Journal articles: '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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Karaslaan, Hatice, Annette Hohenberger, Hilmi Demir, Simon Hall, and Mike Oaksford. "Cross-Cultural Differences in Informal Argumentation: Norms, Inductive Biases and Evidentiality." Journal of Cognition and Culture 18, no. 3-4 (August 13, 2018): 358–89. http://dx.doi.org/10.1163/15685373-12340035.

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AbstractCross-cultural differences in argumentation may be explained by the use of different norms of reasoning. However, some norms derive from, presumably universal, mathematical laws. This inconsistency can be resolved, by considering that some norms of argumentation, like Bayes theorem, are mathematical functions. Systematic variation in the inputs may produce culture-dependent inductive biases although the function remains invariant. This hypothesis was tested by fitting a Bayesian model to data on informal argumentation from Turkish and English cultures, which linguistically mark evidence quality differently. The experiment varied evidential marking and informant reliability in argumentative dialogues and revealed cross-cultural differences for both independent variables. The Bayesian model fitted the data from both cultures well but there were differences in the parameters consistent with culture-specific inductive biases. These findings are related to current controversies over the universality of the norms of reasoning and the role of normative theories in the psychology of reasoning.

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Hidayat, Wahyu, Wahyudin Wahyudin, and Sufyani Prabawanto. "THE MATHEMATICAL ARGUMENTATION ABILITY AND ADVERSITY QUOTIENT (AQ) OF PRE-SERVICE MATHEMATICS TEACHER." Journal on Mathematics Education 9, no. 2 (June 29, 2018): 239–48. http://dx.doi.org/10.22342/jme.9.2.5385.239-248.

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The Mathematical argumentation has been studied before, but no research has a focus on mathematical argumentation and adversity quotient of the pre-service mathematics teacher. This study is experimental research that aims to know and examine in depth about the influence of AQ of pre-service mathematics teacher toward the achievement of mathematical argument ability. The population of this study is the pre-service mathematics teacher in Cimahi City, West Java, Indonesia; while the sample is 60 pre-service mathematics teachers selected purposively. The instruments of this study are tests and non-tests. They are based on the assessment of good characteristics towards students' mathematical argumentation abilities, while the non-test instrument is based on the assessment of good characteristics towards AQ. The results of this research show that: (1) AQ gives positive influence to the development of mathematical argumentation ability of pre-service mathematics teacher with the influence of 60.2%, while the rest of it (39.8%) is influenced by other factors outside AQ; (2) The ability of mathematical argumentation of pre-service mathematics teacher is more developed on AQ of Climber type; (3) Students with the Quitter AQ type still tend to have less ability of mathematical argumentation.

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Lin, Pi-Jen. "The Development of Students’ Mathematical Argumentation in a Primary Classroom." Educação & Realidade 43, no. 3 (September 2018): 1171–92. http://dx.doi.org/10.1590/2175-623676887.

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Abstract: The use of valid argument does not come naturally. It is acquired only through practice. This study was accomplished to provide students intended opportunities of engaging activities for launching argumentation in primary classrooms. The focus of the paper is how argumentation was evolved when students engaged in the conjecturing incorporated into regular mathematics instruction over two consecutive years. Working with a group of 6 teachers was to develop conjecturing tasks and pedagogical strategies to support them in teaching, and then to enhance the quality of students’ argumentation when 24 students were in grades 3 and 4. The collected data mainly consisted of conjecturing tasks, audio - and video - taped recordings of classroom observations, and students’ worksheets. Results indicate that the evolution of argumentation was identified in two aspects: the characteristics and the quality of the argumentation.

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Sukirwan, Sukirwan, Dedi Muhtadi, Hairul Saleh, and Warsito Warsito. "PROFILE OF STUDENTS' JUSTIFICATIONS OF MATHEMATICAL ARGUMENTATION." Infinity Journal 9, no. 2 (September 21, 2020): 197. http://dx.doi.org/10.22460/infinity.v9i2.p197-212.

