How Did Your Math Courses Prepare You For Teaching?

So I saw this today:

Will be giving a talk next month--need to know: How did your math courses/major prepare you for teaching? NB: Math specific, not Ed courses.
— Breedeen Murray (@btwnthenumbers) February 14, 2014

And it got me thinking...

First, a bit of background.  When I was in college, I ended up completing a Computer Science major along with a mathematics major.  I entered college thinking I'd become a secondary teacher, but then never took a single education class since the combination of math and computer science courses filled up all my time!  A couple years later, I found myself earning a masters (this time in education) and now I'm teaching (mathematics) at a four-year liberal arts college.

So, I can easily discuss how my math major prepared me - and how that major compared to the education classes I've since taken.

First, the majority of my math classes taught me how not to teach.  Too much lecture.  Too many book problems.  Almost no interaction.  On the other hand, my later education classes taught me that too much group work is just as bad if not worse.  There's a fine line somewhere between those two extremes.

My math major did have one useful course though in terms of teaching down the road:  Math Colloquium.  It was in colloquium that each math major was required to pick a faculty adviser and a topic.  Over the course of the semester, we had to prepare a 40 minute talk, and then near the end of the semester we actually had to give our talk to our fellow students and all our professors.

Colloquium was a stressful time, but once it was over I realized how much I learned about teaching.  I had to make my first ever PowerPoint (for instruction purposes).  I had to fit a lesson in a time frame.  I had to realize what my audience did (and did not) know coming into the talk.  I had to keep the professors attention while simultaneously not losing the students in the minutia of the mathematics of the topic.  Finally, I also had to impress everyone because my grade hinged on doing well.

I think that colloquium was truly the only class that prepared me to teach at all because it was the only class where I had to stand in the front of the room and actually teach.  I look at teaching a lot like I look at mathematics:  you can watch someone else do it all you want - and it might even make sense - but it isn't until you actually try it that you'll know whether or not you understand it.

Looking at my own teaching from my students point of view, I hope they don't have a lot of the same complaints that I did when I was in their shoes.  I try my best to incorporate more problem solving, less book work, and the occasional class activity.  I attempt to refrain from lecturing for more than five or ten minutes at a time.  I also try to relate the material at hand to true "real world" applications, not the "real world" you read about in textbooks (typically the final six or seven word problems in a chapter or section).

I also think this question deserves a lot more time and thought on my end - but I don't have a lot of time since I have my own teaching to prepare for the upcoming week!  I did, however, think it was worth jotting a few things down in response...and perhaps spark some sort of dialogue with other teachers out there!

Getting Back on Track: A Blog Re-Launch!

I've been reading quite a few different educational blogs (and Twitter accounts) lately which have all served to motivate me into re-launching my own educational blog.  So, here goes:

----

Since I'm starting from scratch (though I won't be deleting any of the previous drivel that I published), I should first introduce myself.

I'm a 30 something (ok, 30 exactly) math professor at a liberal arts college who doesn't have a Ph.D. (and after taking graduate math classes at two different schools, I no longer want a Ph.D.).  The only downside to the extra letters that aren't on the end of my name is that college teaching positions are tenuous at best.

Over the last seven years, I have taught a variety of courses at three different institutions including:

• Pre-Algebra
• Algebra I
• Algebra II
• PreCalculus
• Calculus I
• Calculus II (scheduled to teach in spring 2014)
• Combinatorics
• Intro. to Statistics
• Mathematics of Games & Gambling

It's an eclectic group of courses, but most of them were a lot of fun to teach.  I'd also like to think they were fun for the students, though I in some cases I have my doubts.

It's those doubts that are impetus for this particular blog.  My Fall 2013 schedule looks something like this:

• Calculus I (two sections plus two labs)
• Mathematics of Games & Gambling

It is my goal to make my three courses as fun for the students AND as rigorous as possible.  Can those two ideas coexist?  Well, sure, I believe they can or else I wouldn't be attempting it!

As the summer progresses, I hope to start posting some of my course ideas.  Eventually, I hope to have a vibrant blog following where ideas get bounced back and forth (and by all means, feel free to disagree with me).  Until then, I'll blog like no one's reading.*

*not hard to do when no one is actually reading

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!

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!

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!

The Price Really Is Right!

I've spent a fair bit of time discussing the happenings (and future plans) for my course that I am both developing and teaching this semester.  Today, I figured I would discuss our recent activity mostly to serve as another diary type entry for myself next semester.

