Math Proofs Explained
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Explanation and Proof in Mathematics
Author: Gila Hanna
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-12-04
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Mathematics Explained for Primary Teachers
To help teachers confidently teach mathematics in primary school, this book develops their understanding of mathematical concepts and processes and how children learn them.
Mathematics 436 - Finely Explained
This book deals with the geometric aspects of the Quebec mathematics course numbered 436. The history of this course depicts a difficult and confusing path with results measured in failures and frustration. The course is meant for students expecting to go on to studies in the technical and scientific fields. Unfortunately, there has been a dearth of material to explain the course. The reality is that it has been a source of confusion for administrators, teachers, parents, and most unfortunately students. Rob Shutler has attempted to leave the fighting and finger pointing behind and concentrate on explaining the material. The book follows a traditional path and provides painstaking detail to explain each topic and provide a plethora of examples. The underlying feature of this book is its secure connection to the provincial exam that provides the final and ultimately deciding evaluation for students. The book could be used as a textbook for classroom use, or as a stand alone resource for a committed, besieged student. It is an excellent foundation resource for any mathematics teacher.