**Problem Solving and Reasoning with Discrete Mathematics**. A textbook for high school students, college students, those intending to become middle school math teachers, and for students of all ages (10+) who are mathematically curious.

**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. T*his 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.)

in Books And Journals

- The Role of Teachers in Mathematics Education Reform.

In Volume 2 of the series*Issues in Mathematics Education*published by the American Mathematics Society in cooperation with the Mathematical Association of America. **A Comprehensive View of Discrete Mathematics**(1997). In*Discrete Mathematics in the Schools,*see above.- The Leadership Program in Discrete Mathematics (1997 with Valerie DeBellis). In
*Discrete Mathematics in the Schools,*see above. **Discrete Math in the Schools – An Opportunity to Revitalize School Mathematics**(1997). In*Discrete Mathematics in the Schools,*see above.**Discrete mathematics in primary and secondary schools in the United States**(2004 with Valerie DeBellis).*International Reviews on Mathematical Education*(Zentralblatt für Didaktik der Mathematik), Vol. 36, Number 2, Electronic-Only Publication, ISSN 1615-679X.- Creating an Equitable Learning Environment for Teachers of Grades K-8 Mathematics (2007 with Valerie DeBellis), in
*The Learning of Mathematics,*the Sixty-ninth Yearbook of the National Council of Teachers of Mathematics. **Discrete Mathematics in 21**(2007), in Lesh, R., Hamilton, E., and Kaput, J. (eds.), Foundations for the Future in Mathematics Education, Hillsdale,NJ: Lawrence Erlbaum Associates.^{st}Century Education: An Opportunity to Retreat From the Rush to Calculus

**When Districts Encounter Teacher Shortages**: The Challenges of Recruiting and Retaining Mathematics Teachers in Urban Districts (2008 with Edward Liu, Aubrey Swan and Deena Khalil), in Leadership, Policy, and Schools.-
**How Unique are Urban Districts’ Challenges with Recruiting/Retaining Math Teachers?—A Comparison with Suburban Districts**(2008 with Edward Liu, Aubrey Swan, and Deena Khalil), to appear **Discrete Mathematics and the Chinese Postman Problem**(2010), in the Mathematics Bulletin of the Chinese Mathematical Society and Beijing Normal University.- Putting Brakes on the Rush to AP Calculus (with A. Ahluwalia), in
*The Role of Calculus in the Transition from High School to College Mathematics*(edited by David Bressoud, published by the Mathematical Association of America and the National Council of Teachers of Mathematics) - The Absence of Discrete Mathematics in Primary and Secondary Education in the United States .. and Why That is Counterproductive (2018), in
*Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research*(edited by Eric Hart and James Sandefur, published by Springer) **Mathematical Perspectives on Fairness in Elections**(2021),to appear

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

**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.)**The Evaluation of State Mathematics Standards: New Jersey Perspectives****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.)**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).)

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

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:

**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