Objectual beliefs of two preservice Mathematics teachers about teaching geometric transformations with geometer’s sketchpad
Palavras-chave:
Mathematics Teachers’ Beliefs, Objectual Beliefs, Technology Integration, Radical Constructivist Grounded Theory (RCGT), Geometer’s Sketchpad (GSP), Syntactics of GTs with GSP, Semantics of GTs with GSPResumo
The purpose of this paper is to present pre-service high school mathematics teachers’ objectual beliefs about the use of Geometer's Sketchpad (GSP) for teaching geometric transformations (GTs). The participants of the study were two senior undergraduate pre-service high school mathematics teachers at a public university in the United States of America. The study comprised a series of ten task-based interviews, five with each participant. I conceptualized radical constructivist grounded theory (RCGT) with five assumptions to guide the research process outlining the relationship between the researcher and participants, as well as emergent process of data construction, analysis, and interpretation. The results include three in vivo categories concerning GSP as an object of teaching GTs. The categories were – interface between algebra and geometry, the semantics of GTs with GSP, and syntactic of GTs with GSP. I addressed pedagogical implications of these categories at the end.
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Anfara, V. A., & Mertz, N. T., Jr. (Eds.). (2006). Theoretical frameworks in qualitative research. Thousand Oaks, CA: Sage Publications, Inc.
Audi, R. (2015). Rational beliefs: Structure, grounds, and intellectual virtue. Oxford: Oxford University Press.
Bailyn, L. (1977). Research as a cognitive process: Implications for data analysis. Quality and quantity, 11, 97-107.
Belbase, S. (2013). Images, anxieties, and attitudes toward mathematics. International Journal of Education in Mathematics, Science, and Technology, 1(4), 230-237. Accessed on July 20, 2017 from: http://dergipark.ulakbim.gov.tr/ijemst/article/view/5000036019
Belbase, S. (2014). Radical constructivist grounded theory: A hybrid epistemology. A presentation at the College of Education Research Symposium, University of Wyoming, Laramie, Wyoming (March 7, 2014). Online accessed on May 23, 2017 from: http://repository.uwyo.edu/education_symp/2014/Schedule/4/
Belbase, S. (2015a). A preservice secondary mathematics teacher’s beliefs about teaching mathematics with technology. International Journal of Research in Education and Science, 1(1), 31-44. Accessed on June 15, 2017 from: http://ijres.net/index.php/ijres/article/view/15
Belbase, S. (2015b). Pre-service secondary mathematics teachers’ beliefs about teaching geometric transformations using Geometer’s Sketchpad. A doctoral dissertation, University of Wyoming, Laramie, WY, USA.
Belbase, S. (2016). Reflective and reflexive beliefs of two pre-service secondary mathematics teachers about teaching geometric transformations using Geometer’s Sketchpad. European Journal of Educational and Social Sciences, 1(1), 34-65. Online accessed on May 28, 2017 from: http://ejess.eu/EJESS_vol1_1_MANID243_34-65.pdf
Belbase, S. (2017). Attitudinal and cognitive beliefs of two pre-service secondary mathematics teachers. International Journal of Research in Education and Science (IJRES), 3(2), 307-326. Online accessed from: http://ijres.net/index.php/ijres/article/view/231
Bell, A., Greer, B., Grimison, L., & Mangan, C. (1989). Children’s performance on multiplicative word problems: Elements of a descriptive theory. Journal for Research in Mathematics Education, 20(5), 434–449.
Bergkamp, J. (2010). The paradox of emotionality and competence in multicultural competency training: A grounded theory. A doctoral dissertation, Antioch University, Seattle, WA, USA.
Central Board of Secondary Education (CBSE, India). (2016). Mathematics: Coordinate geometry and transformations. Delhi: CBSE.
Chai, C. S., Wong, B., & Teo, T. (2011). Singaporean pre-service teachers’ beliefs about epistemology, teaching and learning, and technology. Teacher Development: An International Journal of Teachers’ Professional Development, 15 (4), 485-498.
Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Thousand Oaks, CA: Sage Publications, Inc.
Chen, R. J. (2011). Pre-service mathematics teachers’ ambiguous views of technology. School Science and Mathematics, 111(2), 56-67.
Clarke, A. E. (2005). Situational analysis: Grounded theory after the postmodern turn. Thousand Oaks, CA: Sage Publications, Inc.
Corbin, J. M., & Strauss, A. L. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Los Angeles, CA: Sage Publications, Inc.
Cuevas, G. J. (2010). Integrating technology in the mathematics classroom. In K. Cennamo, J. Ross, & P. Ertmer (Eds.), Technology integration for meaningful classroom use: A standard-based approach (pp. 369-386). Belmont, CA: WADSWORTH.
