OUTLINE OF CONTENTS:

EDUCATION
EMPLOYMENT  
GRANTS
SERVICE
DOCTORAL STUDENTS
SELECTED PRESENTATIONS & AWARDS
PUBLICATIONS (books, articles, etc.)
THUMBNAIL SKETCHES

————————————————-
EDUCATION

Pre-College

September 1947 – December 1948, Alice C. Bateman Private School, preK-2A (2nd half of 2nd grade)
Story: My mother took me out of this school when she learned that they had promoted me without her permission to the second half of second grade (because I could read) . She had to wait until my 6th birthday to enroll me at the local public school.

January 1949 – June 1955, Mary Gage Peterson (public) School, 1A through 8th grade – memorable teachers: Rose Bellon, 4A; Herbert Herman, 6A; Helen C. Wright, 8 (full year).
Story: The public school administrators wanted to put me in 1B, the first half of 1st grade, but my mother argued that would be putting me back three semesters. They compromised on 1A for the single month of January, then 2B for the rest of the year. A year later, in 3rd grade I was “skipped” from 2A to 3A due to there being too many students. (It was not at all uncommon for better students to be pushed up a semester.) In 8th grade, influenced by my love of my teacher Mrs. Wright, I decided I wanted to be a teacher.

September 1955 – June 1959, Von Steuben (public) High School, 9th through 12th grade, class salutatorian – memorable teachers: Glenn Hewitt, Mathematics; Charles Stief, choral groups; Frances Beck, Latin and English.
Story: It was in 9th grade that I decided I wanted to teach mathematics.

1958 Summer, Roosevelt College, Analytic Geometry and Conducting
Story: By doubling up on mathematics classes, I had completed all the mathematics offered at Von Steuben by the end of my junior year. I wanted to take calculus and at that time analytic geometry was a pre-requisite. I had been named as the student director of the Von Steuben Choir for my senior year, so I desired to learn (musical) conducting. So between my junior and senior years of high school, I took two courses at Roosevelt College (now Roosevelt University), analytic geometry and conducting.

College

September 1959 – June 1963, University of Illinois – main advisor, J.W. Peters; main professor in mathematics, Colin Blyth; main professor in mathematics education, Kenneth Henderson; main professor in music, Harold Decker.
Story: I went to the U of I because my brother had gone there; it was a safe school because every graduate from a high school in Illinois could get in! I had no idea that the University of Illinois was the place where the “new math” had started in the United States. My first course in mathematics education, taught by Professor Henderson, was essentially a course in the new math curriculum of the University of Illinois Commission on School Mathematics, UICSM. It taught me that the same school mathematics could be approached in significantly different ways, and it was a major influence on my career in mathematics education.

1962 Spring, student teaching, Niles West H.S., Skokie, IL – geometry, 2nd-year algebra, calculus; master teacher, Jim Martin.
Story: The university requested that I do some teaching in a calculus class even while student teaching because of their belief that I would not be a high school mathematics teacher, but a mathematician who would be teaching at the college level.

1962 Summer, North Park College – French (anticipating needing modern languages for a PhD)
Story: By this time, I expected to go to graduate school, for which I would need to show reading proficiency in two languages. Neither of the allowed languages were likely to be Hebrew or Latin, the two languages I had studied until this time. So I took a 6-week concentrated course in French.

Degree: Bachelor of Science (B.S.) in Mathematics (with highest distinction), 1963 (minors in Statistics, Astronomy)
Thesis (not required and quite unusual): Max-min Probabilities in the Voting Paradox. Thesis advisor: Colin Blyth.

Degree: Bachelor of Science (B.S.) in Education (with highest honors), 1963 (major in Mathematics, minor in Music), state certification to teach.
Story: Due to a great deal of classes in the music school, I had enough hours to receive a second degree; the advantage of that is that I could have music (specifically, choral music) as a teaching minor.

Main honors: James Scholar (all four years); Phi Kappa Phi (all-university), Phi Beta Kappa (liberal arts), Outstanding Senior in Education, University Honors (highest honor a graduate can receive)

Graduate work

June 1963 – August 1964, Harvard University – advisor, Edwin Moise
Story: At Illinois I had been introduced as a freshman to the work of the University of Illinois Commission on School Mathematics (UICSM), the first of the “new math” projects in the United States. I had become acquainted with the algebra of UICSM but not the geometry, and I applied to the Harvard Graduate School of Education) because the advisor in mathematics education was Moise, who was mainly responsible for the geometry text of the School Mathematics Study Group (SMSG), the largest of the new math projects.

Degree: Master of Arts in Teaching (M.A.T.) in Mathematics, 1964

1966-1969, University of Michigan - course advisor, Joseph Payne; thesis advisor, Arthur Coxford.
Story: I had applied to three schools for my doctorate: Harvard, Stanford, and Michigan. I was accepted at all three and chose Michigan because I had been told that I could do a dissertation in curriculum there. (By this time I was already co-authoring a pre-calculus text – see the Books section of Publications below.) I received an NDEA Scholarship, which covered my tuition for all three years.

Degree: Doctor of Philosophy (Ph.D.) in Education (Curriculum and Instruction – Mathematics), 1969
Story: Michigan required reading knowledge of two languages but allowed a computer language. French and Fortran became my languages.

Dissertation: The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, 1969, Publication No. AAT 7014670, University Microfilms, Ann Arbor, MI, full text can be found in Dissertation Abstracts.
Dissertation committee: Arthur Coxford (chair), Joseph Payne, Phillip Jones, Stanley Diamond, Roger Lyndon
Story: During my first year at Michigan, Joe Payne suggested that I might be interested in looking at incorporating geometric transformations into the geometry course. When I expressed great interest in this idea, he directed me to Art Coxford, whom he said was very interested in this. The second year at Michigan Art and I both taught geometry classes and wrote the first draft of the materials that became the subject of my dissertation. The third year at Michigan these materials were revised into two-volume paperback form so they could be used by others and tested in schools.

EMPLOYMENT

Full-time high school teaching

1964 Spring, Lexington H.S., Lexington MA (as part of the Harvard M.A.T. program), five classes (3 geometry and 2 2nd-year algebra)

1964-1966, Niles Twp. H.S. West, Skokie (algebra and algebra honors, geometry, advanced algebra trig, math team coach)
Story: While at Harvard, I applied to 8 school districts in the Chicago area for employment: the Chicago Public Schools, Evanston, Glenbrook, New Trier, Niles, Highland Park-Deerfield, Oak Park-River Forest, and the University of Chicago Laboratory Schools. I received five offers and so much liked my student teaching experience at Niles under Jim Martin that I accepted that offer.

Part-time teaching (Sept – June) during my doctoral studies

1966-1967, University of Michigan Laboratory School – 8th grade mathematics
1967-1968, University of Michigan Laboratory School – geometry – writing Geometry – A Transformation Approach (GATA) with Art Coxford
1968-1969, Adrian H.S., Adrian MI – geometry honors – teaching GATA, trying out ideas for a 2nd-year algebra when students are familiar with transformations – department head, Pete Boudreau

Full-time titles and positions at the University of Chicago

1969-1974, Assistant Professor of Education, teaching one class in the Lab School (see below), teaching and advising in the M.A.T. program in mathematics

1974-1976, Associate Professor, Graduate School of Education, teaching and advising in the M.A.T. program in mathematics
Story: In my 5th year at the university, I asked to be considered for tenure and received that with the promotion.

1976-1982, Associate Professor, Department of Education, teaching and advising master’s and doctoral students in mathematics education
Story: In 1975-76, the Graduate School of Education and Department of Education merged into the latter, and the Graduate School no longer existed.

1982-2001, Professor, Department of Education, master’s and doctoral students (until department was closed), teaching and advising master’s and doctoral students in mathematics education, and curriculum and instruction
Story: The Department of Education was closed to new applicants in 1996; doctoral students were given five years to finish and its one-year master’s programs existed through that time.

2001-2007, Professor of Education, Division of Social Sciences
Story: Without a department I reported directly to the Dean of the Division of Social Sciences.

2004-2007, Professor, Harris School of Public Policy and in the College, teaching public policy in education

2008-present, Professor Emeritus
Story: In January 2008, I took advantage of an early-retirement incentive to become an emeritus professor. Supported by UCSMP royalties to the university, I remained full-time for two years and then part-time for nine years to write and to handle various projects and grants, and in June 2019, I retired entirely from professorial duties at the university.

University work elsewhere

Winter 1980, Visiting Professor of Education, University of Georgia
August-September 1991, Visiting Lecturer, East China Normal University

Teaching individual high school mathematics classes for full school years

As part of my University of Chicago position:
1969-1971, University of Chicago Laboratory School, 2nd-year algebra – to work out Advanced Algebra with Transformations and Applications (AATA)
1972-1974, University of Chicago Laboratory School, one class each quarter I was in residence – probability and statistics, computer programming

As part of my curriculum development work:
1974-1975, Addison Trail H.S., Addison IL – algebra – to write Algebra Through Applications with Probability and Statistics (ATA) – Alan Foster, department chair
1975-1976, Proviso West H.S., Hillside, IL – algebra – to write 2nd draft of ATA. – Jerry Cummins, department chair
1978-1979, Rich South H.S., Richton Park, IL – geometry – to write a geometry text with Sharon Senk influenced by van Hiele theory – venture abandoned when we saw that Alan Hoffer had written a book with the same idea (!)
1983-1984, Glenbrook South H.S., Glenview, IL – general mathematics – to write UCSMP Transition Mathematics – John McConnell, department chair

Administrative positions with the University of Chicago School Mathematics Project (UCSMP)

Original funding from the Amoco Foundation obtained by Izaak Wirszup of the Department of Mathematics; other faculty members involved were Paul Sally, Jr. of the Department of Mathematics and Larry Hedges, Susan Stodolsky, and beginning in 1985, Max Bell of the Department of Education. For a history of UCSMP, see https://ucsmp.uchicago.edu/about/history/.
1983-1987, Secondary Component Director – overall project director, Paul Sally, Jr.
1987-2019, Overall UCSMP Director, Secondary Component co-Director with Sharon Senk – assisted by Denisse Thompson, who in the 1990s became Director of Secondary Component Research.

GRANTS (Director or Co-Director)

1974-1978, from the National Science Foundation, for the First-Year Algebra via Applications Development Project
1979-1982, from the National Institute of Education, for the Cognitive Development and Achievement in Secondary School Geometry (CDASSG) Project – with Sharon Senk
1979-1982, from the National Science Foundation, for the Arithmetic and Its Applications Project
1983-1995, from the Amoco Foundation, for the University of Chicago School Mathematics Project (UCSMP) – with Izaak Wirszup, Paul Sally Jr., Max Bell, Susan Stodolsky, and Larry Hedges; later funding from royalties from the sale of UCSMP texts
1985-1993, from the Carnegie Corporation of New York, for UCSMP
1985-1990, from the General Electric Foundation, for UCSMP
1988-1992, from the Ford Motor Company, for UCSMP
1991-1997, from the UCSMP Research Fund for Mathematics Education, numerous grants for testing UCSMP materials
1995, from the National Science Foundation, for the 4th Gateways Conference – a conference of those math and science curriculum projects funded by NSF
1998-1999, from the National Science Foundation, for the 4th UCSMP International Conference on Mathematics Education
1999-2002, from the Stuart Foundation, for the High School Mathematics from an Advanced Standpoint Project (with the University of California – Berkeley) – with Dick Stanley, Anthony Peressini, and Elena Marchisotto
2004-2014, from the National Science Foundation, for the Center for the Study of Mathematics Curriculum (with the Univ. of Missouri, Michigan State Univ., Western Michigan Univ., and Horizon Research) – with Barbara Reys, Robert Reys, Glenda Lappan, Chris Hirsch, and Iris Weiss

SERVICE

1970-1973, Board of Directors, Men’s Mathematics Club of Chicago (during which time MMC became the Metropolitan Mathematics Club of Chicago).
1982-1983, Chicago United Committee on Curriculum and Instruction
1983-2003, Editorial Board, American Journal of Education
1984-1992, Mathematics Advisory Committee, Illinois State Board of Education
1986-1992, National Advisory Board, Children’s Television Workshop Square One TV
1988-1991, Mathematical Sciences Education Board, National Research Council; 1990-1991, Executive Committee
1990-1992, Illinois Mathematics Coalition
1995-2003, National Assessment of Educational Progress (NAEP): various committees
1995-1996, Illinois State Board of Education Mathematics Academic Standards Project
1995-1998, Board of Directors, National Council of Teachers of Mathematics (NCTM)
1995-2001, United States National Commission on Mathematics Instruction: 1995-1997, member; 1998-2001, chair
1996-1998, Member and Steering Committee, Education Partnership, Conference Board of the Mathematical Sciences
1996-2000, Editorial Panel, NCTM Recent History of Mathematics Education
1998-1999, NCTM Dialogues in Mathematics Education: 1997-1998, task force member; 1998-1999, editor
2003-2006, Advisory Board, Mathematical Association of America, Preparing Mathematicians to Educate Teachers
2005-2008, Committee on the Mathematical Education of Teachers, Mathematical Association of America
2017, NCTM Task Forces: Chicago 2020 Task Force, New Journal Task Force, and High School Report Task Force
2018-2021, International Advisory Committee of the Asian Centre for Mathematics Education, East China Normal University
2018-present, National Assessment of Educational Progress (NAEP): various committees

DOCTORAL STUDENTS

These students are those for whom I was chair of their dissertation committee, together with the title of the dissertations, in order of their completing their degrees.

