Category: College Algebra

Learning at Scale Slides from ICTCM

Learning at Scale: Using Research To Improve Learning Practices and Technology for Teaching Math In the last 5 years, there has been a rise in what we might call “large-scale digital learning experiments.”  These take the form of centralized courses, vendor-created courseware, online homework systems, MOOCs, and free-range learning platforms. If we mine the research, successes, and failures coming out of these experiments, what can we discover about designing better digital learning experiences and technology for the learning of mathematics? Learning at Scale: Using Research To Improve Learning Practices and Technology for Teaching Math from Maria Andersen   Possibly...

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Abandoning Ship on Wolfram Alpha?

I am really getting fed up tired of having to explain Wolfram Alpha graphs to students.  For some reason, the default in Wolfram Alpha is to graph everything with imaginary numbers.  This results in bizarre-looking graphs and makes it near-impossible to use Wolfram Alpha as a teaching tool for undergraduate mathematics, a real shame.  Now that Google has entered the online graphing fray, I have a wary hope that the programmers at Wolfram Alpha might finally (after two years of waiting) fix the problem. Here are a few examples.  I’ll show you the graph in Wolfram Alpha, on a...

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Collection of Math Games

To view the collections of Math Games, hover over the Games Menu, and go to one of the dropdown categories.   Possibly Related Posts: Learning at Scale Slides from ICTCM AMATYC Keynote Notes: Challenge and Curiosity Full version of Algeboats is out! Board Games that Change Attitudes Level Up: Video Games for Learning...

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NYT Opinionator Series about Math

For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms. The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University. There are several other articles in this series, and if you haven’t been reading them, you really should go check them out.  Assign them.  Discuss them in your classes. From Fish to Infinity (Jan. 31, 2010) Rock Groups (Feb. 7, 2010) The Enemy of My Enemy (Feb. 14, 2010) Division and Its Discontents (Feb. 21, 2010) The Joy of X (Feb. 28, 2010) Finding Your Roots (March 7, 2010) Square Dancing (March 14, 2010) Think Globally (March 21, 2010) Power Tools (March 28, 2010) Take It to the Limit (April 4, 2010) Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students. 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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Logarithm Graphs in Wolfram Alpha

At the Wolfram Alpha Workshop at ICTCM, there was universal disappointment about the fact that you cannot get a graph of a logarithm that is only over the real numbers.  We tried everything we could think of to remove the complex part of the graph. Personally, I have tried and tried and tried and tried to explain the problem with this in the feedback window for Wolfram Alpha, but been universally unsuccessful.   Every time I suggest a change, I am told that the “After review, our internal development group believes the plots for input “log(x)” are correct.” … yes, I know that … that doesn’t mean it’s the answer that most people will be looking for. I find it ironic that “inverse of e^x” produces the graph we’d like to see, and even gives log(x) as an equivalent. But then ask for a graph of  log(x) or ln(x) and the graph will always include the solution over the complex numbers. What’s worse is that W|A inconsistently decides when to use reals only and when to use both complex and real numbers.  For example, the output for y=ln(x), y=x includes the complex numbered plot, while the output for y=ln(x), y=2x-3 includes only the Reals.  What!?!  Actually, I have some idea why this is … it seems that in some cases, if the extra graph intersects the real part of...

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