Published "Mathematical Investigations" with students

Barry D. Cohen

  1. Pythagoras, Fibonacci, and Lucas Numbers. Mathematics Teaching in the Middle School, 11-12/1996. Reference: Mathematics Teacher, 4/1989.
  2. Fibonaccis and Primes: Fibonacci numbers with prime subscripts are often prime. Mathematics Teaching in the Middle School, 3/2007. Reference: The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Mario Livio, 2002.
  3. The 3n+1 Problem. Mathematics Teaching in the Middle School, 2/1998. Reference: D. Hofstadter (1979) Godel, Escher, Bach, Basic Books. A response was published in Mathematics Teaching in the Middle School, 10/1998.
  4. Unusual appearances of Pi (I)--"Two Investigations": Two randomly chosen positive integers have 6/pi2 probability of being relatively prime. Mathematics Teaching in the Middle School, 2/1998. Reference: R. Honsberger (1970) Ingenuity in Mathematics, Random House.
  5. Unusual appearances of Pi (II)--"Comte de Buffon Needle Experiment": The probability of a randomly tossed needle crossing a line is 2/pi. Mathematics Teaching in the Middle School, 8/2006. Reference: Mathematics Magazine (Mathematical Association of America), 2/1991.
  6. Magic Squares. Mathematics Teaching in the Middle School, 1/1999. References: R. Honsberger (1973) Mathematical Gems, and Kenda & Williams (1995) Math Wizardry for Kids, Barron's.
  7. Working with Primes I: Differences of powers of 2 and powers of 3 in any order yield many primes. Mathematics Teaching in the Middle School, 2/1999. Reference: Mathematics Magazine (Mathematical Association of America), 2/1993.
  8. Working with Primes II: Conjecture--All even numbers can be generated by consecutive primes. Mathematics Teaching in the Middle School, 5/1999. Reference: B. Bolt (1984) The Amazing Mathematical Amusement Arcade, Cambridge University Press.
  9. Working with Primes III: "Germain primes," first studied by Sophie Germain. Mathematics Teaching in the Middle School, 5/2001. Reference: Simon Singh (1997) Fermat's Enigma, Walker and Company.
  10. Working with Primes IV: Primes of the form 4n+1 can be expressed as the sum of not more than four square numbers. Mathematics Teaching in the Middle School, 1/2002. Reference: Simon Singh (1997) Fermat's Enigma, Walker and Company.
  11. Working with Primes V: Primes can be arranged in arithmetic progressions. Mathematics Teaching in the Middle School, 4/2002. Reference: Charles W. Trigg's article in Crux Mathematicorum, 1981.
  12. Working with Primes VI: Even numbers can be expressed as the sums of primes in different ways. Mathematics Teaching in the Middle School, 1/2003. Reference: John Holding (1991) The Investigations Book, Cambridge University Press.
  13. Working with Primes VII: Every odd number > 1 is the sum of a prime and a power of two (DePolignac 1848). Mathematics Teaching in the Middle School, 2/2003. Reference: B. Bolt (1984) The Amazing Mathematical Amusement Arcade, Cambridge University Press.
  14. Working with Primes VIII: There is at least one prime between consecutive square numbers. Mathematics Teaching in the Middle School, 2/2003. Reference: B. Bolt (1984) The Amazing Mathematical Amusement Arcade, Cambridge University Press.
  15. Working with Primes IX: "Symmetric Primes." Mathematics Teaching in the Middle School, 3/2005. Reference: G. Muschla & J. Muschla (1995) The Math Teacher's Book of Lists, Prentice Hall.
  16. Working with Primes X: Constructing primes from Fibonacci numbers. Mathematics Teaching in the Middle School, 2/2007.
  17. Happy Numbers. Mathematics Teaching in the Middle School, 2/2000.
  18. Unhappy Numbers. Mathematics Teaching in the Middle School, 8/2006.
  19. Armstrong Numbers. Mathematics Teaching in the Middle School, 12/2000. Reference: Science Digest, 5/1985.
  20. Four Four's. Mathematics Teaching in the Middle School, 2/2001. Reference: Martin Gardner (1985) The Magic Numbers of Dr. Matrix, Prometheus Books. Two responses were published in Mathematics Teaching in the Middle School, 10/01.
  21. Pythagorean Quintuples. Mathematics Teaching in the Middle School, 4/2002. References: Mathematics Teacher, 11/86; and letter to the Editor in Mathematics Teacher 2/92.
  22. A Diophantine Problem. Mathematics Teaching in the Middle School, 4/2002. Reference: Mathematics Teacher, 5/91.
  23. Square Numbers: Every perfect square can be expressed as the sum of not more than five square numbers. Mathematics Teaching in the Middle School, 4/2002. Reference: See "Waring's Problem" in Calvin C. Clawson (1996) Mathematical Mysteries, Perseus.
The entries above were published as letters to the editor of Mathematics Teaching in the Middle School, the journal of the National Council of Teachers of Mathematics.

Return to the New Hope Academy Middle School teacher introductions page (or the High School teacher introductions page).
See the curricula outlines.
Go to the main New Hope Academy page.
Go to the main New Hope High School page.


[New Hope Academy]
[New Hope Pre-School & Day-Care]
[Summer Day Camp]
[Korean Language & Cultural Center]
[Dance Studio]


7009 Varnum Street
Landover Hills, MD 20784
Phone: (301) 459-7311
Fax: (301) 459-2813


School Motto: Dedicated to academic excellence and supporting parents to raise moral children
[NHA Logo - click for Table of Contents]


Click here to contact us by web form e-mail.