ARAKTERISTIK WARRANT DALAM MENEMUKAN COUNTER EXAMPLE
Keywords:
warrant, argumentation, counter examplAbstract
Warrant is the basis of thought used someone ito generate claims. Argumentation is
mathematical form of communication used to convince ourselves and others about the truth of the
statements that have been made. Arguments will be discussed based on components consisting of
a Toulmin argument data, warrant, claim and rebuttal. This study aims to explore the
characteristics of the warrant in a mathematical argument when students attempted to produce a
counter example. This research is a descriptive qualitative research for characterize warrant in
the students ' argument when generating a counter example. For resolve the problem, the
researchers record, observing and noting all the behaviors include think aloud of students.
Students are then interviewed individually to explain his thinking process when mengonstruksi
evidence. The results showed that the warrant can generate inductive claims are true. Warrant
can be grouped into a warrant that is weak and warrant that is strong.
References
Aberdein, A. (2008). Mathematics and
Argumentation. Kluwer Academic
Publishers. Printed in the
Netherlands
Alcock, L. (2009). Teaching Proof to
Undergraduates: Semantic and
Syntatic Approaches. Procceding
ICMI Study 19, 2009
Arzarello,F., Paola D., Sabena, C. (2009).
Proving In Early Calculus.
Proceeding ICMI 2009
Arzarello,F., Paola D., Sabena, C. (2009).
Logical And Semiotic Levels In
Argumentation. Proceeding ICMI
2009
Boero, P., Garuti, R., Mariotti M. A. (1999).
Some Dynamic Mental Processes
Underlying Producing and Proving
Conjectures» Proceedings of the
20th Conference of the International
Group for the Psychology of
Mathematics Education PME-XX,
vol. 2, (pp. 121 – 128), Valencia.
Bromley, D.B. (1986). The case-study
method in psychology and related
disclipines. Chichester. John Wiey
& Sons
Burton, L. (2004). Mathematicians as
Enquirers. Learning about Learning
Mathematics. Dordecht, Kluwer
Chen, Y.T., dan Wang, J. H. (2016).
Analyzing with Posner’s Conceptual
Change Model and Toulmin’s Model
of Argumentative Demonstration in
Senior High School Students’
Mathematic Learning. International
Journal of Information and
Education Technology, Vol. 6, No. 6,
June 2016
de Villiers, M. (1990). The Role and
Function of Proof in Mathematics.
Pythagoras 24: 17-24
Douek, N. (1999). Some Remark About
Argumentation and Mathematical
Proof and Their Educational
Implication. European Research in
Mathematics Education I: Group 1
Duval. (2007). Struktur Argumentasi.
Educational Studies in Mathematic,
22, 233-261
Ginsburg, H. (1981). The Clinical Interview
in Psychological Research on
Mathematical Thinking: Aims,
Rationales, Techniques. For the
Learning of Mathematics 1 (1), 4-11
Hanna, G., & de Villiers, M. (2012). Proof
and Proving in Mathematics
Education: The 19th ICMI Study.
Dordrecht, Netherlands: Springer.
Harel, G. (2008). DNR perspective on
mathematics curriculum and
instruction, Part I: focus on proving.
ZDM Mathematics Education,
40:487–500. DOI 10.1007/s11858008-0104-1
Hitchcock D., & Verheij, B. (2006). Arguing
on the Toulmin Model: New Essays
in Argument analysis and Evaluation
(p.1-23), Springer.
Hoffkamp, A., Schnieder, J. & Paravicini, W.
(2011). Mathematical Enculturation
– Argumentation And Proof At The
Transition From School To
University
Inglis, M., Ramos M. & Simpson, (2007).
Modelling Mathematical
Argumentation: The Importance of
Qualification. Educational Studies
in Mathematics, 66(1), 3-21.
Knipping, Ch. (2002). Proof and proving
processes: Teaching Geometry in
France and Germany. In H.-G.
Weigand (Ed.), Developments in
Mathematics Education in GermanSpeaking
Countries.
Selected
Papers
From
the Annual Conference on
Didactics of Mathematics, Bern
1999 (pp. 44–54). Hildesheim:
Franzbecker Verlag.
Knipping, Ch. (2003). Argumentation
Structures in Classroom Proving
Situations. European Research in
Mathematics Education III
Krummheuer, G. (1995). The Ethnography of
Argumentation. In: P. Cobb und H.
Bauersfeld (Ed.), The Emergence of
Mathematical Meaning: Interaction
in Classroom Cultures. Hillsdale,
NJ.: Lawrence Erlbaum Associates,
229-269
National Council of Teacher of Mathematics.
(2000). Principles and Standards for
School Mathematics
Pablo, J., Ramos, M., and Inglis,M. (2008).
