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!

So I Played Pong in Math Class Today

That's right, I played pong in my Calculus I class today (assuming today is this past Monday).  No, it wasn't this kind of pong...

Image source:   http://www.aboutdwi.com/blog/tag/teenagers/ 

...but it was based on that idea - with my own "twist" of course.  

My class had their first exam (limits - I'm still doing Calculus I in the "conventional" order).  Anyhow, I often try to do some sort of review game with the class the day before the exam.  During my couple of years of teaching, the review game was almost always Jeopardy.  The students loved it then (they even added me to the "Men of Mathematics" poster in the hallway as the inventor of math jeopardy)  Fun times for them, but honestly, Jeopardy is a total bore from my perspective...especially when done over and over.

A couple of years ago, I managed to create a working "Who Wants to Be a Millionaire" game, complete with the lifeline allowing them to phone a friend using their cell phones.  Great hilarity ensues when a team of four or five is all on the cell phone trying to explain (and then acquire) an answer to a question within the 60 second time limit.

Flash forward to last year, I added in a game based on the bar trivia game (referred to as Quizzo in my neck of the woods).  I guess the bar theme got extended a bit further this year with my Limit Pong game.

Set-up:

I found four identical boxes (I used baseball card boxes - something I have plenty of) and labeled them as Team 1, Team 2, Team 3, and Team 4.  I then took a bunch of styrofoam cups (approximately 30) and used a sharpie to put a point value on the inside of the cup.  The point values varied, the majority of the cups were worth either +1 or +2, though I scattered in a few +5s and one +10.  To keep things interesting (and to add some strategy to the game), I also added in a few -1s and -2s on the cups.

From there, all I needed was a ping pong ball (I happen to advise the table tennis club on campus as well so that was easy enough to acquire).  For the first time, I had to spend a bit of time going over the rules, but I imagine if I play the game again with the same class I could easily fit in a fifth round (and stay within the 65 minute class period).

Rules:

The rules were fairly simple.  I split my class into four equal teams.  Each team member got a worksheet packet for his or her self AND the team got an extra "team packet".  I gave the teams a few minutes to work through the first page of the packet.  The goal of the problem solving round is to fill out the team packet with the team's final answers.  After time was up, the groups swapped packets and graded each other's pages.  At this point, I posted the answers on a PowerPoint slide so that students could copy the solutions on their own, personal packets if they wished.

Each round was worth a set amount of points (usually 1 point per question).  At the end of the scoring phase, one member from each team (this role rotated each round) came up to the front of the class as the "thrower" for that round.  Using the points earned during the round as a currency of sorts, the thrower could attempt to throw the ping pong ball (with a mandatory bounce) into their team's box OR they could select a cup (all cups were facedown so it was a mystery as to the point value) and then place the selected cup in a box.  Positive point cups go in their team's box, negative point cups get to go in one of the other team's boxes.  In my cases, each box could hold up to five cups, so once a box reached five cups you could stack (and therefore, replace less desirable cups).

We repeated the process three more times, with a different student getting the opportunity to throw each round.  At the end of the day, the highest point total (from the throws only) won!  

For the first attempt, I liked the game a lot (and it seemed popular with the students).

The good:

I did this activity in both of my Calculus I classes.  In one class, the students recognized there was a strategy in terms of whether to throw the ball in the hopes of scoring points and grabbing cups (in hopes of making future throws worth more).  By the way, a throw that lands in the box (but not a cup) was worth a single point.  You might even say the teams attempted to optimize their score by carefully choosing throws and cups.

The bad:

The other class didn't grasp the strategy at all.  The initial throwers all opted to fill their box with cups (as much as they could).  The next group also grabbed cups (replacing as necessary).  By the time the third and fourth throwers were up, they only had the option of throwing.  On the other hand, the average team score was much higher with this group - though rumor has it some of them were well-versed in the art of beer pong.

Things to try:

I need to emphasize the solutions a bit better.  Students got too excited about the throwing part and would sometimes not worry about problems they got incorrect.  I suppose that's the danger of any game where the students are emotionally invested, but it's still a problem that I need to fix for next time.  After all, what's the point of reviewing if the students don't make the best of the time and opportunity?

Game modifications:

The game itself worked fine, though I think it might be fun to have a bit more variety in terms of the number of cups.  Scores would have been more impressive if the boxes held more cups - some teams scored zero points simply because they were lousy pong players.  I don't mind skill having a role, but it didn't seem right that teams couldn't land a single ball in the box.  The students really enjoyed it when they grabbed a negative cup and got to place it in one of the opponent's boxes.  Both classes used some strategy in terms of the negative cups (using them to either wipe out big positive gain cups or to try and weaken the first place team).