Senk, Sharon. 1983. Proof-Writing Achievement and Van Hiele Levels among Secondary School Geometry Students
Gustin, William. 1987. Talented research mathematicians: a retrospective study of exceptional cognitive development
Dalida, John. 1988. Risk taking, small groups, and the game of Equations
Hirschhorn, Daniel. 1991. Implementation of the first four years of the University of Chicago School Mathematics Project Secondary Curriculum (later he changed his name to Raven Deerwater)
Flanders, James R. 1992. Textbooks and the SIMS test: comparisons of intended and implemented eighth-grade mathematics
Friedman, Lynn. 1992. A Meta-analysis of Correlations of Spatial and Mathematical Tasks
Thompson, Denisse. 1992. An evaluation of a new course in precalculus and discrete mathematics
Fan, Lianghuo. 1998. The development of teacher's pedagogical knowledge: an investigation of mathematics teachers in three high-performing high schools
Fernandez, Eileen. 1998. Instantiating the Standards: describing attempts by an exceptional group of mathematics teachers to implement the NCTM professional teaching standards
Levin, Suzanne. 1998. Fractions and division: researcher conceptualizations, textbook presentations, and student performance
Li, Jianhua. 2004. A comparative study of U.S. and Chinese elementary mathematics textbook teacher guides

SELECTED PRESENTATIONS & AWARDS

During over fifty years in the field of mathematics education, I have given presentations at universities or professional meetings in every one of the 50 states and the District of Columbia. These include being on the program at every NCTM annual meeting from 1972 until the 2020 pandemic. I have also given presentations in 25 foreign countries, listed here in order of my first engagement in each: Canada, England, Germany, Australia, St. Croix, Taiwan, Hungary, Denmark, Bermuda, Egypt, China, Japan, Thailand, Malaysia, Denmark, Netherlands, Scotland, Mexico, Turkey, Korea, South Africa, Spain, Brazil, Israel, Oman.

Selected presentations (if published, reference is to publication in next section) (M = with music) (Th = a thumbnail sketch can be found at the end of this section.)

1963:  Illinois Section, Mathematical Association of America, student research session
“Max-min Probabilities in the Voting Paradox”
1968:  Michigan Mathematics Conference, Ann Arbor, MI
“A Transformation Approach to High School Geometry”
1981: Illinois Council of Teachers of Mathematics annual meeting banquet speaker, Champaign, IL (Th)
(M) “Mathematics and Diamonds: The Many Facets of Mathematics”
1983: National Council of Teachers of Mathematics annual meeting, secondary level general session, Detroit, MI.
“We Need Another Revolution in School Mathematics” (A36)
1987: Long Island University, Fifth Morton J. Hellman Memorial Lecturer, Brooklyn, NY
“The Real True Understanding of Mathematics” (later version in A109)
1987: Association of Teachers of Mathematics of New England, First Richard H. Balomenos Lecturer, Burlington, VT
“The Enjoyment of Mathematics”
1987: National Council of Teachers of Mathematics annual meeting banquet speaker, Anaheim, CA (Th)
(M) “Mathematics and Diamonds: The Many Facets of Mathematics”
1987: University of Chicago School Mathematics Project Users Conference, opening speaker, Chicago, IL
“The Beliefs Underlying UCSMP” (N1, A48)
1990: Association for Supervision and Curriculum Development, John Dewey Memorial Lecturer, San Antonio, TX
“Reforming the Schools: Is It Deja-vu All Over Again?”
1992: Seventh International Conference on Mathematics Education (ICME -7), Regular Lecture, Quebec City, Canada
“From ‘Mathematics for Some’ to ‘Mathematics for All’” (A60)
1999: Western Illinois University, Centennial Lecturer, Macomb, IL
“From ‘Mathematics for Some’ to ‘Mathematics for All’” (A60)
1999: National Council of Teachers of Mathematics annual meeting banquet speaker, San Francisco, California (Th)
(M) “Sum of the Powers of Mathematics: A Theme and Variations”
2004: Asian Conference on the Teaching of Mathematics, Singapore
“A K-12 Mathematics Curriculum with CAS: What Is It and What Would It Take to Get It?” (A93)
2008: University of Tennessee, Barrett Lecturer, Knoxville, TN
“The Current State of High School Mathematics and Its Implications for the Transition to College Mathematics” (A96, A104)
2009: National Council of Supervisors of Mathematics Annual Meeting, Washington, DC.
“Four Years from First-Year Algebra to Calculus Is Not Enough”. Podcast at
https://poddtoppen.se/podcast/340703550/ncsm-leadership-in-mathematics-education-learning-with-leaders/episode24-zalman-usiskin-four-years-from-first-year-algebra-to-calculus-is-not-enough
2009: Miami University, Buckingham Scholar, Miami, OH
“Teachers’ Mathematics: A Collection of Content Deserving to Be a Field” (A88, N15)
“The Current State of High School Mathematics and Its Implications for the Transition to College Mathematics” (A96, A104)
2012: Twelfth International Conference on Mathematics Education (ICME-12), Invited Regular Lecture, Seoul, Korea
“What Does It Mean to Understand Some Mathematics? (A109)
2012: University of Michigan, Rackham Graduate School Centennial Alumni Lecture, Ann Arbor, MI
“Comparison Studies of Textbooks in a Digital Age”
2012: National Council of Teachers of Mathematics regional meeting, Chicago, IL
“Mathematical Modeling in the School Curriculum”, https://www.youtube.com/watch?v=tqaIL473dys
2013: Association of Mathematics Educators of South Africa (AMESA) annual meeting keynote speaker, Capetown, South Africa
“What Does It Mean to Understand Some Mathematics? (A109)
2013: Illinois Council of Teachers of Mathematics annual meeting closing session, Peoria, IL
“Changes Needed in the Common Core Math Standards”, https://www.youtube.com/watch?v=5M6dHbJqZjA
2014: International Conference on the Teaching of Statistics (ICOTS-9), Flagstaff, Arizona
“On the Relationships between Statistics and Other Subjects in the K-12 Curriculum” (A125)
2017: National Council of Supervisors of Mathematics annual meeting, San Antonio, Texas
“Approaching Ten Tough Mathematical Ideas for High School Students.” (Th) One-page summary by Jill Gough at https://jillgoughnotes.blog/2017/04/
2017: International Conference on Mathematics Textbooks (ICMT-2), Plenary Lecture, Rio de Janeiro, Brazil
“Electronic vs. Paper Textbook Presentations of the Various Aspects of Mathematics” (A130)
2018: International Society for Design and Development in Education (ISDDE) annual meeting, Galway, Ireland
“Beauty and Serendipity in Creating Mathematics Curricula” (A131)
2018: Oman Mathematics Day IV, Sultan Qaboos University, Muscat, Oman
“Assessing Students in Mathematics”
2022: 12th Conference of the International Group for Mathematical Creativity and Giftedness, keynote speaker, Las Vegas, NV
“The Road from Ordinary to Extraordinary”, https://doi.org/10.37626/GA9783959872263.0
2022: National Council of Teachers of Mathematics annual meeting highlighted session, Los Angeles, CA (Th)
(M with Andrew Chukerman) “Circling Through a Century of NCTM: A Celebration Sprinkled with Music”

Lifetime achievement awards
It perhaps need not be stated that each of these awards is a major honor on its own.

1981: Illinois Council of Teachers of Mathematics, Max Beberman Award (for distinguished contributions to mathematics education curriculum or research)
1982: Metropolitan Mathematics Club of Chicago, Lifetime Achievement Award
1994: National Council of Supervisors of Mathematics Glenn Gilbert Award (for contributions to mathematics education)(now called the Ross Taylor/Glenn Gilbert National Leadership Award)
2001: National Council of Teachers of Mathematics Lifetime Achievement Award
2010: Illinois Council of Teachers of Mathematics Distinguished Life Achievement Award
2017: Program in Mathematics, Teachers College, Columbia University International Achievement Award in Mathematics Education
2017: International Society for Design and Development in Education ISDDE Prize for Lifetime Achievement

PUBLICATIONS

Organization of publications
On this website, publications are arranged by type, in the order of these bullets, with entries to types numbered in chronological order (and - in the first four types - coded with a letter before the number).

• Books (B)

• Published Papers (A)

• Unpublished Papers Available Through ERIC in 2012 (E)

• Papers Published in UCSMP Newsletters and/or available on the UCSMP Website (U)

• Essays as Editor of Mathematics Education Dialogues

• Available Videos of Presentations

• Writing Regarding Video and Films

• Published Reviews

• Published Recreations

Within each type, items are numbered chronologically. Multiple editions of the same book with the same publisher and variants and continuations of the same paper are under the same number. If a copy of the publication is known to be available online, a link is provided.

Below, the books, articles, and papers are roughly categorized into areas of interest. For this categorization, each publication is identified by letter and its chronological number: Books = B; Articles = A; unpublished papers in ERIC = E; UCSMP newsletters = U.

Original Mathematics: A1, A5, A6, A9, A12, A22, A25, A41
Arithmetic: B8, A10, A35, A40, A77, A98, A99, A114, A116, E3, E4, E9
Calculators and Technology: B44, A21, A32, A34, A77, A93, A121, A126, E4, U9
Middle School Mathematics: B8, B10, B16, B30, B32, B36, A10, A23, A35, A45, A49, A69, A101, A115, A122, A124, A134, U18
Algebra: B4, B5, B11, B13, B17, B18, B25, B27, B31, B33, B38, B41, A15, A16, A18, A20, A24, A26, A27, A45, A47, A64, A65, A71, A73, A92, A93, A95, A97, A116, A121, A134, U10
Applications and Modeling: B4, B5, B6, B8, A20, A24, A26, A39, A49, A54, A59, A75, A78, A79, A120, A124, A133, E9, U21
Geometry: B1, B2, B7, B12, B19, B28, B34, B37, B41, A3, A8, A13, A16, A17, A26, A27, A29, A31, A43, A74, A97, A116, A119, A123, A127, E8
Transformations: B1, B2, B4, A4, A8, A14, A16, A41, A119, A123, A127, E5
Precalculus and Calculus: B3, B14, B15, B21, B22, B39, B40, A61, A71, A89, A96, U10
Statistics and Probability: B5, B14, B21, B39, A1, A6, A125
Curriculum Development: B20, B35, B41, B44, A8, A21, A23, A27, A33, A36, A42, A45, A50, A66, A73, A76, A89, A100, A102, A103, A104, A112, A128, A129, A131, A132, E6, E7, U2, U7, U19
Curriculum Evaluation: B1, B25, B28, B30, B31, B42, A11, A29, A53, A90, A107, A110, A117, E1, E2, E6, U11, U13
About Textbooks: A4, A18, A57, A90, A108, A122, A123, A130
Mathematics for All: A7, A45, A48, A58, A60, A63, A64, A70, A71, A74, A80, A83, U3, U4, U8, U10
Gifted Students: A19, A80, A83, A135, U4
Teacher Education: B26, B27, A68, A69, A86, A87, A88, A91, U12, U15, U16|
International Math. Ed.: B23, B24, B26, B29, B35, B41, B44, A28, A38, A55, A56, A81, A94, A107, A110|
History of Math. Ed.: A4, A36, A46, A60, A66, A75, A87, A89, A106, A110, A129, A134
General: B9, B23, A2, A30, A34, A37, A46, A50, A51, A73, A76, A85, A86, A90, A92, A101, A105, A106, A109, A111, A118, U6, U7, U11, U14, U20
UCSMP: B10-B19, B21, B22, B25, B28, B30-B33, B36-B40, A42, A44, A48, A49, A52, A54, A57, A67, A84, A87, A91, A100, A122, U1, U5, U13

