THE USE OF EXAMPLES IN MATHEMATICS TEACHING: BASIC DEFINITIONS, CONCEPTS AND APPROACHES
Yıl 2019,
, 569 - 586, 01.07.2019
Duygu Ören Vural
,
Fulya Kula
Öz
The use of examples in
mathematics and its contributions to the learning of mathematics has been
receiving both international and national attention recently. Mathematical
examples are widely studied in the international literature with their
classifications or the development and use of theoretical frameworks. However
examples were limitedly studied in the national level. This study aims to
review the literature of mathematical examples from a historical and
pedagogical approach. The various classifications of examples and the
theoretical framework are introduced. In addition the national studies
conducted about the topic are reviewed to draw an overview about the trends.
According to the
results of this study, although there has been increased national interest in
the subject in the last two decades, it has been determined that the studies
carried out are limited and generally examined at secondary and undergraduate
levels. The results of the national studies examined point out the finding of
the limited and poor use of examples in the teaching contexts. The
current study also gives insights for future research. The most basic
suggestions are the extensive use of examples in teaching settings and books
and the effects on student learning and widespread studies in the primary
level.
Kaynakça
- Akkoç, H. (2006). Fonksiyon kavramının çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 30, 1-9.
- Alcock, L. and Inglis, M. (2008). Doctoral students' use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69:111-129.
- Alkan, S. (2016). Matematik öğretmenlerin kullandıkları örneklerin sınıflandırılması ve öğretimsel açıklama boyutlarıyla ilişkisinin incelenmesi. Yayınlanmamış doktora tezi, Karadeniz Teknik Üniversitesi, Trabzon.
- Alkan, S., & Güven, B. (2018) Ders kitaplarında kullanılan örnek türlerinin analizi: Limit konusu. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 1-1.
- Alkan, S., Güven, B., & Yılmaz, Ş. (2017). The types of examples teachers use in teaching function concept. Bayburt Eğitim Fakültesi Dergisi, 12(23), 367-384.
- Anthony, G. (1994). The role of the worked example in learning mathematics. A. Jones ve diğerleri. (Ed.). SAME papers (s. 129-143). Hamilton, New Zealand: University of Waikato.
- Antonini, S., Presmeg, N., Mariotti, A. ve Zaslavsky, O., (2011). Examples in mathematics thinking and learning from an educational perspective. ZDM Zentralblatt fur Didaktik der Mathematik, 43.(3).
- Asiala, M. Brown, A. DeVries, D. Dubinsky, E. Mathews D. ve Thomas K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1-32.
- Avcu, R. (2014). Exploring middle school mathematics teachers’ treatment of rational number examples in their classrooms: A multiple case study.Yayınlanmamış doktora tezi, Orta Doğu Teknik Üniversitesi, Ankara.
- Aylar, E. (2014). A Study on the forms of perception of 7th grade students towards the concept of proof. Journal of Education and Future, 5, 39-56.
- Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. D. Pimm (Ed.).Mathematics, Teachers and Children, (s. 216-235), London: Hodder and Stoughton.
- Bell, E.T. (1967). Men of Mathematics. New York: Simon and Schuster.
- Bentley, P. (2008) The Book of Numbers: The Secret of Numbers and how They Changed the World.
- Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A. ve Zaslavsky, O. (2006). Exemplification in mathematics education. Proc. 30th Conf. of the Int. Group for the Psychology of Mathematics Education içinde (s. 126-154). Prague, Czech Republic: PME.
- Bills, L. ve Watson, A. (2008). Editorial introduction (Special issue on the role and use of examples in mathematics education). Educational Studies in Mathematics, 69(2), 77–79.
- Bogomolny, M. (2006). The role of example-generation tasks in students’ understanding of linear algebra. Yayınlanmamış doktora tezi, Simon Fraser University, Burnaby, Canada.
- Boyer, C. B. (1949). The History of the Calculus and Its Conceptual Development. New York:Dover Publications.
- Boyer, C. B. (1968). A History of Mathematics. New York: Wiley International Edition.
- Breen, S., O’Shea, A. ve Pfeiffer, K. (2016). Students’ views of example generation tasks. Teaching Mathematics and its Applications. doi: 10.1093/teamat/hrv017
- Bruner, J., Goodnow, J. ve Austin, A. (1956). A study of thinking. New York: Wiley.
