MARCH MADNESS - to Teach Mathematics

My knowledge of basketball goes about as far as my one year on the 6th grade basketball team.  But, what I lack in basketball knowledge I hope I can make up with my knowledge of mathematics.  When I filled out my bracket this year (only to please my overly competitive family) I wanted to use mathematics to help me win the coveted prize, a gift card to my dad's favorite restaurant (you can guess who picked out the prize).  I have two purposes to this post.  First, I want to tell you how I used mathematics to fill out my bracket.   Second, I will give some ideas on how to use march madness in your classroom.

Math and my bracket:
The first thing to know is that there are MANY options for the march madness and the chances of 
guessing a totally perfect bracket is pretty much ZERO.  

For the first round there are 2^32 ways of guessing, that would be
4,292,967,296.  This is because there are 32 games and 2 possible outcomes for each game.  Yup, 4 billion ways for the first round to turn out.  The second is less, but still 2^16 is 65,536.  Continuing on, there are 2^8 for the third round, 2^4 for the fourth round, 2^2 for the fifth round, and finally 2 ways for the final round to turn out.

We multiply these numbers together to get the total number of ways the tournament could turn out and we get....a number too big to fit on my calculator.

9.22 x 10^18

So based on WikiAnswers I found the length from the earth to the moon at it's farthest point from the earth.  From this, I discovered that 9.22 x 10^18 paperclips would make it to the moon and back 363,755,010 times. 

That's why my bracket already isn't perfect, as you can tell below.

Asking your students what the probability of having the perfect bracket is could be a great way to get the real world into your classroom.  

You can also ask them to find out how I came up 363,755,010 times to the moon and back.  This is a great way to look at and explore conversion lengths.

To fill out my bracket I decided to use statistics from the past to try to predict the future.  I found statistics on this website:
http://statistics.about.com/od/Applications/a/March-Madness-Statistics.htm

There is more than one way to apply these statistics.  You could just go by percentages and have the team win who has the higher percentage.  I decided where there was a 70% winning rate for one seed against another to pick about 3/4 of these teams to win and 1/4 of them to loose.  This wouldn't be the statistically perfect way to pick, but I wanted to do something a little different. 

Next, I followed these statistics from the same website as above,

• "Only once (4% of the time) has all four #1 seeds have made it to the Final Four.
• Three times (12% of the time) no #1 seeds have made it to the Final Four.
• 14 times (52% of the time) a #1 seed has won the entire tournament.
• The lowest seed to win the tournament is a #8 seed.
• The lowest seed to make it to the Final Four is a #11 seed."

I checked my bracket to see if it followed these statistics too.  Essentially this means that I made all the number 9 seeds win the first round.
http://www.washingtonpost.com/wp-srv/special/sports/ncaa-march-madness-bracket-guide/
 

Finally, I used these to help pick my final four and championship game.  I used the winning percentages to finalize who would win in the final four.
http://fivethirtyeight.com/interactives/march-madness-predictions/

There are no perfect statistics to use and very few perfect brackets, but you can be a much more informed competitor in your office if you know how to use mathematics.

Good luck and have fun!
 

 

Sensible Mathematics: Second Edition by Steven Leinward

Recently I read this book for my mathematics capstone course.  My summary and review of the book is below.  

Sensible mathematics is a book focused on empowering leaders to push for better mathematics school programs.  The book is written towards school leaders, but gives an interesting perspective for a future teacher like me.  Leinward explains that the common core state standards are the first step in creating a better math program.  It takes leadership and teacher support to implement the common core effectively.  He gives many reasons why change is important.  One example is the way society is changing.  This change demands a different mathematics classroom.  Students must be prepared for the workforce where calculators and excel spreadsheets are readily available.

    According to the author, one person can make a lot of change in a school’s mathematics program.  Schools must provide support for their teachers, but teachers must also provide support to each other.  Just one of these teachers has the power to influence a mathematics program.  As a teacher, helping my future colleges and challenging them to try new thing in the classroom is very important.  There are obstacles according to the author, like the fear of failing.  It is important though to encourage new methods and ideas in the classroom.  As a teacher, if I lead other teachers to try new strategies and share new strategies with my colleges, I am being a helpful leader, according to Leinward.    

    I also learned a lot about the shift in mathematics education from this book.  I would recommend it to leaders and administrators more than I would teachers, but it does provide great arguments for change.  The most interesting part of the book, for me, was looking at examples of lessons that promote sensible mathematics.  He shared one teacher’s story of a classroom exploring the speed at which toy cars go. The students discovered that under the conditions they were testing, the car speed was much slower than the advertised speed.  They used proportions and experiments to come up with data and sent it to the company that made the cars.  The company suggested they look at different situations to test in.  I can only imagine the excitement the students had when they heard back from the company, and to do more math testing.  This is the type of mathematics that I want to teach, mathematics that is real world, fun, and as the title says, sensible.   

Timeline of Mathematics

Below is a link to my prezi I created on the history of mathematics.  It provides a timeline and brief explanation of the topics we have covered so far in my MTH 495 class.

What fascinated me most about creating this timeline is there is a huge gap in time were mathematics wasn't making any strides.  I'm not a historian, but there has to be some reason for the 600 year gap.   Also what is interesting to me is how fast mathematics has moved since 600 AD.  It makes me excited to see the new things coming in the mathematics world!


History of Mathematics