or cell phone app. I hope that Kahn gets that idea and stops putting so much energy into the one-way videos. But did you hear him say that he wants to use his video to free up the teacher’s time for more face-to-face interaction? Isn’t that ironic, computers providing more time for in-person human interaction! Its ironic, but no surprise that bringing automation home can do that.

Long term memory is another big issue that needs better techniques for proper learning.

Richard Feynman asks why math, but can’t answer the question with anything but, math is needed. At the end of part four he explains that as people argue that they prefer one philosophy or another as the best description of nature, that technique never works only the tests will work. Huh, funny the way he puts it.

Richard Feynman asks why math, but can’t answer the question with anything but, math is needed. At the end of part four he explains that as people argue that they prefer one philosophy or another as the best description of nature, that technique never works only the tests will work. Huh, funny the way he puts it.

Wow! Feynman criticizes ARISTA, the National Academy of Science, and the Nobel Price all in one video! Do the math, do the science, don’t publicize yourself… good one.