Demostrar

Un tema que me interesa particularmente (Antonio) es el de enseñar a demostrar y a comprender demostraciones. A medida que leo me encuentro incorporando aspectos generales de cómo leer matemáticas.

Akkurt, Yasemin Yılmaz, and Soner Durmuş. (2022) Tracing proof schemes: some patterns and new perspectives. JRAMathEdu (Journal of Research and Advances in Mathematics Education) 7, no. 1: 1-16.
T.A. Grundmeier (2022) Assumption and Definition Use in an Inquiry-Based Introduction to Proof Course. PRIMUS 32, no. 1: 1-13.
Paul Christian Dawkins, Dov Zazkis, and John Paul Cook. (2022) How Do Transition to Proof Textbooks Relate Logic, Proof Techniques, and Sets?. PRIMUS 32, no. 1: 14-30.
Alexander Schüler-Meyer. (2022) How transition students relearn school mathematics to construct multiply quantified statements. Educational Studies in Mathematics: 1-21.
Darryl Chamberlain Jr, and Draga Vidakovic. (2021) Cognitive trajectory of proof by contradiction for transition-to-proof students. The Journal of Mathematical Behavior 62: 100849.
Morgan Early Sellers, Kyeong Hah Roh, and Erika David Parr. (2021) Student quantifications as meanings for quantified variables in complex mathematical statements. The Journal of Mathematical Behavior 61: 100802.
Tina Rapke and Xiaoheng Yan. (2021) An Asynchronous Online Forum that Supports Undergraduate Students in Proof Validation. PRIMUS: 1-15.
Samuel D. Reed (2021) Connecting Logic and Proof Techniques: Identifying Learning in an Introduction to Proofs Course. PhD diss., Middle Tennessee State University.
Waluya, S. B., and T. S. N. Asih. (2021) Analysis of problem-solving difficulties at limits of sequences. In Journal of Physics: Conference Series, vol. 1722, no. 1, p. 012033. IOP Publishing.
Michael Aristidou (2020) Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?. Athens Journal of Education 7, no. 1: 99-121.
Olivia M. Carducci (2020) Card trick exercise leads to improved reading of mathematics texts. PRIMUS 30, no. 2: 142-146.
Paul Christian Dawkins, and Kyeong Hah Roh. (2020) Assessing the influence of syntax, semantics, and pragmatics in student interpretation of multiply quantified statements in mathematics. International Journal of Research in Undergraduate Mathematics Education 6, no. 1: 1-22.
Erika J. David, and Dov Zazkis. (2020) Characterizing introduction to proof courses: a survey of US R1 and R2 course syllabi. International Journal of Mathematical Education in Science and Technology 51, no. 3: 388-404.
Morgan Early Sellers. (2020) Students’ Quantifications, Interpretations, and Negations of Complex Mathematical Statements from Calculus. PhD diss., Arizona State University.
Melanie Butler (2019) Preparing Our Students to Read and Understand Mathematics. Journal of Humanistic Mathematics 9, no. 1: 158-177.
Silke Neuhaus and Stefanie Rach (2019) "Proof comprehension of undergraduate students and the relation to individual characteristics." In Eleventh Congress of the European Society for Research in Mathematics Education, no. 31. Freudenthal Group; Freudenthal Institute; ERME.
Leander Kempen and Rolf Biehler (2019) "Fostering first-year pre-service teachers’ proof competencies." ZDM 51, no. 5: 731-746.
Leander Kempen and Rolf Biehler (2019) 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, no. 1: 27-55.
Leander Kempen (2018) "How do pre-service teachers rate the conviction, verification and explanatory power of different kinds of proofs?." In Advances in mathematics education research on proof and proving, pp. 225-237. Springer, Cham.
Annie Selden, John Selden, and Ahmed Benkhalti (2018) Proof frameworks: A way to get started. PRIMUS 28, no. 1: 31-45.
Anja Panse, Lara Alcock, and Matthew Inglis (2018) "Reading proofs for validation and comprehension: An expert-novice eye-movement study." International Journal of Research in Undergraduate Mathematics Education 4, no. 3: 357-375.
Gizem Karaali (2017). An “Unreasonable” Component to a Reasonable Course: Readings for a Transitional Class. Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics: 107-118.