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This study investigates the aspects that influence students' justification of the four types of arguments constructed by students, namely: inductive, algebraic, visual, and perceptual. A grounded theory type qualitative approach was chosen to investigate the emergence of the four types of arguments and how the characteristics of students from each type justify the arguments constructed. Four people from 75 students were involved in the interview after previously getting a test of mathematical argumentation. The results of the study found that three factors influenced students' justification for mathematical arguments, namely: students' understanding of claims, treatment given, and facts found in arguments. Claims influence the way students construct arguments, but facts in arguments are the primary consideration for students in choosing convincing arguments compared to representations. Also, factor treatment turns out to change students' decisions in choosing arguments, and these changes tend to lead to more formal arguments.

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Inglis, Matthew, Juan Pablo Mejia-Ramos, and Adrian Simpson. "Modelling mathematical argumentation: the importance of qualification." Educational Studies in Mathematics 66, no. 1 (April 5, 2007): 3–21. http://dx.doi.org/10.1007/s10649-006-9059-8.

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Rumsey, Chepina, Jody Guarino, Rachael Gildea, Christina Y. Cho, and Bethany Lockhart. "Tools to Support K–2 Students in Mathematical Argumentation." Teaching Children Mathematics 25, no. 4 (January 2019): 208–17. http://dx.doi.org/10.5951/teacchilmath.25.4.0208.

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A yearlong professional development project investigated types of discourse and argumentation that students engage in, participation structures and routines that teachers can include to support students, and types of tasks that promote mathematical argumentation.

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UYGUN-ERYURT, Tugba. "Conception and development of inductive reasoning and mathematical induction in the context of written argumentations." Acta Didactica Napocensia 13, no. 2 (December 30, 2020): 65–79. http://dx.doi.org/10.24193/adn.13.2.5.

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Abstract: Nowadays, mathematical reasoning and making proof have taken importance for all students from the grade level of elementary education to university. More specifically, mathematical induction (MI) is a kind of proof and reasoning strategy taking place nearly all grade levels. Moreover, teachers are important factors affecting student learning and they can acquire necessary knowledge and skills developmentally in their teacher education programs. This paper makes contributions to domain of research by investigating the development of PMT’s conception of MI in the context of written argumentations encouraging MI. In other words, the purpose of this multiple case study is to explore how PMT’s conception of mathematical induction develop through their written argumentations. These cases show that there exist improvements in PMT’s written argumentations, conception of MI and proof construction activities related to MI. In other words, the more organized and structured they produced written argumentation, the more successfully they use and make mathematical induction.

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Suhendra, Mr. "ARGUMENTASI MATEMATIK SEBAGAI SEBUAH KOMPETENSI MATEMATIK." Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam 15, no. 1 (January 13, 2015): 1. http://dx.doi.org/10.18269/jpmipa.v15i1.284.

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Teaching and learning mathematics should provide opportunity to student to express, explain, and give reason regarding what they are thinking. In addition, teaching and learning mathematics should make student active, creative, efective, meaningful, and joyful. Students are able to think accurately and communicate properly. These are relevant to the essence of teaching and learning mathematics, mathematical thinking and mathematical communication. By teaching and learning matematics student is supported to catch the idea of concepts, rules, and principles of mathematics, and then revoicing all of them. Even they should be able to defence what they assume as rightness argumentatively (mathematical argumentation or mathematical reasoning). Even though mathematical argumentation is one of important mathematical competences, but it has to make student to proportionaly master. However, mathematical argumentation is mathematical creativity with in tolerances to get the real meaning of learning mathematics. Teaching and learning mathematics can use to (i) highlight ideas that have come directly from students; (ii) help develop students’ understanding that are implicit in those ideas; (iii) negotiate meaning with students, and (iv) add new ideas, or move discussion in another direction.Key words: mathematical argumentation, thinking, communication, express, explain, reason.

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Graham, Melissa, and Kristin Lesseig. "Back-Pocket Strategies for Argumentation." Mathematics Teacher 112, no. 3 (November 2018): 172–78. http://dx.doi.org/10.5951/mathteacher.112.3.0172.

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Salazar-Torres, Juan Pablo, Yudith Liliana Contreras-Santander, and Sandra Susana Jaimes-Mora. "Semiótica: Un recurso fundamental en los procesos de argumentación matemática escrita." Eco matemático 7, no. 1 (January 29, 2016): 20. http://dx.doi.org/10.22463/17948231.1016.

