Author Archive

You’re getting on my last NERV!

We’ve had the opportunity to discuss quite a lot of things in the Math of Sports and Games class.  Right now, they’re working on a project on NERV. 

NERV stands for net expected run value (see here, for more).   It’s a great lesson to talk about that utilizes probability and expected value in a real tangible way.  We’re using math to better create strategies to cause baseball teams to win.  How is that not a cool thing? 

No longer is math a series of steps, but rather a tool that is used to increase success (we’re looking at success on the baseball field, but I think the kids will start to see it as a tool to increase success in other ways too). 


Categories: Other Junk

First week of school

One week (a partial week) is in the books, and this school year looks to be an interesting one.   I introduced SBG to my Calculus class.  We haven’t yet taken a standards assessment (it will be next Tuesday), so they haven’t made any real judgments on the system.  They seem skeptical, but we’ll see how things go.   I’m not used to giving assessments as often as it will be needed with SBG, so it will be different for me as well.

The Math of Sports and Games class has been pretty fun so far.  On the first day of class, I presented them the classic Monty Hall problem. I asked them what they would do, and I then showed them this video clip from the movie 21 (by the way, that’s the best website for math video clips anywhere, so check it).

They were skeptical even after watching it.  The guy sounded smart, but they weren’t sure what to make of it.  I made no comments on anything at this point in time.

At this point, I WANTED to have the kids use their iPads to perform a simulation of the Monty Hall question (I like to program).  However, they decided not to give iPads to the iPad-centered class, so we couldn’t do it.  Instead, I gave them 3 post-its and a little piece of paper and had them simulate it in a “hands-on” method with another classmate.

They recorded their answers and we pooled the results to discuss.

It went pretty well, but the fact that a fellow classmate was choosing where to put it gave us some skewed results (since it wasn’t truly random).

Lebron James vs. Michael Jordan


Who is the better NBA player?


Students discuss in their groups how/if we can determine this with math.   Their goal for this discussion with their groupmates is to create a plan on how to determine which athlete is the better athlete.  I’ll have them record their plan and we’ll come back together and share ideas.

Questions that I hope will come up:

How do we define “better”?  How do we quantify a player’s value?   How do we compare players from different eras/different skillsets?

The key question that will help us determine which is the better athlete is “How do we quantify a player’s value”.

I think it would be a good idea to get the students to come up with their own way (using common stats) of ranking players.

Not all students will know the ins-and-outs of basketball.  I may need to do a primer (read…. “go to gym and play some basketball”) on the different statistics available.

There’s a few useful things I’ve found out there.  Chapter 29 of an excellent book entitled Mathletics by Wayne Winston has a nice discussion on the NBA efficiency rating (points per game + rebounds per game + assists per game + steals per game – turnovers – missed FG per game – missed FT per game) as compared to a much more complicated player efficiency rating abbreviated PER (see the wikipedia page).  They state that the correlation between the NBA’s efficiency rating and PER is at 0.99.  Moral of the story, complicated does not always equal better.

We might decide as a group to come up with our own efficiency rating.  I’ve got a few ideas of what this could look like, but I don’t want to be a “provider of information”.

I liked what Mr. H over at Mathing did in a Tyson Chandler versus Steve Novak argument, and I think it could fit into this discussion quite easily.

When all is said and done and we use an efficiency rating of sorts to compare the two players, I want them to discuss (and this may be difficult without them knowing the sport very well) what the problem(s) are with using an efficiency rating like this to compare two players.   Wayne Winston does a good job of this in Mathletics.

Another good reference for what I’ll call “extended NBA statistics” is 82games.

I see this project hitting on the following math topics:
z-scores, standard deviation, correlation, evaluating expressions

Most importantly, it will hopefully develop problem solving skills in the students.

I thought about having them go through this Lebron vs MJ argument, and then assigning them to pick their own two athletes to compare of any sport (perhaps I could exclude the NBA since that would be too easy after the MJ vs LJ argument).  They then would have to create their own SportsCenter segment similar to my intro piece comparing the two athletes.

Any thoughts on how to improve upon this very rough outline of a project?

Math of Sports and Games description

Since I’ll be referencing it a lot in some of these blog posts, I wanted to share what my Math of Sports and Games course actually is.

Here’s the course description that I wrote for our program of studies:

Mathematics of Sports and Games
Prerequisite: Pass Algebra, Functions, and Data Analysis OR Algebra 2
Standards of Learning Addressed: Various standards will be addressed found in the following courses:

Credit: 1 elective credit
(actually, we were able to modify this to provide an actual math credit to students)

Course Description:
This course will investigate the mathematics behind sports and games. Our investigations will apply the principles of functions, probability, statistics, geometry, and equations to sports and games. This course is designed to strengthen a student’s mathematics skills while looking at practical applications of mathematics as it applies to sports and games.

This next year, I will be teaching the course as part of a pilot program.  We have chosen a group of about 20 students that show academic promise, but perhaps do not believe in themselves.   Kids that need a push.  As part of this program, each kid will be given an ipad for the year, so I’m hoping to be able to come up with some ideas to use those (once they come in, and I can start playing with it).

I wrote up a short blurb to give the kids (or probably their parents) an idea of what’s going on in this course.  It reads as follows:

Is there really such thing as home field advantage?  Can we predict the performance of players?   What strategies should we employ that would give our team the highest possibility of success?  What strategies should we use that would give us the best possibility of success in a particular game?

