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!

The (Hidden) Cost of Higher Education

Anyone who pays attention to politics or the news will have undoubtedly heard plenty about the rising costs of higher education.  Tuition keeps going up, up, up and yet our students still struggle to land jobs upon graduation.  Surely, that's a problem - why keep paying more for something that won't even ensure you have a job at the end to show for you hard spent cash?  I suppose that is, in part, what has led to the rise of online classes (and more recently, free online classes).

Now, the merits of tuition raises and college preparation for the job market can be (and have been) debated by plenty of others.  Since I work at a small liberal arts college (and I have no say in terms of things like the college's budget), I like to focus on things that I can have some input on - namely, the hidden costs of higher education.

What are the hidden costs?

• Books
• Graphing calculators
• Printing costs
• Software costs

And those are just to name a few - certainly the four biggest costs for a potential mathematics, physics, biology, or chemistry student.

How do I help my students minimize their hidden costs?  This coming fall I'll be teaching two sections of Calculus I and one section of The Mathematics of Games and Gambling.  For the gambling class, I do require a textbook but it sells at the campus bookstore for about $40.  Sure, that is still probably $20 too much but at least it's less than fifty bucks.

For my Calculus class, I have decided to forgo a textbook entirely.  On the first day of classes, I'm going to tell my students that they can get virtually any calculus book (late transcendentals) and it should (more or less) follow along with my lectures and homework.  The downside for me is that I have to write all my own homework assignments (complete with answer keys and hints).  Still, I consider that part of my job - and I have a feeling my students (and their parents) will appreciate all my work.

As for the other hidden costs, well, they are a bit trickier.  Actually, the second one isn't hard at all - not only do I not require a graphing calculator, I don't allow them to be used.  I'd much rather have my students know how to graph y = (x + 2)^2 than use a graphing calculator to get the exact graph of y = (2.3x - 3.8)^2.  Sure, in theory the students should be able to graph the second equation, but why?  Keep it simple I say - it's more important to work on intuition, observation, and determination!

My other beef with graphing calculators?  Their costs haven't dropped.

Why can get a Samsung Galaxy S3 (or even an S4) smart phone for under $100 but I can't get a TI-84 graphing calculator for that price?  Why can I buy a brand new WiiU video game system for $299 but a calculator that's essentially over a decade old still costs me over a third of a new HD gaming system?

One reason:  College.

It's a hidden cost.  Each professor that requires a graphing calculator forces students to buy said devices.  Since there are tons of classes that require TI-somethings, Texas Instruments gets to keep the costs of their device artificially high.  For all the grief that textbook companies get, it hardly seems fair that Texas Instruments gets a free pass.  They are clearly just as guilty.

In the end, the only way for the cost of education to go down will be for more professors to take proactive steps to reduce hidden costs for their students.  As more professors move to cheaper (or even free) options for their students, more and more schools will begin to follow suit.  After all, if all a student's professors provide printed handouts (saving the students printing costs), the schools will eventually have to stop charging so much for printing fees (or else start charging professors I suppose).  Unfortunately, I'm guessing I'll get charged for my printing way before my students ever see a discount.

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:

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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!

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?