Research Publications
Articles in refereed international journals
1. A. Arcavi & M. Bruckheimer. 1981.
“How Shall We Teach the Multiplication of Negative Numbers?” Mathematics in
School, 3(5), 31-33.
2. A. Arcavi, M. Bruckheimer & R. Ben-Zvi. 1982.
“Maybe a Mathematics Teacher can Profit from the Study of the History of
Mathematics” For the Learning of Mathematics, 3(1), 30-37.
3. A. Arcavi. 1985.
“History of Mathematics and Mathematics Education. A Suggested Bibliography”
Zentralblatt für Didaktik der Mathematik, 1, 26-29.
4. R. Hershkowitz, A. Arcavi & T. Eisenberg. 1987.
“Geometrical Adventures in Functionland” Mathematics Teacher, 80, 346-352.
5. A. Arcavi, M. Bruckheimer & R. Ben-Zvi. 1987.
“History of Mathematics for Teachers: the Case of Irrational Numbers” For the
Learning of Mathematics, 7 (2), 18-23.
6. A. Arcavi. 1987.
“Using Historical Materials in the Mathematics Classroom” Arithmetic Teacher, 35
(4), 13-16.
7. A. Arcavi & A. H. Schoenfeld1. 1988.
“On the Meaning of Variable” Mathematics Teacher, 81, 420-427. Reprinted in
Moses, B. (Ed.), 1999, Algebraic Thinking, Grades K-12: Reading from NCTM's
School-Based Journals and Other Publications.
8. A. Arcavi & N. Hadas. 1989.
“Large Numbers and Calculators: A Classroom Activity” School Science and
Mathematics , 1989, 89 (5), 412-416.
9. A. Arcavi & M. Bruckheimer. 1989.
“The Didactical De Morgan: A Selection of Augustus De Morgan's Thoughts on
Teaching and Learning Mathematics” For the Learning of Mathematics, 9 (1), 34-39.
10. A. Arcavi, A. Friedlander & R. Hershkowitz. 1989-1990.
“L'algèbre avant la lettre” (In French) Petit X, 24, 61-71.
11. A. Arcavi & R. Nachmias. 1990.
“Desperately Looking for the Focus” Mathematics in School, 19(2), 19-23.
1 In the publication the order of authors was mistakenly reversed. For the correct order, A.
Arcavi and A. Schoenfeld, see "Correction", Mathematics Teacher, 81, p. 774
1
12. R. Nachmias & A. Arcavi. 1990.
“A Parallel Representation of Linear Functions Using a Microcomputer-Based
Environment”. The Journal of Computers in Mathematics and Science Teaching,
9(4), 79-88.
13. A. Arcavi & M. Bruckheimer. 1991.
“Reading Bombelli's x-purgated Algebra”. College Mathematics Journal, 22(3),
212-219. Reprinted in Anderson, M., Katz, V. & Wilson, R. (Eds.), 2004, Sherlock
Holmes in Babylon and other Tales of Mathematical History, The Mathematical
Association of America, 164-168.
14. R. Ofir & A. Arcavi. 1992.
“Word Problems & Equations. An Historical Activity for the Algebra Classroom”
Mathematical Gazette. 1992, 76(475), 69-84.
15. A. Arcavi & A. H. Schoenfeld. 1992.
“Mathematics Tutoring Through a Constructivist Lens: The Challenges of SenseMaking” Journal of Mathematical Behavior. 11(4), 321-335.
16. A. H. Schoenfeld, M. Gamoran, C. Kessel, M. Leonard, R. Orbach
& A. Arcavi. 1992.
“Toward a Comprehensive Model of Human Tutoring in Complex Subject Matter
Domains” Journal of Mathematical Behavior. 1992, 11(4), 293-319.
17. A. Arcavi & R. Nachmias. 1993.
“What is your family name, Ms. Function? - Exploring families of functions with a
non-conventional representation” Journal of Computers in Mathematics and
Science Teaching. 12(3/4), 315-329.
18. A. Arcavi. 1994.
“Symbol sense: informal sense-making in formal mathematics” For the Learning of
Mathematics. 14(3), 24-35.