All told, it was a fun activity that my students really seemed to enjoy.  I haven't finished grading the exams yet, so I can't even begin to make any guesses as to the effectiveness of the activity compared to previous year's games but I'm sure I'll try to make some conclusions at some point in the future.  Until then, if you have any review games or other ideas to share with me, please do so!

First Day Plan: Calculus I

I hope to document some of my classes throughout the upcoming semester on the blog.  I figure it might be a good way to spark some dialogue with other readers on ideas and (especially) improvements.  It will also serve as a nice diary of sorts for myself when it comes time to assess what did and did not work.

For today's post, I present my plans for Day 1 of my Calculus I course.  In the past (I've taught Calculus I for three or four years now), I jumped right into the first lecture on limits after spending about 10 minutes going over the highlights of the syllabus (and explaining our course management software - Moodle).  After the introductory lesson I limits, I usually handed the students a PreCalculus (and algebra) review worksheet.   Here's one page of my review worksheet...

As you can see, the worksheet isn't trivial for the students - but it's terribly boring.  Even worse, there are three more pages of similar work, including a page of graphing.  I have found that my students need the review (hence the worksheet) but based on many of the edu-bloggers posts that I've read over the summer, I decided to try something different this year.

This time around, I have different ideas (most of which I've stolen from a variety of great bloggers).  I plan to greet my students as they arrive in the door with a PowerPoint displaying the course name (and my name).  That way, in case a poor freshman wanders into the wrong classroom he or she will (hopefully) figure it out right away and leave before they get too embarrassed by the gaffe.  As the students file in and admire my beautiful slide (just kidding), I will hand them a survey called "Who Am I?"  I stole the idea (even the name) from Dan over at dy/dan.

This will give the "early birds" something to do and I hope it will also set the tone that my class isn't going to be a "typical" math class (whatever typical means...mostly bad things I'm afraid).  After I introduce myself, we are going to split up and jump right into an ice breaker activity (cup stacking, also stolen from dy/dan).

At this point, I should be able to say that I've spoken to every student in the class and hopefully interacted (either formally with math questions or informally based on something I saw on their Who Am I? page).  Following the cup stacking activity (which I'm estimating about 10 minutes - I have a PowerPoint presentation that will serve as a prompt for each question).  The students will first guess how many cups are necessary by themselves and then answer all remaining questions as a group (including comparing each of the guesses).  I just went through my school's Writing Across the Curriculum training so the idea of writing responses to questions is fresh in my mind!

At this point, there should be about 30 minutes remaining (give or take a few) in a 65 minute class.  With most of the remaining time, I'm going to do a variation of a drawing activity (that I also saw on a blog but I don't remember where - probably dy/dan since that's where everything else came from but I can't be sure).  Basically, the idea is to have one student in each group act as the "eyes" and a second to act as the "hands".  The eyes are looking at a picture on the PowerPoint slide while the hands have their back to the screen.  The eyes have to describe what they see and the hands have to listen to the description and make the best drawing they can.  

My pictures begin with a happy face (very simple) and then progress through an increasingly challenging series of graphs (linear all the way to horrible discontinuous graphs).  In fact, one of the graphs was pulled directly from my Day 3 lesson (foreshadowing - ooooh!).  The final drawing should be a riot - after a bunch of mathematical functions, the final drawing is of a train (and fairly detailed at that).  It should be fun!

Finally, in the last couple of remaining minutes in the class, my students will be given their assignment - essentially a longer survey (with a little bit of mathematical review thrown in).  

I've scanned the final page of the survey, mostly because it's the one original bit (the beginning questions in the survey are inspired by a post on Long tails of \int e^r est) of my day one lesson.

As I write out my lesson (something I rarely do besides the PowerPoint), I think I've got a day that should be more interesting than the usual "syllabus day" for day one.  In fact, you might have noticed that I didn't mention going over the syllabus at all - I actually have three slides dedicated to it (one on my contact information and office hours, one on the grading scheme since that's all students care about anyway, and the final on the Moodle course page password).  The syllabus is wedged in between the two main activities - and will be handed out while students are reorganizing themselves.  

I have no idea if the new plan will make the class any better at algebra and/or PreCalculus as compared to previous semesters where the main assignment was the lengthy worksheet, but if I had to guess I'd say the students won't be any worse on average.  I know for a fact that the day will be more fun - I hate syllabus days as much as anyone, and the students seem to hate it if I jump right into a lecture on day 1.  Hopefully they will be too busy having a good time to realize that they are learning (or at least reviewing) mathematical concepts. 

"Did you just describe that graph with the word multiplicity?  What does that mean again?"

At least, that's what I hope to hear on Monday.  We shall see.