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Gloriana Gonzalez Rivera
Gloriana González's research focuses on how teachers manage students' prior knowledge. She is interested in examining teachers' decision-making when handling students' prior knowledge and the rationality underlying those decisions.
- Ph.D., Mathematics Education, University of Michigan, 2009
- M.S., Mathematics Education, Cornell University, 1995
- B.A., Secondary Mathematics Education, University of Puerto Rico, 1993
Key Professional Appointments
- Assistant Professor, Department of Curriculum and Instruction, University of Illinois at Urbana-Champaign, 2009-present
Activities & Honors
- Reviewer, Journal of Mathematics Teacher Education, 2013-present
- Reviewer, Mathematics Teaching in the Middle School, 2011-present
- Reviewer, Journal of Mathematical Behavior, 2011-present
- Reviewer, Journal of Mathematics Teacher Education, 2011-present
- Outstanding Undergraduate Teaching Award, College of Education, University of Illinois at Urbana-Champaign, College of Education, University of Illinois at Urbana-Champaign,, 2012-2013
- Reviewer, Mathematics Teacher Journal, -2012
- Reviewer, Journal of Mathematical Behavior, 2011-2012
- Reviewer, Psychology of Mathematics Education-North American Chapter, 2005-2012
- Faculty Fellow, Hardie Faculty Fellows Program, College of Education, 2011
- List of Teachers Ranked as Excellent by Their Students, University of Illinois, 2010
- Stanley E. and Ruth B. Dimond Best Dissertation Award, School of Education, University of Michigan - Ann Arbor, 2010
- STaR Fellow, National Science Foundation, 2010
- Reviewer, ZDM - The International Journal on Mathematics Education, 2010-
- Reviewer, Educational Evaluation and Policy Analysis, 2010-
- Susan S. Lipschutz Award for exceptional scholarly achievement, a sense of social responsibility and service, and a lively interest in promoting the success of women in the academic community, University of Michigan - Ann Arbor, 2008
- School of Education Scholars Award, University of Michigan - Ann Arbor, 2003-2008
- Beginning Researcher Award to attend the Discovery Research K-12 Principal Investigators Conference, National Science Foundation, 2007
- Jones, Payne, Coxford Award for outstanding doctoral student in mathematics education, University of Michigan - Ann Arbor, 2006
Research StatementMy research focuses on how teachers manage students’ prior knowledge. I am interested in examining teachers’ decision-making when handling students’ prior knowledge and the rationality underlying those decisions. I have studied this question in the particular case of the high school geometry class, which has special demands for the teaching and learning of mathematics. Methodologically, I apply Systemic Functional Linguistics to the analysis of both classroom talk and discussions among teachers.
I have found that geometry teachers shape<i> the collective memory of the class</i> with timely actions geared towards making students remember something from the past or towards making something memorable in the future. Moreover, geometry teachers not only control what students have to remember, but also what students have to forget as a result of teaching with a problem. In the future, I expect to have a detailed description of teaching moves to manage students’ prior knowledge in problem-based instruction. I am also interested in developing applications of my findings for the purpose of teacher education through the design of innovative rich-media environments that would scaffold how teachers consider students' prior knowledge as they plan mathematical tasks for their students.
I have a special interest in the teaching and learning of geometry. In the past, I have investigated relationships between justifications for teaching geometry and the historical development of the American high school geometry curriculum. I have also studied how the use of dynamic geometry provokes new challenges and possibilities in geometry classrooms.
- Principal Investigator, CAREER: Noticing and Using Students' Prior Knowledge in Problem-Based Instruction, National Science Foundation, 2013-2018
- Principal Investigator, Mathematics teachers' decision-making when activating students' prior knowledge in problem-based instruction, Campus Research Board, 2011-2012
- Herbst, P., Chen, C., Weiss, M., González, G., Nachlieli, T., Hamlin, M., Brach, C., Gonzalez Rivera, G. “Doing proofs” in geometry classrooms. Teaching and learning proof across the grades: A K-16 perspective. Routledge: New York.