19. A. Arcavi. 1995.
“... And in mathematics, those of us who instruct, what do we construct?” (in
Spanish) Substratum, Temas Fundamentales en Psicología y Educación, II(6), 7794. Reprinted in 1999 in Números, Revista de Educación Matemática, 38, 1999,
39-586.
20. A. Arcavi. 1995.
“Teaching and learning algebra: past, present and future” Journal of Mathematical
Behavior. 14 (1), 145-162.
21. M. Bruckheimer, R. Ofir & A. Arcavi. 1995.
“The case for and against casting out nines” For the Learning of Mathematics,
15(2), 24-35.
22. M. Bruckheimer & A. Arcavi. 1995.
“Farey Series and Pick's Theorem” The Mathematical Intelligencer, 17(4), 64-67.
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23. M. Bruckheimer & A. Arcavi. 1995.
“A visual approach to some elementary number theory” Mathematical Gazette,
79(486), 471-478.
24. A. Arcavi, C. Kessel, L. Meira & J. Smith. 1998.
“Teaching Mathematical Problem Solving: An analysis of an Emergent Classroom
Community” Research in Collegiate Mathematics Education. III, 7, 1-70.
25. M. Bruckheimer & A. Arcavi. 1999.
“Of discs and cubes and magic squares: a sort of algebra” The Australian
Mathematics Teacher, 55(1), 17-20.
26. M. Bruckheimer & A. Arcavi. 2000.
“Farey Rabbits” Mathematical Gazette, 84(500), 223-226.
27. A. Arcavi & N. Hadas. 2000.
“Computer mediated learning: An example of an approach” International Journal
of Computers for Mathematical Learning. 5. 25-45.
28. A. Arcavi & M. Bruckheimer, 2000.
“Didactical Uses of Primary Sources from the History of Mathematics”. Themes in
Education, 1(1), 44-64.
29. J. van Dormolen & A. Arcavi. 2000.
“What is a circle?” Mathematics in School, 29(5), 15-19. (Reprinted in the Dutch
journal Euclides, 2001, 76(5), 183-186).
30. A. Arcavi. 2000.
“Problem driven research in mathematics education” Journal of Mathematical
Behavior. 19(2), 141-173.
31. M. Bruckheimer & A. Arcavi. 2001.
“A Herrick among Mathematicians, or dynamic geometry as an aid to proof”
International Journal of Computers for Mathematical Learning. 6(1), 113-126.
32. R. Hershkowitz, A. Arcavi & M. Bruckheimer. 2001.
“Reflections on the status and nature of visual reasoning - The case of the matches”
International Journal of Mathematical Education in Science and Technology.
32(2), 255-265.
33. D. Ben-Zvi & A. Arcavi. 2001.
“Junior High School Students’ Construction of Global Views of Data and Data
Representations” Educational Studies in Mathematics. 45, 35-65.
34. A. Arcavi. 2002.
“The Everyday and the Academic in Mathematics” Everyday and Academic
Mathematics in the Classroom. A Monograph edited by M. Brenner and J.
Moschkovich (Eds.) Journal for Research in Mathematics Education. 12-29.
Reprinted in Spanish, in Números 63, 2006, 3-24.
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35. A. Arcavi, 2003.
“The role of visual representations in the teaching and learning of mathematics”
Educational Studies in Mathematics. 52 (3), 215-241.
36. A. Arcavi, 2004.
“Solving linear equations – Why, how and when?” For the Learning of
Mathematics. 24(3), 25-28.
37. A. Arcavi, 2005.
“Developing and Using Symbol Sense in Mathematics” For the Learning of
Mathematics. 25(2), 50-55. Reprinted in Spanish in Uno, Revista de Didáctica de
las Matemáticas, 44, 2007, 59-75.
38. A. Arcavi, & M. Isoda, 2007.
“Learning to listen: from historical sources to classroom practice”
Educational Studies in Mathematics, 66(2), 111-129.
39. R. Karsenty, A. Arcavi & N. Hadas, 2007.
“Exploring informal mathematical products of low achievers at the secondary
school level” Journal of Mathematical Behavior, 16(2), 156-177.
