After much thought and consideration, I’ve consolidated four sites at one blog/site.  Over the years I’ve drifted from writing about ONLY math-related topics to writing about a more general topics in learning, futuring, and education. While this site will always remain near and dear to my heart, it is being slurped up into a larger body of content now housed at  When you’re at Busynessgirl, all you have to do is click on the button that says MATHEMATICS and you’ll be back at your old friend, Teaching College Math.  But there’s lots more there to see, so maybe you’ll explore a little too.

Click on MATHEMATICS to be back at all the posts about math from TeachingCollegeMath.

All the Resource pages are on the new blog.  There’s still a RESOURCE tab at Busynessgirl.  It’s got Mindmaps, Presentations, and more (in reorganizing, I’ve added more resources).  There’s still a GAMES tab at Busynessgirl.  It’s still got categories for all the math games, broken down by subject.

PLEASE UPDATE ALL YOUR BOOKMARKS AND HANDOUTS SENDING PEOPLE TO TEACHING COLLEGE MATH!!!   Eventually, there will be 301 Redirects on every page of this site (permanent redirects to the new site).

The RSS will automatically move you (I think).

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Navigating WolframAlpha Pro Features

Last week I had to do a workshop about WolframAlpha, and I noticed that there are three different feature sets: not logged in, logged in, logged in to Pro.

I needed to know which login settings provided which features (especially for giving workshops and working with students), so I decided to be thorough about it.  You can download the PDF of this document, Guide to Wolfram Alpha Features, as well.

Hope this makes the decision-making a little easier for you!


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Copyright Math

This is a short TED Talk by Rob Reid (The $8 billion iPad) that tries to infuse a little “reasonability test” into our blind belief in the numbers provided by those with self-interest … in this case, the music/entertainment industry.


There are several examples that you could turn into signed number addition or subtraction problems.  In my favorite example (about 2:57 in the video), Reid uses what he calls “Copyright Math” to “prove” that by their own calculations, the job losses in the movie industry that came with the Internet must have resulted in a negative number of people employed.

Here’s the word problem I’d write:

In 1998, prior to the rapid adoption of the Internet, the U.S. Motion Picture and Video Industry employed 270,000 people (according to the U.S. Bureau of Labor Statistics).  Today, the movie industry claims that 373,000 jobs have been lost due to the Internet.

[Prealgebra] There are many ways to interpret this claim.  If all these jobs were all lost in 1999, how many people would have been left in the motion picture industry in 1999?  If the 373,000 jobs were spread out over the last 14 years, then on average, how many jobs were lost each year? Using this new “annual job-loss” figure and no industry growth, how many jobs would have been left in 1999? Can you think of other ways the quoted figures could be interpreted?  Use the Internet to see if you can find out how many people are employed in the motion picture industry today.  [Prealgebra]

[Intermediate Algebra] If the job market for the motion picture and video industry grew by 2% every year (without the Internet “loss” figures), how many people would be employed in 2012 in the combined movie/music industries?  How many jobs would have been created between 1998 and 2012 at the 2% growth rate?  If the job market grew by 5% every year (without the Internet “loss” figures), how many people would be employed in 2012 in the combined movie/music industries?  How many jobs would be created between 1998 and 2012 at the 5% growth rate?


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Scale of the Universe

One of my former students (who is still a Twitter user) pointed me to this fantastic animation of powers of 10 meters, called “Scale of the Universe 2.”  I think you’ll appreciate the design and relevance of the objects the authors, Cary and Michael Huang, use to help the user to understand the relevance of scale.  Just like Powers of 10, you can zoom from the smallest part of a cell to the edges of the universe.



The authors have a collection of science- and math-oriented animations at that might be worth checking out too.  They also have a clever little game called Get to the Top (with 82 variations).

P.S. If you’ve never seen the 1977 film, Powers of 10, it was a really incredible movie for its time and you can see it on YouTube.  Another animated version of this film can be found at the Powersof10 website.

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The “Secret Technology Club”

During Winter Seminar Days at MCC, I held a breakout session called “The Secret Technology Club” and I just finished a set of slides to mimic the presentation. Here’s the description:

The Secret Technology Club: If you think that technology power-users have a whole bunch of “secret” tricks and shortcut, you might be right. We’ve been immersed in computer-use for decades now, but very few of us have had much formal training. We learn through trial and error, but it’s difficult to learn what you don’t know exists! If you suspect you’ve fallen behind and would like to fill some of those silly technology gaps, this is for you. This will be a random assortment of tips and tricks for a variety of programs and web applications. You can become a member of the “Secret Technology Club” by learning the secret technology handshakes.

You might be surprised by what you don’t know. I learn something new every time I prepare for this presentation.

Here are the slides for The Secret Technology Club.


I’d encourage you to “play along” and try out all the tips as you go through the slides.

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What if you don’t have enough whiteboards?

Just a quick post to share this video from Betty Love (University of Nebraska – Omaha). Betty attended our MCC Math & Technology Workshop in 2011 and really wanted to try paired boardwork with her students during class. The problem? Not enough whiteboards/chalkboards. The solution? Well, just watch!

