Building "Consciousness and Legacies": Integrating Community, Critical, and Classical Knowledge Bases in a Precalculus Class

Persistent Link:
http://hdl.handle.net/10150/305882
Title:
Building "Consciousness and Legacies": Integrating Community, Critical, and Classical Knowledge Bases in a Precalculus Class
Author:
Gutiérrez, Rodrigo Jorge
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Grounded in Freire's (1970) notion that the purpose of education in an unjust society is to bring about equality and justice, Critical Mathematics (CM) scholars consider mathematics to be a tool to understand, critique, and change the world by deconstructing power structures that marginalize certain groups. In particular, Gutstein's (2006) framework for integrating students' Community, Critical, and Classical mathematics knowledge bases (3 Cs) advocates for mathematics instruction that incorporates students' informal and everyday experiences. This involves investigations into social phenomena that draw on students' perspectives and experiences to inform critical analysis, while developing mathematical power. This dissertation presents the findings from a critical ethnographic study of a veteran teacher of color's approach to integrating the 3 Cs in his Precalculus class. In addition to discussing the creation and implementation of CM activities, this study examined the perspectives and participation of students of color during these curricular units. Data from 12 students of color, including interviews, focus groups, classroom observations, and student work, were collected over the course of a school year. Detailed descriptions are presented of three CM activities (i.e., Local Poverty Unit, AIDS Lab, Gini Coefficient Unit).Analysis of student participation found that students engaged most fully when units integrated transparent mathematical concepts into non-traditional social investigations. CM activities that lacked mathematical activity and/or reproduced traditional instructional norms resulted in high levels of open and passive resistance. Analysis of student perspectives found that repeated opportunities to integrate the 3 Cs promoted shifts in students' orientation toward mathematics. Some students came to see new ways of learning and using mathematics that included various means of participation and connections to one's personal life. In the end, students recognized that mathematics could be relevant and powerful for making sense of the world (reading the world), and acknowledged its potential for bringing about change (writing the world). Findings point to the essential role personalization plays in helping students develop a sense of social agency. That is, by prioritizing Community knowledge and inviting students to incorporate personal and family stories, teachers promote students' integration of their personal perspectives and experiences into their critical analyses.
Type:
text; Electronic Dissertation
Keywords:
Critical Mathematics; Funds of Knowledge; Latino; Precalculus; Social Justice; Teaching & Teacher Education; Community
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Teaching & Teacher Education
Degree Grantor:
University of Arizona
Advisor:
Turner, Erin E.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleBuilding "Consciousness and Legacies": Integrating Community, Critical, and Classical Knowledge Bases in a Precalculus Classen_US
dc.creatorGutiérrez, Rodrigo Jorgeen_US
dc.contributor.authorGutiérrez, Rodrigo Jorgeen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractGrounded in Freire's (1970) notion that the purpose of education in an unjust society is to bring about equality and justice, Critical Mathematics (CM) scholars consider mathematics to be a tool to understand, critique, and change the world by deconstructing power structures that marginalize certain groups. In particular, Gutstein's (2006) framework for integrating students' Community, Critical, and Classical mathematics knowledge bases (3 Cs) advocates for mathematics instruction that incorporates students' informal and everyday experiences. This involves investigations into social phenomena that draw on students' perspectives and experiences to inform critical analysis, while developing mathematical power. This dissertation presents the findings from a critical ethnographic study of a veteran teacher of color's approach to integrating the 3 Cs in his Precalculus class. In addition to discussing the creation and implementation of CM activities, this study examined the perspectives and participation of students of color during these curricular units. Data from 12 students of color, including interviews, focus groups, classroom observations, and student work, were collected over the course of a school year. Detailed descriptions are presented of three CM activities (i.e., Local Poverty Unit, AIDS Lab, Gini Coefficient Unit).Analysis of student participation found that students engaged most fully when units integrated transparent mathematical concepts into non-traditional social investigations. CM activities that lacked mathematical activity and/or reproduced traditional instructional norms resulted in high levels of open and passive resistance. Analysis of student perspectives found that repeated opportunities to integrate the 3 Cs promoted shifts in students' orientation toward mathematics. Some students came to see new ways of learning and using mathematics that included various means of participation and connections to one's personal life. In the end, students recognized that mathematics could be relevant and powerful for making sense of the world (reading the world), and acknowledged its potential for bringing about change (writing the world). Findings point to the essential role personalization plays in helping students develop a sense of social agency. That is, by prioritizing Community knowledge and inviting students to incorporate personal and family stories, teachers promote students' integration of their personal perspectives and experiences into their critical analyses.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectCritical Mathematicsen_US
dc.subjectFunds of Knowledgeen_US
dc.subjectLatinoen_US
dc.subjectPrecalculusen_US
dc.subjectSocial Justiceen_US
dc.subjectTeaching & Teacher Educationen_US
dc.subjectCommunityen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineTeaching & Teacher Educationen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorTurner, Erin E.en_US
dc.contributor.committeememberTurner, Erin E.en_US
dc.contributor.committeememberWood, Marcyen_US
dc.contributor.committeememberCivil, Martaen_US
dc.contributor.committeememberGutstein, Ericen_US
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