40. A. Arcavi & A. Friedlander, 2007.
“Curriculum developers and problem solving - The case of Israeli elementary
school projects” Zentralblat für Didaktik de Mathematik, 39(5-6), 355-364.
41. A. Arcavi & Z. Resnick, 2008.
“Generating problems from problems and solutions from solutions” Mathematics
Teacher, 102 (1), 10-14.
43. M. Tabach. A. Arcavi, R. Hershkowitz, 2008.
“Transitions among different symbolic generalizations by algebra beginners in a
computer intensive environment” Educational Studies in Mathematics, 69(1), 5371.
44. A. Arcavi, 2008.
“Modeling with graphical representations” For the Learning of Mathematics, 28(2),
2-10.
45. M. Tabach, R. Hershkowitz & A. Arcavi, 2008.
“Learning beginning algebra with spreadsheets in a computer intensive
environment” Journal of Mathematical Behavior, 27(1), 48-63.
46. A. Arcavi & A. Schoenfeld, 2008.
“Using the unfamiliar to problematize the familiar: the case of mathematics teacher inservice education” Canadian Journal of Science, Mathematics and Technology
Education, 8(3), 1-16 [This paper is an enlarged version of publication 6, listed under
book chapters]
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47. T. Mulat & A. Arcavi, 2009.
“Success in mathematics within a challenged minority: the case of students of
Ethiopian origin in Israel” Educational Studies in Mathematics, 72(1), 77-92.
Book chapters (peer reviewed)
1. A. H. Schoenfeld, J. Smith & A. Arcavi. 1993.
“Learning: The Microgenetic Analysis of One Student's Evolving Understanding of
a Complex Subject Matter Domain”. Advances in Instructional Psychology, Vol.
4. R. Glaser (Ed.). Erlbaum, NJ. 1993, 55-175.
2. J. Moschkovich, A.H. Schoenfeld & A. Arcavi1. 1993.
“Aspects of Understanding: On Multiple Perspectives and Representations of
Linear Relations, and Connections Among Them” Integrating Research on the
Graphical Representation of Function. T. A. Romberg, E. Fennema & T. P.
Carpenter (Eds.), Erlbaum, NJ. 69-100.
3. M. Bruckheimer & A. Arcavi. 2000.
“Mathematics and its History - an Educational Partnership” Using History to Teach
Mathematics: An International Perspective. Katz, V. (Ed.) Mathematical
Association of America, 135-146.
4 . C. Tzanakis & A. Arcavi. 2000.
“Integrating history of mathematics in the classroom” History in Mathematics
Education. The ICMI Study. J. Fauvel & J. van Maanen (Eds.) Dordrecht, Kluwer,
201-240.
5. H. N. Jahnke with A. Arcavi, E. Barbin, O. Bekken, C. N. Dynnikov, F.
Furinghetti, A. El Idrissi & C. Weeks. 2000.
“The use of original sources in the mathematics classrooms” History in
Mathematics Education. The ICMI Study. J. Fauvel & J. van Maanen (Eds.)
Dordrecht, Kluwer, 291-316.
6. A. Arcavi & A.H. Schoenfeld, 2006.
“Using the unfamiliar to problematize the familiar” (In Portuguese) Chapter 4 in M.
Borba (Ed.) Tendencias Internacionais em Formaçâo de Professores de
Matemática (International Perspectives in Mathematics Teacher Education), pp.
87-111.
7. A. Arcavi, 2007.
“Exploring the Unfolding of a Cylinder”, “New Ways of Calculation”, and “I
Understand What You Want to Say” Three Commentaries on study lessons in
Japan. In M. Isoda, M. Stephens, Y. Ohara & T. Miyakawa (Eds.) Japanese Lesson
Study in Mathematics: Its Impact, Diversity and Potential for Educational
Improvement, World Scientific Publishing, 236-247.
1 The order of authorship was determined by a random choice procedure.
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8. M. Tabach, R. Hershkowitz, A. Arcavi & Dreyfus, 2008. “Computerized
environments in mathematics classrooms: A research-design view”. In L. D.
