Redesigning Calculus I - Ideas Appreciated!

The college where I work had finals last weekend and has graduation this coming weekend.  After the festivities, I'll be officially done with work for a few months.

Although I love getting some time off, it's not all fun and games this summer for me.  In fact, I might end up doing as much (or more) work this summer as a I did last summer when I was prepping a brand new course offering.

Why you ask?  Well, I'm hoping to redo the entire Calculus I curriculum.  For the past five years, I've been teaching Calculus I using a variety of textbooks.  Unfortunately, none of them made me super happy - and based on polls I've given my students, the students didn't like them either.

Change #1:  No required textbook

I'm sure many of you have done this already, but for me (and my college), it's a big step.  This means that I'll have to write all my own exercises for the students AND update my notes to make sure all necessary information is contained within the course materials.  Luckily, my notes are fairly thorough so the second half of the problem shouldn't prove to be too difficult.

I suppose I ought to back up and state why I got rid of the textbook.  There were two main reasons.  The first, as I mentioned above, was that I couldn't find a book that pleased both the students and myself.  Some had only super easy problems, others had only hard problems.  The books that fell in the middle seemed to have muddled descriptions within the pages.  Semester after semester, no matter which book I used I would consistently get 60% or more of the students saying they never use the book (except to copy homework problems).  I already provide about half the assignments in worksheet form (homework that I've written myself) so doing the second half hopefully won't be too difficult.

The second reason I got rid of the textbook was because of the cost.  $100+ for a used calculus book is terrible.  It's even worse considering you can find most of the information online with a quick search on your smart phone (and not pay a penny - well, besides that smart phone data fee of course).

Although I've gotten rid of the textbook, I would still like to offer the students a chance for a free open source Calculus book.  Do any of you know of a good book (or multiple books) that are available for free?

This is the first post in what will probably be quite a few posts detailing the changes I'm making to the Calculus I curriculum.  As usual, I'd love to hear what you have to say!

The Calculus Funk.

I'm teaching Calculus I again this semester (two sections) and therein lies the problem.

Again.

And again.  And again.

I've been teaching Calculus I for way too long.  If I'm being honest, it's gotten stale.  My lessons are all on PowerPoints that have been scrubbed clean of errors and ambiguities.  My stash of worksheets cover almost any area where a given class needs more practice.  My review games are carefully tied to the material on the exams.  Heck, even my labs are now a solid representation of how the course material is used "in the real world."

And yet.

I can't shake the funk.

It's a case of "been there, done that."

Even worse is the split of students this semester.  One of my Calculus classes is scoring much, much higher than any previous class (in terms of class average).  The other class?  One of the lowest averages ever.

Sometimes it's luck of the draw I guess.  Sometimes it's the students within the class.  And sometimes, just sometimes, it might be the instructor.

I need to come up with new ideas and methods to engage my lower achieving class - clearly they aren't responding to the same things that my other class is.

I have my theories on why, but there's little time for "why" right now.  Right now, it's time for "how".

How, that is, can I improve the class?

Student Responses on First Day Survey in Games & Gambling

I've been teaching in front of a college classroom every semester since I graduated from my undergrad institution back in 2005.  In that time, I believe I've given a first day survey every semester (except maybe my first).  The classes that I've taught have changed over the years (as has the institutions where I teach) - and the survey has changed as well, but the goal of the survey remains the same.  I want to get to know my students as people AND I want to know what they know (and what they think they know) coming into the course.

I asked the students a variety of questions on the survey - but I've only highlighted the "interesting" questions.

Why did you sign up for this course?

• Looked like a fun and informative course to fill a distribution requirement  (9 people)
• Heard it was a fun class (1 person)
• Love games (1 person)
• For distribution (without any mention of fun/interesting)  (3 people)
• Variety in math classes (3 people)

Note:  The first question was a short answer so I categorized the answers as best I could.

If you had to, which ONE of the following games would you play (with the goal to make money at a casino):  

• Craps:   1
• Roulette:  3
• Blackjack:  11
• Slot Machines:  2
• Keno: 0

The first question was designed to figure out my audience.  The second was designed to figure out what preconceived notions the students had in regards to gambling.  I also had a series of true/false and a few ranking questions on the survey (interesting to me but probably not great blogging fodder).

What information can I glean from the two selected questions?  Looking at question #1, it seems clear that the majority of the students signed up because the class sounded like a fun way to earn their mathematics distribution credit.  While some mathematicians may cringe at that idea, I think it's awesome.  It's not easy to have a non-majors mathematics class that the students are excited about before they even step foot in the classroom.

The second question was interesting to me because the majority of the class decided that Blackjack was the way to go if the goal was making money.  It's clear to me that movies like 21 (plus the glamorized depictions of casinos in movies like Ocean's 11 have an effect on people).  It was also interesting that no one chose Keno (a wise move by the way) despite the fact that Keno is also available at a lot of non-casino locations (including the Maryland state lottery).

