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Relevant bibliographies by topics / Mathematical argumentation

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Academic literature on the topic 'Mathematical argumentation'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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Journal articles on the topic "Mathematical argumentation"

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Rumsey, Chepina, and Cynthia W. Langrall. "Promoting Mathematical Argumentation." Teaching Children Mathematics 22, no. 7 (March 2016): 412–19. http://dx.doi.org/10.5951/teacchilmath.22.7.0412.

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Zhou, Da, Jinqing Liu, and Jian Liu. "Mathematical Argumentation Performance of Sixth-Graders in a Chinese Rural Class." International Journal of Education in Mathematics, Science and Technology 9, no. 2 (March 7, 2021): 213–35. http://dx.doi.org/10.46328/ijemst.1177.

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Researchers have established that solid argumentation is essential for developing, establishing and communicating mathematical knowledge, which attracted substantial attention from researchers, but few have simultaneously investigated the argumentation performance of sixth-graders and their teacher’s potential influence in Chinese rural classrooms. In this pilot study, 33 sixth graders in a Chinese rural class were examined, and the math teacher who had been teaching them for three years was interviewed. Findings related to the students’ performance revealed the need to improve their argumentation competency, including using more diverse modes of arguments and argument representation as well as developing more advanced types of arguments (e.g., deductive argumentation). The interview finding with the math teacher indicated that the teacher’s perception and knowledge might impact students’ learning opportunities to conduct argumentation and, therefore, may influence students’ argumentative performance. Implications and limitations of this study is discussed at the end.

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Knudsen, Jennifer, Teresa Lara-Meloy, Harriette Stallworth Stevens, and Daisy Wise Rutstein. "Advice for Mathematical Argumentation." Mathematics Teaching in the Middle School 19, no. 8 (April 2014): 494–500. http://dx.doi.org/10.5951/mathteacmiddscho.19.8.0494.

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Carrascal, Begoña. "Proofs, Mathematical Practice and Argumentation." Argumentation 29, no. 3 (January 1, 2015): 305–24. http://dx.doi.org/10.1007/s10503-014-9344-0.

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Corneli, Joseph, Ursula Martin, Dave Murray-Rust, Gabriela Rino Nesin, and Alison Pease. "Argumentation Theory for Mathematical Argument." Argumentation 33, no. 2 (January 4, 2019): 173–214. http://dx.doi.org/10.1007/s10503-018-9474-x.

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Salazar-Torres, J., M. Vera, Y. Contreras, E. Gelvez-Almeida, O. Valbuena, D. Barrera, and O. Rincon. "Mathematical argumentation in the classroom." Journal of Physics: Conference Series 1408 (November 2019): 012023. http://dx.doi.org/10.1088/1742-6596/1408/1/012023.

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Singletary, Laura M., and AnnaMarie Conner. "Focusing on Mathematical Arguments." Mathematics Teacher 109, no. 2 (September 2015): 143–47. http://dx.doi.org/10.5951/mathteacher.109.2.0143.

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The importance of collective argumentation is highlighted in the Common Core's third Standard for Mathematical Practice, which states that students should be able to “construct viable arguments and critique the reasoning of others” (CCSSI 2010, p. 6). Researchers have described what productive mathematical argumentation might entail, including students participating in particular ways (Weber et al. 2008; White 2003); classroom environments where sense making is valued (Weber et al. 2008); and argumentation that progresses from intuition toward deductive reasoning (Prusak, Hershkowitz, and Schwarz 2011).

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Kosko, Karl W., and Belinda S. Zimmerman. "Emergence of argument in children’s mathematical writing." Journal of Early Childhood Literacy 19, no. 1 (June 12, 2017): 82–106. http://dx.doi.org/10.1177/1468798417712065.