My school's fall break is this week which means we get Friday off.  Yeah, a one day break isn't overly impressive (but we do get the Wednesday before Thanksgiving off as well which I appreciate).  Anyhow, it's often tough to cover much material in a short week for a distribution class since the students have all of Thursday, Friday, Saturday, and Sunday to forget.  However, thanks to our local community arts center, I got lucky.

You see, the traveling game show The Price is Right LIVE is coming to our town on Sunday.  When I learned about the show, I instantly arranged for tickets (free for the entire class) and rearranged my course schedule to accommodate the game show.  That meant both Monday and Wednesday were used to discuss Price is Right games and strategies.

Image source: http://content.clearchannel.com/cc-common/mlib/2036/01/2036_1264503009.jpg

We spent one and a half days discussing the mathematics behind the game of Plinko!  It ended up being a great way to review choice trees (using a small version of the Plinko! board).  It also natural evolved into a way to discuss using a small problem to help us solve a larger version...and it perfectly illustrated the need for a formula or shortcut when trying to analyze the "real" board.  In our case, the short cut is of course Pascal's triangle...which in itself is an excellent lead in to the next segment of the course where we will discuss the Binomial Theorem (and the MLB World Series).

After spending the better part of two classes on Plinko!, I used the remaining class time to give a crash course on some other games that might be played during the live show (I emailed the producers of the program but they wouldn't divulge which games would be played).

We looked at when to spin and when to "hold" during the Showcase Showdown.

We talked about bidding strategies.

We talked about basic strategies for a few of the games...and we ended yesterday's class with a video of what not to do which drew the expected laughs.

Overall, the students seemed quite excited for the opportunity to attend the show.  The math wasn't easy for the Plinko! board but most students seemed to intently study the various problems and explanations.  I had plenty of great questions about it during the lessons which convinced me that the students were truly engaging the material.  I believe the allure of winning a car (supposedly they play a game where someone could win a car even in the traveling show) was a great motivator!

Now that the lessons are over, I can only sit back and hope at least one of my students get the opportunity to go the stage.  It'd be a lot of fun to say that students can take my class and possibly win a vacation to Bermuda or something!

The Mathematics of Games and Gambling: A Course Update

I haven't done well keeping the blog updated on a daily basis (or even a semi-daily basis) but that doesn't mean that I haven't been keeping track of what has (and hasn't) worked in my classroom.  I've talked about my Mathematics of Games and Gambling course that I'm developing/teaching during the Fall 2012 semester a few times already (most notably here and here).  Since I haven't mentioned much about the course since then, it's probably time to reflect on how things have gone through (almost) five weeks.

So far in class (through five weeks - aka fifteen 65 minute classes), we have:

• Learned the game of Chuck-a-Luck
• Learned the game of Roulette (both American and European)
• Learned the game of Craps (both street and casino)
• Learned the game of Five Card Stud Poker
• Learned about expected values
• Learned about probabilities
• Learned about choice trees
• Learned about combinations and permutations
• plus a variety of other (smaller) topics such as a few brain teasers and card puzzles, plus assorted vocabulary as it arises in various gaming contexts.

We've also had a day where the class played craps, another where they played roulette, and today they happen to have a Five Card Stud Poker tournament.  The class has had five take home assignments so far (all but one spanning multiple classes).  Finally, the class took their first test on Monday of this week.

With all that's been done so far - and, quite honestly, that is a LOT of material for a distribution math class, it's time to reflect on the good, the bad, and the things that I might (or might not) change next time I teach the course.
*Note:  All observations are mine and mine alone.  I have not polled my students yet nor issued any sort of survey thus far in the semester.

Image source: http://singlemindedwomen.com/women-relationships/duchess-digest-the-good-the-bad-and-the-solution/

The Good:
Students love games and they seem to be working to understand the mathematics as a way to get better at the games.  I split the class into two separate tables when playing Craps - one table had every student (except one) turn their $300 into $1000+, while at the other table almost all the students went bankrupt.  It was a great, though unplanned, lesson in the draw of the casino!

The first round of testing had 6 of the 18 students earn an A on the exam.  For a distribution math course, that's awesome.  Even more impressive is the fact that the test was five pages long - and certainly not easy - and yet one-third of the class earned an A.

The best part of the class though isn't the grades or even the "fun" stuff.  Instead, the best part so far has been the students reaction to various problems, homework assignments, and in class activities.  The overall attention and engagement levels are through the roof as compared to a typical distribution class.  I can't say the class is at 100% in terms of engagement, but on any given day I would wager that at least 16 of the 18 students are fully engaged.  Again, a remarkable number considering the fact that most of the students in the class are self-professed math-phobes.