I should mention (for those that are curious) that there isn't exactly a "correct" answer to the second question.  Keno is clearly wrong in terms of things like expected value - but if you only have $1 to bet, you have a slim chance at winning say $10,000 in Keno - unlike any other game in the list!  I didn't ask for any sort of written explanation from the students so I don't have any idea why each student chose the game they did.  The real value (for me) will be the follow-up survey at the end of the semester where I'll put the same question with a spot for a written explanation.  We'll see what they glean from the semester's worth of material!

Another Semester is About to Begin

Another semester is about to begin, only this time my teaching load feels a lot lighter!  Once again, I'm teaching two sections of Calculus I (with labs) and a section of the course I developed last semester (Mathematics of Games and Gambling).  The Games and Gambling course went quite well last semester though I don't have the results of the anonymous survey that all our students take at the end of the semester.  I expect there will be a few complaints but for the most part I'm expecting good things.

So where does that leave me for Spring 2013*?
*It's weird writing 2013 isn't it?

Well, I have two big goals for the semester.
1.  In Games & Gambling:  Tailor the course to the individuals in the class.  In other words, don't fall into the trap of doing exactly what I did last semester simply because the lessons are complete.  Last semester I tried to hit the interests of the students, let's do it again.
2.  In Calculus I:  Come up with some way to make labs enjoyable learning experiences rather than current Mathematica syntax heavy monstrosities that they are now.  I did manage to rewrite one lab last semester and had fairly good results - so I know it's possible.

  What are your teaching goals for the upcoming semester?

Instant Insanity

Although one might take the title of this particular blog post to be an assessment of the craziness that is the end of another semester, I assure it's not meant to be that way.  Quite the opposite in fact.  My semester went quite well, especially the Mathematics of Games and Gambling class that I designed and taught for the first time.  As I've down throughout the semester (though admittedly not nearly as often as I would have liked), it's time for another update for the course (here's a link to my last few course updates...published back in September and another in October).

Throughout the semester, I covered a variety of topics in the class (as a reminder, the class was designed for non-mathematics majors to take as an elective to fulfill distribution requirements).  The topics that covered included (but are not limited to):

• Chuck-a-Luck
• Roulette
• Craps
• Keno
• Five Card Stud
• Texas Holdem
• Lotteries
• Instant Insanity

It is the final topic that shall be the focus of today's entry.  

For a few semesters now, I've lobbied my mathematics department to allow me to teach an experimental course.  For the longest time, I wanted to do a 300-level Introduction to Graph Theory course.  Alas, our mathematics major is quite small (and most of our majors aim to teach at secondary schools so their electives get filled by education required classes like geometry).  As such, it has been deemed unlikely that I could ever get enough students to adequately fill up a Graph Theory course.

Last spring, I changed gears and proposed the Mathematics of Games and Gambling course instead.  As you can guess, that was approved (and has, for the record, been approved for the upcoming spring semester as well).  Although I couldn't teach graph theory, I still managed to find a way to squeeze in a few days of graph theory (at a basic level) by using the 1980s puzzle "Instant Insanity."

Before I describe how I taught the lesson, I will say that overall the lesson went extremely well.  I even put a question on the final exam which almost every student got correct!  If you have taught a lesson using Instant Insanity (or something similar), I'd love to hear about it.  If you happen to be inspired in some way to use what I did in your own classroom, I'd love to hear about your experiences when they happen!

Our class periods are just over an hour long, so for the first class of the unit I showed the students the original Instant Insanity advertisement after a short PowerPoint presentation that covered the various graph vocabulary that I wanted the students to know.  

The terms weren't difficult, but they weren't all simplistic either (bipartite graphs).  

The next class was much more of a riot (for me anyhow).  I gave each student a colored sheet Instant Insanity puzzle blocks which they had to cut-out and tape together.  Watching college students do something that many haven't done since a middle-school art class was definitely amusing (and somehow a bit worrisome too)!

After constructing the blocks, the students spent the remaining time trying to solve the puzzle.  While a few did succeed, the majority of the class did not successfully complete the confounding game.  I didn't provide any hints as they left class that day, though I did encourage them to find a "mathematical way to solve the puzzle."  

The final day of the lesson was the big one - how to solve Instant Insanity puzzles using graph theory. To begin, we discussed how each block could be "unfolded" to a two dimensional image.  

From there, we can easily pair the opposite sides.

Once the three pairs are made (front/back, top/bottom, left/right), all you need is a graph with four vertices (one for each of the four possible colors).  Draw an edge that for each of the three pairings.  For example, if the top color is blue and the bottom color is red, there should be an edge connecting the blue vertex to the red one.  If the left and right colors both happen to be yellow, there would be a loop connecting yellow to itself.  In total, there should be three edges for each graph (one graph per each of the four cubes).  

Using the four graphs (or if you prefer, a single graph that combines the four small graphs), you then look for a path that uses an edge from each cube once and that makes each of the four vertices have degree two.  Once you find one such solution, find a second solution.  The first solution corresponds to the front and back of the four cubes.  The second solution corresponds to the left and right.   Note:  Once you've found the front/back and left/right, the top/bottom is forced (and therefore you do not need to worry yourself about those)!

I've skipped over a few of the finer details, but in essence that's how you solve an Instant Insanity puzzle.  For those who want to give it a go, here are three puzzles.  It should be noted that some puzzles may not be solvable.

Good luck!