Category: College Algebra

The power of a good video (Mobius Transformations)

I remember never really “getting” mobius transformations when I took complex analysis. I could perform the mathematics, but what, really, was I doing? This elegant video (thanks to Karen for the link) reveals the Mobius transformations in a way that is so simple and elegant, it is truly remarkable. I will show it to my intermediate algebra class when we get to complex numbers simply because it is an application of complex numbers that they can at least see visually. You’ll probably want to make the video full screen, and there is nice music to accompany the text and transformations, so turn up your volume! Follow the link to the Science Friday file and scroll down to the Mobius Transformations Revealed. If you visit the website where Arnold and Rogness host this video, they have a downloadable version, in case your classroom does not have Internet. Possibly Related Posts: Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in 2020 AMATYC Keynote Notes: Challenge and...

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Can you say ‘Asymptotic’?

Go on, tell me these aren’t some of the most beautiful real-world exponential graphs you’ve seen lately… I was minding my own business, watching Chris Anderson (of WIRED magazine) discuss Technology’s Long Tail in one of the TedTalks (this is one of the things I do while I do mundane tasks like building PDF files and letting Camtasia build .avi video files) … when I saw some of the most beautiful examples of exponential growth and decay in graph after graph after graph. If you’re teaching pre-calculus or calculus this semester, you’ve got to see this and use it in your classes. Personally, I’m sick of population problems and radioactive decay problems… and I bet our students are too! Apparently, Chris Anderson has written an entire book about the “long tail,” that is, the asymptotic behavior at the end-life of a certain kind of technology, when it begins to approach “FREE.” The book is called “The Long Tail” and is available in bookstores everywhere. If you want to read more of Anderson’s musings about technology and the future, his blog can be found here. Possibly Related Posts: Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in 2020 AMATYC Keynote Notes: Challenge and...

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Graphing puzzles on “Maths Online”

Sorry… I was remiss in my postings last week! The beginning of the semester just sucked the energy right out of me. I ran across this nice website last week called “Maths Online” (the authors are Austrian). Although a lot of the applets they provide are pretty simple (read: not flashy, but quite good), the concept of game-oriented learning is powerful. The human mind naturally likes to solve puzzles, improve ability, and play “matching” games (this is how our schemata, the ideas we form in our heads, become more flexible). I particularly like these “Recognize Graphs” games (see below). These are excellent for helping students recognize characteristics of graphs without pulling out their calculator and graphing every function. Just work out enough information about the given function to rule out some of the graphs and narrow down your choice to one graph. Students can play over and over as there are around a hundred graphs in the database. I think this game could be improved by adding a timer… thus encouraging students to “beat” their own best time. The games run with Java (so you may have to download that plug-in if you do not have it). I found that I had to “right-click” on the red buttons to get the game to show up on my screen. For my online class, I’m having them submit a screenshot of...

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