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Mathematical Thinking and Learning Volume 12, 2010 - Issue 4
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Articles

Mathematics Majors' Perceptions of Conviction, Validity, and Proof

Keith Weber Rutgers UniversityCorrespondence[email protected]
Pages 306-336 | Published online: 05 Oct 2010

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Alison G. Lynch, Elise Lockwood & Amy B. Ellis. (2022) Comprehensive example generation: mathematicians’ uses of examples when developing conjectures. Research in Mathematics Education 0:0, pages 1-23.
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Sarah Erickson & Elise Lockwood. (2022) Experienced provers’ uses of contexts while engaging in combinatorial proof of binomial identities. International Journal of Mathematical Education in Science and Technology 0:0, pages 1-30.
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David Miller, Joshua Case & Ben Davies. (2022) Students' beliefs on empirical arguments and mathematical proof in an introduction to proof class. International Journal of Mathematical Education in Science and Technology 0:0, pages 1-22.
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T. A. Grundmeier, D. Retsek, A. Berg, S. Mann & A. Hamlin Prieto. (2022) Assumption and Definition Use in an Inquiry-Based Introduction to Proof Course. PRIMUS 32:1, pages 1-13.
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Martha B. Makowski. (2021) The written and oral justifications of mathematical claims of middle school pre-service teachers. Research in Mathematics Education 23:1, pages 63-84.
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David Miller & Todd CadwalladerOlsker. (2020) Investigating undergraduate students’ view of and consistency in choosing empirical and deductive arguments. Research in Mathematics Education 22:3, pages 249-264.
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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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Keith Weber, Kristen Lew & Juan Pablo Mejía-Ramos. (2020) Using Expectancy Value Theory to Account for Individuals’ Mathematical Justifications. Cognition and Instruction 38:1, pages 27-56.
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Igor’ Kontorovich. (2019) Why do students not check their solutions to mathematical problems? A field-based hypothesis on epistemological status. International Journal of Mathematical Education in Science and Technology 50:7, pages 1050-1062.
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Ruthmae Sears. (2019) Proof schemes of pre-service middle and secondary mathematics teachers. Investigations in Mathematics Learning 11:4, pages 258-274.
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Keith Weber & Jennifer Czocher. (2019) On mathematicians’ disagreements on what constitutes a proof. Research in Mathematics Education 21:3, pages 251-270.
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Daniel R. Jordan. (2019) Proof-Writing Workshops. PRIMUS 29:2, pages 111-123.
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Christine A. Herrera, Terrance McCabe, Sharon Strictland & Alexander White. (2018) Let’s Draw a Picture. PRIMUS 28:1, pages 46-56.
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Juan Pablo Mejía-Ramos, Kristen Lew, Jimmy de la Torre & Keith Weber. (2017) Developing and validating proof comprehension tests in undergraduate mathematics. Research in Mathematics Education 19:2, pages 130-146.
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Keith Weber, Matthew Inglis & Juan Pablo Mejia-Ramos. (2014) How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition. Educational Psychologist 49:1, pages 36-58.
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Keith Weber & Juan Pablo Mejia-ramos. (2014) Mathematics majors’ beliefs about proof reading. International Journal of Mathematical Education in Science and Technology 45:1, pages 89-103.
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Keith Weber. (2013) On the sophistication of naïve empirical reasoning: factors influencing mathematicians' persuasion ratings of empirical arguments. Research in Mathematics Education 15:2, pages 100-114.
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Keith Weber. (2012) Mathematicians’ perspectives on their pedagogical practice with respect to proof. International Journal of Mathematical Education in Science and Technology 43:4, pages 463-482.
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Articles from other publishers (71)

Fatma Nur AKTAŞ. (2023) The Roles of Argumentation Structures for The Conviction of Proof Types. Acta Didactica Napocensia 16:1, pages 66-81.
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Orly Buchbinder & Sharon McCrone. (2023) Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving. ZDM – Mathematics Education 55:4, pages 779-792.
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Lara Alcock & Nina Attridge. (2023) Refutations and Reasoning in Undergraduate Mathematics. International Journal of Research in Undergraduate Mathematics Education.
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Katharina Kirsten & Gilbert Greefrath. (2023) Proof construction and in-process validation – Validation activities of undergraduates in constructing mathematical proofs. The Journal of Mathematical Behavior 70, pages 101064.
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Alon Pinto & Boris Koichu. (2022) Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition. Educational Studies in Mathematics 113:1, pages 147-164.
