545
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Prospective mathematics teachers’ understanding of the base conceptFootnote*

ORCID Icon & ORCID Icon
Pages 176-199 | Received 20 Dec 2016, Published online: 22 Aug 2017

References

  • Maxedon SJ. Early childhood teacher's content and pedagogical knowledge of geometry [dissertation]. Tucson (AZ): The University of Arizona; 2003.
  • Clements D, Sarama J, Battista M. Development of concepts of geometric figures in a specially designed logo computer environment. Focus Learn Probl Math. 1998;20(2&3):47–64.
  • Cunningham RF, Roberts A. Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPST: J. 2010;1( Content Knowledge):1–17.
  • De Villiers M. To teach definitions in geometry or teach to define. In: Olivier A, Newstead K, editors. Proceedings of the 22nd International Conference for the Psychology of Mathematics Education; Vol. 2; 1998 Jul 12–17; Stellenbosch: University of Stellenbosch; 1998. p. 248–255.
  • Gutiérrez A, Jamie A. Preservice primary teachers’ understanding of the concept of altitude of a triangle. J Math Teach Educ. 1999;2(3):253–275.
  • Işıksal M, Koç Y, Osmanoglu A. A study on investigating 8th grade students’ reasoning skills on measurement: the case of cylinder. Educ Sci. 2010;156:61–70.
  • Matos JM. Cognitive models of the concept of angle. In: Da Ponte JP, Matos JF, editors. Proceedings of the 18th International Conference for Psychology of Mathematics Education; Vol. 3; 1994 Jul 29–Aug 3; Lisbon: University of Lisbon; 1994. p. 263–270.
  • Prescott A, Mitchelmore M, White P. Students’ difficulties in abstracting angle concepts from physical activities with concrete material. In: Barton B, Irwin KC, Pfannkuch M, Thomas MOJ, editors. Proceedings of the 25th Annual Conference of the Mathematics Education Research Group of Australasia; 2002 Jul 7–10; Auckland. Sydney: MERGA; 2002. p. 583–591.
  • Tsamir P, Tirosh D, Levenson E, et al. Early years teachers’ concept images and concept defnitions:triangles, circles, and cylinders. ZDM Math Educ. 2015;47:497–509.
  • Shulman L. Those who understand: knowledge growth in teaching. Educ Res. 1986;15(2):4–14.
  • Toluk Z, Olkun S, Durmuş S. The effect of geometric teaching supported by problem-centered and visual models on the development of geometric thinking levels of elementary school teachers. Paper presented at: 5th National Science and Mathematics Education; 2002 Sep 16–18; Ankara.
  • Bozkurt A, Koç Y. Investigating first year elementary mathematics teacher education students’ knowledge of prism. Educ Sci: Theory Pract. 2012;12(4):2949–2952.
  • Ertekin E, Yazıcı E, Delice A. Investigation of primary mathematics student teachers’ concept images: cylinder and cone. Int J Math Educ Sci Tech. 2014;45(4):566–588.
  • Kaplan A, Hızarcı S. Knowledge levels of mathematics teachers candidate concerning with triangle concept. J Kâzım Karabekir Educ Fac. 2005;11:472–478.
  • Tekin-Sitrava R, Işıksal-Bostan M. In-service mathematics teacher's mathematical knowledge for teaching: a case of volume of prism. In: Potari D, editor. Chair. Proceedings of CERME 8; 2013 Feb 6–10; Antalya. Available from: http://cerme8.metu.edu.tr/wgpapers/ WG17/WG17_Tekin_Sitrava.pdf
  • Vinner S, Hershkowitz R. Concept images and some common cognitive paths in the development of some simple geometric concepts. In: Karplus R, editor. Proceedings of the 4th International Conference for the Psychology of Mathematics Education; 1980 Aug 16–17; Berkeley (CA): PME; 1980. p. 177–184.
  • Horzum T. Visually impaired students’ concept images and representations in some mathematical concepts [dissertation]. Ankara: Gazi University; 2013.
  • Horzum T. Triangle concept from the perspective of blind students. J Kırşehir Educ Fac. 2016;17(2):275–295.
  • Türnüklü E, Ergin AS. 8th year students definitions and figural recognitions of solids: concept images. Element Educ Online. 2016;15(1):40–52.
  • Vinner S. The role of definitions in the teaching and learning of mathematics. In: Tall D, editor. Advanced mathematical thinking. Dordrecht: Kluwer; 1991. p. 65–81.