What are the argumentative activities
associated with proof? Joubert, M.
(Ed.) Proceedings of the British
Society for Research into Learning
Mathematics 28(2) June 2008
Pedemonte, B. (2002). Relation Between
Argumentation and Proof in
Mathematics: Cognitive Unity or
Break? In: Proceedings of the 2
Conference of the European Society for Research in Mathematics
Education, 2, Marienbad, 2001.
Pedemonte, B. (2003). What Kind of Proof
can be Constructed Following an
Abductive Argumentation?
European Research in Mathematics
Education III
Pedemonte, B. (2007). How can the
relationship between argumentation
and proof be analysed. Educ Stud
Math (2007) 66:23–41
Rav, Y. (1999). Why do We Prove
Thorems? Philosophia Mathematica,
7(3), 5-41
Selden, A. & Selden, J. (2013). Persistence
and Self-Efficacy in Proving.
Martinez, M. & Castro Superfine, A
(Eds.). Proceedings of the 35th
annual meeting of the North
American Chapter of the
International Group for the
Psychology of Mathematics
Education,304-307
Stylianides, A. J. (2007). Proof and Proving
in School Mathematics. Journal for
Research in Mathematics Education,
38(3), 289-321
Tetens, H. (2010). Argumentieren lehren.
Eine kleine Fallstudie. In Meyer, K.
(Ed.), Texte zur Didaktik der
Philosophie (198-214). Stuttgart:
Reclam.
Tikva, J.B. (2009). Old Meta-Discursive
Rules Die Hard. Procceding ICMI
Study 19, 2009
Toulmin, S.E. (1958). The Uses of Argument,
Cambridge: Cambridge University
Press.
Toulmin, S. E. (2003). The Uses of
Argument. Cambridge, UK:
Cambridge University Press.
Ubuz, B., Dincer, S., & Bulbul, A. (2012).
Argumentation in undergraduate
math courses: A study on proof
generation. Tso, T. Y. (Ed.),
Proceedings of the 36th Conference of the International Group for the
Psychology of Mathematics
Education, Vol.4, 163-170.
Ubuz B., Dincer S.,& Bülbül A. (2013).
Argumentation in Undergraduate
Math Courses: A Study on
Definition Construction.
Proceedings of the 37th Conference
of the International Group for the
Psychology of Mathematics
Education, vol. 4, pp. 313-320. Kiel,
Germany: PME.
Viholainen, A. (2009). The View Of
Mathematics And Argumentation
Vincent, J., Chick, H., dan McCrae, B.
(2005). Argumentation Profile
Charts As Tools For Analysing
Students’ Argumentations.
Proceedings of the 29th Conference
of the International Group for the
Psychology of Mathematics
Education, Vol. 4, pp. 281-288.
Melbourne: PME
Argumentation. Kluwer Academic
Publishers. Printed in the
Netherlands
Alcock, L. (2009). Teaching Proof to
Undergraduates: Semantic and
Syntatic Approaches. Procceding
ICMI Study 19, 2009
Arzarello,F., Paola D., Sabena, C. (2009).
Proving In Early Calculus.
Proceeding ICMI 2009
Arzarello,F., Paola D., Sabena, C. (2009).
Logical And Semiotic Levels In
Argumentation. Proceeding ICMI
2009
Boero, P., Garuti, R., Mariotti M. A. (1999).
Some Dynamic Mental Processes
Underlying Producing and Proving
Conjectures» Proceedings of the
20th Conference of the International
Group for the Psychology of
Mathematics Education PME-XX,
vol. 2, (pp. 121 – 128), Valencia.
Bromley, D.B. (1986). The case-study
method in psychology and related
disclipines. Chichester. John Wiey
& Sons
Burton, L. (2004). Mathematicians as
Enquirers. Learning about Learning
Mathematics. Dordecht, Kluwer
Chen, Y.T., dan Wang, J. H. (2016).
Analyzing with Posner’s Conceptual
Change Model and Toulmin’s Model
of Argumentative Demonstration in
Senior High School Students’
Mathematic Learning. International
Journal of Information and
Education Technology, Vol. 6, No. 6,
June 2016
de Villiers, M. (1990). The Role and
Function of Proof in Mathematics.
Pythagoras 24: 17-24
Douek, N. (1999). Some Remark About
Argumentation and Mathematical
Proof and Their Educational
Implication. European Research in
Mathematics Education I: Group 1
Duval. (2007). Struktur Argumentasi.
Educational Studies in Mathematic,
22, 233-261
Ginsburg, H. (1981). The Clinical Interview
in Psychological Research on
Mathematical Thinking: Aims,
Rationales, Techniques. For the
Learning of Mathematics 1 (1), 4-11
Hanna, G., & de Villiers, M. (2012). Proof
and Proving in Mathematics
Education: The 19th ICMI Study.
