Rivera, Ferdinand

Publications & Presentations

Rivera, F. (in press). Abduction and the emergence of necessary mathematical knowledge. In L. Magnani & T. Bertolotti (eds.), SpringerHandbook of Model-Based Science.

 

Rivera, F. (2015). Teaching to the Common Core Standards: Focus on Grades 5 Through 8 and Algebra I. New York: Sense.

 

Rivera, F. (2015). The distributed nature of pattern generalization. PNA, 9(2).

 

Rivera, F., Steinbring, H., & Arcavi, A. (2014). Visualization as an Epistemological Tool. ZDM,

47(1).

 

Rivera, F. (2014). From Math Drawings to Algorithms: Emergence of Whole Number

Operations in Children. ZDM, 47(1).

 

Rivera, F. (2014). Teaching to the Common Core Standards: Focus on Kindergarten Through

Grade 5. New York: Sense.

 

Rivera, F. (2013). Teaching and Learning Patterns in School Mathematics: Psychological and

Pedagogical Considerations. New York: Springer.

 

Rivera, F. (2013). Pattern Generalization Processing of US Elementary and Middle School Students: Similarities and Differences. In H. Ainze (Ed.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol.4, 149-56). Kiel, Germany: PME.

 

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. (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.

 

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. & Becker, J. R. (2011). Formation of Pattern Generalization in Middle School. In J. Kai & E. Knuth (eds.), Springer Advances in Mathematics Education. 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. (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.

 

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.

 

Rivera, F. & Becker, J. (2008). From Patterns to Algebra: The Development of Generalized

Thinking. ZDM, 40(1).

 

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. 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. & Becker, J. R. (2007). Abductive-Inductive (Generalization) Strategies of Preservice

Elementary Majors on Patterns in Algebra. Journal of Mathematical Behavior, 26(2), 140-155.

 

Rivera, F. (2007). Visualizing as a Mathematical Way of Knowing: Understanding Figural

Generalization. Mathematics Teacher, 101(1), 69-75.

 

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.

 

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.

 

Rivera, F. (2006). Changing the Face of Arithmetic: Teaching Children Algebra. Teaching

Children Mathematics, 12(6), 306-311.

 

Rivera, F. (2006). Structures of elementary algebraic thinking: Evidence from sixth grade students and implications for classroom practice. Intersection, 7(2), 2-13.

 

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.

 

Rivera, F. & Becker, J. R. (2005). Figural and Numerical Modes of Generalizing in Algebra.

Mathematics Teaching in the Middle School, 11(4), 198-203.

 

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.

 

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.

 

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. 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. (2003). Developing reflective practice in preservice elementary mathematics teachers: Issues and insights. Practice and Policy in Education, 10(2).

 

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.

 

Rivera, F. (2000). What's radical in radical constructivism? The self in the process of coming to know mathematics. Intersection, 1(1), 13-17

 

Forthcoming

Rivera, F. Teaching to the Common Core Standards: Focus on High School Mathematics. New

York: Sense.

 

Rivera, F. & Becker, J. Middle school students’ pattern generalization strategies on free generalization tasks.

 

Rivera, F. (ed.). English Learners in Math Classrooms. ZDM Special Issue, 2017.

 

Peer-Reviewed Conference Papers With No Proceedings

Rivera, F. (2008, March). Technology as experience: Putting instrumentation to work in the

construction of a mathematical reality. Paper presented at the International Congress on

Mathematical Instruction in Rome, Italy, in March 2008.

 

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.

 

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. Denmark. Available online: http://www.icme-organisers.dk/tsg26.

 

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.