Ferdinand D Rivera
Publications
2012
Rivera, F. (in press, 2012). Teaching and Learning Patterns in School Mathematics: Psychological and
Pedagogical Considerations. New York: Springer.
Forgasz, H. & Rivera, F. (2012). Toward Equity: Gender, Culture, and Diversity (Advances in Mathematics
Education Volume 3). Netherlands: Springer.
Rivera, F. (2012). Neural correlates of gender, culture, and race and implications to embodied thinking in
mathematics. In H. Forgasz & F. Rivera (eds.), Toward equity: Gender, culture, and diversity (Advances in
Mathematics Education, Volume 3). Springer.
Rivera, F., Leung, C. H., and Krauthausen, G. (2012). First Grade Students’ Patterning Competence Prior
to Formal Instruction: A Cross-Cultural Comparison Between US and Hongkong. PME in Taipei, Taiwan. &
ICME in Seoul, Korea.
2011
Rivera, F. (2011). Toward a Visually-Oriented School Mathematics Curriculum: Research, Theory,
Practice, and Issues (Mathematics Education Library Vol. 49). New York: Springer.
Rivera, F. (2011). Explaining Differences in Second Grade Students’ Patterning Ability Using Parallel
Distributed Processing. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group
for the Psychology of Mathematics Education (Vol.49-56). Anakara, Turkey: PME.
Rivera, F. & Becker, J. R. (2011). Formation of Pattern Generalization in Middle School. In J. Kai & E.
Knuth (eds.), Springer Advances in Mathematics Education. Springer.
2010
Rivera, F. (2010). Visual Templates in Pattern Generalization Activity. Educational Studies in
Mathematics, 73(3), 297-328.
Rivera, F. (2010). There is More to Mathematics Than Symbols. Mathematics Teaching, 218, 42-47.
Rivera, F. (2010). Spicing Up Counting Through Geometry. Mathematics Teacher, 104(4), 319-324.
Rivera, F. (2010). Second grade students’ preinstructional competence in patterning activity. In M. Pinto
& T. Kawasaki (eds.), Proceedings of the PME 34 (Vol. 4, pp. 81-88). Brazil: PME.
2009
Rivera, F. & Becker, J. (2009). Algebraic Reasoning Through Patterns. Mathematics Teaching in the
Middle School, 15(4), 212-221.
Rivera, F. (2009). Visuoalphanumeric Mechanisms That Support Pattern Generalization. In I. Vale & A.
Barbosa (eds.), Patterns: Multiple Perspectives and Contexts in Mathematics Education (pp. 123-136).
Viana do Castelo, Portugal: Escola Superior de Educacao do Instituto Politecnico de Viana do Castelo.
Rivera, F. & Becker, J. R. (2009a). Visual Templates in Pattern Generalization. In M. Tzekaki, M.
Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the Joint Meeting of 33rd International Group for
the Psychology of Mathematics Education (Vol. 4, pp. 473-480). Thessaloniki, Greece: PME.
Becker, J. R. & Rivera, F. (2009b). Justification Schemes of Middle School Students in the Context of
Generalization of Linear Patterns. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings
of the Joint Meeting of 33rd International Group for the Psychology of Mathematics Education (Vol. 5,
pp. 9-16). Thessaloniki, Greece: PME.
2008
Rivera, F. (2008). On the pitfalls of abduction: Complicities and complexities in patterning activity. For
the Learning of Mathematics, 28(1), 17-25.
Rivera, F. & Becker, J. (2008). From Patterns to Algebra: The Development of Generalized Thinking. ZDM,
40(1).
Rivera, F. & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and
deconstructive generalizations involving linear figural patterns. ZDM, 40(1), 65-82.
Rivera, F. & Becker, J.R. (2008). Ethnomathematics in the Global Episteme: Quo Vadis? In B. Atweh,
M. Borba, A. Barton, N. Gough, C. Keitel, C. Vistro-Yu, & R. Vithal (eds.), Internalisation and
Globalisation in Mathematics and Science Education (pp. 209-226). Dordrecht, Netherlands: Springer.
Rivera, F. & Becker, J. R. (2008a). Sociocultural Intimations on the Development of Generalization
Among Middle School Learners: Results from a Three-Year Study. In O. Figueras, J. L. Cortina, S.
Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PMENA
XXX (Vol. 4, pp. 193-200). Morelia, Mexico: Cinvestav-UMSNH.
Becker, J. R. & Rivera, F. (2008b). Nature and Content of Generalization of 7th- and 8th-Graders
on a Task That Involves Free Construction of Patterns. In O. Figueras, J. L. Cortina, S. Alatorre, T.
Rojano, & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PMENA XXX (Vol. 4,
pp. 201-208). Morelia, Mexico: Cinvestav-UMSNH.
Rivera, F. (2008, March). Technology as experience: Putting instrumentation to work in the construction
of a mathematical reality. Paper to be presented at the International Congress on Mathematical
Instruction in Rome, Italy, in March 2008. Denmark. Available online: http://www.icmeorganisers.dk/tsg26.
2007
Rivera, F. (2007). Accounting for Students’ Schemes in the Development of a Graphical Process for
Solving Polynomial Inequalities in Instrumented Activity. Educational Studies in Mathematics, 65(3),
281-307.
Rivera, F. (2007). Visualizing as a Mathematical Way of Knowing: Understanding Figural
Generalization. Mathematics Teacher, 101(1), 69-75.
Rivera, F. & Becker, J. R. (2007). Abductive-Inductive (Generalization) Strategies of Preservice
Elementary Majors on Patterns in Algebra. Journal of Mathematical Behavior, 26(2), 140-155.