English, M. B. Bussi, G. A. Jones, R. A. Laesh, B. Sriraman, & D. Tirosh (Eds.),
Handbook of International Research in Mathematics Education, Second Edition
(pp. 784-805). NY, USA: Routledge.
9. A. Arcavi, 2008.
“Algebra: Purpose and Empowerment”. Seventieth NCTM Yearbook (2008):
Algebra and Algebraic Thinking in School Mathematics.
10. A. Arcavi, 2009
“The languages of mathematics”. Episteme Reviews - Volume 3 Macmillan
Publishers India Ltd., New Delhi: India
Edited books
1. M. Isoda, A. Arcavi & A. Mena (editors), 2007
El estudio de Clases Japonés (Japanese Lesson Study – In Spanish) Universidad
Católica de Valparaiso, Chile.
Chapters in Refereed Proceedings of International Conferences
1. J. Smith, A. Arcavi & A. H. Schoenfeld. 1989.
“Learning y-intercept: assembling the pieces of an atomic concept” Proceedings of
the 13th International Conference on the Psychology of Mathematics (PME 13),
Paris, Vol. 3, 174-181.
2. A. Friedlander, R. Hershkowitz & A. Arcavi. 1989.
“Incipient algebraic thinking in pre-algebra students” Proceedings of the 13th
International Conference on the Psychology of Mathematics (PME 13), Paris, Vol.
1, 283-290.
3. A. Arcavi & R. Nachmias. 1989.
“Re-exploring familiar concepts with a new representation” Proceedings of the 13th
International Conference on the Psychology of Mathematics Education (PME 13),
Paris, V.1, 77-84.
4. R. Hershkowitz & A. Arcavi. 1990.
“The interplay between student behaviors and the mathematical structure of problem
situations - issues and examples” Proceedings of the 14th International Conference
on the Psychology of Mathematics (PME 14), Mexico, Vol. II, 193-200.
5. A. Arcavi, N. Hadas & T. Dreyfus. 1994.
“Engineering Curriculum Tasks on the Basis of Theoretical and Empirical Findings”
Proceedings of the 18th International Conference on the Psychology of Mathematics
(PME 18), Lisbon, Vol. II, 280-287.
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6. D. Ben-Zvi & A. Arcavi. 1998.
“Towards a characterization and understanding of students’ learning in an interactive
statistics environment.” In L. Pereira-Mendoza (Ed.), Proceedings of the Fifth
International Conference on Teaching of Statistics, Vol. II, 647-653.
7. A. Arcavi. 1999.
“The role of visual representations in the teaching and learning of mathematics”
Proceedings of the 21st Annual Meeting of PME-NA. Hitt, F. & Santos, M. (Eds.)
55-80
8. N. Hadas & A. Arcavi. 2001.
“Relearning mathematics - the case of dynamical geometrical phenomena and their
unexpected Cartesian representations” Proceedings of the 25th International
Conference on the Psychology of Mathematics (PME 25), Utrecht, The Netherlands,
Vol. III, 81-89.
9. A. Arcavi. 2002.
“Developing and using symbol sense in mathematics” In J. Abramsky (Ed.),
Reasoning, explanation and proof in school mathematics and their place in the
intended curriculum Proceedings of the International Seminar. Qualifications and
Curriculum Authority London, England, 29-39.
10. A. Arcavi. 2004.
“Education of Mathematics Teachers” In Strässer, R., Brandell, G., Grevholm, B. &
Helenius, O. (Eds.) Educating for the Future. Proceedings of an International
Symposium on Mathematics Teacher Education. The Royal Swedish Academy of
Sciences, 2004, 227-234.
11. A. Friedlander & A. Arcavi. 2005
“Folding perimeters: Designer concerns and student solutions” (Part of the
Research Forum “The significance of task design in mathematics education:
Examples from proportional reasoning”) Proceedings of the 29th International
Conference on the Psychology of Mathematics (PME 29), Melbourne, Australia,
Vol. I,108-114.
