Understanding Teacher Noticing of Students’ Prior Knowledge: Challenges and Possibilities

I propose a new construct, teacher noticing of students’ prior knowledge, and provide examples of a professional development intervention with the goal of supporting teacher learning. The examples demonstrate that combining discussions of animations of classroom instruction, video clubs, and lesson study can help teachers to attend to students’ prior knowledge and anticipate actions that use that knowledge for promoting mathematical understanding. I discuss challenges and new questions for mathematics education researchers brought about by the new construct. I suggest that the construct is valuable for developing teachers’ professional knowledge

Geometry Students’ Arguments About a 1-Point Perspective Drawing

The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram

INSTRUCTIONAL SITUATIONS AND STUDENTS’ OPPORTUNITIES TO REASON IN THE HIGH SCHOOL GEOMETRY CLASS

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.This manuscript is part of the final report of the NSF grant CAREER 0133619 “Reasoning in high school geometry classrooms: Understanding the practical logic underlying the teacher’s work” to the first author.All opinions are those of the authors and do not represent the views of the National Science Foundation.http://deepblue.lib.umich.edu/bitstream/2027.42/78372/1/Instructional_Situations_in_Geometry.pd

Mathematical Tasks and the Collective Memory: How Do Teachers Manage Students' Prior Knowledge When Teaching Geometry with Problems?

This is a study of how teachers manage students’ prior knowledge in problem-based mathematics teaching. I propose that geometry teachers manufacture a collective memory which they use to hold students accountable for what they should remember and what they should forget when they work on problems. This hypothesis is put to work in analyzing two corpuses of data. I inspect a corpus of video records of a problem-based unit on quadrilaterals, where a teacher made changes to usual practices in two ways, by asking students to call forth knowledge from prior mathematics classes and by having students anticipate a theorem that the teacher had not stated yet. The second corpus consists of proceeds of five focus group sessions in which experienced geometry teachers viewed and discussed records of problem-based teaching in geometry and where they designed tasks in which they would engage their students. The analysis uncovered teachers’ assumptions and normative stances on how to manage students’ prior knowledge. In addition, from the analysis I describe a catalogue of teaching actions that teachers accept they might avail themselves for shaping the collective memory of a class. Methodologically, the study shows how to investigate teachers’ management of prior knowledge by applying tools from Systemic Functional Linguistics to transcripts of mathematics classroom talk and to transcripts of conversations among practitioners. This work is a contribution to the study of teaching by describing the kinds of resources that teachers could use in teaching with problems, and the underlying rationality for teaching actions to manage students’ prior knowledge.Ph.D.EducationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/62441/1/glorigon_1.pd

Geometry Students’ Arguments About a 1-Point Perspective Drawing

The practice of formulating and justifying claims is a fundamental aspect of doing mathematics, and in geometry, students’ use of diagrams is integral to how they establish arguments. We applied Toulmin’s model to examine 23 geometry students’ arguments about figures included in a 1-point perspective drawing. We asked how students’ arguments drew upon their knowledge of 1-point perspective and their use of the diagram provided with the problem. Students warranted their claims based upon their knowledge of perspective, both in an artistic context as well as from experiences in everyday life. Students engaged in multiple apprehensions of the diagram, including using the given features, adding features, or measuring components, to justify claims about the figures. This study illustrates the importance of students’ prior knowledge of a context for formulating arguments, as well as how that prior knowledge is integrated with students’ use of a geometric diagram

REPRESENTATIONS OF MATHEMATICS TEACHING AND THEIR USE IN TRANSFORMING TEACHER EDUCATION: CONTRIBUTIONS TO A PEDAGOGICAL FRAMEWORK

teacher education, technology, representations of practice, teaching, mathematics, comics, cartoon, animation, pedagogy, casesThe use of representations of mathematics teaching, particularly those that are maintained in a digital form, calls for specialized pedagogical practices from teacher developers. They also open new areas for investigation of how future professionals learn to practice and the role that various technologies play in scaffolding that learning. In the discussion paper for the PMENA working group on representations of mathematics teaching, Herbst, Bieda, Chazan, and González (2010) reviewed literature on the use of video records and written cases in teacher education and noted that classroom scenarios sketched as cartoon animations have begun to be utilized for those purposes, arguing that they have affordances that are distinct from those of video and written cases. That document also noted existing literature on the use of written and video cases in teacher education and cited examples that concern mostly face-to-face facilitation and argued that the increased capabilities of information technologies for creating, manipulating, and collaborating over multimedia point to a promising future for teacher development assisted by representations of practice. In this document we complement the previous year’s review by briefly accounting for three areas of emerging scholarship: (1) information technologies that support teachers’ learning from representations of practice; (2) the particular challenge of helping prospective teachers understand students’ thinking; and (3) research and theory about what is important or possible to achieve in having prospective teachers look at or work with representations of teaching. We also describe present developments in the articulation of a pedagogical framework.Some of this material has been produced with the support of NSF grants ESI-0353285 and DRL- 0918425 to Herbst and Chazan.http://deepblue.lib.umich.edu/bitstream/2027.42/86657/1/PMENA2011_RMT_Framework.pd

Investigación (Arte + Diseño): desarrollo de discusiones críticas sobre múltiples experiencias, perspectivas y prácticas investigativas en el CIDEA.

Modalidad de graduación: Seminario para optar por el grado de licenciatrua en Arte y Comunicación VisualEntendiendo que el Seminario constituye una modalidad comprendida en el ámbito de los Trabajos Finales de Graduación como una actividad teórico - práctica dirigida al desarrollo de proyectos de investigación circunscritos a un tema propuesto por la Unidad Académica. El tema de este seminario de graduación, avalado por la mencionada entidad, coincide con el proyecto (PPAA): Nodos activos (Investigación + práctica artística). En síntesis, este tema es la exploración crítica sobre los procesos, formas prácticas y modelos destinados a diferentes formas de vivenciar, asumir y aplicar el concepto de Investigación artística y diseñística1. Por su amplitud y complejidad, este tema se ofrece como matriz para el desarrollo de proyectos de investigación alternos o asociados partiendo de una perspectiva interdisciplinaria y transdisciplinaria capaz de comprender diferentes áreas de especialización más allá incluso de las fronteras de las artes visuales y el diseño.Escuela de Arte y Comunicación Visua