- DeJarnette, A., Dao, J., González, G., Gonzalez Rivera, G. Promoting small-group discussions. Mathematics Teaching in the Middle School, 19(7), 414-419.
- Gonzalez Rivera, G., DeJarnette, A., Deal, J. (2014). Assessing and using students’ prior knowledge in problem-based instruction. New England Mathematics Journal, XLVI.
- González, G., Gonzalez Rivera, G. (2013). A geometry teacher’s use of a metaphor in relation to a prototypical image to help students remember a set of theorems. Journal of Mathematical Behavior, 32, 397-414.
- González, G., DeJarnette, A., Gonzalez Rivera, G. (2013). Leading classroom discussions. Mathematics Teaching in the Middle School, 18(9), 544-551.
- DeJarnette, A., González, G., Gonzalez Rivera, G. (2013). Building students’ reasoning habits by promoting student-led discussions in an Algebra II class. The Mathematics Educator, 23(1), 3-23.
- González, G., DeJarnette, A., Gonzalez Rivera, G. (2013). Geometric reasoning about a circle problem. The Mathematics Teacher, 106(8), 586-591.
- González, G., Herbst, P., Gonzalez Rivera, G. (2013). An oral proof in a geometry class: How linguistic tools can help map the content of a proof. Cognition and Instruction, 31(3), 271-313.
- González, G., DeJarnette, A., Gonzalez Rivera, G. (2012). Agency in a geometry review lesson: A linguistic view on teacher and student division of labor. Linguistics and Education, 23(2), 182-199.
- González, G., Gonzalez Rivera, G. (2011). Who does what?: A linguistic approach to analyzing teachers’ reactions to videos. ZDM-The International Journal on Mathematics Education, 43(1), 65-80.
- González, G., Gonzalez Rivera, G. (2011). Creating analogies about experiences in ordinary life when doing a proof by contradiction. the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. University of Nevada: Reno, NV.
- González, G., Herbst, P., Gonzalez Rivera, G. (2009). Students' conceptions of congruency through the use of dynamic geometry software. International Journal of Computers for Mathematical Learning, 14, 153-182.
- Nachlieli, T., Herbst, P., González, G., Gonzalez Rivera, G. (2009). Seeing a colleague encourage a student to make an assumption while proving: What teachers put to play in casting an episode of geometry instruction. Journal for Research in Mathematics Education, 40(4), 427-459.
- González, G., Herbst, P., Gonzalez Rivera, G. (2006). Competing arguments for the geometry course: Why were American high school students to study geometry in the twentieth century? International Journal for the History of Mathematics Education, 1(1), 7-33.
- Herbst, P., González, G., Macke, M., Gonzalez Rivera, G. (2005). How can geometry students understand what it means to define in mathematics? The Mathematics Educator, 15(2), 17-24.
In The News
Nov. 19, 2013
NSF CAREER grant funds research to help mathematics educators better understand student learning process
Jun. 20, 2013
Professor Gloriana González is the principal investigator of a new CAREER grant funded by the National Science Foundation. The $853,675 grant started in May and will run through April 2018. The grant will fund the mathematics education research project titled "Noticing and Using Students' Prior Knowledge in Problem-Based Instruction." CAREER grants are highly competitive and touted by the NSF as the "most prestigious awards" supporting junior faculty. Read more...
C&I professor and two of her students address teaching methods and classroom discussions in mathematics journal articles
May 23, 2013
Gloriana González (left photo) and Anna F. DeJarnette are the authors of two recently published journal articles. The first, which appeared in the April 2013 issue of "Mathematics Teacher," was titled "Geometric Reasoning about a Circle Problem." The second was featured in the May 2013 issue of "Mathematics Teaching in the Middle School" (MTMS) and was titled "Leading Classroom Discussions." Read more...