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Mathematical Thinking and Learning Volume 10, 2008 - Issue 2
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Article

Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning

Gabriel J. Stylianides University of Pittsburgh—Pennsylvania, Correspondence[email protected]
&
Andreas J. Stylianides University of Oxford—United Kingdom,
Pages 103-133 | Published online: 25 Apr 2008

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Yusuke Shinno & Taro Fujita. (2022) Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach. International Journal of Mathematical Education in Science and Technology 53:12, pages 3326-3351.
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Maria Blanton, Angela Murphy Gardiner, Ingrid Ristroph, Ana Stephens, Eric Knuth & Rena Stroud. (2022) Progressions in young learners’ understandings of parity arguments. Mathematical Thinking and Learning 0:0, pages 1-32.
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Yavuz Karpuz & Ercan Atasoy. (2020) High school mathematics teachers’ content knowledge of the logical structure of proof deriving from figural-concept interaction in geometry. International Journal of Mathematical Education in Science and Technology 51:4, pages 585-603.
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Ioannis Kanellos, Elena Nardi & Irene Biza. (2018) Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof. Mathematical Thinking and Learning 20:4, pages 277-294.
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AnnaMarie Conner, Laura M. Singletary, Ryan C. Smith, Patty Anne Wagner & Richard T. Francisco. (2014) Identifying Kinds of Reasoning in Collective Argumentation. Mathematical Thinking and Learning 16:3, pages 181-200.
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Konstantinos Flegas & Lemonidis Charalampos. (2013) Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students. Canadian Journal of Science, Mathematics and Technology Education 13:1, pages 70-89.
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AndreasJ. Stylianides & Thabit Al-Murani. (2010) Can a proof and a counterexample coexist? Students' conceptions about the relationship between proof and refutation. Research in Mathematics Education 12:1, pages 21-36.
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Gabriel J. Stylianides. (2009) Reasoning-and-Proving in School Mathematics Textbooks. Mathematical Thinking and Learning 11:4, pages 258-288.
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Elena Nardi, Ioannis Kanellos & Irene Biza. Nascent deductive proof schemes and proof readiness in adolescence. Research in Mathematics Education 0:0, pages 1-22.
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Articles from other publishers (32)