The Bad:
I mentioned the results of the first exam in "The Good" section, but I would be remiss if I didn't mention it in "The Bad" section as well.  Out of the 18 students, 4 of them ended up with Fs, including one student who left a pair of 21 point problems (out of 100 total exam points) blank.  As I said above, the engagement is there for most, but not all, students.

I think it's a bad thing that I have been unable to fit in time to play most of the games with the students and let them figure out their own strategies before we go over the mathematical analysis of each game.  I was able to do that for Roulette but not for Craps.

Things to think about changing:
I don't think I have the exact right balance of rigor and exploration.  I have a tendency to automatically analyze games logically as soon as I am introduced to them (my wife hates that, especially if we are playing against each other)!  However, just because that's a natural thought process for me, it most definitely is not for the majority of the students in the class.  I need to be better at guiding them through the analytical process.  In the beginning of the semester, I used a few brainteasers/puzzles as warm-ups which worked quite well.  Unfortunately, I haven't done much of that lately (mostly because the amount of material in the daily lessons hasn't allowed extra time).

I think the first exam should have been in week 4 rather than week 5.  I probably should have spent a full day on permutations and then a second day on combinations.  I ended up doing both on the same day and while it worked for 80% of the students, that's not close enough to 100% for my tastes.

Finally, I need to come up with a way to assess learning besides exams.  Many of the students in the class that didn't score great on the exam actually seem to know the material but they "froze" during the exam.  I think old math paranoia habits die hard...

I guess there's not really much purpose to this blog entry other than as a self-diary of sorts.  Of course, if you have any ideas for the course, by all means share them!

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!

Week 1 is in the Books!

Happy (day after) Labor Day!  While I’m guessing most of you had yesterday off, my school held classes.  I’ve worked there for five or six years now so I’m used to working on Labor Day (and honestly, it’s hard to complain about working on the holiday when I just had roughly four months “off”).  No one feels sorry for me.

One of my goals for the blog is to keep a running diary of thoughts and observations from my classes.  After one full week, I have to admit that I’m looking forward to the semester!  I have a pair of sections of Calculus I, the first class has 16 students and the second has 19 students.  I appreciate having two sections with roughly the same number of students as it makes planning activities easier!  My first day of theCalculus course went extremely well, but I do fear that I’ve lost a little steam and enthusiasm from the students now.  I attribute that to a string of mostly lectures and problem solving in regards to limits.  If there is one giant weakness to my teaching, it’s that I don’t have a steady stream of varied activities.  Each semester I seem to plug in one or two new things to try (and I usually keep them for future semesters) but even so the course can get a bit monotonous. 

Historically, about half of my students fail to fully grasp limits (and continuity) by the first exam.  Most of the students are able to pass the exam, but limits at the Calculus I level are easy enough that I believe all the students should be able to muster at least a B on the exam.  So far, my current crop of students is right on pace – most have grasped the concept but there are still four or five in each class that still don’t understand.  I keep thinking that if I could come up with an activity that demonstrates the concept of the limit those students might also find themselves understanding all the course material.  Unfortunately, I have yet to come across a suitable activity.

My third class is the Mathematics of Games and Gambling – a course that I am currently developing from scratch.  I had ambition plans for the course but it didn’t even take a full week for me to realize that I am going to have to go quite a bit slower than I had initially planned.  After a week and a day, we have covered finite probabilities and played both Chuck-a-Luck and Roulette.  In the next class, we do a mathematical analysis of Roulette (other than explaining the rules, I didn’t say much about Roulette in class yesterday).  My goal was for the students to experiment as they played to see if they could come up with a strategy that was either good or bad. 

In terms of bad strategies, the students offered some advice like “don’t bet a dollar on black and a second dollar on red at the same time” and “don’t bet on single numbers.”  The first piece of advice is perfectly valid – and quite honestly, the second was as well in the sense that I only gave each student $10 to “bet” with.  Of course, we all know that betting strategies in roulette are about as helpful as a beach volleyball in the arctic circle.

All things considered, I’m moderately pleased with the first week of classes.  I wish I could figure out a way to teach Calculus without resorting to as many lectures but otherwise things have gone quite well.  I should have a better handle on my Gambling students’ abilities once I grade their first homework assignment (which was collected yesterday). I think I've managed to display most of the traits that my students consider important in a good mathematics teacher, though I don't think most of them find me funny*.

*When explaining the floor and ceiling functions, I like to ask my students what the floor of pi is.  After getting the correct answer, I point out to them that they now know the floor of pi(e) is not actually crust but three.  Each class produced three of four groans, a chuckle or two, and a lot of eyes (and heads) rolling.  