In a compilation of 38 of my articles published by NCTM (B43) – I selected the articles: A4b, A7, A8, A14, A16, A21, A24b, A27, A36, A43, A45, A47, A54, A58, A60, A61, A64, A66, A70, A71, A74, A75, A76, A79, A77, A82, A85, A90, A99, A104, A114, A115, A116, A117, A118, A119, A120, A121, E7, U18, U21, U22

As of January 2022, abstracted at https://eric.ed.gov by searching “Usiskin” – I had nothing to do with the selection. Those publications in bold can be downloaded in full from the site: A4b, A6, A7, A8, A16a, A16b, A20, A21, A23, A25, A27, A29, A31, A32, A34, A35, A42, A45, A53, A56, A57, A62, A64, A65, A75, A78, A82, A85, A98, A102, A107, A124, A127, A130, B1, B5b, B7, B8, B20, B26. E1, E2, U2, U4, U6, U11

Books

B1. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, Publication No. AAT 7014670, University Microfilms, Ann Arbor, MI, 1969 (available for download from ProQuest Dissertations and Abstracts)

B2. Arthur Coxford and Zalman Usiskin. Geometry - A Transformation Approach.
a. research 2-volume paperback edition, Ann Arbor, MI: the authors, 1968
b. commercial edition, River Forest, IL: Laidlaw Brothers, 1971

B3. Kenneth B. Henderson, Zalman Usiskin, and Wilson M. Zaring. Precalculus Mathematics. New York: McGraw-Hill, 1971

B4. Zalman Usiskin. Advanced Algebra with Transformations and Applications.
a. as Intermediate Mathematics, research 2-volume paperback edition, Chicago, IL: the author, 1972
b. commercial edition, River Forest, IL: Laidlaw Brothers, 1975

B5. Zalman Usiskin. Algebra Through Applications with Probability and Statistics.
a. research 2-volume paperback edition, Chicago, IL: First-Year Algebra via Applications Development Project, University of Chicago, 1976
b. corrected edition, Reston, VA: National Council of Teachers of Mathematics, 1979

B6. Donald Bushaw, Max Bell, Henry Pollak, Maynard Thompson, and Zalman Usiskin. A Sourcebook of Applications of School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 1980

B7. Zalman Usiskin. Van Hiele Levels and Achievement in Secondary School Geometry. Chicago, IL: CDASSG Project, University of Chicago, 1982. Available online at http://ucsmp.uchicago.edu/resources/van-hiele/ .

B8. Zalman Usiskin and Max Bell. Applying Arithmetic, Parts I-III. Chicago, IL: Arithmetic and Its Applications Project, University of Chicago, 1983. Available online at http://ucsmp.uchicago.edu/resources/applying-arithmetic-handbook/ .

B9. Uncle Zal’s Mathacrostics. Palo Alto, CA: Dale Seymour Publications, 1984.

(B10-B15) University of Chicago School Mathematics Project texts published by Scott Foresman (series co-editor with Sharon Senk of all published editions; author of all teacher editions; consultant and editor on all other ancillary materials)
B10. UCSMP Transition Mathematics. Zalman Usiskin, James Flanders, Cathy Hynes, Lydia Polonsky, Susan Porter, and Steven Viktora. Project versions 1983-85; Project hardcover version 1986; Scott, Foresman editions 1990, 1992
B11. UCSMP Algebra. John W. McConnell, Susan Brown, Susan Eddins, Margaret Hackworth, Leroy Sachs, Ernest Woodward, James Flanders, Daniel Hirschhorn, Cathy Hynes, Lydia Polonsky, and Zalman Usiskin. Project versions 1985-88; Scott, Foresman editions 1990, 1993
B12. UCSMP Geometry. Arthur F. Coxford, Jr., Daniel Hirschhorn, and Zalman Usiskin. Project versions 1986-89; Scott Foresman editions 1991, 1993
B13. UCSMP Advanced Algebra. Sharon L. Senk, Denisse R. Thompson, Steven S. Viktora, Rheta Rubenstein, Judy Halvorson, James Flanders, Cathy Hynes, Natalie Jakucyn, Gerald Pillsbury, and Zalman Usiskin. Project versions 1985-88; Scott, Foresman editions 1990, 1993
B14. UCSMP Functions, Statistics, and Trigonometry. Rheta N. Rubenstein, James E. Schultz, Sharon L. Senk, Margaret Hackworth, John W. McConnell, Steven S. Viktora, Dora Aksoy, James Flanders, Barry Kissane, and Zalman Usiskin. Project versions 1986-89; Scott, Foresman edition 1992
B15. UCSMP Precalculus and Discrete Mathematics. Anthony L. Peressini, Susanna S. Epp, Kathleen A. Hollowell, Susan Brown, Wade Ellis, Jr., John W. McConnell, Jack Sorteberg, Denisse R. Thompson, Dora Aksoy, Geoffrey D. Birky, Greg McRill, and Zalman Usiskin. Project versions 1987-90; Scott, Foresman edition 1992

(B16-B19, B21-B22) University of Chicago School Mathematics Project texts published by Scott Foresman and successor companies (series co-editor with Sharon Senk of all published editions, Natalie Jakucyn, managing editor; author of all teacher editions; consultant and editor on all other ancillary materials)
B16. UCSMP Transition Mathematics. Second edition. Zalman Usiskin, Cathy Hynes Feldman, Suzanne Davis, Sharon Mallo, Gladys Sanders, and David Witonsky. Test version 1992-93; ScottForesman edition 1995; Scott Foresman – Addison Wesley edition 1998; Prentice Hall edition 2002
B17. UCSMP Algebra. Second edition. John W. McConnell, Susan Brown, Sharon L. Senk, Ted Widerski, Scott Anderson, and Zalman Usiskin. Test version 1992-93; ScottForesman edition 1996, Scott Foresman – Addison Wesley edition 1998; California edition, 2000; Prentice Hall edition 2002]
B18. UCSMP Advanced Algebra. Second edition. Sharon L. Senk, Denisse Thompson, Steven S. Viktora, Zalman Usiskin, Nils P. Ahbel, Suzanne Levin, and Marcia Weinhold. Test version 1993-94; ScottForesman edition 1996; Prentice Hall edition 2002
B19. UCSMP Geometry. Second edition. Zalman Usiskin, Daniel B. Hirschhorn, Virginia Highstone, Hester Lewellen, Nicholas Oppong, Richard DiBianca, and Merilee Maeir. Test version 1993-94; ScottForesman edition 1997; Prentice Hall edition 2002

B20. Zalman Usiskin (ed). Reforming the Third R: Changing the School Mathematics Curriculum. Special issue, American Journal of Education 106:1 (November 1997)

B21. UCSMP Functions, Statistics, and Trigonometry. Second edition. Sharon L. Senk, John W. McConnell, Steven S. Viktora, Zalman Usiskin, Nils P. Ahbel, Virginia Highstone, and David Witonsky. Scott Foresman - Addison Wesley, 1997
B22. UCSMP Precalculus and Discrete Mathematics. Second edition. Anthony L. Peressini, John W. McConnell, Zalman Usiskin, Nils P. Ahbel, and David Witonsky. Scott Foresman - Addison Wesley, 1998

B23. Zalman Usiskin (ed). Developments in School Mathematics Around the World, Volume 4. Proceedings of the Fourth UCSMP International Conference on Mathematics Education. Reston, VA: NCTM, 1999

B24. John Dossey and Zalman Usiskin. Mathematics Education in the United States 2000. A Capsule Summary Written for the Ninth International Congress on Mathematical Education, Tokyo/Makuhari, Japan, July – August 2000. Reston, VA: National Council of Teachers of Mathematics, 2000

B25. Denisse R. Thompson, Sharon L. Senk, David Witonsky, Zalman Usiskin, and Gurcharn Kaeley. An Evaluation of the Second Edition of UCSMP Advanced Algebra. University of Chicago: UCSMP, 2001

B26. Hyman Bass, Gail Burrill, and Zalman Usiskin (eds.). Studying Classroom Teaching as a Medium for Professional Development. Proceedings (text and videotape) of a U.S.-Japan Workshop (Tokyo/Makuhari, Japan July 31-August 6, 2000. Washington, DC: National Academy Press, 2002

B27. Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto, and Dick Stanley. Mathematics for High School Teachers: An Advanced Perspective. High School Mathematics from an Advanced Standpoint Project versions. Berkeley, CA: Department of Mathematics, University of California at Berkeley, 2000-02; commercial edition, Upper Saddle River NJ: Prentice-Hall, 2003, 2005. Available for free download from https://knowledge.uchicago.edu/record/5793.

B28. Denisse R. Thompson, David Witonsky, Sharon L. Senk, Zalman Usiskin, and Gurcharn Kaeley. An Evaluation of the Second Edition of UCSMP Geometry. University of Chicago: UCSMP, 2003

B29. Zalman Usiskin and John Dossey. Mathematics Education in the United States 2004. A Capsule Summary Fact Book written for The Tenth International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark, July 2004. Reston, VA: National Council of Teachers of Mathematics, 2004

B30. Denisse R. Thompson, Sharon L. Senk, David Witonsky, Zalman Usiskin, and Gurcharn Kaeley. An Evaluation of the Second Edition of UCSMP Transition Mathematics. University of Chicago: UCSMP, 2005

B31. Denisse R. Thompson, Sharon L. Senk, David Witonsky, Zalman Usiskin, and Gurcharn Kaeley. An Evaluation of the Second Edition of UCSMP Algebra. University of Chicago: UCSMP, 2006

(B32-B33, B36-B40) University of Chicago School Mathematics Project texts published by Wright Group/McGraw -Hill (series director; author of all teacher editions; consultant and editor on all other ancillary materials; Clare Froemel, managing editor; Denisse Thompson, director of research); UChicagoSolutions editions directed by Natalie Jakucyn
B32. UCSMP Transition Mathematics. Third edition. Steven S. Viktora, Erica Cheung, Virginia Highstone, Catherine Capuzzi, Deborah Heeres, Neva Metcalf, Susan Sabrio, Natalie Jakucyn, and Zalman Usiskin. Field test version 2005-06; Wright Group/McGraw-Hill edition 2008; UChicagoSolutions edition 2016
B33. UCSMP Algebra. Third edition. Susan Brown, R. James Breunlin, Mary H. Wiltjer, Katherine M. Degner, Susan K. Eddins, Michael Todd Edwards, Neva Metcalf, Natalie Jakucyn, and Zalman Usiskin. Field test version 2005-06; Wright Group/McGraw-Hill edition 2008; UchicagoSolutions edition 2016

B34. Zalman Usiskin. Jennifer Griffin, David Witonsky, and Edwin Willmore. The Classification of Quadrilaterals: A Study of Definition. Charlotte, NC: Information Age Publishing, 2008

B35. Zalman Usiskin and Edwin Willmore, editors. Mathematics Curriculum in Pacific Rim Countries – China, Japan, Korea, and Singapore: Proceedings of a Conference. Charlotte, NC: Information Age Publishing, 2008

