Argumentation: Building Students’ Capacity for Reasoning Essential to Learning Mathematics and Sciences

REFERENCES

• Allen, M. L. and D. Kelly-Riley. 2005. Promoting Undergraduate Critical Thinking in Astro 101 Lab Exercises. Astronomy Education Review. 4(2): 10–19.
   Google Scholar
• Andrews, R. 2010. Argumentation in Higher Education: Improving Practice Through Theory and Research. New York, NY: Routledge.
   Google Scholar
• Ausubel, D. P. 1963. The Psychology of Meaningful Verbal Learning. New York: Grune and Stratton.
   Google Scholar
• Ball, D. L. and H. Bass. 2000. Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In Phillips, D. (Ed.), Yearbook of the National Society for the Study of Education, Constructivism in Education, pp. 193–224. Chicago, IL: University of Chicago Press
   Google Scholar
• Barker, W., D. Bressoud, S. Epp, S. Ganter, B. Haver, and H. Pollatsek. 2004. Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide, 2004. Washington, DC: Mathematical Association of America.
   Google Scholar
• Bartlett, F. C. 1932. Remembering: A Study in Experimental and Social Psychology. New York: Cambridge University Press.
   Google Scholar
• Bass, J. E., T. L. Contant, and A. A. Carin. 2009. Teaching Science as an Inquiry, fifth edition. Boston, MA: Allyn and Bacon.
   Google Scholar
• Bedford, D. 2010. Agnotology as a teaching tool: Learning climate science by studying misinformation. Journal of Geography. 109(4): 159–165.
   Web of Science ®Google Scholar
• Blanton, M. L., D. A. Stylianou, and M. M. David. 2009. Understanding instructional scaffolding in classroom discourse on proof. In Stylianou, D. A., M. L. Blanton,. and E. J. Knuth (Eds), Teaching and Learning Proof Across the Grades: A K-16 Perspective pp. 290–306. New York: Routledge.
   Google Scholar
• Borasi, R. 1994. Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education. 25(2): 166–208.
   Web of Science ®Google Scholar
• BouJaoude, S. B. 1992. The relationship between students’ learning strategies and the change in their misunderstandings during a high school chemistry course. Journal of Research in Science Teaching. 29(7): 687–699.
   Web of Science ®Google Scholar
• Bransford, J. D., A. L. Brown, and R. R. Cocking. 1999. How People Learn: Brain, Mind, Experience, and School. Washington, DC: National Academy Press.
   Google Scholar
• Carver, S. and Risinger, S. 1987. Improving children’s debugging skills. In Olson, G., S. Sheppard and E. Soloway (Eds), Empirical Studies of Programmers: Second Workshop, pp. 147–171. Norwood, NJ: Ablex.
   Google Scholar
• Cavallo, A. M. L. 1996. Meaningful learning, reasoning ability and students’ understanding and problem solving of genetics topics. Journal of Research in Science Teaching. 33: 625–656.
   Web of Science ®Google Scholar
• Cavallo, A. M. L. and L. E. Schafer. 1994. Relationships between students’ meaningful learning orientation and their understanding of genetics topics. Journal of Research in Science Teaching. 31(4): 393–418.
   Web of Science ®Google Scholar
• Çelik, A. Y. and Z. Kiliç. 2014. The impact of argumentation on high school chemistry students’ conceptual understanding, attitude towards chemistry and argumentativeness. Eurasian Journal of Physics and Chemistry Education. 6(1): 58–75.
   Google Scholar
• Chi, M. T., P. J. Feltovich, and R. Glaser. 1981. Categorization and representation of physics problems by experts and novices. Cognitive Science. 5(2): 121–152.
   Web of Science ®Google Scholar
• Chi, M. T. H., N. de Leeuw, M. Chiu, and C. LaVancher. 1994. Eliciting self-explanations improves understanding. Cognitive Science. 18: 439–477.
   Web of Science ®Google Scholar
• Chmiel, R. and M. Loui. 2004. Debugging: From novice to expert. Inroads. 36(1): 17–21.
   Google Scholar
• Cohen, E. 1994. Designing Group Work: Strategies for the Heterogeneous Classroom, second edition. New York: Teachers College Press.
   Google Scholar
• Cross, D. I. 2009. Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education. 7(5): 905–930.
   Web of Science ®Google Scholar
• Derry, S. J. 1996. Cognitive schema theory in the constructivist debate. Educational Psychologist. 31: 163–174.
   Web of Science ®Google Scholar
• DiSessa, A. 1993. Toward an epistemology of physics. Cognition and Instruction. 10(2/3): 105–225.
