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E-raamat: Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

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This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.      


Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education 1(12)
Megan Staples
AnnaMarie Conner
Part I Argumentation, Justification and Proof in an Elementary Classroom
Overview of the Elementary Level Data
13(6)
Karl W. Kosko
Argumentation in the Context of Elementary Grades: The Role of Participants, Tasks, and Tools
19(16)
Chepina Rumsey
Ian Whitacre
Sebnem Atabas
Jessica L. Smith
Justification in the Context of Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning
35(14)
Eva Thanheiser
Amanda Sugimoto
Proof in the Context of Elementary Grades: A Multimodal Approach to Generalization and Proof in Elementary Grades
49(16)
Candace Walkington
Dawn M. Woods
On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes
65(10)
Andreas J. Stylianides
Gabriel J. Stylianides
Part II Argumentation, Justification and Proof in a Middle Grades Classroom
Overview of Middle Grades Data
75(4)
Megan Staples
Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation
79(16)
Carlos Nicolas Gomez Marchant
Stacy R. Jones
Hilary Tanck
Justification in the Context of Middle Grades: A Process of Verification and Sense-Making
95(14)
Kristin Lesseig
Jerilynn Lepak
Proof in the Context of Middle Grades: Can We Label Middle School Arguments as Proof with a Capital P?
109(20)
David A. Yopp
Rob Ely
Anne E. Adams
Annelise W. Nielsen
Argumentation, Justification, and Proof in Middle Grades: A Rose by Any Other Name
129(10)
Eric Knuth
Orit Zaslavsky
Hangil Kim
Part III Argumentation, Justification and Proof in High School Mathematics
Overview of High School-Level Data
139(6)
Anna Marie Conner
Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation
145(14)
Markus Hahkioniemi
Justification in the Context of High School: Co-constructing Content and Process
159(18)
Jill Newton
Ema Yackel
Proof in the Context of High School: A First Approach Through Discussion, with Occasions and Missed Opportunities
177(18)
Francesca Morselli
Reasoning Is in the Eye of the Lens-Holder: Observations Made Through the Lenses of Justification, Argumentation, and Proof at the High School Level
195(16)
Michelle Cirillo
Dana C. Cox
Part IV Argumentation, Justification and Proof at the Tertiary Level
Overview of Tertiary Level Data
211(8)
David Plaxco
Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves
219(20)
David Plaxco
Megan Wawro
Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group
239(12)
Shiv Smith Karunakaran
Mariana Levin
Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof
251(14)
Timothy Fukawa-Connelly
Sera Karahoca
Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary
Chapters on Argumentation, Justification, and Proof
265(12)
Paul Christian Dawkins
Part V Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels
Participation in Argumentation: Teacher and Student Roles Across the Grades
277(10)
Anna Marie Conner
Justification Across the Grade Bands
287(12)
Amy B. Ellis
Megan Staples
Kristen N. Bieda
Lens, Blinders, or Kaleidoscope? Using a Definition of Proof to Make Sense of Classroom Activity
299(14)
Sean Larsen
Tenchita Alzaga Elizondo
Conclusion: Considering the Consequences of Our Conceptions of Argumentation, Justification, and Proof
313(12)
Karl W. Kosko
Kristen N. Bieda
Index 325
Kristen Bieda is an associate professor of Teacher Education and Mathematics Education at Michigan State University. She also holds an appointment as the Associate Director of Mathematics for the CREATE for STEM Institute. Prior to her appointment at Michigan State, she taught mathematics at the middle school, high school and community college levels. Her research interests include understanding how to incorporate mathematical justification into school mathematics, particularly at the middle school level. She is also interested in the design of clinical experiences that support prospective teachers in learning to teach ambitiously. She is currently the subject area leader for secondary mathematics for Michigan States secondary mathematics teacher preparation program.





AnnaMarie Conner is a professor of Mathematics Education in the Mary Frances Early College of Education at the University of Georgia. She investigates teachers beliefs and identity construction during teacher education and how teachers learn to support collective argumentation in mathematics classes. These two lines of research come together in findings describing how teachers beliefs impact their classroom practice with respect to collective argumentation. Dr. Conners work investigates the complex connections between teacher education, teacher characteristics, and teacher practice. She is currently collaborating with secondary mathematics teachers in supporting mathematical arguments as well as investigating how elementary teachers navigate infusing argumentation into integrative STEM instruction.





Karl W. Kosko is an associate professor of Mathematics Education at Kent State University. His work focuses on how mathematical meaning is conveyed, and has addressed classroom argumentation and discourse, multiplicative reasoning, and use of representations of practice in teacher education.





Megan Staples is an associate professor of Mathematics Education in the NeagSchool of Education, University of Connecticut. Her teaching focuses on the preparation of secondary math teachers. Her research focuses on how teachers organize classroom environments that support powerful practices such as collaboration, justification and argumentation. She has served as PI and Co-PI on multiple grants focused on justification and argumentation including the NSF-funded JAGUAR project, and a state-level Math-Science Partnership grant, Bridging Math Practices.