B36. UCSMP Pre-Transition Mathematics. John W. McConnell, Cathy Hynes Feldman, Deborah Heeres, Emily Kallemeyn, Enrique Ortiz, Noreen Winningham, Karen Hunt, Troy P. Regis, Mihaela Florence Singer, John Wolfe, Natalie Jakucyn, and Zalman Usiskin. Field test version 2006-07; Wright Group/McGraw-Hill edition 2009
B37. UCSMP Geometry. Third edition. John Benson, Ray Klein, Matthew J. Miller, Catherine Capuzzi-Feuerstein, Michael Fletcher, George Marino, Nancy Powell, Natalie Jakucyn, and Zalman Usiskin. Field test version 2006-07; Wright Group/McGraw-Hill edition 2009; UChicagoSolutions edition 2016
B38. UCSMP Advanced Algebra. Third edition. James Flanders, Marshall Lassak, Jean Sech, Michelle Eggerding, Paul J. Karafiol, Lin McMullin, Neal Weisman, and Zalman Usiskin. Field test version 2006-07; Wright Group/McGraw-Hill edition 2009; UChicagoSolutions edition 2016
B39.  UCSMP Functions, Statistics, and Trigonometry. Third edition. John W. McConnell, Susan A. Brown, Paul J. Karafiol, Sara Brouwer, Mary Ives, Rosa McCullagh, Natalie Jakucyn, and Zalman Usiskin. Field test version 2007-08; Wright Group/McGraw-Hill edition 2010; UChicagoSolutions edition 2016
B40.  UCSMP Precalculus and Discrete Mathematics. Third edition. Anthony L. Peressini, Peter D. DeCraene, Molly A. Rockstroh, Steven S. Viktora, Ward E. Canfield, Mary Helen Wiltjer, and Zalman Usiskin. Field test version 2007-08; Wright Group/McGraw-Hill edition 2010; UChicagoSolutions edition 2016

B41. Zalman Usiskin, Kathleen Andersen, and Nicole Zotto, editors. Future Curricular Trends in School Algebra and Geometry: Proceedings of a Conference. Charlotte, NC: Information Age Publishing, 2010

B42. Denisse Thompson and Zalman Usiskin, editors. The Enacted Mathematics Curriculum: A Conceptual Framework and Research Needs. Charlotte, NC: Information Age Publishing, 2014

B43. Barbara Reys and Robert Reys, editors. We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: National Council of Teachers of Mathematics, 2014. The 38 papers in this compilation are identified in purple below.

B44. Meg Bates and Zalman Usiskin, editors. Digital Curricula in School Mathematics. Charlotte, NC: Information Age Publishing, 2016.

Published articles
The notation (Th) in the entry for an article indicates that a Thumbnail Sketch of the article can be found at the very end of this section. To find the sketch, search for the article by its number or a distinguishing word in its title.

A1. Max-min Probabilities in the Voting Paradox, Annals of Mathematical Statistics 35:2 (June 1964) 857-862; follow-up September 1965 (Th)

A2. Six Non–trivial Equivalent Problems
a. The Mathematics Teacher 61 (April 1968), 388-390.
b. reprinted in Mathematics in the Secondary School Classroom: Selected Readings, by Gerald R. Rising and Richard A. Wiesen, Crowell, 1972

A3. A New Approach to the Teaching of Constructions, The Mathematics Teacher 61 (December 1968), 749-757.

A4. Transformations in High School Geometry - A History
a. Points and Angles, the newsletter of the Men's Mathematics Club of Chicago and Metropolitan Area, 4:1 (May 1970), 1, 3-8; 4:2 (October 1970)1, 3-8
b. revised version as "Transformations in High School Geometry before 1970", The Mathematics Teacher 67:4 (April 1974), 353-360.
c. abstracted in Historia Mathematica 1 (1974), p. 351
d. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 303-310

A5. (with R.W. Freese and Ann K. Miller, St. Louis University) Can Every Triangle Be Divided Into n Triangles Similar To It?, American Mathematical Monthly 77:8 (October 1970), 867-869.

A6. Two Preference Paradoxes
a. Illinois Council of Teachers of Mathematics Newsletter 22:1 (March 1971), 13-14
b. revised version in The Mathematics Teacher 67:6 (October 1974), 515-518.
c. reprinted in Applications of Secondary School Mathematics – Readings from the Mathematics Teacher (Reston, VA: NCTM, 1991)

A7. (with Max Bell, University of Chicago) Improving Mathematics for All Students
a. School Review 79:3 (May 1971), 433-440.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 2-6

A8. (with Arthur F. Coxford, Jr., University of Michigan) A Transformation Approach to Tenth–Grade Geometry|
a. The Mathematics Teacher 65:1 (January 1972), 21-30.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 292-302

A9. (with Stanley J. Wayment, Utah State University) Partitioning a Triangle into 5 Triangles Similar To It, Mathematics Magazine 45:1 (January 1972), 37-42.

A10. Some Remarks on the Symbol .99999..., Illinois Council of Teachers of Mathematics Newsletter (March 1972)

A11. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth–Grade Geometry, Journal for Research in Mathematics Education 3:4 (November 1972), 249-259.

A12. Perfect Square Patterns in the Pascal Triangle, Mathematics Magazine 46:4 (September 1973), 203-208.

A13. (with Richard F. Marr, Rolling Meadows H.S.) Similarity and Some Area Formulas, Illinois Mathematics Teacher (October 1973)

A14. The Case for Transformations in High School Geometry (Th)
a. Texas Mathematics Teacher (March 1974) 4-6.
b. reprinted in New York State Mathematics Teachers' Journal 25:1 (January 1975), 37-42.
c. revised version in the Ontario Mathematics Gazette (December 1978)
d. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 311-316.

A15. Some Corresponding Properties of Real Numbers and Implications for Teaching, Educational Studies in Mathematics 5 (May 1974), 279-290. (Th)

A16. Applications of Groups and Isomorphic Groups to Topics in the Standard Curriculum, Grades 9-11
a. Part I, The Mathematics Teacher 68:2 (February 1975), 99-106; see https://www.msri.org/attachments/workshops/454/Usiskin-Application%20of%20Groups%20I.pdf; Part II, 68:3 (March 1975), 235-246.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 226-248

A17. Graphing Pythagorean Triples, Illinois Mathematics Teacher (March 1975)

A18. First and Second Year Algebra - Should They Have the Same Orientation?
a. Virginia Mathematics Teacher (October 1977)
b. reprinted in the West Virginia CTM Newsletter 3:2 (December 1977), 2-8.

A19. The Mathematically Gifted and the Curriculum, Illinois Council for the Gifted Newsletter (Fall 1977)

A20. The Greatest Integer Symbol - An Applications Approach
a. The Mathematics Teacher 70:9 (December 1977), 739-743.
b. reprinted in Applications of Secondary School Mathematics – Readings from the Mathematics Teacher (Reston, VA: NCTM, 1991)

A21. Are Calculators a Crutch?
a. The Mathematics Teacher 71:5 (May 1978), 412-413.
b. reprinted in Calculators: Readings from the Arithmetic Teacher and the Mathematics Teacher, edited by Bruce Burt (Reston, VA: NCTM, 1979)
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 408-409

A22. (with Adam Stephanides, undergraduate student, The University of Chicago) Magic Triangular Regions of Order 4 and 5, Journal of Recreational Mathematics (Winter 1978–79)

A23. The Future of Fractions
a. Arithmetic Teacher 27:5 (January 1979), 18-20.
b. reprinted in Mathematics Teaching in the Middle School 12:7 (March 2007), 366-369.

A24. An Applications Approach to Beginning Algebra (Th)
a. Oregon Mathematics Teacher (October–November 1979)
b. reprinted under the title "Beginning Algebra - An Applications Approach" in Illinois Mathematics Teacher 31:2 (March 1980), 8-15.
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 249-255

A25. Products of Sines, Two–Year College Mathematics Journal 10:5 (November 1979), 334-340. (Th)

A26. Applications in Algebra and Geometry, Chapter 3 in Applications of Mathematics, the 1979 Yearbook of the National Council of Teachers of Mathematics, edited by Sidney Sharron and Robert E. Reys (Reston, VA: NCTM, 1979), 20-30.

A27. What Should Not Be In the Algebra and Geometry Curricula of Average Students? (Th)

a. The Mathematics Teacher 73:6 (September 1980), 413-424.

b. reprinted in condensed form in The Education Digest 46:3 (November 1980), 50-53.

c. one of four articles reprinted for the Seventy-Fifth-Anniversary Retrospective of the National Council of Teachers of Mathematics in The Mathematics Teacher 88:2 (February 1995), 156-164.

d. reprinted in abridged form as “What Should Not Be in the Algebra Curriculum of Average College-Bound Students”, Algebraic Thinking, Grades K-12, edited by Barbara Moses (Reston, VA: NCTM, 1999), 76-81.

e. reprinted in “100 Years of Mathematics Teacher”. Mathematics Teacher Special Issue, volume 100 (January 2007), 68-77. (see also article 96)

f. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 109-121

A28. Decision–Making in Mathematics Education, in Teaching Teachers, Teaching Students, L.A. Steen and D.J. Albers, editors (Boston: Birkhaüser, 1981), 43-55.

A29. (with Sharon Senk) Geometry Proof-Writing: A New View of Sex Differences in Mathematics Ability, American Journal of Education 91:2 (February 1983), 187-201. (Th)

A30. Policy Implications of Problem Solving and Mathematics Learning, The School Administrator (January 1983) (rewrite by William Spady of "Problem Solving and Mathematics Learning: Implications for Curriculum Policy", paper presented at the American Association of School Administrators Summer Instructional Leadership Conference, July 1981)

A31. Enrichment Activities for Geometry, The Mathematics Teacher 76:4 (April 1983), 264-266.

A32. (One Point of View) Arithmetic in a Calculator Age, Arithmetic Teacher 30:9 (May 1983), 2.

A33. What Should Be Dropped from the Secondary School Mathematics Curriculum?, in Proceedings of the Fourth International Congress on Mathematical Education, Marilyn Zweng et al., editors (Boston: Birkhaüser, 1983)

A34. (Soundoff) Mathematics is Getting Easier, The Mathematics Teacher 77:2 (February 1984), 82-83.

A35. (with Max S. Bell, The University of Chicago) Ten Often Ignored Rational Number Application Concepts, Arithmetic Teacher 31:6 (February 1984), 48-50.

A35.5. Needed Changes in Mathematics Curricula. In School Mathematics: Options for the 1990s, Vol. 2, proceedings of a conference edited by Thomas A. Romberg and Deborah M. Stewart. Reston, VA: NCTM, June 1984.

A36. We Need Another Revolution in Secondary School Mathematics (Th)
a. Chapter 1 in The Secondary School Mathematics Curriculum, the 1985 Yearbook of the National Council of Teachers of Mathematics, edited by Christian R. Hirsch and Marilyn J. Zweng (Reston, VA: NCTM, 1985)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 129-146

A37. What Constitutes an Integrated Curriculum?, New York State Mathematics Teachers' Journal (January 1985)

A38. We Are Not Behind the World, American Perspectives on the Fifth International Congress on Mathematical Education (ICME 5), MAA Notes Number 5 (Washington DC: Mathematical Association of American, 1985)

A39. Mathematical Applications: Secondary Schools, in The International Encyclopedia of Education (Oxford, England: Pergamon Press, 1985)

A40. Reasons for Estimating (Th)
a. In Estimation, Approximation, and Mental Computation, the 1986 Yearbook of the National Council of Teachers of Mathematics (Reston, VA: NCTM, 1986)
b. Chinese translation by Huang Ming-Huang in Science Education Today, Taiwan (October 1986)

A41. A Pretrigonometry Proof of the Reflection Property of the Ellipse, The College Mathematics Journal (November 1986)

A42. The UCSMP: Translating Grades 7-12 Mathematics Recommendations into Reality
a. Educational Leadership 44:4 (December 1986/January 1987) 30-35.
b. available also from the Association for Supervision and Curriculum Development as an audio tape
c. reprinted in Phi Delta Kappa's Exemplary Practice Series: Mathematics (September 1987)

A43. Resolving the Continuing Dilemmas in School Geometry
a. Chapter 2 in Learning and Teaching Geometry, K-12, the 1987 Yearbook of the National Council of Teachers of Mathematics, edited by Mary Montgomery Lindquist and Albert P. Shulte (Reston, VA: NCTM, 1987)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 317-328

A44. Some Lessons Learned from the First Eighteen Months of the Secondary Component of UCSMP, in Developments in School Mathematics Around the World, Proceedings of the UCSMP International Conference on Mathematics Education (Reston, VA: NCTM, 1987)