- Burn, R. (2002). The genesis of mathematical structures. P. Kahn ve J. Kyle (Ed.). Effective learning and teaching in mathematics and its applications. (s. 20-33). Kogan Page.
- Charles, R. (1980). Exemplification and characterization moves in the classroom teaching of geometry Concepts. Journal for Research in Mathematics Education.11(1), 10-21.
- Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). New York, NY: Routledge.
- Colburn, W. (1826). Intellectual arithmetic: Upon the inductive method of instruction. Boston, USA: Reynolds ve Co.
- Confrey, J. (1991). Steering a course between Vygotsky and Piaget. Educational Researcher, 20(2), 29-32.
- Cook, J. P. ve Fukawa-Connelly, T. (2015) The pedagogical examples of groups and rings that algebraists think are most important in an introductory course. Canadian Journal of Science, Mathematics and Technology Education, 15(2), 171-185.
- Courant, R. (1981). Reminiscences from Hilbert’s Gottingen. Mathematical Intelligencer, 3(4), 154–164.
- Dahlberg, R. ve Housman, D. (1997). Facilitating learning events through example generation. Educational Studies in Mathematics, 33, 283-299.
- Davis, R. (1984). Learning mathematics: the cognitive science approach to mathematics education. Norwood, NJ, USA: Ablex.
- Davis, P. ve Hersh, R. (1981). The Mathematical Experience. Brighton UK: Harvester.
- De Morgan, A. (1831). On mathematical instruction. Quarterly Journal of Education,1, 264-279.
- Dienes, Z. (1960). Building up Mathematics. London, UK: Hutchinson Educational.
- Dienes, Z. P. (1963). An Experimental Study of Mathematics Learning. London: Hutchinson.
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MATEMATİK ÖĞRETİMİNDE ÖRNEKLER: TEMEL TANIM, KAVRAM VE YAKLAŞIMLAR
Yıl 2019,
, 569 - 586, 01.07.2019
Duygu Ören Vural
,
Fulya Kula
Öz
Matematikte örnek kullanımı ve örneklerin matematik
öğretimine katkısı ulusal ve uluslararası alanyazında son yıllarda ilgi gören
çalışma başlıklarıdır. Uluslararası alanyazında örneklerle ilgili
sınıflandırmalar ve kuramsal çerçeve oluşturma çalışmaları yaygın olarak
mevcuttur. Ulusal alanyazında ise örnek kullanımı sınırlı şekilde
incelenmektedir. Bu çalışmada örnek kullanımının matematikte ve matematik
öğretimindeki tarihsel gelişimi ve pedagojik sınıflandırma çalışmaları
incelenmiştir. Ayrıca matematikte örnekler ile ilgili geliştirilen kuramsal
çerçeveler derlenmiş ve konu ile ilgili ulusal çalışmalar incelenmiştir. Bu
çalışmanın sonuçlarına göre ulusal alan yazında son yirmi yılda konuya olan
ilgi artmış olsa da yapılan çalışmaların sınırlı sayıda olması ve genellikle
ortaöğretim ve lisans seviyelerinde incelendiği belirlenmiştir. İncelenen
ulusal çalışmalar doğrultusunda matematik öğretiminde sınırlı ve zengin olmayan
örnek kullanımı dikkat çekicidir. Ayrıca bu çalışmada elde edilen bulgular
doğrultusunda ileride yapılacak çalışmalar için kimi önerilerde bulunulmuştur.
En temel öneriler ise çalışmaların daha yaygın olarak kitaplarda ve derste
zengin örnek kullanımının ve bunun matematik öğrenmeye katkısının incelenmesi
ve ilköğretim seviyesinde yapılacak çalışmaların daha yaygınlaştırılmasıdır.
Kaynakça
- Akkoç, H. (2006). Fonksiyon kavramının çoklu temsillerinin çağrıştırdığı kavram görüntüleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 30, 1-9.
- Alcock, L. and Inglis, M. (2008). Doctoral students' use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69:111-129.
- Alkan, S. (2016). Matematik öğretmenlerin kullandıkları örneklerin sınıflandırılması ve öğretimsel açıklama boyutlarıyla ilişkisinin incelenmesi. Yayınlanmamış doktora tezi, Karadeniz Teknik Üniversitesi, Trabzon.
