patrick honner

Math teacher in Brooklyn, New York

Graphing the Collatz Conjecture

This a beautiful representation of the infamous Collatz Conjecture:

http://www.jasondavies.com/collatz-graph/

The Collatz conjecture is one of the great unsolved mathematical puzzles of our time, and this is a wonderful, dynamic representation of its essential nature.

One compelling aspect of the Collatz conjecture is that it’s so easy to understand and play around with.   Start by choosing any positive integer, and then apply the following steps.

Step 1)  If the number is even, cut it in half; if the number is odd, multiply it by 3 and add 1

Step 2)  Take your new number and repeat Step 1.

For example, starting with 10 yields the sequence

10 \longrightarrow 5 \longrightarrow 16 \longrightarrow 8 \longrightarrow 4 \longrightarrow 2 \longrightarrow 1 \longrightarrow 4 \longrightarrow 2 \longrightarrow 1 \longrightarrow ...

The Collatz conjecture simply hypothesizes that no matter what number you start with, you’ll always end up in the 4 \longrightarrow 2 \longrightarrow 1 loop.

Have fun!

By patrick honner, ago

2011 Sloan Award Winners

I would like to extend my congratulations to the recipients of the 2011Sloan Awards for Excellence in Teaching Science and Mathematics.

These awards, presented by the Fund for the City of New York, recognize outstanding teachers in the New York City Public School System.  I am very proud to have received this award in 2010.

As a teacher, the current public discourse that focuses mainly on what is “broken” in public education can be deflating.  It is wonderful to be a part of something that honors the great work teachers do every day.

Here’s a short write-up in the New York Times about the winners, and bios and videos of this year’s recipients can be found here:  http://www.fcny.org/fcny/core/sae/.

By patrick honner, ago

Google Public Data Explorer

Google’s Public Data Explorer is a great, free resource for students and teachers interested in data science and statistics.

http://www.google.com/publicdata/home

The site allows you to create custom graphs of available data sets, making it easy to experiment with different representations and explore the meaning of data.

There are several data sets available to play around with.   The OECD Factbook alone provides a wealth of raw data on education, energy, employment, population and migration, and many other categories.  There are also data sets available from the U.S. Census and the U.S. Bureau of Economic Analysis.  There appears to be support for using your own data sets, as well.

The data can be represented in a variety of ways:  histograms, line graphs, and even dynamic time series are all available.  It’s a great way to play around with data, and to build skill and intuition in data analysis, interpretation, and representation.

By patrick honner, ago
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