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Recent educational policy documents have encouraged engaging students in mathematical argumentation via discussion and writing. Most recently in the U.S., the Common Core State Standards recommend that children construct viable arguments and critique the reasoning of others. One often advocated means of engaging students in this mathematical practice is mathematical writing. This requires students to develop mathematical writing that demonstrates careful analysis, a command of sequence, and a level of detail considered fundamental for constructing effective argumentative, persuasive and informative mathematical explanations. However, there is currently little to no research examining how mathematical writing develops in elementary grades. The present study examined K-3 students’ mathematical writing using modified Piagetian tasks. Incorporating elements of Toulmin’s argumentation scheme, a set of classifications for mathematical writing emerged from K-3 student samples. Further, these classifications are sequential, with strong statistical correlations associated with children’s grade levels. The findings indicate a potentially useful set of classification schemes for identifying children’s writing and examining how such writing develops in early grades.

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Čyras, Kristijonas, Dimitrios Letsios, Ruth Misener, and Francesca Toni. "Argumentation for Explainable Scheduling." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 2752–59. http://dx.doi.org/10.1609/aaai.v33i01.33012752.

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Mathematical optimization offers highly-effective tools for finding solutions for problems with well-defined goals, notably scheduling. However, optimization solvers are often unexplainable black boxes whose solutions are inaccessible to users and which users cannot interact with. We define a novel paradigm using argumentation to empower the interaction between optimization solvers and users, supported by tractable explanations which certify or refute solutions. A solution can be from a solver or of interest to a user (in the context of ‘what-if’ scenarios). Specifically, we define argumentative and natural language explanations for why a schedule is (not) feasible, (not) efficient or (not) satisfying fixed user decisions, based on models of the fundamental makespan scheduling problem in terms of abstract argumentation frameworks (AFs). We define three types of AFs, whose stable extensions are in one-to-one correspondence with schedules that are feasible, efficient and satisfying fixed decisions, respectively. We extract the argumentative explanations from these AFs and the natural language explanations from the argumentative ones.

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Sukirwan, Darhim, T. Herman, and R. C. I. Prahmana. "The students’ mathematical argumentation in geometry." Journal of Physics: Conference Series 943 (December 2017): 012026. http://dx.doi.org/10.1088/1742-6596/943/1/012026.

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Dissertations / Theses on the topic "Mathematical argumentation"

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Macmillan, Emily. "Argumentation and Proof : Investigating the Effect of Teaching Mathematical Proof on Students' Argumentation Skills." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517230.

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Brinkerhoff, Jennifer Alder. "Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1960.pdf.

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Vincent, Jill. "Mechanical linkages, dynamic geometry software, and argumentation : supporting a classroom culture of mathematical proof /." Connect to thesis, 2002. http://eprints.unimelb.edu.au/archive/00001399.

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Stoyle, Keri L. "SUPPORTING MATHEMATICAL EXPLANATION, JUSTIFICATION, AND ARGUMENTATION, THROUGH MULTIMEDIA: A QUANTITATIVE STUDY OF STUDENT PERFORMANCE." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1460722361.

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Kellen, Matthew. "Observing and evaluating creative mathematical reasoning through selected VITALmaths video clips and collaborative argumentation." Thesis, Rhodes University, 2017. http://hdl.handle.net/10962/6107.

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Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.

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Nordin, Anna-Karin. "Matematiska argument i helklassdiskussioner : En studie av elevers och lärares multimodala kommunikation i matematik i åk 3-5." Licentiate thesis, Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-136495.

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This study aimed at investigating and analysing the communication occurring during whole class discussions, with a specific focus on the nature of the mathematical arguments. The investigation was a qualitative case study where the communication during eight whole class discussions in grade 3-5 were analysed. Three types of arguments, wich are functional in the communication and convey different aspects of mathematics, were identified in the study. The types are (a) argument conveying a solution to a task/ a problem (b) argument conveying conceptual properties, and (c) argument conveying a mathematical relationship. The arguments types explain why an answer to a task is correct (type a), illuminate properties of a mathematical object (b), and clarify a mathematical relationship (c). The findings also reveal that arguments may be expressed through the use of a broad range of communicative resources, such as spoken language, written language, symbols, drawings, the use of manipulatives, and gestures. This highlights the importance of taking into account more than speech when construing arguments/reasoning communicated in mathematics classroom. The study also points to the importance of paying attention to arguments/reasoning that are created during other occasions than during task work or problem solving, and that arguments can enable the discerning of mathematical aspects for learners.

