May 7- Finding the zen of mathematics on a meditative long training run

Note: I anticipate that this topic will be a chapter in my forthcoming book. I have lots to say about math and running, so when my book does come out, instead of grumbling about how I have shared these ideas before, think of yourself as special, because you right now are part of the process and get to hear these ideas first! <3

I have grown to love long run training days.

When I started running, which I did only a couple of years ago, I did it just to see if I could. I figured I'd try to run a 5k, and took up one of those couck-to-5k programs.  Little did I know that a sport that I once detested would become part of who I am.

I ran a few little races, and found I really liked the 10ks better than the 5ks.  The 5k races were populated by so many fast runners, I always felt so sluggish. The 10k races didn't have so many sprinters, but people more like me, who paced themselves. 

I ran my first half marathon a little over two years ago, and loved it.  When you run a half marathon, it isn't about winning, or being fast, but you are amazing if you finish!  My first goal was to finish before the sweeper van picked up stragglers, which I did!  I also found that running these longer races was different in that people who ran had dedicated months to training, and often still had energy to dance at the after party! This was my jam.

But even more than the actual half marathon races, I found that I absolutely fell in love with the training.  The rituals of it, the rhythms, the long runs, this is what I thrive on.  Here's how you train for a long run: You start at least three months out.  You start by running three-five times a week.  You need some shorter runs, some speed/hill training runs, and always one long run a week.  Long run days are my absolute favorite day of the week.

Because I work in academia, I rarely work on Fridays, so generally long run day is then (although these last few weeks, I've had to shift to Saturday or Sunday).  Oh, what bliss.  I wake, have a light breakfast, grab my running partner (Copper), lace up my shoes and head out. 

My friend calls her long training runs "Meditative runs" which I think is a great name.  During a long run, I generally contemplate everything that has been on my mind.  I have conversations with myself, and with the dog. I make plans, and promptly forget them.  I find incredible peace in the beauty of the nature around me.  I look for birds, I save turtles, I smell the plants, I feel the wind, the sun, the rain.  Sometimes I listen to audio books, sometimes I listen to music, and sometimes I just listen to the sound of my breathing, my feet hitting the ground, and the wildlife on the trail.

 

One thing I always think about through my meditative run are my running statistics.  I have a Garmin watch which calculates data for me.  My distance is calculated with GPS.  The watch also tallies my average pace per mile, and my steps per minute.  Plugging it in at home, I can also see other data, like temperatures, elevations, fastest miles, etc.  I love seeing the data collected while I run.  I constantly do little math problems along the way.

If I maintain this average pace per mile, what time will I finish my run?

If I increase my steps per minute, how does that affect my pace per mile?

If I increase my stride, how does that affect my steps per minute?

Lately, Rob and I have done a number of long training runs together.  He's finally agreed to run a half marathon with me, and has been training for the Wilds HM next week with me.  When I run with Rob, I don't listen to music or audio books, and I don't think quite as much, but we do have a great time talking about everything along the way.  I was super tickled today to learn that he  likes to do running math, too!  I thought it was just something nerds like myself did.

Maybe math isn't as nerdy as I thought...

May 5- Weighted averages

One beautiful thing about my job is that everything happens in cycles.  A semester begins, a semester ends. There's a certain comfort in knowing that no matter how weird my teaching schedule is, or if there's a time-consuming student or two, that in a few months, all of that will change. I will have a different but equally weird teaching schedule, and a different but equally time-consuming student.

I teach, I test, I grade. There's a bit of zen in all of that.

It is nearing the end of the spring semester.  There is one question I get over and over again, so I thought I'd address it here.

"What do I need to get on the (last graded assignment of choice) to get an A/pass the class?"

This is a concept that most students struggle a bit with, and it isn't hard, you just have to think about weighted averages.

You know that to find an average, or the mean of a set of values, you would simply add those values together, then divide the sum by the number of values you added.  Well, a weighted average takes into account that not every assignment given in a course is weighted evenly.

In order to calculate the weighted average, you multiply each score by the weight it carries as a decimal.

For instance, Tommy has an average of 75% on his homeworks which are worth 10%.  He had an average of 84% on the quizzes which are worth 15%.  The exams were all worth 25%, and he got a 90% on the first exam, an 80% on the second exam, and hasn't yet taken the last exam.

So, Tommy needs to set up what he has:
(75)(.10)+(84)(.15)+(90)(.25)+(80)(.25)=62.5

So, if he skips taking the last test, he would receive a D in the class. That's not good enough! Tommy wants an A! Well, even if he geta a perfect score on the last test, that isn't possible.

62.5+(100)(.25)=87.5 that's a B.

Hrmmm, Tommy thinks. Well, if the best he can do is a B, what's the lowest grade he could get on the test to get that B? Just replace the test score with a variable, and solve.

62.5 + .25x = 80
-62.5                 -62.5

.25x = 17.5
/.25        /.25

X = 70

As long as Tommy gets a 70 on the test, he'll have that B.

So, clearly, if the last assignment is worth 20% of the overall grade, then how well a student does on that assignment could have a big impact on the overall grade.  But if the last assignment is only worth 5% of the overall grade, well, it's not such a big deal.

It's funny, students will get all worked up about a little assignment, but flake off during the big assignments.  For example, a student who came into my office today told me that he was so busy completing the extra credit problems (worth 10 points) that he forgot to study for the exam (worth 100 points).  See the problem?

But honestly, it's not just students and grades.  

I'm guilty, too.

What is worth the most? 

Tonight's post is late because I was taking care of high point things today: work, a run, making great food, spending this evening with my love.

The rest can wait for tomorrow!