A45. Why Elementary Algebra Can, Should, and Must Be an 8th Grade Course for Average Students (Th)
a. Mathematics Teacher 80:6 (September 1987), 428-438.
b. reprinted in Algebraic Thinking, Grades K-12, edited by Barbara Moses (Reston, VA: NCTM, 1999), 40-48.
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 256-266

A46. Secondary School Mathematics in the United States: Past, Present, and Future, in Proceedings of Sino-American Secondary Mathematics Education Seminar/Workshop, National Kaohsiung Teachers' College, Kaohsiung, Taiwan, ROC (January 1988)

A47. Conceptions of School Algebra and Uses of Variables (Th)
a. in The Ideas of Algebra, K-12, the 1988 Yearbook of the National Council of Teachers of Mathematics (Reston, VA: NCTM, 1988) See https://www.msri.org/attachments/workshops/454/Usiskin-Conceptions%20of%20School%20Algebra.pdf .
b. reprinted in Algebraic Thinking, Grades K-12, edited by Barbara Moses (Reston, VA: NCTM, 1999), 7-13. See https://atcm.mathandtech.org/EP/2004/2004S332/fullpaper.pdf .
c. reprinted in Defining Mathematics Education – Presidential Yearbook Selections 1926-2012, the Seventy-Fifth Yearbook of the National Council of Teachers of Mathematics, edited by Frances (Skip) Fennell and William R. Speer (Reston, VA: NCTM, 2013).
d. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 267-276

A48. The Beliefs Underlying UCSMP (original in U2, Winter, 1988)) (Th)
a. variant in Developments in School Mathematics Around the World, Proceedings of the 2nd UCSMP International Conference on Mathematics Education (Reston, VA: NCTM, 1990)
b. abridged version in The Elementary Mathematician (Winter, 1988)

A49. The Sequencing of Applications and Modelling in the University of Chicago School Mathematics Project (UCSMP) 7-12 Curriculum, Chapter 26 of Applications and Modelling in Learning and Teaching Mathematics, edited by W. Blum, J.S. Berry, R. Biehler, J.D. Huntley, G. Kaiser-Messmer, and L. Profke (London: Ellis Horwood, Ltd., 1989)

A50. The Fundamental Problems in Implementing Curricular Change, and How to Overcome Them, AMP Line, quarterly newsletter of the American Mathematics Project (Fall 1989)

A51. Visions of the Future, National Council of Supervisors of Mathematics Newsletter (October 1989)

A52. The University of Chicago School Mathematics Project (UCSMP): Preparing Teachers and Students for the Present, Excerpts of Proceedings from the Fourth Annual Conference sponsored by the Texas Higher Education Coordinating Board (January, 1989)

A53. (with Sharon Senk, Michigan State University) Evaluating a Test of van Hiele Levels: A Response to Crowley and Wilson, Journal for Research in Mathematics Education 21:3 (May 1990), 242-245.

A54. Building Mathematics Curricula with Applications and Modelling (Th)
a. Chapter 3 of Teaching of Mathematical Modelling and Applications, edited by M. Niss, W. Blum, and I. Huntley (London: Ellis Horwood, Ltd., 1991)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 347-357

A55. Competition and Cooperation in School Mathematics, in Developments in School Mathematics Around the World, Proceedings of the 3rd UCSMP International Conference on Mathematics Education (Reston, VA: NCTM, 1992)

A56. Glimpses of ICME-7, For the Learning of Mathematics 12:3 (November 1992), 19-24. See https://flm-journal.org/Articles/592179E8471469D2F42A1A1375F4CF.pdf .

A57. Lessons Learned from the University of Chicago School Mathematics Project, Educational Leadership 50:8 (May 1993),14-18.

A58. If Everybody Counts, Why Do So Few Survive?
a. Chapter 2 in Reaching All Students with Mathematics, edited by Mark Driscoll (Reston, VA: NCTM, 1993)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 7-18

A59. Conceptions of Mathematical Modelling and Their Implications for the Future, in Teaching and Learning Mathematics in Context, edited by T. Breiteig, I. Huntley, and G. Kaiser-Messmer (New York: Ellis Horwood, 1993)

A60. From "Mathematics for Some" to "Mathematics for All"
a. In Didactics of Mathematics as a Scientific Discipline, edited by R. Biehler, R.W. Scholz, R. Sträßer, and B. Winkelmann (Dordrecht, Netherlands: Kluwer Publ., 1994)
b. also in Selected Lectures from the 7th International Congress on Mathematical Education, edited by David F. Robitaille, David H. Wheeler, and Carolyn Kieran (Sainte-Foy, QUE: Les Presses de L'Université Laval, 1994)
c. abstracted in Proceedings of the 7th International Congress on Mathematical Education (Sainte-Foy, QUE: Les Presses de L'Université Laval, 1994)
d. shortened version "Algebra for All?" in Mathematics Teaching 1995 Conference Report (Edinburgh, Scotland: University of Edinburgh, 1996)
e. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 19-28

A61. Recent Developments in Secondary School Mathematics, and Their Implications
a. in Preparing for a New Calculus, edited by Anita Solow, MAA Notes #36 (Washington, DC: Mathematical Assoociation of America, 1994)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 147-155

A62. What Changes Should Be Made for the Second Edition of the NCTM Standards? Humanistic Mathematics Network Journal 10 (August 1994), 31-38. (on line at <https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1134&context=hmnj>)

A63. Individual Differences in the Teaching and Learning of Mathematics, Teaching Thinking and Problem Solving, bimonthly newsletter of Research for Better Schools, Philadelphia (Part I, Volume 16, Issue 3, 1994; Part II, Volume 16, Issue 4, 1994)

A64. Why Is Algebra Important To Learn? (Th)
a. American Educator 19:1 (Spring 1995), 30-37, 46. See https://www.garnermath.com/downloads/Usiskin_Why-is-Algebra-Important.pdf .reprinted in Algebraic Thinking, Grades K-12, edited by Barbara Moses (Reston, VA: NCTM, 1999), 22-30.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 277-289

A65. Thoughts Preceding the Algebra Colloquium, in The Algebra Initiative Colloquium, Volume 2, edited by Carole B. Lacampagne, William Blair, and Jim Kaput (Washington, DC: U.S. Department of Education, May 1995).

A66. Stages of Change (Th)
a. NCSM Newsletter, Vol. XXIV, No. 4 (July 1995)
b. reprinted in variant form along with #50 for the NSF Local Systemic Change Projects PI meeting 22 Jan 1999 (on line at <http://lsc-net.terc.edu/do.cfm/conference_material/6857/show/use_set-oth_conf_arch/page-1>)
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 156-165

A67. (with Daniel Hirschhorn, Denisse Thompson, and Sharon Senk) Rethinking the First Two Years of High School Mathematics: The University of Chicago School Mathematics Project, Mathematics Teacher 88:8 (November 1995), 640-647

A68. The Training of Teachers in New Curricula, in Proceedings of the ICMI-China Regional Conference on Mathematical Education, edited by Lee Peng Yee, Jerry Becker, John Mack, and Dianzhou Zhang, Shanghai: Shanghai Educational Publishing House, 1995

A69. (with Zu Chenghou) Middle Secondary School Teacher Preparation, in Proceedings of the ICMI-China Regional Conference on Mathematical Education, edited by Lee Peng Yee, Jerry Becker, John Mack, and Dianzhou Zhang, Shanghai: Shanghai Educational Publishing House, 1995

A70. Mathematics as a Language (Th)
a. Chapter 28 in Communication in Mathematics, K-12 and Beyond, the 1996 Yearbook of the National Council of Teachers of Mathematics, edited by Portia C. Elliott and Margaret J. Kenney (Reston, VA: NCTM, 1996)
b. Polish translation, Matematyka jako je’zyk, in Nauczyciele i Matematyki + Technologia Informacyjna, Autumn 2009, pp. 21-29.
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 29-38

A71. Algebra and Calculus for All? (Th)
a. Illinois Mathematics Teacher (September 1996)
b. also in Journal of Mathematics and Science: Collaborative Explorations (Spring 1999)
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 39-50

A72. Le direzioni del cambiamento, Lettera Pristem (December 1996), 37-43. Translation of unpublished paper, “Directions of Change in Secondary Mathematics Education, and the Difficulties They Spawn”, presented in TSG-13 at the 8th International Congress on Mathematical Education, July 1996

A73. Doing Algebra in Grades K-4 (Th)
a. Teaching Children Mathematics 3 (6) (February 1997), 346-356
b. abridged version in Algebraic Thinking, Grades K-12, edited by Barbara Moses (Reston, VA: NCTM, 1999), 5-6
c. Hebrew translation at http://mathcenter-k6.haifa.ac.il/articles(pdf)/article41.pdf

A74. The Implications of “Geometry for All”
a. Mathematics Education Leadership 1:3 (October 1997), 5-14
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 51-61

A75. Applications in the Secondary School Mathematics Curriculum: A Generation of Change
a. American Journal of Education 106:1 (November 1997), 62-84.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 358-374

A76. On the Relationships between Mathematics and Science in Schools
a. Journal of Mathematics and Science: Collaborative Explorations 1: 9-25 (Fall 1997)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 375-385

A77. Paper and Pencil Algorithms in a Calculator/Computer Age (Th)
a. Chapter 2 in Algorithms in School Mathematics, edited by Lorna J. Morrow and Margaret J. Kenney, the 1998 Yearbook of the National Council of Teachers of Mathematics (Reston, VA: NCTM, 1998)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 410-421

A78. Fitting Tasks to Curriculum, in High School Mathematics at Work (Washington, DC: National Research Council, 1998)

A79. Teaching Applications of Mathematics – A K-12 Perspective, in Ideas & Resources for Teachers of Mathematics, 9th Edition, edited by Mike Fulton (Saskatoon, Saskatchewan: Saskatchewan Teachers' Federation, January 1999)

A80. The Mathematically Promising and the Mathematically Gifted
a. Chapter 5 in Developing Mathematically Promising Students, edited by Linda Jensen Sheffield (Reston, VA: NCTM, 1999)
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 62-72

A81. Is There a World-Wide Mathematics Curriculum?
a. Developments in School Mathematics Around the World, Proceedings of the 4th UCSMP International Conference on Mathematics Education (Reston, VA: NCTM, 1999), 213-227.
b. also in delta-K, journal of the Mathematics Council of the Alberta (CAN) Teachers’ Association 38:2 (May 2001), 35-44.

A82. The Development into the Mathematically Talented (Th)
a. Journal of Secondary Gifted Education 11:3 (Spring 2000), 152-162.
b. also in 2001: A Mathematical Odyssey: Teaching-Learning-Curriculum, Proceedings of the NCTM Eastern Regional Conference, edited by R.F. Cunningham and E. Milou (Somerset, NJ: Association of Teachers of Mathematics of New Jersey, 2002)
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 73-84

A83. Quantitative Literacy for the Next Generation of Adults,
a. in Mathematics and Democracy: The Case for Quantitative Literacy, edited by Lynn Arthur Steen (Princeton, NJ: National Council on Education and the Disciplines, 2001), 79-86.
b. on line at http://www.maa.org/sites/default/files/pdf/QL/MathAndDemocracy.pdf .

A84. University of Chicago School Mathematics Project, in Encyclopedia of Mathematics Education, edited by Louise S. Grinstein and Sally I. Lipsey (New York: RoutledgeFalmer, 2001).

A85. Educating the Public About School Mathematics
a. Humanistic Mathematics Network Journal 24 (May 2001), 26-34 (reviewed in The College Mathematics Journal 33: 1 (January 2002), 66-67). See also U14.
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 85-96

A86. Teachers’ Mathematics: A Collection of Content Deserving To Be a Field
a. in Proceedings of the National Summit on the Mathematical Education of Teachers (Washington, DC: Conference Board of the Mathematical Sciences, http://www.cbmsweb.org/NationalSummit/WG_Speakers/usiskin.pdf).
b. in The Mathematics Educator (Singapore) 6:1 (2001), 85-98.
c. short version, as What Mathematics Do Teachers Need That They Are Likely not to Encounter in Their Mathematics Courses?, in Studying Classroom Teaching as a Medium for Professional Development, edited by Hyman Bass, Gail Burrill, and Zalman Usiskin. Proceedings of a Workshop. Washington, DC: National Academy Press, 2002.
d. on line at http://www.maa.org/cbms/NationalSummit/Speakers/Usiskin/htm .
e. on CD-ROM, "Mathematics Teacher Preparation in Appalachia – Mathematics Content". Huntington, WV: ACCLAIM (Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics, August 8-9, 2003.