   Web of Science ®Google Scholar
• Dorier, J. L. 1995. Meta level in the teaching of unifying and generalizing concepts in mathematics. Educational Studies in Mathematics. 29(2): 175–197.
   Web of Science ®Google Scholar
• Doyle, W. 1988. Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist. 23(2): 167–180.
   Web of Science ®Google Scholar
• Duschl, R. A. and J. Osborne. 2002. Supporting and promoting argumentation discourse in science education. Studies in Science Education. 38(1): 39–72.
   Google Scholar
• Firmender, J. M., M. K. Gavin, and D. B. McCoach. 2014. Examining the relationship between teachers’ instructional practices and students’ mathematics achievement. Journal of Advanced Academics. 25(3): 214–236.
   Google Scholar
• Fukawa-Connelly, T. and J. Silverman. 2015. The development of mathematical argumentation in an unmoderated, asynchronous multi-user dynamic geometry environment. Contemporary Issues in Technology and Teacher Education. 15(4): 445–488.
   Google Scholar
• Hart, K. 1981. Children’s Understanding of Mathematics: 11–16. London, UK: Murray.
   Google Scholar
• Henningsen, M. and M. K. Stein. 1997. Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education. 28(5): 524–549.
   Web of Science ®Google Scholar
• Herbst, P., C. Chen, M. Weiss, G. González, T. Nachlieli, M. Hamlin, and C. Brach. 2009. Doing proofs in geometry classrooms. In Blanton, M., D. Stylianou, and E. Knuth, (Eds), Teaching and Learning Proof Across the Grades: A K–16 perspective pp. 250–263. New York: Routledge.
   Google Scholar
• Hynd, C. and D. E. Alvermann. 1986. The role of refutation text in overcoming difficulty with science concepts. Journal of Reading. 29(5): 440–446.
   Google Scholar
• Inglis, M., J.P. Mejia-Ramos, K. Weber, and L. Alcock. 2013. On mathematicians’ different standards when evaluating elementary proofs. Topics in Cognitive Science. 5(2): 270–282.
   PubMed Web of Science ®Google Scholar
• Kilpatrick, J., J. Swafford, and B. Findell. (Eds). 2001. Adding it up: Helping Children Learn Mathematics. Washington, DC: National Academies Press.
   Google Scholar
• Kindfield, A. C. 1994. Biology diagrams: Tools to think with. The Journal of the Learning Sciences. 3(1): 1–36.
   Google Scholar
• Kosko, K. W., A. Rougee, and P. Herbst. 2014. What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal. 26(3): 459–476.
   Google Scholar
• Kowalski, P. and A. K. Taylor. 2009. The effect of refuting misconceptions in the introductory psychology class. Teaching of Psychology. 36: 153–159.
   Web of Science ®Google Scholar
• Kozma, R. B. and J. Russell. 1997. Multimedia and understanding: Expert and novice responses to different representations of chemical phenomena. Journal of Research in Science Teaching. 34(9): 949–968.
   Web of Science ®Google Scholar
• Kuhn, D. 2010. Teaching and learning science as argument. Science Education. 94(5): 810–824.
   Web of Science ®Google Scholar
• Larkin, J. H. 1983. The role of problem representation in physics. In Gentner, D. and A. Stevens, (Eds.), Mental Models pp. 75–98. New York: Lawrence Erlbaum.
   Google Scholar
• Larson, R., R. P. Hostetler, and B. H. Edwards. 2002. Calculus with Analytic Geometry, seventh edition. Boston, MA: Houghton Mifflin Company.
   Google Scholar
• Lemke, J. 1990. Talking Science: Language, Learning, and Values. Westport, CT: Ablex.
   Google Scholar
• Lomibao, L. S., C. A. Luna, and R. A. Namoco. 2016. The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research. 4(5): 378–382.
   Google Scholar
• Lowe, R. K. 1987. Drawing out ideas: A neglected role for scientific diagrams. Research in Science Education. 17(1): 56–66.
   Google Scholar
• Magnusson, S. J. and A. S. Palincsar. 2005. Teaching to promote the development of scientific knowledge and reasoning about light at the elementary school level. In Donovan, M. S. and J. D. Bransford (Eds), How Students Learn Science in the Classroom pp. 421–474. Washington, DC: The National Academies Press.
   Google Scholar
• Martin, T., S. Soucy, M. Wallace, and J. Dindyal. 2005. The interplay of teacher and student actions in the teaching and learning of geometric proof. Educational Studies in Mathematics. 60: 95–124.