Qualities of a Good Math Teacher

I had a highly successful first day (more on that another day perhaps).  For today's post, I thought it would be fun to see what qualities my students thought a successful math teacher must possess.  They answered this question (along with a host of others) within the first 10 minutes of the opening class.

I have three classes to teach this semester:
The Mathematics of Games and Gambling - a distribution level course.  There is a mix of freshman through seniors in the course.  Class size is 18.  There is one math major in the course (a senior who needs credits).

Calculus I - Section A - Mostly upperclassmen, about a third of which had me for a previous class.  Class size is 21.

Calculus II - Section B - All freshman (except two).  Only one student had me for a previous class.  Class size is currently 15 - it could potentially rise to 20 by the end of the week (though I doubt it).

With that in mind, let's see what the students claimed as the qualities of a good math teacher (divided by class).

Mathematics of Games and Gambling student responses:

• Fun & Interesting
• Thorough, patient
• Interactive, knows the material, is excited about the material
• Explains well, takes time, offers homework to help prepare for tests
• Helpful & receptive to questions I may have; Makes subject matter interesting
• Multiple ways to find a solution
• Patient, eloquent, sense of fun
• Explains lessons and hands on
• Patient
• Understanding, approachable
• Knows what he is talking about; Is clear when explaining steps
• Explains well and is hands on
• Answers students' questions
• Knows math;  Gets the students interested in math (Texas Hold 'em?  Yes please)
• Strict, but fun, explains things, not everyone's BFF
• Explanation skills, patience

As you can see, there is quite a diversity in what makes for a good math teacher.  However, the one word that appeared a lot is patience.  By my count 7 of the 16 respondents either named patience outright or alluded to patience in their qualities.  The other attribute that was named a lot was fun or excitement (four out of the 16 alluded to fun in their comments).  For a distribution class, I thought the comments were quite telling!  The students want to see why the subject of math is interesting or fun, but they want to be shown in a clear, precise, (and perhaps slow) manner.  If I had to try to summarize this class' thoughts into a single sentence, it would be:  A successful (distribution) math teacher has a love for the subject which they can translate into thoughtful, fun, and well-structured lessons.

Moving out of the distribution course, I have a pair of Calculus I sections.  First up, the (mostly) freshman section of Calculus and their thoughts on makes for a good math teacher.

• Understanding of info, communication
• Interactive, Hands on
• Engaging, able to make course interesting and fun
• Experience
• They can somehow make class fun and not all lecture
• Gives a lot of problems to practice with
• Helpful, insightful, explains things well and goes over things extra times
• Funny, helpful, smart
• Can teach a topic in different ways to help better understand something
• Organized, smart
• Explains/teaches well, interactive, approachable
• Enthusiasm

For my (mostly) freshman section of Calculus I, the differences in what makes for a good teacher (as compared to the distribution course) were quite stark.  The idea of being fun wasn't nearly as prevalent.  The idea of patience was essentially non-existent.  Instead, words like "smart", "insightful", and "organized" make an appearance.  Since the majority of the students in the class hadn't had more than one college class (as in, a single meeting of one class since this class meets in the morning), it seems that many of the qualities are a direct response to the stereotypical college professor.

Finally, my second section of Calculus I (a class in which there were only a couple of freshman and plenty of students who have had me for previous courses) had this to say about successful math teachers.

• Able to fully answer questions & visibly demonstrate answer; able to make learning fun
• Approachable
• Explains everything
• Patience, intelligence
• Funny, respectful, patient
• Someone who explains well and works problems on the board
• Explains new material in detail
• Goes at a good pace and is clear
• Funny, helpful, interesting, knowledgeable
• Patience, clarity, authority
• Good at math
• If they can teach me, they can teach anyone
• Answers every question
• Approachable
• Interactive, entertaining, available
• Doesn't assume we remember how to do everything from precalc*

*not one of my former students for the record!

I wasn't surprised by the across the board responses from this class based on the heterogeneous mix of students in the course.  The freshman all said things to the freshman in the previous class while the upperclassmen usually went with something along the lines approachable or explains things well.

Can you make any broad assumptions or observations from my data?  I don't know (well, you can make assumptions but how accurate are they)?  If you put all the responses into a single list, it's interesting how much higher "fun" and "patient" rank as compared to "knowledgeable".  Even more telling, I teach at a liberal arts college so the answer of "prepares me for a future job" was essentially non-existent!

Do you ask your students anything along the lines of what I did?  Or, if you are a non-student reading this, what qualities do you think a good math teacher should exhibit?