A87. Mathematics Teacher Education in Grades 7-12 the United States. In Studying Classroom Teaching as a Medium for Professional Development, edited by Hyman Bass, Gail Burrill, and Zalman Usiskin. Proceedings of a Workshop. Washington, DC: National Academy Press, 2002.

A88. Teachers Need a Special Type of Content Knowledge
a. in ENC [Eisenhower National Clearinghouse] Focus, May 2002.
b. reprinted in News You Can Use, The CPM [College Preparatory Mathematics] Educational Program Newsletter, November 2002.
c. abridged version in Northern Nevada Mathematics Association Newsletter (2003).

A89. The Integration of the School Mathematics Curriculum in the United States – History and Meaning (Th)
a. in Integrated Mathematics: Choices and Challenges, edited by Sue Ann McGraw (Reston, VA: NCTM, 2003), pp. 13-31
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 166-178

A90. A Personal History of the UCSMP Secondary Curriculum, Chapter 17 in A History of School Mathematics, edited by George M.A. Stanic and Jeremy Kilpatrick (Reston, VA: NCTM, 2003), pp. 673-736. (Th)

A91. Next Steps in High School Mathematics Teacher Development. In Next Steps in Mathematics Teacher Development, Grades 9-12, edited by Solomon Garfunkel, Carole Lacampagne, and Vicki Stohl. Washington, DC: National Academy Press (2003).

A92. Should All Students Learn a Significant Amount of Algebra?
a. as “A Significant Amount of Algebra”, in Nieuw Archief voor Wiskunde (Netherlands), 5/5 No. 2 (June 2004), pp. 147-151. See http://www.nieuwarchief.nl/serie5/pdf/naw5-2004-05-2-147.pdf .
b. in Developing Students’ Algebraic Reasoning Abilities, edited by Carole Greenes and Carol Findell. National Council of Supervisors of Mathematics Monograph Series, Volume 3, pp. 4-16 (2005).
c. in Secondary Lenses on Learning: Team Leadership for Mathematics in Middle and High Schools, Catherine Miles Grant, Valerie L. Mills, Mary Bouck, and Ellen Davidson,with Barbara Scott Nelson and Steve Benson (eds.) Thousand Oaks, CA: Corwin Press (2009).

A93. A K-12 Mathematics Curriculum with CAS: What Is It and What Would It Take To Get It? In Proceedings of the 9th Asian Technology Conference in Mathematics, edited by Wei-Chi Yang, Sung-Chi Chu, Tilak de Alwis, and Keng-Cheng Ang. Blacksburg, VA: ATCM, Inc. (December 2004), pp. 5-16. See https://atcm.mathandtech.org/EP/2004/2004S332/fullpaper.pdf . (Th)

A94. What We Can Learn about Teaching and Learning Mathematics through U.S.-Japan Collaboration? U.S. – Japan Panel Discussion, in Learning Across Boundaries: U.S.-Japan Collaboration in Mathematics, Science and Technology Education, proceedings from conferences in San Francisco, March 2003, and Chicago, May 2005.

A95. TSG 1: The Teaching and Learning of Algebra. In Proceedings of The Ninth International Congress on Mathematical Education, edited by Hiroshi Fujita, Yoshihiko Hashimoto, Bernard R. Hodgson, Peng Yee Lee, Stephen Lerman, and Toshio Sawada. Tokyo: Research Institute of Mathematics Education, Tokyo University of Science, 2005, pp. 297-300.

A96. High School Overview and the Transition to College. In A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus, MAA Notes #69, edited by Nancy Baxter Hastings. Washington, DC: Mathematical Association of America, 2006).

A97. What Should Not Be in the Algebra and Geometry Curricula of Average College-Bound Students? – A Retrospective after a Quarter Century. Mathematics Teacher Special Issue, volume 100 (2007), pp. 68-77. (see also A27)

A98. Some Thoughts About Fractions. Mathematics Teaching in the Middle School. 12:7 (March 2007), 370-373. (see also article 23)

A99. The Arithmetic Operations as Mathematical Models (Th)
a. in Modelling and Applications in Mathematics Education, ICMI Study No. 14, edited bv Werner Blum, Peter L. Galbraith, Hans-Wolfgang Henn and Mogens Niss. New York: Springer, 2007, pp. 257-264.
b. slightly revised form, as The Arithmetic Curriculum and the Real World, in Research and Development in the Teaching and Learning of Number Systems and Arithmetic, Proceeedings of ICME-11 Topic Study Group 10, edited by Dirk De Bock, Bettina Dahl Søndergaard, Bernardo Gómez Alfonso, and Chun Chor Litwin Cheng. Leuven, Belgium: the editors, 2008.
c. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 386-391.

A100. The Case of the University of Chicago School Mathematics Project – Secondary Component. In Perspectives on the Design and Development of School Mathematics Curricula, edited by Christian R. Hirsch. Reston, VA: National Council of Teachers of Mathematics, 2007, pp. 173-182.

A101. DG 1: Issues, movements, and processes in mathematics education reform. In Proceedings of the 10th International Congress on Mathematical Education, edited by Mogens Niss. Roskilde, Denmark: Roskilde University, 2008, pp. 426-428.

A102. Do We Need Math Standards with Teeth? Educational Leadership 65:3 (November 2007), pp. 38-42.

A103. Grades 7-12 Learning Progressions in Mathematics Content. In Proceedings of the APEC Conference on Replicating Exemplary Practices in Mathematics Education, Koh Samui, Thailand (March 2010). https://www.apec.org/docs/default-source/Publications/2010/7/Replicating-Exemplary-Practices-in-Mathematics-Education-among-APEC-Economies-July-2010/TOC/Zalman-Usiskin--Grades-7-12-Learning-Progression-in-Mathematics-Content.pdf

A104. The Current State of the School Mathematics Curriculum
a. in Mathematics Curriculum: Issues, Trends, and Future Directions, the 72nd Yearbook of the National Council of Teachers of Mathematics, edited by Barbara J. Reys and Robert E. Reys. Reston, VA: National Council of Teachers of Mathematics (Reston, VA: NCTM, 2010).
b. reprinted in We Need Another Revolution: Five Decades of Curriculum Papers by Zalman Usiskin. Reston, VA: NCTM, 2014, 201-211.

A105. Reflections from a Retiring Mathematics Curriculum Developer. In Future Curricular Trends in School Algebra and Geometry: Proceedings of a Conference, edited by Zalman Usiskin, Kathleen Andersen, and Nicole Zotto. Charlotte, NC: Information Age Publishing, 2010, pp. 305-312.

A106. Interview with Zalman Usiskin.
a. The International Journal for the History of Mathematics Education. Vol. 6, No. 1 (2011), pp. 39-52
b. in Leaders in Mathematics Education: Experience and Vision. Rotterdam: Sense Publishers (2014).

A107. Misidentifying the Reasons for Singapore’s High Test Scores. Mathematics Teacher Vol. 105, No. 9 (May 2012), pp. 666-671.

A107.5  Reflections of a United States mathematics educator in South Africa for the first time.  Mail & Guardian (Johannesburg, S.A.), Vol. 29, No. 30 (July 26 to August 1, 2013), pp. 47-48. 

A108. Studying Textbooks in an Information Age – A United States Perspective. ZDM Mathematics Education DOI 45:713 – 723; 10.1007/s11858-013-0514-6 (September 2013).

A109. What Does It Mean to Understand Some Mathematics? (Th)
a. Selected Regular Lectures from the 12th International Congress on Mathematical Education, edited by Cho Sung Je. Springer (2015), pp. 821-842. https://www.mathunion.org/fileadmin/ICMI/Conferences/ICME/ICME12/www.icme12.org/upload/submission/1881_F.pdf
b. slightly modified form in Rekenen-wiskunde op niveau, edited by M. van Zanten. Utrecht, Netherlands: FISME, 2013.

A110. Forty-Eight Years of International Comparisons in Mathematics Education from a United States Perspective: What Have We Learned? In Mathematics Curriculum in School Education, edited by Yeping Li and Glenda Lappan. Dordrecht, Holland: Springer, 2014, pp. 581-606.

A111. Mathematics and Mathematics Education: Two Quite Different Perspectives on the Same Subject. In Reflections on Policy, Chapter 16 in Mathematics & Mathematics Education: Searching for Common Ground, Michael N. Fried & Tommy Dreyfus (Eds.), pp. 289-293. New York: Springer, 2014.

A112. Postscript. In Enacted Mathematics Curriculum, Denisse Thompson and Zalman Usiskin (eds.). Charlotte, NC: Information Age Publishing, 2014, pp. 177-180.

A113. (with Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer, Alan Schoenfeld, Cathy Seeley, and Dan Teague) The Future of High School Mathematics.
a. Mathematics Teacher Vol. 107, No. 7 (March 2014), pp. 488-490.
b. in The Best Writing on Mathematics 2015. Princeton, NJ: Princeton U. Press, pp. 181-186.

A114. The Performance with Fractions: A Demonstration of Cultural Differences within the United States and Overseas, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 97-105

A115. Motivation and the Sequencing of Mathematics Content, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 122-128.

A116. The Importance of the Transition Years, Grades 7-10, in School Mathematics, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 179-189.

A117. (with Barbara J. Reys, University of Missouri, and John P. Smith, Michigan State University) Setting the Record Straight: An Examination of the Curriculum Recommendations of the National Mathematics Advisory Panel Report, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 190-200.

A118. Unpacking Mathematical Understanding in the Common Core, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 212-224.

A119. The Shape of Geometry and the Geometry of Shape, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 329-344.

A120. Mathematical Modeling in the Curriculum, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 392-406.

A121. The Ethics of Using Advanced Technologies in a CCSSM Environment, in We Need Another Revolution: Five Decades of Mathematics Curriculum Papers by Zalman Usiskin. Barbara Reys and Robert Reys, editors. Reston, VA: NCTM, 2014, 422-437.

A122. Development and Features of the UCSMP Curriculum for Grades 6-12. In Proceedings of the International Forum on Mathematics Textbooks, Seoul National University, Korea, December 2014, pp. 95-113.

A123. Transformations in U.S. Commercial High School Geometry Textbooks Since 1960: A Brief Report. In Proceedings of the International Conference on Mathematics Textbook Research and Development (ICTM-2014), Keith Jones, Christian Bokhove, Geoffrey Howson and Lianghuo Fan (Eds.). Southampton: University of Southampton, pp. 471-476, 2014. Available for download at http://eprints.soton.ac.uk/374809.

A124. Mathematical Modeling and Pure Mathematics. Mathematics Teaching in the Middle School, 20:8 (April 2015), pp. 476-483.

A125. The Relationships Between Statistics and Other Subjects in the K-12 Curriculum. (Th) Chance, 28:3 (2015). Also on line at http://chance.amstat.org/2015/09/28-3-editors-letter/

A126. Closing Remarks. In Digital Curricula in School Mathematics. Meg Bates and Zalman Usiskin, editors. Charlotte, NC: Information Age Publishing, 2016, 297-301.

A127. Approaching Euclidean Geometry Through Transformations. In Mathematics Matters in Education. New York: Springer, 2017, 233-244.

A128. (with Anita Rampal, Delhi University) Topic Study Group No. 37: Mathematics Curriculum Development. In Proceedings of the 13th International Congress on Mathematical Education. Gabriele Kaiser, editor. Cham, Switzerland: Springer Open, 2017, 555-559.

A129. The Four-Page Document that Made NCSM and Its Implications for the Near Future. In Fifty Years of Leadership in Mathematics Education: Where Do We Go From Here? Johnny W. Lott, Carolyn J. Lott, Carol A. Edwards, and Linda Fulmore, editors. Englewood, CO: National Council of Supervisors of Mathematics, 2018, 11-22.

A130. Electronic vs. Paper Textbook Presentations of the Various Aspects of Mathematics. ZDM 50(6), April, 2018.

A131. Beauty and Serendipity in Teaching Mathematics. (Th) Educational Designer 12 (March 2019), at https://www.educationaldesigner.org/ed/volume3/issue12/article47/.