Dordrecht, Netherlands: Springer.
Harel, G. (2008). DNR perspective on
mathematics curriculum and
instruction, Part I: focus on proving.
ZDM Mathematics Education,
40:487–500. DOI 10.1007/s11858008-0104-1
Hitchcock D., & Verheij, B. (2006). Arguing
on the Toulmin Model: New Essays
in Argument analysis and Evaluation
(p.1-23), Springer.
Hoffkamp, A., Schnieder, J. & Paravicini, W.
(2011). Mathematical Enculturation
– Argumentation And Proof At The
Transition From School To
University
Inglis, M., Ramos M. & Simpson, (2007).
Modelling Mathematical
Argumentation: The Importance of
Qualification. Educational Studies
in Mathematics, 66(1), 3-21.
Knipping, Ch. (2002). Proof and proving
processes: Teaching Geometry in
France and Germany. In H.-G.
Weigand (Ed.), Developments in
Mathematics Education in GermanSpeaking
Countries.
Selected
Papers
From
the Annual Conference on
Didactics of Mathematics, Bern
1999 (pp. 44–54). Hildesheim:
Franzbecker Verlag.
Knipping, Ch. (2003). Argumentation
Structures in Classroom Proving
Situations. European Research in
Mathematics Education III
Krummheuer, G. (1995). The Ethnography of
Argumentation. In: P. Cobb und H.
Bauersfeld (Ed.), The Emergence of
Mathematical Meaning: Interaction
in Classroom Cultures. Hillsdale,
NJ.: Lawrence Erlbaum Associates,
229-269
National Council of Teacher of Mathematics.
(2000). Principles and Standards for
School Mathematics
Pablo, J., Ramos, M., and Inglis,M. (2008).
What are the argumentative activities
associated with proof? Joubert, M.
(Ed.) Proceedings of the British
Society for Research into Learning
Mathematics 28(2) June 2008
Pedemonte, B. (2002). Relation Between
Argumentation and Proof in
Mathematics: Cognitive Unity or
Break? In: Proceedings of the 2
Conference of the European Society for Research in Mathematics
Education, 2, Marienbad, 2001.
Pedemonte, B. (2003). What Kind of Proof
can be Constructed Following an
Abductive Argumentation?
European Research in Mathematics
Education III
Pedemonte, B. (2007). How can the
relationship between argumentation
and proof be analysed. Educ Stud
Math (2007) 66:23–41
Rav, Y. (1999). Why do We Prove
Thorems? Philosophia Mathematica,
7(3), 5-41
Selden, A. & Selden, J. (2013). Persistence
and Self-Efficacy in Proving.
Martinez, M. & Castro Superfine, A
(Eds.). Proceedings of the 35th
annual meeting of the North
American Chapter of the
International Group for the
Psychology of Mathematics
Education,304-307
Stylianides, A. J. (2007). Proof and Proving
in School Mathematics. Journal for
Research in Mathematics Education,
38(3), 289-321
Tetens, H. (2010). Argumentieren lehren.
Eine kleine Fallstudie. In Meyer, K.
(Ed.), Texte zur Didaktik der
Philosophie (198-214). Stuttgart:
Reclam.
Tikva, J.B. (2009). Old Meta-Discursive
Rules Die Hard. Procceding ICMI
Study 19, 2009
Toulmin, S.E. (1958). The Uses of Argument,
Cambridge: Cambridge University
Press.
Toulmin, S. E. (2003). The Uses of
Argument. Cambridge, UK:
Cambridge University Press.
Ubuz, B., Dincer, S., & Bulbul, A. (2012).
Argumentation in undergraduate
math courses: A study on proof
generation. Tso, T. Y. (Ed.),
Proceedings of the 36th Conference of the International Group for the
Psychology of Mathematics
Education, Vol.4, 163-170.
Ubuz B., Dincer S.,& Bülbül A. (2013).
Argumentation in Undergraduate
Math Courses: A Study on
Definition Construction.
Proceedings of the 37th Conference
of the International Group for the
Psychology of Mathematics
Education, vol. 4, pp. 313-320. Kiel,
Germany: PME.
Viholainen, A. (2009). The View Of
Mathematics And Argumentation
Vincent, J., Chick, H., dan McCrae, B.
(2005). Argumentation Profile
Charts As Tools For Analysing
Students’ Argumentations.
Proceedings of the 29th Conference
of the International Group for the
Psychology of Mathematics
Education, Vol. 4, pp. 281-288.
Melbourne: PME
Downloads
Published
2017-09-01
Issue
Section
Articles
