Can K-12 Math Teachers Train Students to Make Valid Logical Reasoning?

Valid logic is the mortar that binds all building blocks of critical thinking and analytical thinking. It is the common factor and foundation of three 21st century cognitive skills—critical thinking, analytical thinking and problem solving. According to the Common Core Standards of K-12 mathematics in the United States, proposition and basic first order predicate logic is embedded as a small topic in geometry courses. However, its applications crosscut almost all topics in STEAM (Sciences, Technology, Engineering, Arts and Mathematics) subjects. We inspected how logic is expected to be taught according to the USA K-12 Common Core State Standards and compared with the Singapore curriculum. We found that the difference is not about what should be taught, but how it is taught. The question of this chapter is: How can our K-12 teachers effectively teach logic lessons so that our students can use basic logic to connect concepts and recognize typical logical fallacies? We argued that the answer to that question affects the 21st century skills of the workforce. We hope that our analysis may shed light on the difficult problem in reforming math education and promoting 21st century skills in the workforce.

[1]  J. Michael Spector,et al.  Handbook of Research on Educational Communications and Technology, 3rd Edition , 2012 .

[2]  Daytona Beach,et al.  AC 2008-2721: PROBLEM-SOLVING EXPERIENCE THROUGH LIGHT-DOSE COMPUTATIONAL MATHEMATICAL MODULES FOR ENGINEERING STUDENTS , 2008 .

[3]  J. Michael Spector,et al.  Highly integrated model assessment technology and tools , 2010, CELDA 2008.

[4]  Marguerite Miriam Joseph,et al.  The trivium : the liberal arts of logic, grammar, and rhetoric : understanding the nature and function of language , 2002 .

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

[6]  Dov Dori,et al.  Object-process methodology - a holistic systems paradigm , 2013 .

[7]  Teaching logic: Cracking the hard nut , 2014 .

[8]  Hong Liu,et al.  A Mathematical Modeling Module with System Engineering Approach for Teaching Undergraduate Students to Conquer Complexity , 2009, ICCS.

[9]  G. Harel,et al.  PROOF FRAMES OF PRESERVICE ELEMENTARY TEACHERS , 1989 .

[10]  Angel M. Recio,et al.  Institutional and personal meanings of mathematical proof , 2001 .

[11]  Andreas J. Stylianides,et al.  Proof constructions and evaluations , 2009 .

[12]  Guershon Harel,et al.  Two Dual Assertions: The First on Learning and the Second on Teaching (or Vice Versa) , 1998 .

[13]  Miriam Liston,et al.  The use of video analysis and the Knowledge Quartet in mathematics teacher education programmes , 2015 .

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

[15]  C. Rasmussen,et al.  A framework for characterizing students’ thinking about logical statements and truth tables , 2015 .

[16]  Kosta Dosen,et al.  Models of Deduction* , 2006, Synthese.

[17]  Jonathan Evans,et al.  Human Reasoning: The Psychology Of Deduction , 1993 .

[18]  D. Kahneman.  Thinking, Fast and Slow , 2011 .

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

[20]  Ton de Jong,et al.  Model-facilitated learning , 2007 .

[21]  J. Michael Spector,et al.  Assessing Progress of Learning in Complex Domains , 2010 .

[22]  Susanna S. Epp.  The Role of Logic in Teaching Proof , 2003, Am. Math. Mon..

[23]  Keith Devlin,et al.  The math gene: How mathematical thinking evolved and why numbers are like gossip , 2002 .

[24]  P. Johnson-Laird.  The history of mental models , 2004 .

[25]  Mária Bakó.  Why we need to teach logic and how can we teach it ? , 2022 .

[26]  Eric J. Knuth,et al.  Secondary School Mathematics Teachers' Conceptions of Proof , 2002 .

[27]  J. Michael Spector,et al.  The Handbook of Research on Educational Communications and Technology 3rd ed. , 2008 .