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ResumenTodo proceso de argumentación matemática escrito exige un alto nivel de manejo de registros semióticos articulando estructuras semánticas capaces de significar. El presente artículo muestra los resultados del proyecto de investigación titulado “Análisis e interpretación de la semiótica en los procesos de argumentación matemática escrita por los estudiantes de 9º grado del colegio Gonzalo Rivera Laguado de Cúcuta”, el estudio fue asumido desde las teorías en torno a la semiótica y argumentaciónmatemática planteadas por Peirce, Bachelard, Vygotsky y Duval. La investigación sed esarrolló bajo la metodología cuantitativa con un alcance descriptivo. Los resultados evidenciaron que en los procesos analizados de argumentación matemática escrita, se pierde fuerza y pertinencia del argumento debido al uso inapropiado de los recursos semióticos, evidenciando vacíos conceptuales que generan vacíos epistemológicos en el saber matemático.Palabras claves: Argumentación matemática, lenguaje matemático, semiótica de la matemática.AbstractEvery process of written mathematical argumentation, requires a high level of management of semiotic records, articulating semantic structures capable of meaning. This manuscript shows the results of the research project entitled “Analysis and interpretation of semiotics in the processes of mathematical argumentation, written by the 9th grade students of the Gonzalo Rivera Laguado School in Cúcuta”, the study was assumed from theories surrounding the semiotics and mathematical argumentation, proposed by Peirce, Bachelard, Vygotsky and Duval. The research was developed under the quantitative methodology with a descriptive scope. The esults showed that in the analyzed processes of written mathematica argumentation, the argument loses its strength and relevance due to the inappropriate use of semiotic resources, evidencing conceptual gaps that generate epistemological gaps in mathematical knowledge.

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Walter, Janet G., and Tara Barros. "Students build mathematical theory: semantic warrants in argumentation." Educational Studies in Mathematics 78, no. 3 (June 15, 2011): 323–42. http://dx.doi.org/10.1007/s10649-011-9326-1.

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Todd Edwards, Michael, Michael S. Meagher, and S. Asli Özgün-Koca. "Nurturing Argumentation and Reasoning with Pentominoes." Mathematics Teaching in the Middle School 23, no. 1 (September 2017): 54–59. http://dx.doi.org/10.5951/mathteacmiddscho.23.1.0054.

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Nagel, Kathrin. "Análisis de la argumentacion matematica de estudiantes de primer año." Pensamiento Educativo: Revista de Investigación Educacional Latinoamericana 55, no. 1 (2018): 1–12. http://dx.doi.org/10.7764/pel.55.1.2018.10.

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ZACK, VICKI. "Everyday and Mathematical Language in Children's Argumentation about Proof." Educational Review 51, no. 2 (June 1999): 129–46. http://dx.doi.org/10.1080/00131919997579.

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Lin, Pi-Jen. "Improving Knowledge for Teaching Mathematical Argumentation in Primary Classrooms." Journal of Mathematics Education 11, no. 1 (March 31, 2018): 17–30. http://dx.doi.org/10.26711/007577152790018.

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Cervantes-Barraza, Jonathan Alberto, Antonia Hernandez Moreno, and Chepina Rumsey. "Promoting mathematical proof from collective argumentation in primary school." School Science and Mathematics 120, no. 1 (January 2020): 4–14. http://dx.doi.org/10.1111/ssm.12379.

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Tristanti, Lia Budi, and Toto Nusantara. "Improving Students’ Mathematical Argumentation Skill Through Infusion Learning Strategy." Journal of Physics: Conference Series 1783, no. 1 (February 1, 2021): 012103. http://dx.doi.org/10.1088/1742-6596/1783/1/012103.

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Conner, AnnaMarie, and Laura Marie Singletary. "Teacher Support for Argumentation: An Examination of Beliefs and Practice." Journal for Research in Mathematics Education 52, no. 2 (March 2021): 213–47. http://dx.doi.org/10.5951/jresematheduc-2020-0250.

