Congressional Apportionment

Resources

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Charles Biles, Teaching Apportionment, 14 March 2017 (6 pages).  This essay was written for classroom teachers of apportionment.  The essay describes the two math skills needed for understanding apportionment.  Further, the essay describes how to exploit the history of congressional apportionment to motivate the mathematical description of apportionment as the distribution of a fixed number of integral resources.  [PDF format]

 

Charles Biles, An Average Lesson, (revised) 13 February 2017 (8 pages).  This essay is intended as a classroom textbook section to cover the topic of how to take an average of two numbers using five methods: minimum, arithmetic mean, geometric mean, harmonic mean and maximum.  Explanations, examples, and exercises are included.  A key example includes: how to round a decimal.  It is very useful to cover this material in the classroom before launching into apportionment.           [PDF format]   

 

Charles Biles, The Congressional Apportionment Problem Based on the Census 1790-1840: The Basic Divisor Method,

17 October 2015 (9 pages).  Most textbooks treat congressional apportionment as a mathematical apportionment problem; i.e., how to distribute a fixed resource.  However, this approach was not used to make a re-apportionment act until the act based on the 1850 census.  Accordingly, this essay summarizes reapportionment based on the first six censuses.      [PDF format]

 

Charles Biles, Congressional Apportionment: A Liberal Arts Perspective, 4 November 2015.  This is a textbook chapter augmenting the chapter on apportionment in the open source textbook Math and Society by David Lippman.  This work has five sections: An Average Lesson, The Basic Divisor Method, The Quotient Method, The Modified Divisor Method, and Priority Techniques.  [PDF format]

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Shannon Guerrero and Charles Biles, The History of the Congressional Apportionment Problem Through a Mathematical Lens.

This is a 14 page paper describing the overall history of congressional apportionment in the United States.  The paper also provides a mathematical description of the various methods of congressional apportionment used in U.S. history.

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