Leander Kempen (2017) "Pre-service teachers’ abilities in constructing different kinds of proofs." In Proceedings of the khdm Conference 2015: Didactics of Mathematics in Higher Education as a Scientific Discipline, pp. 387-391. Kassel: Universität Kassel.
Keith Weber (2015) Effective Proof Reading Strategies for Comprehending Mathematical Proofs. International Journal of Research in Undergraduate Mathematics Education 1, no. 3: 289-314.
Leander Kempen and Rolf Biehler (2015) "Pre-service teachers' perceptions of generic proofs in elementary number theory." In CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, pp. 135-141.
Aaron Weinberg, Tim Fukawa-Connelly and Emilie Wiesner (2015) Characterizing instructor gestures in a lecture in a proof-based mathematics class. Educational Studies in Mathematics 90, no. 3: 233-258.
Anne E. Adams, Jerine Pegg, and Melissa Case. Anticipation guides: Reading for mathematics understanding. The Mathematics Teacher 108, no. 7 (2015): 498-504.
Mark Hodds, Lara Alcock, & Matthew Inglis (2014) Self-Explanation Training Improves Proof Comprehension. Journal for Research in Mathematics Education, 45(1), 62–101. https://doi.org/10.5951/jresematheduc.45.1.0062
Jana T. Beitlich, Andreas Obersteiner, Gabriele Moll, Julio G. Mora Ruano, Jiafang Pan, Sarah Reinhold, Kristina Reiss (2014) The Role of Pictures in Reading Mathematical Proofs: An Eye Movement Study. North American Chapter of the International Group for the Psychology of Mathematics Education. p121-128
Alejandro S. González-Martín, Isabelle Bloch, Viviane Durand-Guerrier and Michela Maschietto (2014) Didactic situations and didactical engineering in university mathematics: Cases from the study of calculus and proof. Research in Mathematics Education 16, no. 2: 117-134.
Rolf Biehler and Leander Kempen (2014) "Using generic proofs as an element for developing proof competencies in the course." Introduction into the culture of mathematics,” in Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue Between Mathematics and Didactics of Mathematics. Oberwolfach Report 56 (2014): 44-45.
Ann Wheeler and Joseph Champion (2013) Students’ Proofs of One-to-One and Onto Properties in Introductory Abstract Algebra. International Journal of Mathematical Education in Science and Technology 44, no. 8: 1107-1116.
Zhihui Fang and Suzanne Coatoam. "Disciplinary literacy: What you want to know about it." Journal of Adolescent & Adult Literacy 56, no. 8 (2013): 627-632.
Juan Pablo Mejia-Ramos, Evan Fuller, Keith Weber, Kathryn Rhoads and Aron Samkoff (2012) An assessment model for proof comprehension in undergraduate mathematics. Educ Stud Math 79, 3–18. https://doi.org/10.1007/s10649-011-9349-7
Tommy Dreyfus, Elena Nardi, and Roza Leikin. "Forms of proof and proving in the classroom." In Proof and proving in mathematics education, pp. 191-213. Springer, Dordrecht, 2012.
Timothy Shanahan and Cynthia Shanahan. "What is disciplinary literacy and why does it matter?." Topics in language disorders 32, no. 1 (2012): 7-18.
Aaron Weinberg, Emilie Wiesner, Bret Benesh, and Timothy Boester. "Undergraduate students' self-reported use of mathematics textbooks." Primus 22, no. 2 (2012): 152-175.
Aaron Weinberg and Emilie Wiesner (2011) Understanding mathematics textbooks through reader-oriented theory. Educational Studies in Mathematics 76, no. 1: 49-63.
Keith Weber and Juan Pablo Mejia-Ramos (2011) Why and how mathematicians read proofs: an exploratory study. Educational Studies in Mathematics 76, no. 3: 329-344.
S. Brown "An investigation of students proof preferences: The case of indirect proofs." In Proceedings of the 14th Annual Conference on Research in Undergraduate Mathematics Education, vol. 4, pp. 31-36. 2011.
Caroline Yoon, Michael OJ Thomas, and Tommy Dreyfus. "Gestures and insight in advanced mathematical thinking." International Journal of Mathematical Education in Science and Technology 42, no. 7 (2011): 891-901.
Robert A. Powers, Cathleen Craviotto, and Richard M. Grassl. "Impact of proof validation on proof writing in abstract algebra." International Journal of Mathematical Education in Science and Technology 41, no. 4 (2010): 501-514.