12. A. Arcavi. 2006.
“An integrated vision of mathematical competencies” (In Spanish – Invited
Plenary). Memorias de la Conferencia sobre Competencias Matemáticas, Ministerio
de Educación, Bogotá, Colombia (CD Rom).
13. A. Arcavi, M. Artigue, C. Knipping, W. Khoon Yoong, M. Trigueros, W. Uegaki,
M. Isoda & S. Lerman, 2007.
“Mathematics Education in Senior Secondary Schools (Working Group for Action
3)” In H. Fujita, Y. Hashimoto, B. R. Hodgson, P. Yee Lee, S. Lerman &
T. Sawada (Eds.) Proceedings of the Ninth International Congress on Mathematical
Education, (Part 4), 2000 Makuhari, Japan, 232-237.
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14. T. Mulat & A. Arcavi, 2009
“Mathematical behaviors of successful students from a challenged ethnic minority”
Prooceedings (to appear) of the CERME 6 - Sixth Conference of European
Research in Mathematics Education, Lyon, France.
15. T. Mulat & A. Arcavi, 2009
“Mathematics Success among Students of Ethiopian Origin in Israel (SEO): a Case
Study” Proceedings of the 33th International Conference on the Psychology of
Mathematics (PME 33), Thessaloniki, Greece.
16. R. Hershkowitz & A. Arcavi, 2009
“Are second graders able to explain their mathematical ideas?” Proceedings of the
33th International Conference on the Psychology of Mathematics (PME 33),
Thessaloniki, Greece.
Reports
1. M. Jay & A. Arcavi. 1991.
“Educational software design analysis with special emphasis on mathematics” The
Foundation for Educational Software, S. Francisco, USA, 85 pages.
2. A. Arcavi & N. Hadas. 1994.
“Mathematics at the level of 2-3 units. A proposal for a new curriculum - Approach
and Rationale” (In Hebrew) Submitted to the Chief Scientist of the Ministry of
Education, Israel, 23 pages.
3. N. Hadas & A. Arcavi. 1996
“Summary of results from an experimental program with new learning materials” (In
Hebrew) Submitted to the Chief Scientist of the Ministry of Education, Israel, 25
pages.
4. A. Arcavi. 1999.
“Non-mathematically oriented students - a Research Report” Submitted to the
Curriculum planning Department of the Ministry of Education, Israel, 47 pages.
5. R. Karsenty & A. Arcavi. 2003
“Learning characteristics of ‘low achieving’ students in mathematics – Final report
of activities for the years 2000-2002” Submitted to the Curriculum planning
Department of the Ministry of Education, Israel, 121 pages.
6. A. Arcavi. 2005
"Report of activities (research and development)", submitted to the Center for
Research on International Cooperation In Educational Development (CRICED),
University of Tsukuba, Japan, 151 pages.
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7. A. Arcavi, A. Friedlander, B. Fresko, M. Carmeli, Rina Hershkowitz, Zvia
Markovits. 2006.
“Evaluation of Six Mathematics Curriculum Projects for First and Second Grade”
Submitted to the Chief Scientist of the Ministry of Education, Israel, 110 pages.
The following reports were written under Arcavi's supervision:
8. R. Bouhadana & R. Karsenty
“Selected problem solutions by low achieving students of mathematics who learned
according to the 3U program” Internal report, 22 pages.
9. S. Magidson
“Learning on the job: Instructional design as professional development” Internal
report, 20 pages.
10. R. Fried
“Low achieving students in junior-high school - A review of thinking processes and
teaching methods” Internal report (as a duty of the program for tachers on sabbatial
leave), 37 pages.
Other papers and abstracts
1. R. Nachmias & A. Arcavi, 1989.
“Multiple representations of linear functions: A case study” Proceedings of the 2nd
International Jerusalem Convention on Education: Interaction Between Research
and Practice, 369-75.
2. A. Arcavi, D. Tirosh & R. Nachmias, 1989.
“Effects of exploring a new representation on prospective mathematics teachers'
conceptions of function” Proceedings of the 2nd International Jerusalem Convention
on Education: Interaction Between Research and Practice, 269-277.