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Supporting students in making mathematical arguments is an important part of discourse practices in mathematics classrooms. Differences in teachers’ support for collective argumentation have been observed and documented, and the importance of the teacher’s role in supporting collective argumentation is well established. This article seeks to explain differences in teachers’ support for argumentation by examining two student teachers’ beliefs about mathematics, teaching, and proof to see which beliefs are visible in their support for argumentation. Assisted by a framework for argumentation and a commitment to teachers’ beliefs and actions as sensible systems, we found that teachers’ beliefs about the role of the teacher, particularly with respect to giving explanations, were more visible in their support for collective argumentation than other beliefs about mathematics or proof.

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Mukuka, Angel, Overson Shumba, Sudi Balimuttajjo, and Vedaste Mutarutinya. "An Analysis of Prospective Teachers’ Mathematical Reasoning on Number Concepts." African Journal of Educational Studies in Mathematics and Sciences 15, no. 2 (December 30, 2020): 119–28. http://dx.doi.org/10.4314/ajesms.v15i2.10.

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This paper presents and discusses the results of a case study that was carried out to understand the mathematical reasoning of 73 second-year student teachers at a university in Zambia. The paper also demonstrates why it is important to develop the reasoning abilities of mathematics student teachers during their initial training programs. The questionnaire items presented to student teachers required them to justify the validity of selected algebraic statements and arguments on odd and even numbers. Factors that influenced participants’ modes of argumentation were also identified, clearly highlighting their implications for mathematics teacher education. Findings of the study revealed that 70% of the participants gave explanations that were aligned to an empirical or inductive mode of argumentation while 7% used the analytical or deductive argumentation mode. The rest of the participants gave explanations that did not reflect valid mathematical justification of the given algebraic statements and arguments. These results clearly indicate that only the minority of participants exhibited an adequate understanding of representing odd and even numbers in general form. Analysing and developing prospective teachers’ mathematical reasoning abilities are necessary to anticipate how they would practice when they are professionally qualified.

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Muir, Tracey. "Always, Sometimes, Never True." Teaching Children Mathematics 21, no. 6 (February 2015): 384. http://dx.doi.org/10.5951/teacchilmath.21.6.0384.

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To promote reasoning, mathematical argumentation, and the importance of justifying answers, we can use always, sometimes, never true statements, which can span a range of age groups, abilities, and mathematical topics.

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Foutz, Timothy L. "Collaborative Argumentation As A Learning Strategy To Improve Student Performance In Engineering Statics: A Pilot Study." American Journal of Engineering Education (AJEE) 9, no. 1 (July 3, 2018): 11–22. http://dx.doi.org/10.19030/ajee.v9i1.10185.

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Educators have used argumentation to help students understand mathematical ideas which often appear abstract to the novice learner. A preliminary investigation was conducted to determine if collaborative argumentation is a strategy that can improve the student’s conceptual understanding of the topics taught in the engineering course commonly titled Statics. The academic performance of students enrolled in a traditional problems-solving session was compared to the academic performance of students enrolled in a problem-solving session where collaborative argumentation was used. Results suggest that argumentation improved student performance as measured by grades associated with one-hour long exams, although student written responses on a course evaluation survey responses indicate that students did not believe argumentation was a learning strategy was effective.

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Reiser, Elana. "Exploring Triangles." Mathematics Teaching in the Middle School 23, no. 3 (November 2017): 171–73. http://dx.doi.org/10.5951/mathteacmiddscho.23.3.0171.

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Indrawatiningsih, N., Purwanto, A. R. As’ari, C. Sa’dijah, and Dwiyana. "Students’ mathematical argumentation ability in determining arguments or not arguments." Journal of Physics: Conference Series 1315 (October 2019): 012053. http://dx.doi.org/10.1088/1742-6596/1315/1/012053.

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Conner, AnnaMarie. "Authentic Argumentation With Prospective Secondary Teachers: The Case of 0.999…" Mathematics Teacher Educator 1, no. 2 (March 2013): 172–80. http://dx.doi.org/10.5951/mathteaceduc.1.2.0172.