A132. Mathematics as a Native Language (2019). In If I Ruled the World Conference Proceedings, 1-11. Cambridge, MA; COMAP.

A133. (in Chinese) 数学建模与算术的基本运算（上 and 下） [Mathematical Modelling and the Fundamental Operations of Arithmetic (I and II).] 小学教学（数学版）Primary School Teaching (Mathematics Edition), 2020, Issue 4 (April), pp. 8-11 and Issue 5 (May) pp.4-6.

A134. The Timing of the First Concentrated Study of Algebra in the Past Century in the United States. Mathematics Teacher: Learning & Teaching PK-12, 113:6 (June 2020), pp. 524-6.

A135.  The Road from Ordinary to Extraordinary.  (Th) In On the Road to Mathematical Expertise and Innovation, Proceedings of the 12th International Conference on Mathematical Creativity and Giftedness, September 2022, pp. 38-57, at https://d-nb.info/1268386723/34.  Also available by open access at https://doi.org/10.37626/GA9783959872263.0.

A136.  Lessons Learned from the Development of Innovative Mathematics Materials.  In Lessons Learned from Research on Mathematics Curriculum, Denisse R. Thompson, Mary Ann Huntley, and Christine Suurtamm, editors.  Charlotte, NC:  Information Age Publishing, 2024, pp. 563-579.

Unpublished papers formerly available through the Educational Resources Information Center (ERIC) (http://www.eric.ed.gov/)

As of February 2012, 43 published and unpublished papers were available on this site. Below are the unpublished papers with their original ERIC numbers, not the current download numbers.

E1. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, paper presented at the 48th Annual Meeting of the National Council of Teachers of Mathematics (April 1970) ED 036 670

E2. (with Jeanne Bernhold, student, University of Chicago) Three Reports on a Study of 11th Grade Mathematics (July 1973) SE 017 077 (not available Mar 2019)

E3. Uses of the Fundamental Operations (1974) ED 195 417

E4. (with Max Bell, University of Chicago) Calculators and School Arithmetic: Some Perspectives, in Electronic Hand Calculators: The Implications for Pre–College Education, Marilyn Suydam and Richard Shumway, editors (February 1976) ED 127 206

E5. (with Faustine Perham, Central YMCA Community College) A Summary of Research in the Learning of Geometric Transformations, paper presented at the 56th Annual Meeting of the National Council of Teachers of Mathematics (April 1978) ED 153 840 (summary)

E6. The First-Year Algebra Through Applications Development Project. Summary of Activities and Results. Final Technical Report (1979) ED 210 191

E7. Motivation and the Sequencing of Mathematics Content, paper presented at the 60th Annual Meeting of the National Council of Teachers of Mathematics (April 1982) SE 038 813
see also A115 above

E8. Van Hiele Levels and Achievement in Secondary School Geometry, final report of the Cognitive Development and Achievement in Secondary School Geometry Project (June 1982) ED 220 288

E9. (with Max Bell, University of Chicago) Applying Arithmetic, Part I, Numbers; Part II, Operations; Part III, Maneuvers (1983) ED 264 087, ED 264 088, ED 264 089

E10. (editor) Who Should Determine What You Teach? Mathematics Education Dialogues 2 (2) (April 1999) ED 460 836

E11. Trends in High School Preparation for Calculus and Their Implications for the Transition to College (Jan 2003) ED 474435

Papers published in UCSMP Newsletters

These papers are available at ucsmp.uchicago.edu/newsletters/ or at ucsmp.uchicago.edu/resources/conferences/.

U1. The Beliefs Underlying UCSMP, UCSMP Newsletter No. 2 (Winter 1988)
see also A48 above

U2. The Fundamental Problems in Implementing Curricular Change, and How To Overcome Them, UCSMP Newsletter No. 4 (Winter 1989)
see also A50 above

U3. If Everybody Counts, Why Do So Few Survive?, UCSMP Newsletter No. 6 (Winter 1990)
see also A58 above

U4. The Creation and Destruction of a Myth: Either You Have It in Math or You Don’t, talk given at the NCTM Annual Meeting, New Orleans LA, April 1991

U5. What We Have Learned from Seven Years of UCSMP, UCSMP Newsletter No. 8 (Winter 1991)
see also A57 above

U6. Teaching and Testing in the 1990s, UCSMP Newsletter No. 10 (Winter 1992)

U7. What Changes Should Be Made for the Second Edition of the NCTM Standards?, UCSMP Newsletter No. 12 (Winter 1993)
see also A62 above

U8. Individual Differences in the Teaching and Learning of Mathematics, UCSMP Newsletter No. 14 (Winter 1994)
see also A63 above

U9. Paper and Pencil Skills in a Calculator/Computer Age, UCSMP Newsletter No. 16 (Winter 1995)
seee also A77 above

U10. Algebra and Calculus for All?, UCSMP Newsletter No. 18 (Winter 1996)
see also A71 above

U11. Pseudomath and Pseudoresearch: Some Consequences of Mathematical Ignorance, UCSMP Newsletter No. 20 (Winter 1997)

U12. The Beleaguered Mathematics Teacher, UCSMP Newsletter No. 22 (Winter 1998)

U13. Which Curriculum Is Best?, UCSMP Newsletter No. 24 (Winter 1999)

U14. Educating the Public about School Mathematics Today, UCSMP Newsletter No. 26 (Winter 2000)
see also A85 above

U15. Teachers’ Mathematics: A Collection of Content Deserving to Be a Field, UCSMP Newsletter No. 28 (Winter 2001)
see also A88 above

U16. The Shortage of Qualified Mathematics Teachers: A Major Problem and Some Suggested Solutions, UCSMP Newsletter No. 30 (Winter-Spring 2002)

U17. Reexamining the Beliefs Underlying UCSMP, UCSMP Newsletter No. 31 (Spring 2003)

U18. The Importance of the Transition Years, Grades 7-10, in School Mathematics, UCSMP Newsletter No. 33 (Winter-Spring 2005)
see also A114 above

U19. A K-12 Mathematics Curriculum with CAS, UCSMP Newsletter No. 36 (Fall 2006-07) (Th)

U20. Would National Curriculum Standards with Teeth Benefit U.S. Students and Teachers?, UCSMP Newsletter No. 37 (Spring 2007)
see also A100 above

U21. Mathematical Modeling in the School Curriculum, a talk presented at Teachers College, Columbia University (September 201
see also A117 above

U22. The Ethics of Using Computer Algebra Systems (CAS) in High School Mathematics, an adaptation of talks given at the 2010 USACAS and 2012 T3 conferences.
see also A118 above

U23. What Changes Should Be Made for the Next Edition of the Common Core Standards?, a talk given at the NCTM 2014 annual meeting, see also Video 4 below.

U24. The Common Core in Mathematics at Nine Years: An Analysis, a combination of talks given at the 2019 NCTM and NCSM annual meetings and at USACAS 11 (June 2019)

Essays as editor of Mathematics Education Dialogues (NCTM, 1998-1999)

E1. Who Should Determine What You Teach? (April 1999).
E2. Groping and Hoping for a Consensus on Calculator Use (May/June 1999).

Available videos of presentations (as of January 2022)

• Curriculum and Teacher Education in Light of the Common Core. Panelist at the Conference on The Mathematical Education of Teachers, Mathematical Sciences Research Institute, Berkeley, CA, 12 May 2011. On line at http://www.youtube.com/watch?v=MZUz1iQdzzE (begins around 25:00)

• Mathematical Modeling in the School Curriculum. Presentation at the Regional Meeting of the National Council of Teachers of Mathematics, Chicago IL, 30 Nov 2012. On line at http://www.youtube.com/watch?v=tqaIL473dys

• What Changes Should Be Made for the Next Edition of the Common Core Standards? Closing session at the annual meeting of the Illinois Council of Teachers of Mathematics, Peoria, IL, 18 Oct 2013. On line at https://www.youtube.com/watch?v=5M6dHbjqZjA

• On the Relationships between Statistics and Other Subjects in the K-12 Curriculum. Major session at the 9th International Conference on the Teaching of Statistics (ICOTS-9), Scottsdale, AZ, 5 Nov 2015. On line at https://www.youtube.com/watch?v=GWUNtecSr7s

Multimedia
Videotapes and programs:
for the Educational Television Branch of the Ontario (Canada) Department of Education
1. Introduction to Transformations (February 1970)
2. Isometries (February 1970)
3. Similarity (February 1971)
4. Applications of Transformations (February 1971)

for Educational Progress, Tulsa OK
5. Applying Mathematics in Everyday Situations, part of the series The Third R: Teaching Basic Mathematics Skills (1980)

for the North Central Regional Educational Laboratory and PBS
6. Restructuring to Promote Learning in America's Schools
Video Conference 3: The Collaborative Classroom (March 1989)

for Kentucky Educational Television Foundation
7. GED Connections: Mathematics (parts of 13 programs) (2000)

Papers and consulting
1. Some Thoughts About Mathematics Films, Media Review (March 1973)
2. Conceptualization Paper, Secondary Level General Mathematics Project, Agency for Instructional Television (August 1979)
3. Consultant, "Body Unlimited", WLS-TV Chicago (aired September 1982)
4. Square One TV, Children's Television Workshop, advisor on Mathnet segments (1988-1992)

Published reviews

1. of Unified Mathematics, Courses 1-3, by Howard Fehr, James Fey, and Thomas Hill, in Curriculum Advisory Quarterly (1973)

2. of Effects of the Analytic–Global and Reflectivity–Impulsivity Cognitive Styles on the Acquisition of Geometry Concepts Presented Through Emphasis or No Emphasis and Discovery or Expository Lessons, by Barbara A. Nelson, in Investigations in Mathematics Education (Fall 1973)

3. of The Concept of Exponentiation at the Undergraduate Level and the Definitional Approach, by Shlomo Vinner, in Investigations in Mathematics Education (Fall 1977)

4. of Electronic Calculators in Further Education, by P.H. Coward, in Investigations in Mathematics Education (Spring 1979)

5. of Mindstorms: Children, Computers, and Powerful Ideas, by Seymour Papert, in Contemporary Psychology (July 1981)

6. of Women and the Mathematical Mystique, edited by Lynn H. Fox, Linda Brody, and Dianne Tobin, in American Journal of Education (November 1981)

7. of Algebra: An Incremental Approach, by John Saxon, in The Mathematics Teacher (October 1982; also see letters to editor February 1983)

8. of Mathematics Counts, Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the Chairmanship of Dr W H Cockcroft, in Journal of Curriculum Studies (April-June 1983)

9. of Didactical Phenomenology of Mathematical Structures, by Hans Freudenthal, in Educational Studies in Mathematics (1985)

10. of Street Mathematics and School Mathematics, by Terezinha Nunes, Analucia Dias Schliemann, and David William Carraher, and Multicultural Mathematics, by David Nelson, George Gheverghese Joseph, and Julian Williams, in American Journal of Education (1994)

11. of International Perspectives on Gender and Mathematics Education, edited by Helen J. Forgasz, Joanne Rossi Becker, Kyeong-Hwa Lee, and Olof Bjor Steinthorsdottir, in Comparative Education Review (February 2012)

Published recreations

1. Mathacrostics 1-100, in Points and Angles (doublecrostics on mathematical themes, one per issue in most issues from 1972 to 1990), the newsletter of the Metropolitan Mathematics Club of Chicago

2. Uncle Zal’s Mathacrostics. Palo Alto, CA: Dale Seymour Publications, 1984. (same as B9 above)

3. MMC Math Contests 1-24 (unique single-problem contest open to students, teachers, and interested others), in the December issues of Points and Angles, the newsletter of the Metropolitan Mathematics Club of Chicago, 1985-2008

THUMBNAIL SKETCHES (Th)

This section contains brief summaries of selected publications and a few presentations not turned into publications.

Selected Publications
Max-min Probabilities in the Voting Paradox (A1, 1964)
Given distributions X1, X2, … Xn it is possible to have P(X1>X2), P(X2>X3, …, P(Xn-1>Xn and P(Xn>X1) all greater than 1/2.  When n = 3, the max-min of these probabilities is (√5 – 1)/2, when n = 4, the max-min is 2/3, and, as n increases, so does the max-min, with a limit of 3/4  as n gets larger.