3. A. Arcavi, 1990.
“The teaching and learning of algebra in the secondary school”
Boletim Gepem (Publicação do Gepem - Grupo de Estudos e Pesquisas em
Educação Matemática). Ano XV (26), 12-23.
4. A. Arcavi, 1991.
“Two Benefits of Using History” Paper at the Conference “History in Mathematics
Education”, Leicester, England. For the Learning of Mathematics. 11(2), 11.
5. A. Arcavi, 1995.
“El Sentido de los Símbolos: Generación de Intuiciones en la Matemática formal” (In
Spanish). Actas de las VII Jornadas para el Aprendizaje y la Enseñanza de las
Matemáticas (7as JAEM) , Madrid, 77-83.
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6. A. Arcavi, 1996,
“A partial, simplified, and biased story about expectations”. For the Learning of
Mathematics, 16(3), 27-28.
7. R. Hershkowitz and A. Arcavi, 2000.
“Some brief and informal speculations on linguistic and cultural aspects related to
proof”. http://www.lettredelapreuve.it/EthnoPreuve/Israel.html
8. A. Arcavi & A. Flores, 2000.
n
n
n
“   min i, j    k 2 ” College Mathematics Journal, 31(5), 392.
i 1 j 1
k 1
9. A. Arcavi, 2005.
“Open letter mathematics teachers at the Elementary School of the University of
Tsukuba” (In Japanese). Journal of Mathematics Lesson Study at Elementary School,
42, 30-31.
10. A. Arcavi, 2006.
“Solving problems and their solutions” (Abstract).
Proceedings of the History and Pedagogy of Mathematics Meeting (HPM2004) &
the Fourth European Summer University on the History and Epistemology in
Mathematics Education. Edited by F. Furinghetti, S. Kaijser and C. Tzanakis
(Revised Edition).
Articles in Hebrew
1. A. Arcavi. 1980.
“The Meeting of Three Ships - A Mathematical Problem” Shevavim, Journal for
Mathematics Teachers (in Israel), Vol. 15.
2. A. Arcavi. 1982.
“How Shall We Teach the Multiplication of Negative Numbers?” Shevavim, Journal
for Mathematics Teachers (in Israel), Vol. 20.
3. R. Hershkowitz & A. Arcavi. 1985.
“Geometrical Adventures with the Function Concept” Shevavim, Journal for
Mathematics Teachers (in Israel), Vol. 24.
4. N. Hadas & A. Arcavi. 1985.
“The Importance of Thoughtful Use of Calculators” Shevavim, Journal for
Mathematics Teachers (in Israel), Vol. 25.
5. A. Arcavi. 1985-87
“Once Upon a time” (A sequence of episodes from the history of mathematics)
E'arot VeE'arot , Newsletter for Israeli Mathematics Teachers.
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6. R. Nachmias & A. Arcavi. 1989.
“A Microcomputer-Based Environment for the Parallel Axes Representations of
Functions” Mesarim-Misparim, Journal for Mathematics Teachers, 2(3), 7-17.
7. A. Arcavi, A. Friedlander & R. Hershkowitz. 1990.
“The Algebra Before Algebra” Mesarim-Misparim, Journal for Mathematics
Teachers 3(3), 48-62.
8. A. Arcavi & R. Nachmias. 1990.
“Looking for the Focus” Aleh, Journal for Mathematics Teachers, 7,
49-56.
9. M. Bruckheimer & A. Arcavi. 1996.
“A visual approach to basic topics in number theory” Aleh, Journal for Mathematics
Teachers, 19, 11-14.
10. R. Hershkowitz & A. Arcavi. 1997
“Take it with a grain of salt” (Some comments on the international comparison
studies). Aleh, Journal for Mathematics Teachers, 21, 41.
11. A. Arcavi. 2000.
“A conversation with Professor Fischbein (on intuitions in science and
mathematics)” Aleh, Journal for Mathematics Teachers, 26,1
3-16.
12. Alex Friedlander & A. Arcavi. 2001.




“Why my daughter has to solve 14  2  20  2  6 3  4(23  7)  7 and thousands
5
of exercises like it?” Aleh, Journal for Mathematics Teachers, 27,47-48.

11