Cuoco, A. A., & Goldenberg, E. P. (1997). Dynamic geometry as a bridge from Euclidean Geometry to Analysis. In J. R. King & D. Schattschneider (Eds.), Geometry turned on!: Dynamic software in learning, teaching, and research (pp. 33-44). Washington, D. C.: The Mathematical Association of America.
Curriculum Development Center (CDC, Nepal). (2012). Basic education curriculum. Sanothimi, Bhaktapur, Nepal: CDC.
De Corte, E., & Verschaffel, L. (1987). The effect of semantic structure on first graders’ strategies for solving addition and subtraction word problems. Journal of Research in Mathematics Education, 18(5), 363-381.
Department for Education (DfE, UK). (2014). National curriculum in England: Mathematics programmes of study (July 16, 2014). Manchester, UK: DfE.
Erbas, A. K., Ledford, S. D., Orrill, C. H., & Polly, D. (2005). Promoting problem solving across geometry and algebra by using technology. Mathematics Teacher, 98(9), 599-603.
Erens, R., & Eichler, A. (2016). Beliefs and technology. In C. Bernack-Schüler, R. Erens, A. Eichler, & T. Leuders (Eds.), Views and beliefs in mathematics education: Results of the 19th MAVI Conference (pp. 133 – 144). Germany: Springer Spektrum.
Ertmer, P. A. (2006). Teacher pedagogical beliefs and classroom technology use: A critical link. Online resource document retrieved on May 24, 2013 from: http://www.edci.purdue.edu/ertmer/docs/AERA06_TchrBeliefs.pdf
Ertmer, P. A., Ottenbreit-Leftwich, A. T., Sadik, O., Sendurur, E., & Sendurur, P. (2012). Teacher beliefs and technology integration practices: A critical relationship. Computer & Education, 59(2012), 423-435. DOI: 10.1016/j.compedu.2012.02.001
Friedhoff, S., Zu Verl, C. M., Pietsch, C., Meyer, C., Vomprass, J., & Liebig, S. (2013). Social research data: Documentation, management, and technical implementation within the SFB 882. SFB 882 Working Paper Series, 16 (February).
Garry, T. (1997). Geometer’s Sketchpad in the classroom. In J. R. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching, and research (pp. 55-62). Washington, D. C.: The Mathematical Association of America.
Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. New York, NY: Aldine de Gruyter.
Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A.E. Kelly & R.A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 35-44). Mahwah, NJ: Lawrence Erlbaum Associates.
Goldin, G. A. (2002). Affect, meta-affect, and mathematical beliefs structures. In G. C. Leder, E. Pehkonen, & G. TÓ§rner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Hertz, R. (Ed.). (1997). Reflexivity and voice. Thousand Oaks, CA: Sage Publications, Inc.
Hoong, L. Y. (2003). Use of the Geometer’s Sketchpad in secondary schools. The Mathematics Educator, 7(2), 86-95.
Hoong, L. Y., & Khoh, L.-T. S. (2003). Effects of Geometer’s Sketchpad on spatial ability and achievement in transformation geometry among secondary two students in Singapore. The Mathematics Educator, 7(1), 32-48.
Hunter, J. (2015). Technology integration and high possibility classrooms: Building from TPACK. New York, NY: Routledge.
Jiang, Z. (2011). Participant research essay for TTAME Research Team. In S. A. Chamberlin, L. L. Hatfield, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education: Papers from a planning conference for WISDOMe. Laramie, WY: College of Education, University of Wyoming.
Kim, S. (2016). Relationship between pre-service secondary mathematics teachers’ beliefs, knowledge, and technology use. A doctoral dissertation, University of Georgia, Athens, GA.
Kissane, B., McConney, A., & Ho, K. F. (2015). Review of the use of technology in mathematics education. Perth, Western Australia: Government of Western Australia School Curriculum and Standards Authority.
Layder, D. (1998). Sociological practice: Linking theory and social research. London: Sage Publications, Inc.
Leatham, K. R. (2002). Pre-service secondary mathematics teachers’ beliefs about teaching with technology. A doctoral dissertation, University of Georgia, Athens, GA.
Lempert, L. B. (2007). Asking questions of the data: Memo writing in the grounded theory tradition. In A. Bryant & K. Charmaz (Eds.), The SAGE handbook of grounded theory (pp. 245-264). Los Angeles, CA: Sage Publications, Inc.
Lichtenstein, B. B. (2000). The matrix of complexity: A multi-disciplinary approach for studying emergence in coevolution. Online retrieved on January 20, 2014 from: http://www.hsdinstitute.org/learn-more/library/articles/MatrixOfComplexity.pdf
Lye, S. Y., & Churchill, D. (2013). Teaching with technology in a Future School in Singapore: A mathematics teacher’s experience. In L. Y. Tay & C. P. Lim (Eds.), Creating holistic technology-enhanced learning experiences: Tales from a Future School in Singapore (pp. 39-58). Rotterdam, The Netherlands: Sense Publishers.