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Engaging prospective secondary teachers in mathematical argumentation is important, so that they can begin to learn to engage their own students in creating and critiquing arguments. Often, when we attempt to engage prospective secondary teachers in argumentation around topics from secondary mathematics classes, the argumentation is not authentic, as they believe they already know the answers. I suggest that there are problems related to the secondary curriculum around which we can engage students in authentic argumentation, and I propose one of them is whether 0.999… = 1. Purposefully engaging and supporting students in discussing this problem, and others like it, can lead to productive discussions that go beyond the answer to the question, including, for instance, what counts as evidence in mathematics.

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Ginat, David. "Mathematical operators and ways of reasoning." Mathematical Gazette 89, no. 514 (March 2005): 7–14. http://dx.doi.org/10.1017/s0025557200176582.

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Given a mathematical operator, how should one reason about the outcome of its repeated invocation? This question is relevant in both mathematics and computer science, where iterative operator invocations are core, algorithmic elements.An initial approach, which one may naturally follow, is to try the operator in diverse situations, observe the results, and suggest a general outcome. Such an approach embodies operational reasoning, where inference derives from ‘behaviours’ of invocation sequences. This may indeed reveal some behavioural characteristics, but is it sufficient for rigorous argumentation of the general outcome? Not quite.

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Staples, Megan, and Jillian Cavanna. "Student Argumentation Work Sample Sorting Task and Teachers’ Evaluations of Arguments." Mathematics Teacher Educator 9, no. 2 (February 1, 2021): 94–109. http://dx.doi.org/10.5951/mte.2020.0001.

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To support teachers in implementing ambitious reform efforts, professional developers and teacher educators need to know more about teachers’ thinking about argumentation. Specifically, there is a need to understand more about teachers’ views and evaluations of students’ mathematical arguments as they play out in practice. In this article, we share a tool developed to elicit teachers’ pre- and postevaluations of students’ mathematical arguments on a problem-solving task. We discuss the design of the tool and provide evidence of its utility. Our findings indicate that the tool can be used to (a) identify changes in teachers’ evaluations of student mathematical arguments over time and (b) inform the design of professional learning experiences.

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Hoffman, Brittany L., M. Lynn Breyfogle, and Jason A. Dressler. "The Power of Incorrect Answers." Mathematics Teaching in the Middle School 15, no. 4 (November 2009): 232–38. http://dx.doi.org/10.5951/mtms.15.4.0232.

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Metaxas, Nikolaos. "Mathematical Argumentation of Students Participating in a Mathematics – Information Technology Project." International Research in Education 3, no. 1 (January 19, 2015): 82. http://dx.doi.org/10.5296/ire.v3i1.6767.

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Stein, Mary Kay. "Take Time for Action: Mathematical Argumentation: Putting Umph into Classroom Discussions." Mathematics Teaching in the Middle School 7, no. 2 (October 2001): 110–12. http://dx.doi.org/10.5951/mtms.7.2.0110.

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Perhaps the most difficult recommendation of the NCTM's Standards to put into practice is that of orchestrating classroom discourse—moving from a teacher-centered classroom to one that is centered on student thinking and reasoning. Some researchers argue that traditional “chalk and talk” classrooms put all the intellectual authority in the hands of the teacher and little or no responsibility for thinking and reasoning on the shoulders of the students. Classroom discussions, in contrast, are viewed as encouraging students to construct and evaluate their own knowledge, as well as the ideas of their classmates. Few examples or guidelines exist, however, to help teachers orchestrate such discussions.

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Muhtadi, D., Sukirwan, R. Hermanto, Warsito, and A. Sunendar. "How do students promote mathematical argumentation through guide-redirecting warrant construction?" Journal of Physics: Conference Series 1613 (August 2020): 012031. http://dx.doi.org/10.1088/1742-6596/1613/1/012031.

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Salazar-Torres, J., M. Vera, Y. Contreras, E. Gelvez-Almeida, Y. Huérfano, and O. Valbuena. "The rubric as an assessment strategy in the mathematical argumentation process." Journal of Physics: Conference Series 1514 (March 2020): 012026. http://dx.doi.org/10.1088/1742-6596/1514/1/012026.

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Tristanti, Lia Budi, and Toto Nusantara. "Identifying Students’ Mathematical Argumentation Competence in Solving Cubes and Pyramid Problems." Journal of Physics: Conference Series 1933, no. 1 (June 1, 2021): 012118. http://dx.doi.org/10.1088/1742-6596/1933/1/012118.

