The Role of Logic in Teaching Proof

 Respect for careful use of language 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. What Learning Proof Teaches

[1]  Maurice Eggen,et al.  A transition to advanced mathematics , 1983 .

[2]  Ed Dubinsky,et al.  Introduction to discrete mathematics with ISETL , 1996 .

[3]  Denisse R. Thompson.  Learning and Teaching Indirect Proof. , 1996 .

[4]  C. Raymond Perrault.  Gennaro Chierchia and Sally McConnell-Ginet, Meaning and Grammar: An Introduction to Semantics , 1993, Artif. Intell..

[5]  Ted Hodgson,et al.  Exploration, Explanation, Formalization: A Three-Step Approach to Proof. , 1996 .

[6]  Janice A. Gifford,et al.  Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics , 1997 .

[7]  Robert C. Moore.  Making the transition to formal proof , 1994 .

[8]  Diane Baker,et al.  FOSTERING THE DEVELOPMENT OF MATHEMATICAL THINKING: OBSERVATIONS FROM A PROOFS COURSE , 2004 .

[9]  John F. Lucas.  Introduction to Abstract Mathematics , 1986 .

[10]  J. Barwise,et al.  The language of first-order logic , 1991 .

[11]  Uri Leron,et al.  Students' Use and Misuse of Mathematical Theorems: The Case of Lagrange's Theorem , 1996 .

[12]  Peter Fletcher,et al.  Foundations of Higher Mathematics , 1992 .

[13]  Susanna S. Epp.  Logic and Discrete Mathematics in the Schools , 1992, Discrete Mathematics in the Schools.

[14]  Annie Selden,et al.  Unpacking the logic of mathematical statements , 1995 .

[15]  Raymond M. Smullyan,et al.  What is the name of this book , 1978 .

[16]  Gennaro Chierchia,et al.  Meaning and Grammar: An Introduction to Semantics , 1990 .

[17]  Donald R. Chalice,et al.  HOW TO TEACH A CLASS BY THE MODIFIED MOORE METHOD , 1995 .

[18]  Annie Selden,et al.  The Role of Logic in the Validation of Mathematical Proofs. Technical Report. No. 1999-1. , 1999 .

[19]  Susanna S. Epp.  The Language of Quantification in Mathematics Instruction , 1999 .

[20]  David Smith,et al.  Toward a Lean and Lively Calculus , 1987 .

[21]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[22]  L. Rips.  The Psychology of Proof: Deductive Reasoning in Human Thinking , 1994 .

[23]  Robert Crumley Moore.  College students' difficulties in learning to do mathematical proofs , 1990 .

[24]  J. A. Mercer,et al.  The role of logic , 2021, The Problem of Plurality of Logics.

[25]  David Tall,et al.  The Psychology of Advanced Mathematical Thinking , 2002 .

[26]  H. Simon,et al.  Applications and Misapplications of Cognitive Psychology to Mathematics Education , 2000 .

[27]  Uri Leron.  Heuristic Presentations: The Role of Structuring. , 1985 .

[28]  Fred B. Schneider,et al.  A Logical Approach to Discrete Math , 1993, Texts and Monographs in Computer Science.

[29]  Michael S. Gazzaniga,et al.  The Social Brain: Discovering the Networks of the Mind , 1985 .

[30]  Susanna S. Epp.  A Unified Framework for Proof and Disproof. , 1998 .

[31]  Alan Levine,et al.  THE TRANSITION TO ADVANCED MATHEMATICS , 2000 .

[32]  K. Holyoak,et al.  Pragmatic versus syntactic approaches to training deductive reasoning , 1986, Cognitive Psychology.

[33]  Alan H. Schoenfeld,et al.  Research in Collegiate Mathematics Education. III , 2000 .

[34]  P. Gerdes,et al.  Ethnomathematics and Mathematics Education , 1996 .

[35]  Herbert A. Simon,et al.  Radical constructivism and cognitive psychology , 1998 .

[36]  Kenneth H. Rosen,et al.  Discrete Mathematics and its applications , 2000 .

[37]  S. Senk.  How Well Do Students Write Geometry Proofs , 1985 .

[38]  P. Freire,et al.  A Conversation with Paulo Freire. , 1997 .

[39]  John R. Anderson.  Cognitive Psychology and Its Implications , 1980 .

[40]  Hector J. Levesque,et al.  The Language of First-Order Logic , 2004 .

[41]  Mike Thomas,et al.  Research on Mathematical Proof , 2002 .

[42]  David Tall,et al.  Concept image and concept definition in mathematics with particular reference to limits and continuity , 1981 .

[43]  Daniel Solow,et al.  How to Read and Do Proofs : An Introduction to mathematical Thought Processes/Daniel Solow , 1982 .

[44]  G. Reeke.  Marvin Minsky, The Society of Mind , 1991, Artif. Intell..