   Google Scholar
• McClain, K. 2009. When is an argument just an argument?. The refinement of mathematical argumentation. In Stylianou, D. A., M. L. Blanton, and E. J. Knuth (Eds), Teaching and Learning Proof Across the Grades: A K-16 Perspective pp. 222–234. New York: Routledge.
   Google Scholar
• National Council of Teachers of Mathematics. 2000. Principles and Standards for School Mathematics. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices and Council of Chief State School Officers. 2010. Common Core State Standards for Mathematics. Washington, DC: Author.
   Google Scholar
• National Research Council. 2000. Inquiry and the National Science Education Standards: A Guide for Teaching and Learning. Washington, DC: National Research Press.
   Google Scholar
• National Research Council. 2005. How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press.
   Google Scholar
• National Research Council. 2012. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. Washington, DC: The National Academies Press.
   Google Scholar
• Olafson, L. and G. Schraw. 2006. Teachers’ beliefs and practices within and across domains. International Journal of Educational Research. 45(1-2): 71–84.
   Google Scholar
• Olson, S. and S. Loucks-Hurley. 2000. Inquiry and the National Science Education Standards: A Guide for Teaching and Learning. Washington, DC: National Academy of Sciences.
   Google Scholar
• Osborne, J. 2010. Arguing to learn in science: The role of collaborative, critical discourse. Science. 328(5977): 463–466.
   PubMed Web of Science ®Google Scholar
• Pontecorvo, C. and H. Girardet. 1993. Arguing and reasoning in understanding historical topics. Cognition and Instruction. 11(3-4): 365–395.
   Web of Science ®Google Scholar
• Rittle-Johnson, B. and M. Schneider. 2014. Developing Conceptual and Procedural Knowledge of Mathematics. Oxford Handbook of Numerical Cognition. Oxford, UK: Oxford University Press.
   Google Scholar
• Roth, K. J. 1986. Conceptual-Change Learning and Student Processing of Science Texts. East Lansing: Michigan State University.
   Google Scholar
• Schneps, M. H., P. M. Sadler, S. Steinberg, and L. Crouse. 1989. A Private Universe. Burlington, VT: Annenberg Media.
   Google Scholar
• Schoenfeld, A. H. 1988. When good teaching leads to bad results: The disasters of ‘well-taught’ mathematics courses. Educational Psychologist. 23(2): 145–166.
   Web of Science ®Google Scholar
• Smith, J. C., S. R. Nichols, S. Yoo, and K. Oehler. 2009. Building a community of inquiry in a problem-based undergraduate number theory course. The refinement of mathematical argumentation. In Stylianou, D. A., M. L. Blanton, and E. J. Knuth (Eds), Teaching and Learning Proof Across the Grades: A K-16 Perspective pp. 307–322. New York: Routledge.
   Google Scholar
• Sowder, L. 1988. Children’s solutions of story problems. Journal of Mathematical Behavior. 7: 227–238.
   Google Scholar
• Stein, M. K. and M. S. Smith. 1998. Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School. 3(4): 268–275.
   Google Scholar
• Stewart, J. 2005. Single Variable Calculus: Concepts and Contexts. Belmont, CA: Thomson Brooks/Cole.
   Google Scholar
• Toulmin, S. 1958. The Uses of Argument. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Watanabe, M. 2012. Heterogenius Classrooms: Detracking Math and Science: A Look at Groupwork in Action. New York: Teachers College.
   Google Scholar
• Weber, K. 2004. Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior. 23: 115–133.
   Google Scholar
• Wertheimer, M. 1959. Productive Thinking. New York, NY: Harper & Row.
   Google Scholar
• Willis, J. 2010. Learning to Love Math: Teaching Strategies that Change Student Attitudes and Get Results. Alexandria, VA: Association for Supervision and Curriculum Development.
   Google Scholar
• Yackel, E. 2002. What we can learn from analyzing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior. 21(4): 423–440.
   Google Scholar
• Yackel, E. and Hanna, G. 2003. Reasoning and proof. In Kilpatrick, J., G. Martin, and D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics pp. 227–236. Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Yopp, D. A. 2012. Valuing informal arguments and empirical investigations during collective argumentation. PRIMUS. 22(8): 643–663.
   Google Scholar
• Zohar, A. and F. Nemet. 2002. Fostering students’ knowledge and argumentation skills through dilemmas in human genetics. Journal of Research in Science Teaching. 39(1): 35–62.
   Web of Science ®Google Scholar