Brian J. Frasier. "Secondary school mathematics teachers' conceptions of proof." University of Massachusetts Lowell, 2010.
Xiaobao Li (2010) Cognitive analysis of students' errors and misconceptions in variables, equations, and functions." PhD diss., Texas A & M University.
Lane Andrew (2009) "Creating a proof error evaluation tool for use in the grading of student-generated “proofs”." Primus 19, no. 5: 447-462.
P. Karen Murphy, Ian AG Wilkinson, Anna O. Soter, Maeghan N. Hennessey, and John F. Alexander. "Examining the effects of classroom discussion on students’ comprehension of text: A meta-analysis." Journal of educational psychology 101, no. 3 (2009): 740.
Margaret G. McKeown, Isabel L. Beck, and Ronette GK Blake. "Rethinking reading comprehension instruction: A comparison of instruction for strategies and content approaches." Reading Research Quarterly 44, no. 3 (2009): 218-253.
Guershon Harel and Larry Sowder. Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning 2 (2007): 805-842.
Kimber Hershberger, Carla Zembal-Saul, and Mary L. Starr. "Evidence helps the KWL get a KLEW." Science and Children 43, no. 5 (2006): 50-53.
Li, X., 2010. Cognitive analysis of students' errors and misconceptions in variables, equations, and functions (Doctoral dissertation, Texas A & M University).
Lara Alcock and Keith Weber. "Proof validation in real analysis: Inferring and checking warrants." The Journal of Mathematical Behavior 24, no. 2 (2005): 125-134.
Andreas J. Stylianides, Gabriel J. Stylianides, and George N. Philippou. "Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts." Educational Studies in Mathematics 55, no. 1 (2004): 133-162.
Annie Selden and John Selden (2003) Validations of Proofs Considered as Texts: Can Undergraduates Tell Whether an Argument Proves a Theorem?. Journal for research in mathematics education, 34(1), 4-36.
Eric J. Knuth "Secondary school mathematics teachers' conceptions of proof." Journal for research in mathematics education 33, no. 5 (2002): 379-405.
Keith Weber. "Student difficulty in constructing proofs: The need for strategic knowledge." Educational studies in mathematics 48, no. 1 (2001): 101-119.
Almeida, Dennis. "Pupils' proof potential." International Journal of Mathematical Education in Science and Technology 32, no. 1 (2001): 53-60.
Suzanne E. Wade and Elizabeth Birr Moje. "The role of text in classroom learning: Beginning an online dialogue." Reading Online 5, no. 4 (2001): n4.
Tabitha TY Mingus and Richard M. Grassl. "Preservice teacher beliefs about proofs." School Science and Mathematics 99, no. 8 (1999): 438-444.
Guershon Harel and Larry Sowder. "Students’ proof schemes: Results from exploratory studies." American Mathematical Society 7 (1998): 234-283.
Carolyn A. Maher and Amy M. Martino. "The development of the idea of mathematical proof: A 5-year case study." Journal for Research in Mathematics Education 27, no. 2 (1996): 194-214.
Gila Hanna. "Challenges to the importance of proof." For the learning of Mathematics 15, no. 3 (1995): 42-49.
Carl C. Cowen. Teaching and testing mathematics reading. The American Mathematical Monthly 98, no. 1 (1991): 50-53.
Michael D. De Villiers. "The role and function of proof in mathematics." Pythagoras 24 (1990): 17-24.
Annie Selden and John Selden. "Errors and misconceptions in college level theorem proving." In Proceedings of the second international seminar on misconceptions and educational strategies in science and mathematics, vol. 3, pp. 457-470. Cornell University, 1987.
Donna M. Ogle. "KWL: A teaching model that develops active reading of expository text." The reading teacher 39, no. 6 (1986): 564-570.

Victor Byers. "Why study the history of mathematics?." International Journal of Mathematical Education in Science and Technology 13, no. 1 (1982): 59-66.

Bell, A.W., 1976. A study of pupils' proof-explanations in mathematical situations. Educational studies in mathematics, pp.23-40.

Videos

Charla de Keith Weber.

Otros

Proof Comprehension Research Group.