Gloriana Gonzalez's research while affiliated with University of Illinois, Urbana-Champaign and other places

Publications (8)

Article
Recommendations that teachers promote argument and discourse in their mathematics classrooms anticipate researchers’ needs for methods for examining and analyzing such talk. One form of discourse is oral arguments, including proofs. We ask: How can we track the development of an oral argument by a teacher and her/his students?We illustrate amethod...
Article
Full-text available
teacher education, technology, representations of practice, teaching, mathematics, comics, cartoon, animation, pedagogy, cases
Article
Full-text available
We outline a theory of instructional exchanges and characterize a handful of instructional situations in high school geometry that frame some of these exchanges. In each of those instructional situations we inspect the possible role of reasoning and proof, drawing from data collected in intact classrooms as well as in instructional interventions. T...
Article
This paper describes students’ interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK¢ model of conceptions, suggests that incorporating technology in mathematics classrooms enabled a measur...
Conference Paper
This paper lays out the basis for a professional development model based on conversations about practice spurred by stories of instruction represented using rich media. It describes on the one hand the learning potential of these stories, as well as what participants of a series of face-to-face study group meetings have identified as design feature...
Article
This study contributes to the historical examination of the justification question for the particular case of the high school geometry course in the United States. The 20th century saw the emergence of competing arguments to justify the geometry course. Four modal arguments are identified including that geometry provides an opportunity for students...

Citations

... Examples of social norms are: (i) active listening, intellectual risk-taking (sharing incomplete ideas), and building on the ideas of others [2]; and (ii) assuming the responsibility of solving the given task [3]. Examples of socio-mathematical norms are: research in mathematics involves creatively solving problems; valid arguments should be based on properties of mathematical objects [1,4,5]; open-ended problems require exploration, formulation of conjecture, and argumentation of conjecture [3]. ...
... Geometry and reasoning have been connected at least since the writing of Euclid's Elements, which provided a paradigm for deductive reasoning in the context of geometric proof. This connection has motivated, in part, the inclusion of geometric proof in high school mathematics curricula in the US (González & Herbst, 2006;Sinclair, 2008). For example, over a century ago, the Committee on Secondary School Studies argued that geometric proof "is the most elaborate illustration of the mechanism of formal logic in the entire curriculum of the student" (National Educational Association, 1893). ...
... Also, Hessamy and Hemedi(2013) revealed "additive" as the most frequently used conjunction in independent and integrated essays written by 95 upper-intermediate Iranian EFL learners, while causal, temporal, adversative and continuative conjunctions were all represented in the texts. Gonzalez and Herbst(2013) researched the logical relationships in mathematics classroom and submit that teachers and students often used the conjunctions "then" and "if" to denote consequences of events and premises of events, respectively. In another study by Ionescu (2011), results show that the use of sequential connective markers increase with age and the frequency of causal connectors decrease in Romanian and English as children grow older, but reached the lowest in adult. ...
... This collaboration supported the students in carrying out the activities successfully [36][37][38]. The students managed to define the concepts correctly and gradually based on arguments and constructions [39]. These results show that it is necessary to allow students to construct, explore and investigate mathematical concepts by themselves, as well as to encourage them to develop their knowledge of mathematics through collaboration with each other. ...
... It allows the user to perform investigations and thus affords the possibility of a dynamic visual representation of geometry concepts in a physical sense. Such investigatory activities are hard to experience in a static environment such as paper and pencil (González & Herbst, 2009). In later sections we shall see how students of grade 2 and grade 6 worked with geometrical shapes via GeoGebra applets and made conjectures about them. ...
... The work-specific practice of StoryCircles coupled with the possibility to retrofit MKT-G items to a DCM model suggests the possibility to align StoryCircles content and the attributes being assessed. In a future study, StoryCircles could focus on lessons that make use of instructional situations such as calculating in geometry, doing proofs, or exploring figures (Herbst, 2010) and we could use DCM and the national sample to assess change, providing even more focused evidence than what could be provided in this study. ...