# Publications & Presentations

## Rivera, Ferdinand

### Publications & Presentations

Rivera, F. (in press). Abduction and the emergence of necessary mathematical knowledge.
In L. Magnani & T. Bertolotti (eds.), *Springer**Handbook 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.