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K. Ann Renninger, Allison L. Gantt & D. Abram Lipman. (2022) Comprehension of argumentation in mathematical text: what is the role of interest?. ZDM – Mathematics Education 55:2, pages 371-384.
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Kathleen Melhuish, Kristen Vroom, Kristen Lew & Brittney Ellis. (2022) Operationalizing authentic mathematical proof activity using disciplinary tools. The Journal of Mathematical Behavior 68, pages 101009.
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Muhammed Fatih Dogan. (2022) 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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Orly Buchbinder, Sharon McCrone, Michelle Capozzoli & Rebecca Butler. (2022) Mathematical Knowledge for Teaching Proof: Comparing Secondary Teachers, Pre-Service Secondary Teachers, and Undergraduate Majors. International Journal of Research in Undergraduate Mathematics Education.
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Anita Valenta & Ole Enge. (2022) Teaching practices promoting meta-level learning in work on exploration-requiring proving tasks. The Journal of Mathematical Behavior 67, pages 100997.
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Scott Viteri & Simon DeDeo. (2022) Epistemic phase transitions in mathematical proofs. Cognition 225, pages 105120.
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Tuğba Öztürk & Bülent Güven. (2022) A study on pre-service mathematics teachers’ criteria of proof evaluation. LUMAT: International Journal on Math, Science and Technology Education 10:1.
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Kristen Vroom & Tenchita Alzaga Elizondo. (2022) Students’ Thinking about the Structure of Constructive Existence Proofs. International Journal of Research in Undergraduate Mathematics Education.
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Keith Gallagher & Nicole Engelke Infante. (2021) A Case Study of Undergraduates’ Proving Behaviors and Uses of Visual Representations in Identification of Key Ideas in Topology. International Journal of Research in Undergraduate Mathematics Education 8:1, pages 176-210.
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Yi-Yin Ko & Mary K. Rose. (2021) Are self-constructed and student-generated arguments acceptable proofs? Pre-service secondary mathematics teachers’ evaluations. The Journal of Mathematical Behavior 64, pages 100912.
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Lia Budi Tristanti & Toto Nusantara. (2021) Identifying Students’ Mathematical Argumentation Competence in Solving Cubes and Pyramid Problems. Journal of Physics: Conference Series 1933:1, pages 012118.
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Warli, P Rahayu & I Cintamulya. (2021) Scaffolding worksheets as a medium of student learning during the COVID-19 pandemic in constructing proof of group problems. Journal of Physics: Conference Series 1832:1, pages 012055.
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Ben Davies, Lara Alcock & Ian Jones. (2021) What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views. The Journal of Mathematical Behavior 61, pages 100824.
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Lia Budi Tristanti & Toto Nusantara. (2021) Improving Students’ Mathematical Argumentation Skill Through Infusion Learning Strategy. Journal of Physics: Conference Series 1783:1, pages 012103.
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Warli, P Rahayu & I Cintamulya. (2021) Scaffolding as a strategy to help student difficulties in proving group problems. Journal of Physics: Conference Series 1776:1, pages 012037.
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Mohamad Waluyo & Tibor Vidákovich. (2021) Assessment of Students’ Mathematical Proof Comprehension: Gender and Year Level Background. Journal of Physics: Conference Series 1776:1, pages 012017.
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Keith Weber & Matthew Inglis. 2020. Handbook of the History and Philosophy of Mathematical Practice. Handbook of the History and Philosophy of Mathematical Practice 1 28 .
Ben Davies, Lara Alcock & Ian Jones. (2020) Comparative judgement, proof summaries and proof comprehension. Educational Studies in Mathematics 105:2, pages 181-197.
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Pradip Narain & Andreas J. Stylianides. (2020) Demystifying Proofs Through Structured Interaction: A Case Study of One Instructor’s Teaching in an Undergraduate Analysis Course. Journal of Educational Research in Mathematics 30:S, pages 69-90.
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Kristen Lew, Keith Weber & Juan Pablo Mejía Ramos. (2020) Do Generic Proofs Improve Proof Comprehension?. Journal of Educational Research in Mathematics 30:S, pages 229-248.
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Leander Kempen & Rolf Biehler. (2020) Using Figurate Numbers in Elementary Number Theory – Discussing a ‘Useful’ Heuristic From the Perspectives of Semiotics and Cognitive Psychology. Frontiers in Psychology 11.