  • Tall D. Concept image and concept definition. In: De Lange J, Doorman M, editors. Senior secondary mathematics education. Utrecht: OW & OC; 1988. p. 37–41. Available from: http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1988e-concept-image-icme.pdf
  • Tall D, Vinner S. Concept image and concept definition in mathematics with particular reference to limits and continuity. Educ Stud Math. 1981;12(2):151–169.
  • Dienes ZP. An example of the passage from the concrete to the manipulation of formal systems. Educ Stud Math. 1971;3(3/4):337–352.
  • National Council of Teachers of Mathematics. Principles and standards for school mathematics. Reston (VA): NCTM Publications; 2000.
  • Toptaş V. An analysis of the elementary school mathematics curriculum and presentation of geometry concepts in textbooks. Element Educ Online. 2010;9(1):136–149.
  • Shaughnessy JM, Burger WF. Spadework prior to deduction in geometry. Math Teach. 1985;78(6):419–428.
  • Ward RA. An investigation of K-8 preservice teacher's concept images and mathematical definition of polygons. Issues Teach Educ. 2004;13(2):39–56.
  • Clements DH, Battista MT. Geometry and spatial reasoning. In: Grouws DA, editor. Handbook on mathematics teaching and learning. New York (NY): Macmillan; 1992. p. 420–464.
  • Grossman PL. The making of a teacher: teacher knowledge and teacher education. London: Teachers College Press; 1990.
  • Ball DL. The subject matter preparation of prospective mathematics teachers: challenging the myths. East Lansing: Michigan State University, National Center for Research on Teacher Education; 1988. ( Research Report 88-3).
  • Post TR, Harel G, Behr MJ, et al. Intermediate teachers’ knowledge of rational number concepts. In: Fennema E, Carpenter TP, Lamon SJ, editors. Integrating research on teaching and learning mathematics. Albany (NY): State University of New York Press; 1991. p. 194–217.
  • Çakmak Z, Konyalıoğlu AC, Işık A. The investigation of pre-service elementary mathematics teachers’ content knowledge on three dimensional objects. Middle East Afr J Educ Res. 2014;8:28–44.
  • Erşen ZB, Karakuş F. Evaluation of preservice elementary teachers’ concept ımages for quadrilaterals. Turk J Comput Math Educ. 2013;4(2):124–146.
  • Gökbulut Y, Ubuz B. Prospective primary teachers’ knowledge on prism: generating definitions and examples. Element Educ Online. 2013;12(2):401–412.
  • Türnüklü E, Alaylı FG, Akkaş EN. Investigation of prospective primary mathematics teachers’ perceptions and images for quadrilaterals. Educ Sci: Theory Pract. 2013;13(2):1213–1232.
  • Vighi P. The triangle as a mathematical object. In: Mariotti MA, editor. Proceedings of CERME 3; 2003 Feb 28–Mar 3; Bellaria. Available from: http://www.dm.unipi.it/∼didattica/ CERME3/proceedings/Groups/TG7/TG7_Vighi_cerme3.pdf
  • Vinner S, Dreyfus T. Images and definitions for the concepts of functions. J Res Math Educ. 1989;20(4):356–366.
  • Barnard AD, Tall DO. Cognitive units, connections, and mathematical proof. In: Pehkonen E, editor. Proceedings of the 21st International Conference for the Psychology of Mathematics Education; Vol. 2; 1997 Jul 14–19. Lahti (Finland): University of Helsinki; 1997. p. 41–48.
  • Viholainen A. Incoherence of a concept image and erroneous conclusions in the case of differentiability. Mont Math Enthus. 2008;5(2–3):231–248.
  • Vinner S. Concept definition, concept image and the notion of function. Int J Math Educ Sci Tech. 1983;14:293–305.
  • Rösken B, Rolka K. Integrating intuition: the role of concept image and concept definition for students’ learning of integral calculus. Mont Math Enthus. 2007;3:181–204.
  • Smith E, Shoben E, Rips L. Structure and process in semantic memory: a featural model for semantic decisions. Psychol Rev. 1974;81:214–241.
  • Tsamir P, Tirosh S, Levenson E. Intuitive nonexamples: the case of triangles. Educ Stud Math. 2008;69:81–95.
  • Olkun S, Toluk Uçar Z. İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics education in primary education]. 3rd ed. Ankara: Maya Akademi Yayın Dağıtım; 2007. Turkish.
  • Fujita T, Jones K. Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing. Res Math Educ. 2007;9(1–2):3–20.
  • Fujita T. Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. J Math Behav. 2012;31:60–72.