In math of sports and games, students will examine question such as these and the mathematical relationships that exist within the realm of sports and games.  Students will develop problem solving skills while working collaboratively with peers.  This course will help students develop the critical thinking skills (as well as mathematical content knowledge) necessary to be successful in their future endeavours in further education.

I don’t really know what all will happen in this course.  I know that it will be project driven.  The math content will come as the projects dictate.  I won’t be presenting math content as much as providing math content as they realize the need for it.  I could easily turn this course into a very statistic heavy one, but I’d like it to be more of a balance of statistics with their other mathematics knowledge.

I’ll share some of my project ideas as time goes on.

Standards Based Grading – Calculus

I’ve read about SBG for a few years now.   My first exposure to the idea coming from Dan Meyer.  I liked some aspects of it, but had some misgivings.   This next year, I’ll be giving it a trial run in my Calculus class.

The problems that I have now with my current grading system are as follows:

  • Rampant cheating on homework due to the 30% chunk of the grade
  • Pursuit of grades/points more than knowledge of the topics
  • Gradebook doesn’t let me identify quickly what kids have trouble with
  • Students can’t identify what they have trouble with
  • No clear path of remediation for kids (can’t search on youtube for p. 154: #’s 3, 8, 12, and 16)

In my previous system, all homework was graded for correctness and could be fixed.   There was a process that went on (with lots of work on my time) where kids did and re-did problems over and over again (with my feedback) until they could figure things out.  The cheating that occurred with the homework and the other things I listed lead me to think a change is necessary.

I believe that SBG can rectify many of these problems.  I’ll be borrowing some things from Sam Shah at Continous Everywhere but Differentiable, John at Quantum Progress, Shawn at Think Thank Thunk, and Bowman Dickson.

I haven’t quite worked through the nitty gritty details of it all, but I’ve thought about a few obstacles.

Obstacle #1:  Discretizing the Subject

I do lots and lots of work to get students to see the big picture of the subject.  Learning is not the mastering of 85 discrete standards (as SBG might make it look), but rather the understanding of the overarching themes of the subject.  A true understanding of the overarching themes will manifest itself as the mastering of the 85 discrete topics.  However, it is possible (and done in many math classrooms across the country including my own at times) for students to never understand the overarching themes but still show mastery of the procedural aspects of the many different topics.  I believe SBG, if not done carefully, can turn a course into the mastery of discrete skills instead of the overarching themes.  Though of course there are probably large chunks of math teachers that don’t use SBG and still turn the subject into the mastery of skills.  I further think that an extremely valuable tool for students to have at their disposable is the ability to decide when to use which tool at their disposal. I think carefully written questions (and perhaps standards) can help avoid this obstacle.

Obstacle #2:  Grade breakdown

How do I breakdown the student’s grades?   Some people use a 100% standard-based model.  I’m wary to place such a huge emphasis on standards.   I don’t want to reward slackers.   There should be some penalty for students who aren’t ready for assessments (due to their own neglect) when they are given.  I believe that SBG doesn’t intrinsically reward slackers, but I moreso am afraid that students will think when they system is presented to them that they can put forth less than a stellar effort and it won’t harm them in the long run.    I’m also afraid that students won’t do homework if there is no credit for it.  For that reason, I believe that a hybrid system is something more up my ally.

Bowman has this breakdown in his hybrid SBG system:

  • 35% – Standards – How much I understand right now
  • 10% – Quizzes – I am keeping up with the pace of the class
  • 30% – Tests – Connecting topics and converting short term knowledge into long-term knowledge
  • 5% – Homework – I am doing my part in learning by practicing on my own
  • 20% – Final – Retained knowledge and have the big picture of Calculus.

I think the small percentage of homework would negate most of the cheating, but still allow me to track who is doing their part.  I think that I can ditch the quiz part of Bowman’s system.  Tests will determine that, and I don’t want to over-assess them.   I want to add  in some space for projects.  These projects would allow me to test for the bigger connections and, more importantly, give them some space for problem solving.   Here is my tentative grading system:

  • 50% – Standards
  • 20% – Final
  • 5% – Homework
  • 25% – Projects/Tests
Categories: Calculus

First post!

So, I decided to join the foray into the blogging world.  I teach math at Waynesboro High School, where I’ve been for 6 years.   It’s a relatively small school with around 900 students, but has a pretty diverse student body.    This summer I hope to rethink how I’m currently doing things for my classes and I started this blog to share my progress (or lack thereof).

I don’t quite know everything that will be on my teaching slate for next year, but I do have an idea of what most of my classes are.  I’ll start my work with these classes.  They are:

  • Calculus
    My Calculus class is a non-AP, non-DE Calculus class.   I’ve taught it for about 4 years and am looking to do some major changes as you’ll surely read about.
  • Algebra 3
    I’ve never taught this class before.   It’s supposed to be the Virginia Math Capstone course.   The teacher who is teaching it now is retiring, and I know that this class will push me a bit more than I’m comfortable.
  • Math of Sports and Games
    This class was one I actually pushed to get approved last year.  I was able to get the school board to approve the course, but we didn’t have enough interest to offer it.   This coming year, we have the numbers to offer it.  The class is designed to be taken by upperclassmen  (meaning that students need to have taken Algebra 1, Geometry, and one more math class).   I’ll speak more on this class later.
  • Dual Enrollment Statistics
    I just completed my master’s degree in Math, and I’m already taking advantage of it with this class.   This will be the first year that our school offers a Dual Enrollment Statistics course, and I’m excited about it.

I believe that I should have one more course besides these ones, so I’ll surely have a lot of preps this year.  I’m looking forward to it though.


Categories: Other Junk