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Elise Lockwood, John S. Caughman & Keith Weber. (2020) An essay on proof, conviction, and explanation: multiple representation systems in combinatorics. Educational Studies in Mathematics 103:2, pages 173-189.
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Jennifer A. Czocher & Keith Weber. (2020) Proof as a Cluster Category. Journal for Research in Mathematics Education 51:1, pages 50-74.
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Warli, I Cintamulya & P Rahayu. (2020) Scaffolding process based on students diagnostic difficulties in proving group problems by using mathematics mapping. Journal of Physics: Conference Series 1422:1, pages 012012.
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Recai AKKUŞ. (2019) Change in the Level of Justification in Problem Solving Over TimeProblem Çözmede Gerekçelendirme Seviyelerinin Zamana Göre Değişimi. Kastamonu Eğitim Dergisi 27:4, pages 1481-1494.
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Fuat, T Nusantara, E B Irawan & S Irawati. (2019) Students’ mathematical conviction in Mathematics proof. IOP Conference Series: Earth and Environmental Science 243, pages 012133.
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Leander Kempen & Rolf Biehler. (2018) Pre-Service Teachers’ Benefits from an Inquiry-Based Transition-to-Proof Course with a Focus on Generic Proofs. International Journal of Research in Undergraduate Mathematics Education 5:1, pages 27-55.
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Orly Buchbinder & Orit Zaslavsky. (2019) Strengths and inconsistencies in students’ understanding of the roles of examples in proving. The Journal of Mathematical Behavior 53, pages 129-147.
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Andreas J. Stylianides. (2018) Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation. Review of Education 7:1, pages 156-182.
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Emine Çontay & Asuman Duatepe Paksu. (2018) The Proof Schemes of Preservice Middle School Mathematics Teachers and Investigating the Expressions Revealing These Schemes. Turkish Journal of Computer and Mathematics Education (TURCOMAT).
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Ashley L. Suominen, AnneMarie Conner & Hyejin Park. (2018) Prospective mathematics teachers’ expectations for middle grades students’ arguments. School Science and Mathematics 118:6, pages 218-231.
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Anja Panse, Lara Alcock & Matthew Inglis. (2018) Reading Proofs for Validation and Comprehension: an Expert-Novice Eye-Movement Study. International Journal of Research in Undergraduate Mathematics Education 4:3, pages 357-375.
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Sean P. Yee, Justin D. Boyle, Yi-Yin (Winnie) Ko & Sarah K. Bleiler-Baxter. (2018) Effects of constructing, critiquing, and revising arguments within university classrooms. The Journal of Mathematical Behavior 49, pages 145-162.
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Alon Pinto & Ronnie Karsenty. (2018) From course design to presentations of proofs: How mathematics professors attend to student independent proof reading. The Journal of Mathematical Behavior 49, pages 129-144.
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David Miller, Nicole Infante & Keith Weber. (2018) How mathematicians assign points to student proofs. The Journal of Mathematical Behavior 49, pages 24-34.
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Kotaro Komatsu, Tomoyuki Ishikawa & Akito Narazaki. 2018. Advances in Mathematics Education Research on Proof and Proving. Advances in Mathematics Education Research on Proof and Proving 131 144 .
Keith Weber & Paul Christian Dawkins. 2018. Advances in Mathematics Education Research on Proof and Proving. Advances in Mathematics Education Research on Proof and Proving 69 82 .
Orly Buchbinder. 2018. Scripting Approaches in Mathematics Education. Scripting Approaches in Mathematics Education 89 113 .
Emily Cilli-Turner. (2017) Impacts of inquiry pedagogy on undergraduate students conceptions of the function of proof. The Journal of Mathematical Behavior 48, pages 14-21.
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Somali Roy, Matthew Inglis & Lara Alcock. (2017) Multimedia resources designed to support learning from written proofs: an eye-movement study. Educational Studies in Mathematics 96:2, pages 249-266.
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Kotaro Komatsu, Keith Jones, Takehiro Ikeda & Akito Narazaki. (2017) Proof validation and modification in secondary school geometry. The Journal of Mathematical Behavior 47, pages 1-15.
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Alison G. Lynch & Elise Lockwood. (2017) A comparison between mathematicians’ and students’ use of examples for conjecturing and proving. The Journal of Mathematical Behavior.
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Zekiye Ozgur, Amy B. Ellis, Rebecca Vinsonhaler, Muhammed Fatih Dogan & Eric Knuth. (2017) From examples to proof: Purposes, strategies, and affordances of example use. The Journal of Mathematical Behavior.