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Pugalee, David K. "Plenary Address: Language and Mathematics, A Model for Mathematics in the 21st Century." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79258.

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Sommerhoff, Daniel [Verfasser], and Stefan [Akademischer Betreuer] Ufer. "The individual cognitive resources underlying students' mathematical argumentation and proof skills : from theory to intervention / Daniel Sommerhoff ; Betreuer: Stefan Ufer." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1163949361/34.

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Nnanyereugo, Iwuanyanwu Paul. "An analysis of pre-service teachers' ability to use a dialogical argumentation instructional model to solve mathematical problems in physics." University of the Western Cape, 2017. http://hdl.handle.net/11394/6252.

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Philosophiae Doctor - PhD (Education)
This study chronicles a teacher training education programme. The findings emerged from the observation of argumentation skills employed by students in a physical science education classroom for pre-service high school teachers. Their task was to use the nature of arguments to solve mathematical problems of mechanics in a physics classroom. Forty first-year students were examined on how they used a dialogical argumentation instructional model (DAIM) based on Toulmin's (1958/2003) Argument Pattern (TAP), Downing's (2007) Analytical Model (DAM) and Ogunniyi's (2007a & b) Contiguity Argumentation Theory (CAT) to solve mathematical problems in physics. Thus efforts to judge the pre-service teachers' capability to solve mathematical problems in physics with respect to mechanics were compounded by the demand for the inclusion of a self-efficacy framework. According to Bandura (2006) self-efficacy is the judgment of capability. Selfefficacy plays a key role in human functioning in that it affects not only people's behaviour but other issues such as goals and aspirations, outcome expectations, affective proclivities and perception of impediments and opportunities in the social environment (Bandura, 1995, 1997 & 2006).

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Sommerhoff, Daniel Verfasser], and Stefan [Akademischer Betreuer] [Ufer. "The individual cognitive resources underlying students' mathematical argumentation and proof skills : from theory to intervention / Daniel Sommerhoff ; Betreuer: Stefan Ufer." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://nbn-resolving.de/urn:nbn:de:bvb:19-226879.

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Books on the topic "Mathematical argumentation"

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Descartes, René. Reglas para la dirección del espíritu. Madrid: Alianza Editorial, 2003.

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Descartes, René. Regulae ad directionem ingenii =: Rules for the direction of the natural intelligence : a bilingual edition of the Cartesian treatise on method. Amsterdam: Rodopi, 1998.

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Simon, Parsons, Rahwan Iyad, and SpringerLink (Online service), eds. Argumentation in Multi-Agent Systems: 8th International Workshop, ArgMAS 2011, Taipei, Taiwan, May 3, 2011, Revised Selected Papers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Iyad, Rahwan, Parsons Simon, and SpringerLink (Online service), eds. Argumentation in Multi-Agent Systems: 7th International Workshop, ArgMAS 2010 Toronto, ON, Canada, May 10, 2010 Revised, Selected and Invited Papers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011.

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Apollonius. On cutting off a ratio: An attempt to recover the original argumentation through a critical translation of the two extant medieval Arabic manuscripts. Fairfield, Conn: Golden Hind Press, 1987.

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Harré, Rom. Greenspeak: A study of environmental discourse. Thousand Oaks, Calif: Sage Publications, 1999.

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Extending the Frontiers of Mathematics: Inquiries into proof and argumentation. Key College, 2007.

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Mathematical Argumentation in Middle School - The What, Why, and How: A Step-by-Step Guide with Activities, Games, and Lesson Planning Tools. Corwin Press, 2017.

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Walton, Douglas. Methods of Argumentation. Cambridge University Press, 2013.

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Methods of Argumentation. Cambridge University Press, 2013.

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Book chapters on the topic "Mathematical argumentation"

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Gilmore, Camilla, Silke M. Göbel, and Matthew Inglis. "Mathematical Argumentation and Proof." In An Introduction to Mathematical Cognition, 154–66. Matthew Inglis. Description: Abingdon, Oxon ; New York, NY : Routledge, 2018. |: Routledge, 2018. http://dx.doi.org/10.4324/9781315684758-9.