If you’ve got pictures or video you’d like to share of your Math ELITE Classroom redesign, or how you’ve incorporated the principles into your teaching, please do!

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Teaching Social Media

You may have noticed a significant drop-off in posting here lately. Well, there are several big projects afoot and they rob me of writing time. While I can’t openly discuss some things I’m involved in, I can tell you about the Social Media course I’m teaching this semester.

I’m team-teaching the course with a colleague from the Business Department (@cvmuse) and it is cross-listed as a Business / Communications course.  We’ve been planning the course for almost a year and it’s been great fun to teach so far (we’re two weeks in to it now).  I will say that my day of teaching Calculus II, then Social Media, then Calculus II makes me feel like I have mental whiplash by the end of the day.  You couldn’t find two topics that are more different to study or teach than these two.

The course consists of three units:

  1. Relate (looking at the human-aspect: psychology, identity, psychology, anthropology, relationships)
  2. Connect (how we create communities, share ideas and information, interact, and manage all these things)
  3. Protect (examining the legal and ethical issues surrounding social media, like privacy and copyright)

Social Media is an open course, which means all the materials, assignments, and class summaries are publicly available and you can participate by using the class hashtag on Twitter (#297SM).  Just follow the RSS on the Studying Social Media site if you’d like to join us.

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Email Manifesto

There are lots of email annoyances that make us groan:

  • When “Reply All” is used instead of “Reply”
  • When someone has a bad grammar or spelling error
  • When someone replies to the wrong person (the “wrong Bob” problem)
  • Weird formatting errors (like sudden font changes)
But these aren’t the reason we hate email, and most of these types of errors are just simple human error.  A consequence of too much multitasking and scattered thinking.The reason we hate opening our inboxes is that many emails, like the “kitchen sink” email (see below), are too difficult to tackle. Emails like this paralyze us and stall our to-do lists.  These “kitchen sink” emails (and other annoying email types) arise from senders who still treat email as the equivalent of a written letter of correspondence to Grandma.  But email (which is now 40 years old) is no longer a substitute for formal written conversation.  It’s now a substitute for conversation.If we could just agree on a few things within organizations, email could be easier for everyone.

I was intrigued by Chris Anderson’s Email Charter (from June 2011) but I didn’t think it was quite right for my organization (a Community College) and a little too technical when dealing with students.  So I wrote the following “Email Manifesto” that I think would improve dealing with the most time-sucking email problems at my college and presented it to the faculty yesterday.  It consists of eight basic axioms:

1.  An email should have one clear subject.

2.  Emails should be simple to respond to and to dismiss when completed.

3.  When an email “conversation” takes a U-turn into new territory, a new subject line is in order.

4.  Need to arrange for an in-person meeting? Suggest several possible meeting times in the first email communication.

  • If the person has a secretary, include them in the meeting request.
  • If there are several people involved, use a Doodle.

5.  If you want the recipient to take additional action outside their normal routine, make it as easy as possible for them to do so.

  • Don’t place the text of the message within an attached document if it can be pasted into the body of the email.
  • Include an easy-to-share blurb and link to website for more information for events, in particular.
  • Don’t link to files on drives that are only available on-site.

6.  If the message contains a lot of information, make required actions clear (bold them or use another color of text).

  • Use phrasing like “What I need from you is …
  • Consider placing the actions at the beginning of the email, followed by the rationale.

7.  There’s nothing wrong with a short email message or response – don’t take offense when you get one. The important thing is that the recipient took the time to read and respond. Lots of emails get answered from a very tiny keyboard or touch-keyboard.

8.  Because it’s difficult to read voice inflection, facial expressions, or body language from an email, consider using emoticons or expressions to convey these emotions.

  • Perhaps this is a jestful comment: Are you kidding me? ;-)
  • Perhaps it makes you sad: Are you kidding me? :-(
  • Perhaps it makes you angry: Are you kidding me? <fuming>
  • Perhaps you are sympathizing: Are you kidding me? <hug>

There are handouts (short and long) and a slide presentation.


Please feel free to share the Email Manifesto, modify it, and give the presentation – just include the author slide with my contact information.  Just a note about the presentation, when you get to the slides about Axiom #8, have your audience read each statement out loud.  This will quickly make the point about why we should use emoticons in email.

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10 Things Our Kids WILL Worry About Thanks to the Information Revolution

After reading this list of “10 Things our Kids will Never Worry About Thanks to the Information Revolution” from Forbes, I was inspired to remind people that technology usually creates just as many problems as it solves.  So here’s my list of the new worries created by the Information Revolution.

1. [Will never have to worry about Taking a Typing Class] They will have to worry about … Mastering multiple input methods and keeping track of which ones autocorrect which words badly.  Now you have to master typing on a keyboard, typing on a tablet device, sliding over touch-keys on a Smartphone, using a numeric-only keyboard on a cellphone, using the voice-input from Apple, using the voice-input from Google, or using the voice-input from Microsoft. Each one of these uses different AutoCorrect features and has different oddities.  That’s plenty to worry about.  One bad autocorrect could lose you a job if you’re not careful.

