Joe Rosenstein

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Mathematics

Books

Problem Solving and Reasoning with Discrete Mathematics

Copies of this book are no longer available, but I hope to print additional copies soon.  Email me and I will notify you when copies are again available. 

  • New Jersey Mathematics Curriculum Framework. Developed by the New Jersey Mathematics Coalition, with the co-sponsorship of the New Jersey Department of Education, to serve as a guide for teachers in implementing the 1996 New Jersey Mathematics Standards.  The development of the standards and framework in 1996 was a collaborative effort involving hundreds of New Jersey teachers, carried out by Janet Caldwell, Warren Crown, and Joseph Rosenstein, who also served as project director and Editor-in-chief of the framework. This version of the mathematics standards was adopted by the New Jersey State Board of Education in 1996 and a revised version was adopted in 2002.
  • Mathematics Activities for High School Teams: From the Rutgers Academic Challenge. Team activities in mathematics created for the statewide competitions in 1999 to 2004 for high school teams; the competitions were sponsored by Rutgers University in order to celebrate the academic achievements of New Jersey students.
  • Linear Orderings. A 487-page research monograph in mathematics, presented in textbook style, which provides a comprehensive treatment of what was known about linear orderings as of its publication in 1982 (in the Pure and Applied Mathematics Series of Academic Press). This book is now out of print.
  • Discrete Mathematics in the Schools (1997). A collection of articles describing and promoting the adoption of topics from discrete mathematics into the elementary and secondary school curriculum.  This is the only book ever published jointly by the American Mathematical Society and the National Council of Teachers in Mathematics, from whom the book can be obtained.  (With Fred Roberts and Deborah Franzblau as co-editors.)
  • Navigating Through Discrete Mathematics in Prekindergarten through Grade 5 (2009) and Navigating Through Discrete Mathematics in Grades 6-12, (2008). Part of a series of books commissioned by the National Council of Teachers of Mathematics (NCTM) to help teachers navigate through the mathematics standards that it had published earlier.  (With co-authors Valerie DeBellis, Eric Hart, and Margaret Kenney, published by NCTM.)

Articles On Mathematics Education
in Books And Journals

Newspaper Articles on Mathematics Education

  1. Calculators in Instruction and Assessment (An article that appeared in the Star Ledger on June 28, 1992.)
  2. Standards-Based Education (An article that appeared in the Star Ledger on July 24, 1993.)
  3. Putting the Early Warning Test (EWT) Results into Perspective (An article, written with Warren Crown, that appeared in the Star Ledger in June 1994.)
  4. How the Business Community Can Help New Jersey Implement the Content Standards (An article that appeared in the Star Ledger in September 1996.)
  5. Mathematics Standards, Division, and Constructivism (An article that was submitted to the New York Times on August 18, 1997.)
  6. The California War over Math Standards (An article that was submitted to the New York Times on November 28, 1997.)
  7. Algebra II + all high schoolers = overkill.  (An article that appeared on April 29, 2008 in the Star Ledger – title given by editor.)

Selected Presentations on Mathematics Education

  1. Content Standards, Curriculum Frameworks, and Teacher Professional Development (A briefing paper prepared for the White House Forum on “Making It Happen: First in the World in Science and Mathematics Education” on July 26-27, 1995.)
  2. The Evaluation of State Mathematics Standards: New Jersey Perspectives (A presentation at an MAA/AMS/NASSMC-sponsored panel in San Antonio on January 16, 1999.)
  3. Standards and Assessment in New Jersey (A presentation at the “Math Summit” sponsored by the Association of American Publishers in Washington, D.C. on October 3, 2001.)
  4. Standards and Assessment in New Jersey (A presentation at the January 14, 2005 Conference on “Keeping Math on Track:  Bridging the Gap Between High School and College Mathematics” sponsored by the Association of Mathematics Teachers of New Jersey (AMTNJ).)

Articles in Mathematics

  1. A Note on a Theorem of Vaught
  2. Aleph-0 Categoricity is not Inherited by Factor Groups
  3. Aleph-0 Categoricity of Groups
  4. Aleph-0 Categoricity of Linear Orderings
  5. Aleph-0 Categoricity of Rings Without Nilpotent Elements and for Boolean Structures (with A. Macintyre)
  6. Aleph-0 Categorical Abelian by Finite Groups (with G. Cherlin)
  7. Concerning Partial Recursive Similarity Transformations of Linearly Ordered Sets
  8. Correction to Aleph-0 Categoricity of Groups
  9. Effective Matchmaking (Recursion Theoretic Aspects of a Theorem of Philip Hall)
  10. Effective Matchmaking and k-Chromatic Graphs
    Initial Segments of Degrees
  11. On GL-2(R) where R is a Boolean Ring
  12. Recursive Linear Orderings
  13. Theories that are not Aleph-0 Categorical
  14. Two-Dimensional Partial Orderings – Recursive Model Theory
  15. Two-Dimensional Partial Orderings – Undecidability

Quora articles

Quora is an electronic platform that provides people around the world an opportunity to ask questions and obtain responses to those questions from other participants.  Following is a selection of my responses, grouped by topic:

  1. Counting Numbers and Sets
  2. Math Education
  3. General
  4. Set Theory

YouTube Recordings

  • The Disappearance of Discrete Mathematics from the K-12 Curriculum in the United States.
    This video was intended for presentation at the ICME-13 conference in Hamburg, Germany in July 2016. {ICME = International Congress for Mathematics Education}  Watch Video
  • What is Missing from the National Mathematics Standards
    This 2015 video discusses some of the flaws of the Core Curriculum Content Standards in Mathematics, with particular focus on topics that are missing from the national standards and that were, from 1996 to 2008, part of the New Jersey mathematics standards — that is, topics in discrete mathematics.  It discusses why those topics are important in themselves and why they would contribute significantly to achieving the goals of the standards, including the “mathematical practices” of problem-solving, reasoning, and mathematical modeling.  (The video appears to have some gaps.) Watch Video
  • Four-Minute Interview with NJ Spotlight News in 2015 on Mathematics Standards Watch Video