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Castro, Walter F., John Henry Durango-Urrego, and Luis R. Pino-Fan. "Preservice Teachers’ Argumentation and Some Relationships to Didactic-Mathematical Knowledge Features." Eurasia Journal of Mathematics, Science and Technology Education 17, no. 9 (August 14, 2021): em2002. http://dx.doi.org/10.29333/ejmste/11139.

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Toro Uribe, Jorge A., and Walter F. Castro. "Condiciones que activan la argumentación del profesor de matemáticas en clase." Revista Chilena de Educación Matemática 12, no. 1 (April 20, 2020): 35–44. http://dx.doi.org/10.46219/rechiem.v12i1.11.

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¿Cuáles son las condiciones que activan la argumentación del profesor de Matemáticas durante la discusión de tareas en clase? En este artículo se presentan posibles respuestas a esta pregunta, en el marco de un estudio que pretende comprender la argumentación del profesor de Matemáticas en un ambiente habitual de clase. Para ello se presenta una fundamentación teórica sobre la argumentación en la clase de Matemáticas. Los datos forman parte de un estudio más amplio, los cuales se tomaron durante lecciones de clase de décimo grado (estudiantes de 15 a 16 años), mientras la profesora y sus estudiantes discutían tareas sobre trigonometría. Se discuten fragmentos de episodios de clase, donde se describen indicadores de las condiciones que podrían activar la argumentación del profesor. Referencias Boero, P. (2011). Argumentation and proof: Discussing a “successful” classroom discussion. En M. Pytlak, T. Rowland, y E. Swoboda (Eds.), Actas del 7th Congress of the European Society for Research in Mathematics Education (pp. 120-130). Rzeszów, Polonia: ERME. Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Recuperado desde http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf Conner, A., Singletary, L., Smith, R., Wagner, P., y Francisco, R. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401-429. https://doi.org/10.1007/s10649-014-9532-8 van Eemeren, F., Grassen, B., Krabbe, E., Snoeck Henkemans, F., Verheij, B., y Wagemans, J. (2014). Handbook of Argumentation Theory. Dordrecht, Países Bajos: Springer. van Eemeren, F. y Grootendorst, R. (2011). Una Tteoría Sistemática de la Argumentación. La Perspectiva Pragmadialéctica. Buenos Aires, Argentina: Editorial Biblos. Knipping, C., y Reid, D. (2015). Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interactions. En A. Bikner-Ahsbahs, C. Knipping, y N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 75-101). New York: Springer. Krummheuer, G. (2011). Representation of the notion ‘‘learning-as-participation’’ in everyday situations of mathematics classes. ZDM Mathematics Education, 43(1), 81-90. https://doi.org/10.1007/s11858-010-0294-1 Metaxas, N. (2015). Mathematical argumentation of students participating in a mathematics–information technology project. International Research in Education, 3(1), 82-92. https://doi.org/10.5296/ire.v3i1.6767 Metaxas, N., Potari, D., y Zachariades, T. (2016). Analysis of a teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes. Educational Studies in Mathematics, 93(3), 383-397. https://doi.org/10.1007/s10649-016-9701-z Pino-Fan, L., Assis, A., y Castro, W. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. EURASIA Journal of Mathematics, Science & Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/eurasia.2015.1403a Prusak, N., Hershkowitz, R., y Schwarz, B. (2012). From visual reasoning to logical necessity through argumentative design. Educational Studies in Mathematics, 79(1), 19-40. https://doi.org/10.1007/s10649-011-9335-0 Santibáñez, C. (2015). Función, funcionalismo y funcionalización en la teoría pragma-dialéctica de la argumentación. Universum, 30(1), 233-252. https://dx.doi.org/10.4067/S0718-23762015000100014 Schoen, R. C., LaVenia, M., y Ozsoy, G. (2019). Teacher beliefs about mathematics teaching and learning: Identifying and clarifying three constructs. Cogent Education, 6(1), 1-29. https://doi.org/10.1080/2331186X.2019.1599488 Selling, S., Garcia, N., y Ball, D. (2016). What does it take to Develop Assessments of Mathematical Knowledge for Teaching?: Unpacking the Mathematical Work of Teaching. The Mathematics Enthusiast, 13(1), 35-51. Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge, Reino Unido: Cambridge University Press. Solar, H. (2018). Implicaciones de la argumentación en el aula de matemáticas. Revista Colombiana de Educación, 74, 155-176. https://doi.org/10.17227/rce.num74-6902 Solar, H., y Deulofeu, J. (2016). Condiciones para promover el desarrollo de la competencia de argumentación en el aula de matemáticas. Bolema, 30(56), 1092-1112. http://dx.doi.org//10.1590/1980-4415v30n56a13 Staples, M., y Newton, J. (2016). Teachers' Contextualization of Argumentation in the Mathematics Classroom. Theory into Practice, 55(4), 294-301. https://doi.org/10.1080/00405841.2016.1208070 Stylianides, A., Bieda, K., y Morselli, F. (2016). Proof and Argumentation in Mathematics Education Research. En Á. Gutiérrez, G. Leder, y P. Boero (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education (pp. 315-351). Rotterdam, Países Bajos: Sense Publishers. Toro, J. y Castro, W. (2019a). Features of mathematics’ teacher argumentation in classroom. En U. T. Jankvist, M. van den Heuvel-Panhuizen, y M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 336-337). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. Toro, J., y Castro, W. (2019b). Purposes of mathematics teacher argumentation during the discussion of tasks in the classroom. En M. Graven, H. Venkat, A. Essien, y P. Valero (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 458-477). Pretoria, Sudáfrica: PME. Toulmin, S. (2007). Los usos de la argumentación. Barcelona, España: Ediciones Península.

