Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Argumentation leads to deeper understanding Many students' interest in mathematics fades as they are asked to solve seemingly endless disconnected problems. Despina Stylianou and Maria Blanton show how building daily instruction around mathematical argumentation can enliven your classroom and re-engage your students. Teaching with Mathematical Argument explores how argumentation-discussing and debating a rich mathematical problem-provides all students a deeper understanding of mathematics. You'll find guidance for: understanding what argumentation is and building a classroom culture that supports it engaging every student in argumentation, not just "strong" or "high performing" students assessing your students' arguments and designing instruction responsive to their learning. The potential to transform student engagement At its core, argumentation helps students delve deeply into foundational mathematical concepts, enhancing their understanding and confidence along the way. Research shows that this type of instruction has the potential to transform student engagement and success in mathematics, and so Despina and Maria argue that mathematical arguments should have a far more central role in teaching and learning than most of us have ever considered. With ideas for structuring discussions and suggested tasks to try, this book will show you how to elevate argumentation in your instruction and harness its power for enhancing student learning.

If you ask students, "Why does that work?" do they know what you're asking and do you know what to listen for in their responses? Do you have images of what mathematical argument looks like in the elementary grades and how to help students learn to engage in this important practice? Do you have so much content to cover that finding time for this kind of work is difficult? But Why Does It Work? offers a simple, efficient teaching model focused on mathematical argument for developing the ability of students to justify their thinking and engage with the reasoning of others. Designed for individuals as well as study groups, this book includes access to classroom-ready instructional sequences, each built on a model supporting students in: noticing relationships across sets of problems, equations, or expressions articulating a claim about what they notice investigating their claim through representations such as manipulatives, diagrams, or story contexts using their representations to demonstrate why a claim must be true or not extending their thinking from one operation to another. Establishing a classroom culture where students gain confidence in their own mathematical voice and learn to value the contributions of their peers is a critical part of this work. The authors tell us, "If the idea underlying a student's reasoning is not made explicit, the opportunity for all students to engage in such thinking is lost." As students become a true community of mathematicians, they heighten each other's understanding by investigating questions, conjectures, and examples together. Enhanced with extensive video showing the instructional sequences in action-along with guiding focus questions and math investigations-But Why Does It Work? is a flexible approach that will help students confidently articulate and defend their reasoning, and share their deep thinking with others.

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

As discrete fields of inquiry, rhetoric and mathematics have long been considered antithetical to each other. That is, if mathematics explains or describes the phenomena it studies with certainty, persuasion is not needed. This volume calls into question the view that mathematics is free of rhetoric. Through nine studies of the intersections between these two disciplines, Arguing with Numbers shows that mathematics is in fact deeply rhetorical. Using rhetoric as a lens to analyze mathematically based arguments in public policy, political and economic theory, and even literature, the essays in this volume reveal how mathematics influences the values and beliefs with which we assess the world and make decisions and how our worldviews influence the kinds of mathematical instruments we construct and accept. In addition, contributors examine how concepts of rhetoric—such as analogy and visuality—have been employed in mathematical and scientific reasoning, including in the theorems of mathematical physicists and the geometrical diagramming of natural scientists. Challenging academic orthodoxy, these scholars reject a math-equals-truth reduction in favor of a more constructivist theory of mathematics as dynamic, evolving, and powerfully persuasive. By bringing these disparate lines of inquiry into conversation with one another, Arguing with Numbers provides inspiration to students, established scholars, and anyone inside or outside rhetorical studies who might be interested in exploring the intersections between the two disciplines. In addition to the editors, the contributors to this volume are Catherine Chaput, Crystal Broch Colombini, Nathan Crick, Michael Dreher, Jeanne Fahnestock, Andrew C. Jones, Joseph Little, and Edward Schiappa.

In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible. (Philosophy)

The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.