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Samuel Otten, Sarah K. Bleiler-Baxter & Christopher Engledowl. (2017) Authority and whole-class proving in high school geometry: The case of Ms. Finley. The Journal of Mathematical Behavior 46, pages 112-127.
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Paul Christian Dawkins & Keith Weber. (2016) Values and norms of proof for mathematicians and students. Educational Studies in Mathematics 95:2, pages 123-142.
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Esra Demiray & Mine Işıksal Bostan. (2015) An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs, Methods Used, and Reasons for Invalid Arguments. International Journal of Science and Mathematics Education 15:1, pages 109-130.
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Dov Zazkis, Keith Weber & Juan Pablo Mejía-Ramos. (2016) Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context. Educational Studies in Mathematics 93:2, pages 155-173.
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Kamila Jooganah & Julian S. Williams. (2016) Contradictions between and within school and university activity systems helping to explain students’ difficulty with advanced mathematics. Teaching Mathematics and its Applications 35:3, pages 159-171.
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Elise Lockwood, Amy B. Ellis & Alison G. Lynch. (2016) Mathematicians’ Example-Related Activity when Exploring and Proving Conjectures. International Journal of Research in Undergraduate Mathematics Education 2:2, pages 165-196.
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Bo Zhen, Keith Weber & Juan Pablo Mejia-Ramos. (2015) Mathematics Majors’ Perceptions of the Admissibility of Graphical Inferences in Proofs. International Journal of Research in Undergraduate Mathematics Education 2:1, pages 1-29.
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Keith Weber. (2015) Effective Proof Reading Strategies for Comprehending Mathematical Proofs. International Journal of Research in Undergraduate Mathematics Education 1:3, pages 289-314.
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Aron Samkoff & Keith Weber. (2015) Lessons learned from an instructional intervention on proof comprehension. The Journal of Mathematical Behavior 39, pages 28-50.
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David S. Dickerson & Helen M. Doerr. (2014) High school mathematics teachers’ perspectives on the purposes of mathematical proof in school mathematics. Mathematics Education Research Journal 26:4, pages 711-733.
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Stacy A. Brown. (2014) On skepticism and its role in the development of proof in the classroom. Educational Studies in Mathematics 86:3, pages 311-335.
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Sarah K. Bleiler, Denisse R. Thompson & Milé Krajčevski. (2013) Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education 17:2, pages 105-127.
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Hye Mi Oh & Oh Nam Kwon. (2014) An investigation in learnability of counter-examples in secondary school mathematics textbooks. The Mathematical Education 53:1, pages 41-55.
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Juan Pablo Mejia-Ramos & Keith Weber. (2013) Why and how mathematicians read proofs: further evidence from a survey study. Educational Studies in Mathematics 85:2, pages 161-173.
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Mark Hodds, Lara Alcock & Matthew Inglis. (2014) Self-Explanation Training Improves Proof Comprehension. Journal for Research in Mathematics Education 45:1, pages 62-101.
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Hye Mi Oh & Oh Nam Kwon. (2013) The Study on the Process of Undergraduate Students' Generating Counter-Examples and Proposing True Statements. Journal for History of Mathematics 26:5_6, pages 401-416.
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Andrew Aberdein. (2013) Mathematical Wit and Mathematical Cognition. Topics in Cognitive Science 5:2, pages 231-250.
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Keith Weber & Juan Pablo Mejia-Ramos. (2013) The Influence of Sources in the Reading of Mathematical Text. Journal of Literacy Research 45:1, pages 87-96.
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Yi-Yin Ko & Eric J. Knuth. (2013) Validating proofs and counterexamples across content domains: Practices of importance for mathematics majors. The Journal of Mathematical Behavior 32:1, pages 20-35.
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Matthew Inglis & Juan Pablo Mejía-Ramos. 2013. The Argument of Mathematics. The Argument of Mathematics 101 117 .
Richard Lehrer & Richard Lesh. 2012. Handbook of Psychology, Second Edition. Handbook of Psychology, Second Edition.
Matthew Inglis & Lara Alcock. (2012) Expert and Novice Approaches to Reading Mathematical Proofs. Journal for Research in Mathematics Education 43:4, pages 358-390.
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Orit Zaslavsky, Susan D. Nickerson, Andreas J. Stylianides, Ivy Kidron & Greisy Winicki-Landman. 2012. Proof and Proving in Mathematics Education. Proof and Proving in Mathematics Education 215 229 .

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