 The Case for Transformations in High School Geometry (A14, 1974)
Transformations enable one to deal with a much greater variety of figures in geometry, bring geometry much closer to the intuition of the child, make geometry more accessible to the slower student, provide assistance (and a strong weapnn) for future work in mathematics, and give a unifying concept to the geometry course which is geometric in nature.  These ideas underlie B1 and B2.

Some Corresponding Properties of Real Numbers and Implications for Teaching (A15, 1974)
Seventy-eight corresponding properties of multiplication and addition, of division and subtraction, and of powers and multiples are1/ presented and applied to the solving of equations and inequalities and to functions.  The underlying mathematics is the isomorphism between the group of positive real numbers under multiplication and the group of all real numbers under addition.  These ideas are found in B4.

An Applications Approach to Beginning Algebra (A24, 1979)
A description of the approach taken in B5.

Products of Sines (A25, 1979)
Although the sines of n° angles with n an integer are almost all irrational, products of k of some of these sines are of the form 1/(2^k).  For example, sin 5°sin 25°sin 35°sin 55°sin 65°sin 85° = 1/64.  Many other examples are provided.

What Should Not Be in the Algebra and Geometry Curricula of Average Students? (A27, 1980; A97, 2007)
Based on the criteria of importance in: understanding or coping in society, for future work in mathematics, and understanding what mathematics is about, proposed are the following deletions from algebra:  the traditional word problems, trinomial factoring, and complicated fractional expressions; and from geometry: some proof and the least important theorems.

(with Sharon Senk) Geometry Proof-Writing: A New View of Sex Differences in Mathematics Ability (A29, 1983)
Results from a study of 1364 geometry students in 74 classes from 5 states showed that girls and boys performed equally well on both simple and difficult proof items even though other research had showed that boys outperform girls on tests of problem-solving, spatial reasoniinng, and logic that are the components of the thinking needed in proofs.  The explanation for this divergent result from other research is that unlike other aspects of mathematics that might be encountered outside of class, geometry proof is encountered only in geometry classes and thus shows that, given equal opportunity to learn, girls and boys are equally capable.  This study contradicted the views of Benbow and Stanley that were widely accepted at the time.

We Need Another Revolution in School Mathematics (A36, 1985)
The biggest problem in secondary school mathematics today…is that a large number – perhaps a majority – of high school graduates lack the mathematical knowhow to cope effectively in society, qualify for the jobs they would like, or qualify for the training programs (including those in college) leading to the jobs they would like.”  The full implications of computer technology force a substantial reworking of the curriculum in which calculus loses some of its pre-eminence.  Reports of NCTM, NCSM, and government-funded panels are recommended for guidance.

Reasons for Estimating (A40, 1986)
Estimation is often viewed as a weak alternate to exact computation.  This paper argues that estimation is or should often be preferred, because constraints force estimates, estimates bring clarity and ease of understanding, estimates are typically easier to use than exact values, and estimating often gives consistency to data.  These ideas are found in Part III of B8.

Why Elementary Algebra Can, Should, and Must Be an Eighth-Grade Course for Average Students (A45, 1987)
Six reasons are provided and defended:
1.      For students who know sixth-grade mathematics, not much is new in seventh or eighth grade. 
2.      Eighth-grade algebra is successful.
3.      What is called “enrichment” is not a suitable alternative to eighth-grade algebra.
4.      It is probably easier (and certainly no harder) to learn algebra at age 13 than at age 14.
5.      Our current practices with respect to placement of students in algebra are the exact opposite of reasonable logic.
6.      Taking algebra in eighth grade reduces pressure on students in grades 9-12.

Conceptions of School Algebra and Uses of Variables (A47, 1988)
Viewing algebra as generalized arithmetic, variables are pattern generalizers; we translate, generalize.  Viewing algebra as a study of procedures for solving certain kinds of problems, variables are unknowns or constants; we solve, simplify.  Viewing algebra as the study of relationships among quantities, variables are arguments or parameters; we relate, graph.  Viewing algebra as the study of structures, variables are arbitrary marks on paper; we manipulate, justify.

The Beliefs Underlying UCSMP (A48, 1988; U2)
1.      Mathematics is valuable to the average citizen.
2.     Virtually every student has the ability to learn a significant amount of mathematics.
3.     Huge numbers of students leaving high school are ill-prepared in mathematics for the activities they will undertake.
4.     We can learn from other countries.
5.     A major cause of #3 above lies in the curriculum.
6.     A major deficiency in the curriculum is that time is wasted.  The current curriculum underestimates what students know when they enter the classroom and needlessly reviews what students have already learned. 
7.     Calculators and computers make some content obsolete, make other content more important, and change the ways in which we should view still other country. They also give us new possibilities for instruction.
8.     The scope of mathematics should be expanded at all levels.

9.     The classroom should not be divorced from the real world.
10.  To accomplish any significant change at the elementary school level, we need teachers who feel a responsibility to mathematics.
11.  To make significant change in any school, teachers and administrators must work together.
12.  Reality does not always coincide with our impressions of reality; impartial examinations of reality are necessary.

Building Mathematics Curricula with Applications and Modeling (A54, 1991)
Building curricula in applications and modeling requires that we structure the subject. Some structures arise from: learning hierarchies; use meanings for numbers, operations, points in geometry, functions, and processes; analogies between the learning of modeling and the learning of proof; considering the use dimension of mathematics as parallel to other dimensions of mathemcatical understanding (algorithms, proof, representations); incorporating technology

Why Is Algebra Important To Learn? (A64, 1995)
“Without a knowledge of algebra: you are kept from doing many jobs or even entering programs that will get you a job; you lose control over parts of your life and must rely on other to do things for you; you are more likely to make unwise decisions, financial and otherwise; and you will not be able to understand many ideas discussed in chemistry, physics, the earth science, economics, business, psychology, and many other areas.  The article goes on to discuss ideas that are in A47 and gives examples of meaningful applications.

Stages of Change (A66, 1995)
Eleven stages are described for the new math. Some of these stages already occurred with the NCTM Standards of 1989; the rest are predicted.
1.     Work by the pioneers
2.     Proselytizing of and by the apostles
3.     Use by those disenchanted with the old
4.     Acceptance by the establishment
5.     Joining by the piggybackers
6.     Forcing of the enchanted
7.     Oversimplification and overapplication of the change
8.     Failure of the oversimplified and overapplied theory
9.     Test scores that do not bear out people’s desires
10.  Public perception of the failure of the change
11.  Fatigue of the establishment

Mathematics as a Language (A70, 1996)
Many of the difficulties children have with mathematics are caused by treating mathematics as a dead, nonsense, or foreign language rather than as a native language with written, oral, and pictorial aspects.

Algebra and Calculus for All (A71, 1996)
Algebra and calculus play parallel roles in high school and college.

Doing Algebra in Grades K-4 (A73, 1997
A look at the approach taken to algebra in the Soviet materials translated by UCSMP.

Paper and Pencil Algorithms in a Calculator/Computer Age (A77, 1998)
Types of algorithms, basic principles about teaching algorithms, reasons for algorithms, dangers inherent in all algorithms, choosing between paper-and-pencil and calculator/computer algorithms, and peering into the future.

The Development into the Mathematically Talented (A82, 2000)
Levels of talent:  (0) No talent.  (1) Basic talent – the culture level.  (2) The honors student.  (3) The terrific student. (4) The exceptional student. (5) The productive mathematician.(6) The exceptional mathematician.  (7) The all-time greats.  Getting from each level to the next is discussed.

The Integration of the School Mathematics Curriculum in the United States – History and Meaning (A89, 2003)
Different kinds of curricular approaches called “integration” are discussed:  integration through unifying concepts, by merging areas of mathematics, by removing distinctions between areas of mathematics, by strands that are taught in the same year but separately, by integrating disciplines such as mathematics and science.  

A Personal History of the UCSMP Secondary Curriculum (A90, 2003)
A detailed history of the curriculum work and the events preceding UCSMP and during the development of the mathematics textbooks B10-B19 and B21-B22 for grades 7-12.  Related is A100.

A K-12 Mathematics Curriculum with CAS (A93, 2004; N19, 2006)
We have a moral obligation to utilize CAS if we are serious about bringing significant mathematical competence to all our students.  But to achieve this we must change societal attitudes towards algebra.  Some examples are given of the use of CAS at the primary and secondary levels.  See also A121.

The Arithmetic Operations as Mathematical Models (A99, 2007)
Based on Part II of B8, use meanings for each of the arithmetic operations.

What Does It Mean to Understand Some Mathematics? (A109, 2015)
A detailed description of the SPUR (Skills, Properties, Uses, and Representations) dimensions of understanding employed in the organization and tests in UCSMP secondary component materials.  See also A122.

The Relationships Between Statistics and Other Subjects in the K-12 Curriculum (A125, 2015)
As one of the mathematical sciences, the study of statistics in grades K-12 naturally has been considered as a part of the school mathematics curriculum. But as statistics has become more important, its connections with everyday literacy, science, health, and the social sciences suggest teaching statistics across the curriculum in addition to a reconsideration of its relationships with mathematics.

Beauty and Serendipity in Teaching Mathematics (A131, 2019)
Examples of how beauty and serendipity have influenced what I would like to see in mathematics classrooms and my curriculum development work to engender them, prior to and through the work of UCSMP.

The Road from Ordinary to Extraordinary. (A135, 2022)
When enough of the population becomes out-of-the-ordinary, then what has been out-of-the-ordinary performance in mathematics becomes ordinary.  Then the road builders (we who create curriculum) and the bus drivers (we who teach students), have hopefully enriched and improved the lives of a generation, and we have increased the likelihood of extraordinary performance among those we touch.

Selected presentations not turned into publications
Mathematics and Diamonds: The Many Facets of Mathematics (1981, ICTM; 1987, NCTM) (M)
Facets of mathematics and their opposites: 
beautiful but often ugly (“Best of All Possible Worlds”);
unified but many isolated results;
predictable but subject to paradoxes and surprises (“The Square of the Hypotenuse”);
elegant but often messy;
hard but makes it easier to solve many problems (“I Can’t Do the Sum”);
easy but often hard methods are taught as preferred;
changes over time though theorems once proved are forever;
widely applicable but often taught with phony applications (“I Am the Very Model of a Modern Major General”);
precise but precision often masks inaccuracy;
based on logic but built from assumed truths;
fosters creativity but most time is spent on algorithms (“I Believe”).

Sum of the Powers of Mathematics: A Theme and Variations (1999, NCTM) (M)
Theme:  Base 10 numeration – a sum of powers (“Seventy-six Trombones”)
Variation 1:  different bases
Variation 2:  extension to fractions
Variation 3:  generalization to Taylor series
Variation 4:  specification to perfect numbers (“What Can We Do with a Perfect Number?”
Variation 5:  Reversal: sums of two squares {“On a Clear Day You Cannot See Forever”
Variation 6:  Extension to sums of two powers (“I Am the Very Model of a Modern Mathematics Man”)
Variation 7:  Equal sums of powers of different numbers
Variation 8:  Annuities (“Seven and a Half Cents”)
Coda:  (“Goodnight, My Someone”)

Approaching Ten Tough Mathematical Ideas for High School Students (2017, NCSM)
1.      Imaginary numbers
2.      0^0
3.      Chunking
4.     Glide reflections are single transformations
5.     Slope
6.     Powers with non-integer exponents
7.     Logarithms
8.     Difficulties with distributivity
9.     Proof
10.  Indirect proof

Circling Through a Century of NCTM: A Celebration Sprinkled with Music (with Andrew Chukerman) (2022, NCTM) (M)
Setting the scene: School Days (group sing)
Theme: “The Windmills of Your Mind”
1920s: Prejudice (“You’ve Got to Be Carefully Taught”) and the ‘23 Report
1930s: Depression, backtracking
1940s: WWII and its recovery
1950s: Good feelings, then Sputnik
1960s: Major growth of NCTM with new curricula (“New Math”)
1970s: Back-to-basics reversal
1980s: Problem-solving and NCTM Standards ("I’ve Got a Little List”)
1990s: NSF curricula and applications (“Ballad of the Shape of Things”)
2000s: Height of NCTM influence
2010s: Common Core
current: My beliefs (“I Believe”)