2. [Will never have to worry about Paying Bills by Writing Countless Checks]  They will have to worry about … Losing control of finances because it’s too easy to make impulse purchases.   When all it takes to make an impulse buy is one click on your phone, tablet, or computer, it’s pretty easy to overspend your income.  And, while $0.99 or $4.99 is a pretty inexpensive purchase, those small impulse App purchases add up pretty quickly.

3. [Will never have to worry about Buying an Expensive Set of Encylopedias] They will have to worry about …  Evaluating the Source of their Information.  I’m sure you know an educator or parent who has “banned” Wikipedia.  Now information comes from Twitter, Facebook, Internet Search, online journals, firewalled “scholarly” research journals, Wikipedia, and more.  Is it good information or bad information?  Well, now you have to make that determination too.

4. [Will never have to worry about Using a Pay Phone or Racking Up a Long Distance Bill]  They will have to worry about … Racking Up a Roaming Charge or Data Overage Bill.  The last time I roamed on my phone in Canada (for about 30 minutes), it cost me $27.  The current overage on a wifi hotspot on Sprint is $50 per GB (after you surpass 5 GB a month).   And, for the record, most phone plans DO come with a limitation on certain types of minutes, and the overages on those are NOT cheap.

5. [Will never have to worry about Having to Pay Somebody Else to Develop Photographs]  They will have worry about Managing the Storage and Rights on their Digital Photos and Videos.  Now they need to decide on their photo- and video-sharing strategy.  Where will they store their photos?  On a hard-drive only? (better have a backup system in case the computer is stolen or lost)  In the cloud? (Flickr, Facebook, Picasa, Vimeo, YouTube …)  What kind of access do you want to give to your photos?  Should they be private or public? Private to specific groups or all your friends?  Do you want to copyright the photos?  If so, which copyright should you use? Oh, and did you still want hard copies of some photos? Then you’ll have to purchase and maintain a printer that is capable of printing color photos (together with proper toner or ink + special photo paper).

6. [Will never have to worry about Driving to a Store to Rent a Movie]   They will have to worry about … Violating Copyright by Accident when they Make their own Videos.  The U.S. Copyright laws have become so complex and confusing that you can accidentally violate them when you make a home movie in your living room while some copyrighted song plays on the radio in the background.  One can imagine a future when being sued for copyright infringement is an almost daily occurrence for the average person.

7. [Will never have to worry about  Buying or storing music, movies, or games on physical media.]  They will have to worry about … Being Locked in to a Single Media Device (and Format) Forever.  Kindle books won’t work on Nooks, Nook books won’t work on Kindle, and iTunes songs won’t play on Android.  Once you make your choice of digital format for books, music, and note-taking, you are either locking yourself in forever, or facing a very expensive switch to a new provider at some point.  The choice of media network not only locks you in to a format, but might lock you out of a sharing network with some of your friends.

8. [Will never have to worry about Having to Endlessly Search to Find Unique Content.]  They will have to worry about … Managing the flow from the firehose of information. When I was a kid, you could write a research paper after consulting your school library and your set of Encylopedias.  With the information now available (and having recently written a dissertation) I can say that having too much access to information can make it incredibly difficult to know whether you’ve thoroughly researched your topic.  How much searching is “enough” to say you’re done?

9. [Will never have to worry about Sending Letters.] They will have to worry about … Responding to Communication on a Multitude of Platforms and Networks.  A professional will have to communicate with their colleagues through email, several social networks, texts, and synchronous communication systems.  Not only is this a lot to manage, but each medium requires different etiquette. If you screw up the etiquette of the medium (for example, you use text-speak in an email) you’ll look like an idiot to the receiver.

10. [Will never have to worry about Being without the Internet & instant, ubiquitous connectivity.]  They will have to worry about … Getting enough Sleep and Managing Stress.  In an always-on world, you have to be able to disconnect to stay sane.  Many youth go to sleep with their cell phone on their pillow, unable to disconnect from their social network for even one minute.  As these sleep-deprived teenagers become adults and parents, one can only imagine the damage to their psychological well-being if they are unable to learn to disconnect.

So, yes, there are some things that our kids will not have to worry about thanks to the Information Revolution.  However, I don’t think technology has exactly made it less worrisome to grow up in today’s world.


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Abandoning ship on using Wolfram Alpha with Students

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 TI-84 Plus emulator (TI-SmartView), from Google Search, and from Desmos Graphing Calculator.  These are all the “default” looks.  Wolfram Alpha consistently shows this confusing imaginary view as the default whenever working with graphs involving variables in radicals.

Example 1:

Example 2:

Example 3:

I was hoping to really teach my College Algebra students to use Wolfram Alpha next semester.  But, between the Logarithm Issues and this graphing issue, I’m afraid I’m going to have to abandon ship on using Wolfram Alpha as a teaching tool for students. Students simply don’t have enough mathematical sophistication to look at the graphs and realize that they aren’t seeing what they are supposed to be seeing and I’m seeing far too much confusion on assessments that are caused by the oddities in graphs and logarithms on Wolfram Alpha.  What a shame that we can’t work this out, huh?

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