  • Jones K. Providing a foundation for deductive reasoning: students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educ Stud Math. 2000;44(1–3):55–85.
  • Monaghan F. What difference does it make? children views of the difference between some quadrilaterals. Educ Stud Math. 2000;42(2):179–196.
  • Pratt D, Davison I. Interactive whiteboards and the construction of definitions for the kite. In: Pateman NA, Dougherty BJ, Zillox JT, editors. Proceedings of the 27th International Conference for the Psychology of Mathematics Education; Vol. 4; 2003 Jul 13–18. Honolulu (HI): College of Education, University of Hawaii; 2003. p. 31–38.
  • Hershkowitz R. Visualization in geometry – two sides of the coin. Focus Learn Probl Math. 1989;11(1):61–76.
  • Hershkowitz R, Vinner S. Basic geometric concepts –  definitions and images. In: Vermandel A, editor. Proceedings of the 6th International Conference for the Psychology of Mathematics Education; 1982 Jul 18–23. Antwerp: Universitaire Instelling Antwerpen; 1982. p. 18–23.
  • Hershkowitz R, Vinner S. The role of critical and non- critical attributes in the concept image of geometrical concepts. In: Hershkowitz R, editor. Proceedings of the 7th International Conference for the Psychology of Mathematics Education; Vol. 1; 1983 Jul 24–29; Jerusalem. Rehovot: Weizmann Institute of Science; 1983. p. 223–228.
  • Hershkowitz R, Vinner S. Children's concept in elementary geometry – a reflection of teacher's concepts? In: Southwell B, Eyland R, Cooper M, Conroy J, Collis K, editors. Proceedings of the 8th International Conference for the Psychology of Mathematics Education; 1984 Aug 16–19; Sydney. Darlinghurst: Mathematical Association of New South Wales; 1984. p. 63–69.
  • Attneave F. Transfer of experience with a class schema to identification of patterns and shapes. J Exp Psychol. 1957;54:81–88.
  • Cheung LH. Enhancing students’ ability and ınterest in geometry learning through geometric constructions [master's thesis]. Hong Kong: The University of Hong Kong; 2011.
  • Napitupulu B. An exploration of students’ understanding and Van Hieles of thinking on geometric constructions [master's thesis]. Burnaby (BC): Simon Fraser University; 2001.
  • Posamentier AS. Making geometry come alive: student activities and teacher notes. Thousand Oaks (CA): Corwin Press; 2000.
  • Posner MI, Keele SW. On the genesis of abstract ideas. J Exp Psychol. 1968;77:353–363.
  • Reed SK. Pattern recognition and categorization. Cognit Psychol. 1972;3:382–407.
  • Rosch E. Natural categories. Cognit Psychol. 1973;4:328–350.
  • Dienes ZP. Building up mathematics. London: Hutchison Education; 1960.
  • Gningue S. Students working within and between representations: an application of Dienes's variability principles. Learn Math. 2006;26(2):41–47.
  • Clements DH, Sarama J. Young children's ideas about geometric shapes. Teach Child Math. 2000;6:482–488.
  • Hannibal MA. Young children's developing understanding of geometric shapes. Teach Child Math. 1999;5(6):353–357.
  • Van De Walle JA, Karp KS, Bay-Williams JM. Elementary and middle school mathematics: teaching developmentally. 7th ed. Toronto: Pearson Allyn and Bacon; 2013.
  • Okazaki M, Fujita T. Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In: Woo JH, Lew HC, Park KS, Seo DY, editors. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education; Vol. 4; 2007 Jul 8–13; Seoul: PME; 2007. p. 41–48.
  • Merriam SB. Qualitative research: a guide to design and implementation. 3rd ed. San Francisco (CA): Jossey-Bass; 2009.
  • Strauss A, Corbin J. Basics of qualitative research techniques and procedures for developing grounded theory. 2nd ed. Thousand Oaks (CA): Sage; 1998.
  • Miles MB, Huberman AM. Qualitative data analysis. Thousand Oaks (CA): Sage; 1994.
  • Büyük Türkçe Sözlük [Internet]. Ankara (Turkey): Turkish Language Institution; [cited 2016]. Available from: http://www.tdk.gov.tr/index.php?option=com_bts&arama=kelime& guid=TDK.GTS.58453aa7443b07.96781626
  • Moyer PS, Jones MG. Controlling choice: teacher, students, and manipulatives in mathematics classrooms. Sch Sci Math. 2004;104(1):16–21.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.