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Rosita, Cita Dwi. "THE DEVELOPMENT OF COURSEWARE BASED ON MATHEMATICAL REPRESENTATIONS AND ARGUMENTS IN NUMBER THEORY COURSES." Infinity Journal 5, no. 2 (October 1, 2016): 131. http://dx.doi.org/10.22460/infinity.v5i2.219.

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Courseware have an important role in the achievement of the objectives of education. Nevertheless, it does not mean any learning resources can be used for a type of learning. The teacher should provide and develop materials appropriate to the characteristics and the social environment of its student. Number Theory courses is one of the basic subjects that would be a prerequisite for courses at the next level, such as Linear Algebra, Complex Analysis, Real Analysis, Transformation Geometry, and Algebra Structure. Thus, the student’s understanding about the essential concepts that exist in this course will determine their success in studying subjects that mentioned above. In trying to understand most of the topics in Number Theory required the abilities of mathematical argumentation and representation. The ability of argumentation is required in studying the topic of complex number system, special operations, mathematical induction, congruence and divisibility. Ability representation especially verbal representations and symbols required by almost all the topics in this course. The purpose of this paper is to describe the development of teaching and learning Number Theory materials which facilitate students to develop the ability of mathematical argumentation and representation. The model used is a Thiagarajan development model consisting phases of defining, planning, development, and deployment. This paper is restricted to the analysis of the results of the materials validation from number theory experts.

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Rosita, Cita Dwi. "THE DEVELOPMENT OF COURSEWARE BASED ON MATHEMATICAL REPRESENTATIONS AND ARGUMENTS IN NUMBER THEORY COURSES." Infinity Journal 5, no. 2 (September 30, 2016): 131. http://dx.doi.org/10.22460/infinity.v5i2.p131-140.

Full text

Abstract:

Courseware have an important role in the achievement of the objectives of education. Nevertheless, it does not mean any learning resources can be used for a type of learning. The teacher should provide and develop materials appropriate to the characteristics and the social environment of its student. Number Theory courses is one of the basic subjects that would be a prerequisite for courses at the next level, such as Linear Algebra, Complex Analysis, Real Analysis, Transformation Geometry, and Algebra Structure. Thus, the student’s understanding about the essential concepts that exist in this course will determine their success in studying subjects that mentioned above. In trying to understand most of the topics in Number Theory required the abilities of mathematical argumentation and representation. The ability of argumentation is required in studying the topic of complex number system, special operations, mathematical induction, congruence and divisibility. Ability representation especially verbal representations and symbols required by almost all the topics in this course. The purpose of this paper is to describe the development of teaching and learning Number Theory materials which facilitate students to develop the ability of mathematical argumentation and representation. The model used is a Thiagarajan development model consisting phases of defining, planning, development, and deployment. This paper is restricted to the analysis of the results of the materials validation from number theory experts.

