Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

lt;p>Kristen Bieda is an Associate Professor of Teacher Education and in the Program in Mathematics Education at Michigan State University. She also holds the appointment of Associate Director for Mathematics for the CREATE for STEM Institute at MSU. Her most recent externally-funded projects involve research on the design and development of field experiences that support prospective teachers in learning to teach, as well as how technology can enhance middle grades students' productive disciplinary engagement in mathematics classrooms. In 2013, Dr. Bieda was awarded the Early Career Publication Award by the AERA SIG-Research in Mathematics Education for her paper "Challenges and Opportunities: Enacting Proof-Related Tasks in Middle School Mathematics" published in Journal for Research in Mathematics Education in 2010. She is currently the outgoing Associate Editor of Mathematics Teacher Educator, a joint publication of NCTM and AMTE focusing on building a knowledge base for the practice of mathematics teacher education.

AnnaMarie Conner is an Associate Professor of Mathematics Education at University of Georgia. She is also an on-site instructor for the University of Georgia Professional Development School District. Dr. Conner's research examines teachers' beliefs about mathematics, teaching, and proof and how this relates to their support for students' arguments in secondary mathematics classes. In her current study, CAREER: Learning To Support Productive Collective Argumentation In Secondary Mathematics Classes, funded by the National Science Foundation, she is following a cohort of secondary mathematics teachers through their on-campus coursework, student teaching, and into their first three years of teaching to examine how they learn to support collective argumentation in mathematics classes. As part of this work, she have been investigating how their identities as teachers of mathematics develop and grow through their experiences. Other current research with colleagues in the College of Education and College of Engineering explores how elementary teachers can support argumentation in their teaching of mathematics, science, and coding in the CALC (Collective Argumentation Learning and Coding) project.

Karl W. Kosko is an Associate Professor of Mathematics Education at Kent State University. His research focuses on how mathematical meaning is conveyed, and the influence of individual and social factors on the conveyance of mathematical meaning. This includes work on mathematical argumentation and multiplicative reasoning, with a particular focus on how a child's multiplicative reasoning interacts with the structure of their argumentative writing. Dr. Kosko has published his work in various peer-reviewed journals including, the Journal of Mathematics Teacher Education, Journal of Teacher Education, Journal of Mathematical Behavior, and others.

Megan Staples is an Associate Professor of Mathematics Education in the Neag School 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. 

Introduction: Conceptualizing Argumentation, Justification, and Proof in Mathematics Education.- Part 1: Argumentation, Justification and Proof in an Elementary Classroom.- Overview of the Elementary Level Data.- Argumentation in the Elementary Grades: The Role of Participants, Tasks, and Tools.- Justification in the Elementary Grades: Justification to Develop and Provide Access to Mathematical Reasoning.- Proof in the Elementary Grades: A Multimodal Approach to Generalization and Proof.- On the Meanings of Argumentation, Justification, and Proof: General Insights from Analyses of Elementary Classroom Episodes.- Part 2: Argumentation, Justification and Proof in a Middle Grades Classroom.- Overview of Middle Level Data.- Argumentation in the Middle Grades: Exploring a Teacher's Support of Collective Argumentation.- Justification in the Middle Grades: A Process of Verification and Sense-Making.- Proof in the Middle Grades: Can we Label Middle Grades Arguments as Proof with a Capital P?.- Argumentation, Justification, and Proof in Middle School: A Rose by Any Other Name.- Part 3: Argumentation, Justification and Proof in High School Mathematics.- Overview of High School Level Data.- Argumentation in the Context of High School Mathematics: Examining Dialogic Aspects of Argumentation.- Justification in the Context of High School Mathematics: Co-Constructing Content and Process.- Proof in the Context of High School Mathematics: A First Approach through Discussion, with Occasions and Missed Opportunities.- Reasoning is in the Eye of the Lens-Holder: Observations Made through the Lenses of Justification, Argumentation, and Proof at the High School Level.- Part 4: Argumentation, Justification and Proof at the Tertiary Level.- Overview of Tertiary Level Data.- Argumentation in the Context of Tertiary Mathematics: A Case Study of Classroom Argumentation and the Role of Instructor Moves.- Justification in the Context of Tertiary Mathematics: Undergraduate Students Exploring the Properties and Relations of the Dihedral Group.- Proof in the Context of Tertiary Mathematics: Undergraduate Inquiry-Based Learning in Abstract Algebra as a Precursor to Mathematical Proof.- Mathematics Educators as Polymaths, Brokers, and Learners: Commentary on the Tertiary Chapters on Argumentation, Justification, and Proof.- Part 5: Lenses on Researching Argumentation, Justification and Proof Across the Grade Levels.- Participation in Argumentation: Teacher and Student Roles across the Grades.- Justification Across the Grade Bands.- Lens, Blinders, or Kaleidoscope? Using a Definition of Proof to Make Sense of Classroom Activity.- Conclusion: Considering the Consequences of Our Conceptions of Argumentation, Justification, and Proof.