- Alkan, S., & Güven, B. (2018) Ders kitaplarında kullanılan örnek türlerinin analizi: Limit konusu. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 1-1.
- Alkan, S., Güven, B., & Yılmaz, Ş. (2017). The types of examples teachers use in teaching function concept. Bayburt Eğitim Fakültesi Dergisi, 12(23), 367-384.
- Anthony, G. (1994). The role of the worked example in learning mathematics. A. Jones ve diğerleri. (Ed.). SAME papers (s. 129-143). Hamilton, New Zealand: University of Waikato.
- Antonini, S., Presmeg, N., Mariotti, A. ve Zaslavsky, O., (2011). Examples in mathematics thinking and learning from an educational perspective. ZDM Zentralblatt fur Didaktik der Mathematik, 43.(3).
- Asiala, M. Brown, A. DeVries, D. Dubinsky, E. Mathews D. ve Thomas K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education, 6, 1-32.
- Avcu, R. (2014). Exploring middle school mathematics teachers’ treatment of rational number examples in their classrooms: A multiple case study.Yayınlanmamış doktora tezi, Orta Doğu Teknik Üniversitesi, Ankara.
- Aylar, E. (2014). A Study on the forms of perception of 7th grade students towards the concept of proof. Journal of Education and Future, 5, 39-56.
- Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. D. Pimm (Ed.).Mathematics, Teachers and Children, (s. 216-235), London: Hodder and Stoughton.
- Bell, E.T. (1967). Men of Mathematics. New York: Simon and Schuster.
- Bentley, P. (2008) The Book of Numbers: The Secret of Numbers and how They Changed the World.
- Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A. ve Zaslavsky, O. (2006). Exemplification in mathematics education. Proc. 30th Conf. of the Int. Group for the Psychology of Mathematics Education içinde (s. 126-154). Prague, Czech Republic: PME.
- Bills, L. ve Watson, A. (2008). Editorial introduction (Special issue on the role and use of examples in mathematics education). Educational Studies in Mathematics, 69(2), 77–79.
- Bogomolny, M. (2006). The role of example-generation tasks in students’ understanding of linear algebra. Yayınlanmamış doktora tezi, Simon Fraser University, Burnaby, Canada.
- Boyer, C. B. (1949). The History of the Calculus and Its Conceptual Development. New York:Dover Publications.
- Boyer, C. B. (1968). A History of Mathematics. New York: Wiley International Edition.
- Breen, S., O’Shea, A. ve Pfeiffer, K. (2016). Students’ views of example generation tasks. Teaching Mathematics and its Applications. doi: 10.1093/teamat/hrv017
- Bruner, J., Goodnow, J. ve Austin, A. (1956). A study of thinking. New York: Wiley.
- Burn, R. (2002). The genesis of mathematical structures. P. Kahn ve J. Kyle (Ed.). Effective learning and teaching in mathematics and its applications. (s. 20-33). Kogan Page.
- Charles, R. (1980). Exemplification and characterization moves in the classroom teaching of geometry Concepts. Journal for Research in Mathematics Education.11(1), 10-21.
- Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). New York, NY: Routledge.
- Colburn, W. (1826). Intellectual arithmetic: Upon the inductive method of instruction. Boston, USA: Reynolds ve Co.
- Confrey, J. (1991). Steering a course between Vygotsky and Piaget. Educational Researcher, 20(2), 29-32.
- Cook, J. P. ve Fukawa-Connelly, T. (2015) The pedagogical examples of groups and rings that algebraists think are most important in an introductory course. Canadian Journal of Science, Mathematics and Technology Education, 15(2), 171-185.
- Courant, R. (1981). Reminiscences from Hilbert’s Gottingen. Mathematical Intelligencer, 3(4), 154–164.
- Dahlberg, R. ve Housman, D. (1997). Facilitating learning events through example generation. Educational Studies in Mathematics, 33, 283-299.
- Davis, R. (1984). Learning mathematics: the cognitive science approach to mathematics education. Norwood, NJ, USA: Ablex.
- Davis, P. ve Hersh, R. (1981). The Mathematical Experience. Brighton UK: Harvester.
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