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Giannakoulias, Eusthathios, Eleutherios Mastorides, Despina Potari, and Theodossios Zachariades. "Studying teachers’ mathematical argumentation in the context of refuting students’ invalid claims." Journal of Mathematical Behavior 29, no. 3 (September 2010): 160–68. http://dx.doi.org/10.1016/j.jmathb.2010.07.001.

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Meyer, Michael, and Susanne Schnell. "What counts as a “good” argument in school?—how teachers grade students’ mathematical arguments." Educational Studies in Mathematics 105, no. 1 (September 2020): 35–51. http://dx.doi.org/10.1007/s10649-020-09974-z.

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Abstract As argumentation is an activity at the heart of mathematics, (not only) German school curricula request students to construct mathematical arguments, which get evaluated by teachers. However, it remains unclear which criteria teachers use to decide on a specific grade in a summative assessment setting. In this paper, we draw on two sources for these criteria: First, we present theoretically derived dimensions along which arguments can be assessed. Second, a qualitative interview study with 16 teachers from German secondary schools provides insights in their criteria developed in practice. Based on the detailed presentation of the case of one teacher, the paper then illustrates how criteria developed in practice take a variety of different aspects into account and also correspond with the theoretically identified dimensions. The findings are discussed in terms of implications for the teaching and learning about mathematical argumentation in school and university: An emphasis on more pedagogical criteria in high school offers one explanation to the perceived gap between school and university level mathematics.

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Jacquette, Dale. "Mathematical Proof and Discovery Reductio ad Absurdum." Informal Logic 28, no. 3 (September 2, 2008): 242. http://dx.doi.org/10.22329/il.v28i3.596.

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The uses and interpretation of reductio ad absurdum argumentation in mathematical proof and discovery are examined, illustrated with elementary and progressively sophisticated examples, and explained. Against Arthur Schopenhauer’s objections, reductio reasoning is defended as a method of uncovering new mathematical truths, and not merely of confirming independently grasped mathematical intuitions. The application of reductio argument is contrasted with purely mechanical brute algorithmic inferences as an art requiring skill and intelligent intervention in the choice of hypotheses and attribution of contradictions deduced to a particular assumption in a contradiction’s derivation base within a reductio proof structure.

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Alden, Kieran, Paul S. Andrews, Fiona A. C. Polack, Henrique Veiga-Fernandes, Mark C. Coles, and Jon Timmis. "Using argument notation to engineer biological simulations with increased confidence." Journal of The Royal Society Interface 12, no. 104 (March 2015): 20141059. http://dx.doi.org/10.1098/rsif.2014.1059.

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The application of computational and mathematical modelling to explore the mechanics of biological systems is becoming prevalent. To significantly impact biological research, notably in developing novel therapeutics, it is critical that the model adequately represents the captured system. Confidence in adopting in silico approaches can be improved by applying a structured argumentation approach, alongside model development and results analysis. We propose an approach based on argumentation from safety-critical systems engineering, where a system is subjected to a stringent analysis of compliance against identified criteria. We show its use in examining the biological information upon which a model is based, identifying model strengths, highlighting areas requiring additional biological experimentation and providing documentation to support model publication. We demonstrate our use of structured argumentation in the development of a model of lymphoid tissue formation, specifically Peyer's Patches. The argumentation structure is captured using A rtoo ( www.york.ac.uk/ycil/software/artoo ), our Web-based tool for constructing fitness-for-purpose arguments, using a notation based on the safety-critical goal structuring notation. We show how argumentation helps in making the design and structured analysis of a model transparent, capturing the reasoning behind the inclusion or exclusion of each biological feature and recording assumptions, as well as pointing to evidence supporting model-derived conclusions.

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Journal articles on the topic 'Mathematical argumentation'

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