Maria Chimoni, Demetra Pitta-Pantazi & Constantinos Christou. (2023) Unfolding algebraic thinking from a cognitive perspective. Educational Studies in Mathematics 114:1, pages 89-108.
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Ieva Kilienė & Rimas Norvaiša. (2022) Solving word problems with reasoned judgement*. Lithuanian Mathematical Journal 62:4, pages 467-480.
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Andreas J. Stylianides & Gabriel J. Stylianides. (2022) Introducing students and prospective teachers to the notion of proof in mathematics. The Journal of Mathematical Behavior 66, pages 100957.
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Freydis Vogel, Ingo Kollar, Frank Fischer, Kristina Reiss & Stefan Ufer. (2022) Adaptable scaffolding of mathematical argumentation skills: The role of self-regulation when scaffolded with CSCL scripts and heuristic worked examples. International Journal of Computer-Supported Collaborative Learning 17:1, pages 39-64.
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Andreas J. Stylianides, Kotaro Komatsu, Keith Weber & Gabriel J. Stylianides. 2022. Handbook of Cognitive Mathematics. Handbook of Cognitive Mathematics 727 761 .
David A. Yopp, Rob Ely, Anne E. Adams & Annelise W. Nielsen. 2022. Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof. Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof 109 127 .
Andreas J. Stylianides, Kotaro Komatsu, Keith Weber & Gabriel J. Stylianides. 2021. Handbook of Cognitive Mathematics. Handbook of Cognitive Mathematics 1 36 .
Tuğba ÖZTÜRK & Damla KUTLU. (2021) Türkiye’de İspat Üzerine Yapılan Çalışmaların Analizi: Bir Meta-Sentez Çalışması. Pamukkale University Journal of Education.
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Tijs Kleemans & Eliane Segers. (2020) Linguistic precursors of advanced math growth in first-language and second-language learners. Research in Developmental Disabilities 103, pages 103661.
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Susana Carreira, Nélia Amado & Hélia Jacinto. (2020) Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning. Education Sciences 10:6, pages 169.
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Muhammed Fatih DOĞAN. (2020) Pre-Service Teachers’ Criteria for Evaluating Mathematical Arguments That Include Generic Examples. International Journal of Contemporary Educational Research 7:1, pages 267-279.
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Jonathan Alberto Cervantes-Barraza, Antonia Hernandez Moreno & Chepina Rumsey. (2020) Promoting mathematical proof from collective argumentation in primary school. School Science and Mathematics 120:1, pages 4-14.
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Azita Manouchehri & Bharath Sriraman. 2020. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 520 529 .
Zehra TOPRAK & Mehmet Fatih ÖZMANTAR. (2019) A Comparative Analysis of Turkey and Singapore 5th Grade Mathematics Textbooks in Terms of Worked Examples and Questions. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10:2, pages 539-566.
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Maryam Alqassab, Jan-Willem Strijbos & Stefan Ufer. (2018) The impact of peer solution quality on peer-feedback provision on geometry proofs: Evidence from eye-movement analysis. Learning and Instruction 58, pages 182-192.
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Maria Chimoni, Demetra Pitta-Pantazi & Constantinos Christou. (2018) Examining early algebraic thinking: insights from empirical data. Educational Studies in Mathematics 98:1, pages 57-76.
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Tijs Kleemans, Eliane Segers & Ludo Verhoeven. (2018) Role of linguistic skills in fifth-grade mathematics. Journal of Experimental Child Psychology 167, pages 404-413.
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Azita Manouchehri & Bharath Sriraman. 2018. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 1 10 .
Jazim Jazim, Rahmad Bustanul Anwar & Dwi Rahmawati. (2017) The Use of Mathematical Module Based on Constructivism Approach as Media to Implant the Concept of Algebra Operation. International Electronic Journal of Mathematics Education 12:3, pages 579-583.
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David A. Yopp. (2017) Eliminating counterexamples: A Grade 8 student’s learning trajectory for contrapositive proving. The Journal of Mathematical Behavior 45, pages 150-166.
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Paul Christian Dawkins & Kyeong Hah Roh. (2016) Promoting Metalinguistic and Metamathematical Reasoning in Proof-Oriented Mathematics Courses: a Method and a Framework. International Journal of Research in Undergraduate Mathematics Education 2:2, pages 197-222.
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Olugbenga Oluwagbemi, Folakemi Oluwagbemi & Chisom Ughamadu. (2016) Android Mobile Informatics Application for some Hereditary Diseases and Disorders (AMAHD): A complementary framework for medical practitioners and patients. Informatics in Medicine Unlocked 2, pages 38-69.
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Nélia Amado, Juan Sanchez & Jorge Pinto. (2015) A Utilização do Geogebra na Demonstração Matemática em Sala de Aula: o estudo da reta de Euler. Bolema: Boletim de Educação Matemática 29:52, pages 637-657.
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Emine Nur (UNVEREN) Bilgic & Devrim Uzel. (2014) The Attitudes of the Elementary School Mathematics Teacher Candidates towards Proof in the Mathematical Modelling Proccess. Procedia - Social and Behavioral Sciences 116, pages 1083-1087.
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Gabriel J. Stylianides. (2014) Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research 64, pages 63-70.
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Jinfa Cai & Michelle Cirillo. (2014) What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research 64, pages 132-140.
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Gabriel J. Stylianides, Andreas J. Stylianides & Leah N. Shilling-Traina. (2013) PROSPECTIVE TEACHERS’ CHALLENGES IN TEACHING REASONING-AND-PROVING. International Journal of Science and Mathematics Education 11:6, pages 1463-1490.
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AnnaMarie Conner. (2013) Authentic Argumentation With Prospective Secondary Teachers: The Case of 0.999…. Mathematics Teacher Educator 1:2, pages 172-180.
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Andreas J. Stylianides. (2011) Towards a comprehensive knowledge package for teaching proof: A focus on the misconception that empirical arguments are proofs. Pythagoras 32:1.
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Michal Ayalon & Ruhama Even. (2010) MATHEMATICS EDUCATORS’ VIEWS ON THE ROLE OF MATHEMATICS LEARNING IN DEVELOPING DEDUCTIVE REASONING. International Journal of Science and Mathematics Education 8:6, pages 1131-1154.
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Eleanor K. Seaton. (2009) The Influence of Cognitive Development and Perceived Racial Discrimination on the Psychological Well-being of African American Youth. Journal of Youth and Adolescence 39:6, pages 694-703.
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Andreas J. Stylianides & Gabriel J. Stylianides. (2009) Proof constructions and evaluations. Educational Studies in Mathematics 72:2, pages 237-253.
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