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Cellucci, Carlo. "The Limitations of Mathematical Logic." In Logic, Argumentation & Reasoning, 215–25. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6091-2_12.

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Van Bendegem, Jean Paul. "The Heterogeneity of Mathematical Research." In Logic, Argumentation & Reasoning, 73–94. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-20762-9_5.

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Hanna, Gila. "Mathematical Proof, Argumentation, and Reasoning." In Encyclopedia of Mathematics Education, 561–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-15789-0_102.

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Corfield, David. "Argumentation and the Mathematical Process." In Appraising Lakatos, 115–38. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-0769-5_8.

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Hanna, Gila. "Mathematical Proof, Argumentation, and Reasoning." In Encyclopedia of Mathematics Education, 404–8. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-4978-8_102.

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Askevold, Gjert-Anders, and Silke Lekaus. "Mathematical Argumentation in Pupils’ Written Dialogues." In ICME-13 Monographs, 155–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70996-3_11.

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Serfati, Michel. "On the “Sum of All Differences” and the Origin of Mathematics According to Leibniz: Mathematical and Philosophical Aspects." In Logic, Argumentation & Reasoning, 69–80. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-7131-4_7.

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Van Bendegem, Jean Paul, and Bart Van Kerkhove. "Another Look at Mathematical Style, as Inspired by Le Lionnais and the OuLiPo." In Logic, Argumentation & Reasoning, 233–45. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-017-9011-6_12.

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Johansen, Mikkel Willum, and Morten Misfeldt. "An Empirical Approach to the Mathematical Values of Problem Choice and Argumentation." In Mathematical Cultures, 259–69. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28582-5_15.

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Conference papers on the topic "Mathematical argumentation"

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Albano, Giovannina, Umberto Iacono, and Giuseppe Fiorentino. "A Technological Storytelling Approach to Nurture Mathematical Argumentation." In 12th International Conference on Computer Supported Education. SCITEPRESS - Science and Technology Publications, 2020. http://dx.doi.org/10.5220/0009416904200427.

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Vandoulakis, Ioannis M. "On The Significance Of Argumentation In Searching For Mathematical Proof." In EEIA 2018 - International Conference "Education Environment for the Information Age". Cognitive-Crcs, 2018. http://dx.doi.org/10.15405/epsbs.2018.09.02.102.

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Bambut, Klaudia E. N., and Sri Rahayu. "The patterns of discussion in teaching argumentation skills in chemistry learning." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000529.

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Laily, Tsaniyatur Rizqi Nurul, Ari Prastika, Siti Marfu’ah, and Suharti Suharti. "Learning buffer solution through modified POGIL justified by student’s scientific argumentation skills." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000690.

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Soewardini, Herfa Maulina Dewi, Heni Sukrisno, and Meilantifa. "Detection of College Students' Anxiety in Carrying Out Mathematical Argumentation about Geometry Problems." In Proceedings of the 6th International Conference on Community Development (ICCD 2019). Paris, France: Atlantis Press, 2019. http://dx.doi.org/10.2991/iccd-19.2019.61.

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Magiera, Marta T. "Prospective K-8 teachers’ problem posing: Interpretations of tasks that promote mathematical argumentation." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-143.

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Amelia, Rena, Endang Budiasih, and Yahmin. "Promoting the scientific argumentation skills of students using ADI-S and ADI models in chemical kinetics teaching." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000753.

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Rohayati, Yulista Trias, Siti Zubaidah, Susriyati Mahanal, and Deny Setiawan. "The correlation between student scientific argumentation skills and cognitive achievement on PBL and RICOSRE learning models in biology classes." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000561.

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Sukardi, Rendi R., and Yanti V. Agustrianti. "Analysis of Students' Argumentation Skill and Conceptual Knowledge in Friction Force Lesson through Argumentative Task." In International Conference on Mathematics and Science Education. Paris, France: Atlantis Press, 2017. http://dx.doi.org/10.2991/icmsed-16.2017.18.

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Pajela, Hannali, Sarah Roberts, and Mary E. Brenner. "Undergraduate mathematics majors’ problem solving and argumentation." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-188.

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