Becker, J. R. & Rivera, F. (2007a). Factors Affecting Seventh Graders’ Cognitive Perceptions of Patterns
Involving Constructive and Deconstructive Generalizations. In J-H Woo, H-C Lew, K-S Park, & D-Y Seo
(Eds.), Proceedings of the 31th Conference of the International Group for the Psychology of Mathematics
Education (Vol.4, pp. 129-136). Seoul, Korea: The Korea Society of Educational Studies in Mathematics.
Becker, J. R. & Rivera, F. (2007b). Seventh Graders’ Generalization Strategies Involving Decreasing
Linear Patterns: Cognitive Complexities of Transfer. Proceedings of the 29th Conference of the North
American Chapter of the Psychology of Mathematics Education. Lake Tahoe, Nevada.
Rivera, F. & Becker, J. R. (2007c). Abduction in Pattern Generalization. In J-H Woo, H-C Lew, K-S
Park, & D-Y Seo (Eds.), Proceedings of the 31th Conference of the International Group for the
Psychology of Mathematics Education (Vol.4, pp. 97-104). Seoul, Korea: The Korea Society of
Educational Studies in Mathematics.
2006
Rivera, F. (2006). Changing the Face of Arithmetic: Teaching Children Algebra. Teaching Children
Mathematics, 12(6), 306-311.
Becker, J. R. & Rivera, F. (2006a). Establishing and Justifying Algebraic Generalization at the Sixth
Grade Level. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th
Conference of the International Group for the Psychology of Mathematics Education (Vol.4, pp. 465 472). Prague, Czechovslovakia: Charles University.
Becker, J. R. & Rivera, F. (2006b). Sixth Graders' Figural and Numerical Strategies for Generalizing
Patterns in Algebra. In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th
Annual Meeting of the North American Chapter of the International Group for the Psychology of
Mathematics Education (Vol.2, pp. 95-101). Mérida, México: Universidad Pedagógica Nacional.
Rivera, F. & Becker, J. R. (2006c) Sixth Graders’ Ability to Generalize Patterns in Algebra: Issues and
Insights. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference
of the International Group for the Psychology of Mathematics Education (Vol.1, p. 320).
Prague, Czechovslovakia: Charles University.
.
Rivera, F. & Becker, J. R. (2006d). Accounting for Sixth Graders’ Generalization Strategies in Algebra.
In S. Alatorre, J. Cortina, M. Sáiz, & A. Méndez (Eds.), Proceedings of the 28th Annual Meeting of
the North American Chapter of the International Group for the Psychology of Mathematics
Education (Vol.2, pp. 155-157). Mérida, México: Universidad Pedagógica Nacional.
2005
Rivera, F. & Becker, J. R. (2005). Figural and Numerical Modes of Generalizing in Algebra.
Mathematics Teaching in the Middle School, 11(4), 198-203.
Becker, J. R. & Rivera, F. (2005). Generalization Schemes in Algebra of Beginning High School
Students. In H. Chick & J. Vincent (Eds.), Proceedings of the 29th Conference of the International Group
for the Psychology of Mathematics Education (pp. 4-121 – 4-128). Melbourne, Australia: University of
Melbourne.
Rivera, F. (2005). An anthropological account of the emergence of mathematical proof and related
processes in technology-based environments. In W. Masalski (Ed.), Technology-Supported Math
Learning Environments: Sixty-Seventh Yearbook (pp. 125-136). Reston, VA: National Council of
Teachers of Mathematics.
Rivera, F. (2005, April). How Qualitative Research Can Be Made to Mean: The Work of Praxis in the
Postmodern. Paper presented at the American Educational Research Association. Montreal, Canada.
Becker, J. R. & Rivera, F. (2005, April). Emerging Perspectives of Research on Gender and
Mathematics: A Global Synthesis. Paper Discussion presented at the American Educational Research
Association sponsored by the Special Interest Group on Research on Women and Education. Montreal,
Canada.
2004
Vistro-Yu, C. and Rivera, F. (2004). The Effective Learning Environment: The Delivery Modes of
Model Schools. In Effective Practices in Science and Mathematics Education: A Benchmarking Project
(Ibe, Ogena, and Brawner, Eds.). Quezon City, Philippines: Vibal.
Rivera, F. D. & Becker, J. (2004). A Sociocultural Account of Students’ Collective Mathematical
Understanding of Polynomial Inequalities in Instrumented Activity. In M. Hoines & A. Fuglestad (Eds.),
Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics
Education (pp. 4-81 – 4-88). Bergen, Norway: Bergen University College.
Rivera, F. (2004, April). The Status of (Difficult) Knowledge in Qualitative Research: Why We Still Need
Objectivity, or Why We Need to Change the Way We Think About It. Paper presented at the American
Educational Research Association. San Diego, CA.
Becker, J. R. & Rivera, F. (2004). Emerging Perspectives of Research on Gender and Mathematics: A
Global Analysis. Paper presented at the 11th International Conference of Mathematical Education.
2003
Rivera, F. (2003). Developing reflective practice in preservice elementary mathematics teachers: Issues
and insights. Practice and Policy in Education, 10(2).
Rivera, F. D. (2003). In Southeast Asia: Conjunctions and Collisions in the Global Cultural Economy. In
W. Pinar (Ed.), International Handbook of Curriculum Research (pp. 572-595). New Jersey: Lawrence
Erlbaum.
Rivera, F.D. & Becker, J. (2003). The Effects of Figural and Numerical Cues on the Induction Processes
of Preservice Elementary Mathematics Teachers. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.),
Proceedings of the 2003 Joint Meeting of PME and PMENA (pp. 4-63 – 4-70). Honolulu, Hawai’i:
University of Hawaii.