Maher, C. A. (1998). Constructivism and constructivist teaching: Can they co-exist? In O. Bjorkqvist (Ed.), Mathematics teaching from a constructivist point of view (pp. 29 – 42). Finland: Abo Akademi.
Maher, C. A., & Sigley, R. (2014). Task-based interviews in mathematics education. Encyclopedia of Mathematics Education (pp. 579-582). DOI: 10.1007/978-94-007-4978-8_147.
Mauther, N. S., & Doucet, A. (2003). Reflexive accounts and accounts of reflexivity in qualitative data analysis. Sociology, 37(3), 413-431.
Meng, C. C. (2009). Engaging students’ geometric thinking through phase-based instruction using Geometer’s Sketchpad: A case study. Journal Pendidik dan Pendidikan, 24, 89- 107.
Meng, C. C., & Sam, L. C. (2013). Developing pre-service teachers’ technological pedagogical content knowledge for teaching mathematics with the Geometer’s Sketchpad through lesson study. Journal of Education and Learning, 2(1), 1-8.
Misfeldt, M., Jankvist, U. T., & Aguilar, M. S. (2016). Teacher beliefs about the discipline of mathematics and the use of technology in the classroom. Mathematics Education, 11(2), 395-419. DOI: 10.12973/iser.2016.2113a
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
Morse, J. M. (1994). Emerging from the data: The cognitive process of analysis in qualitative inquiry. In J. Morse (Ed.), Critical issues in qualitative research methods (pp. 23–43). Thousand Oaks, CA: Sage Publications, Inc.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.
Nesher, P. (1988). Multiplicative school word problems: Theoretical approaches and empirical findings. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 19–40). Hillsdale, NJ: Erlbaum.
Nordin, N., Zakaria, E., Mohamed, N. K., & Embi, M. A. (2010). Pedagogical usability of the Geometer’s Sketchpad (GSP) digital module in the mathematics teaching. The Turkish Online Journal of Educational Technology, 9(4), 113-117. Parveva, T., Noorani, S., Ranguelov, S., Motiejunaite, A., & Kerpanova, V. (2011). Mathematics education in Europe: Common challenges and national policies. Education, Audiovisual and Culture Executive Agency, European Commission.
Pierre, E. A. (2009). Decentering voice in qualitative inquiry. In A. Y. Jackson & L. A. Mazzei (Eds.), Voice in qualitative inquiry: Challenging conventional, interpretive, and critical conceptions in qualitative research (pp. 221-236). New York, NY: Routledge.
Polly, D. (Ed.). (2015). Cases on technology integration in mathematics education. Hershey, PA: Information Science Reference.
Rahim, M. H. (2000). A classroom use of the Geometer’s Sketchpad in a mathematics pre-service teacher education program. Thunder Bay, Ontario: Faculty of Education, Lakehead University.
Ramli, R., & Mustapha, R. (2014). An investigation on the GSP implementation in the teaching of mathematics at a Malaysian Technical School. Journal of Asian Vocational Education and Training, 7, 74-83.
Rodwell, M. K. (1998). Social work constructivist research. New York, NY: Garland Publishing Inc.
Shafer, K. G. (2004). Two high school teachers’ initial use of Geometer’s Sketchpad: Issues of implementation. A doctoral dissertation, Western Michigan University, Kalamazoo, MI.
Steffe, L. P. (2002). The constructivist teaching experiment: Illustrations and implications. In E. Von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177 – 194). New York, NY: Kluwer Academic Publishers.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267 – 307). Hillsdale, NJ: Erlbaum.
Steketee, S., & Scher, D. (2012). Sensations to teach composition of functions. Mathematics Teacher, 106(4), 261-268.
Strauss, A. L., & Corbin, J. M. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage Publications, Inc.
Thornberg, R., & Charmaz, K. (2014). Grounded theory and theoretical coding. In U. Flick (Ed.), The SAGE handbook of qualitative data analysis (pp. 153-169). Los Angeles: Sage Publications, Inc.
Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141–162). Hillsdale, NJ: Erlbaum.
Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. New York, NY: Routledge Falmer.
Von Glasersfeld, E. (Ed.). (1991). Radical constructivism in mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Wachira, P., & Keengwe, J. (2011). Technology integration barriers: Urban school mathematics teachers’ perspective. Journal of Science Education and Technology, 20(1), 17-25. DOI 10.1007/s10956-010-9230-y
Warfield, H. A. (2013). The therapeutic value of pilgrimage: A grounded theory study North Carolina State University. A doctoral dissertation, Raleigh, North Carolina.
Welsh, R. (2009). International barriers to small business development: A study of independent retailers from the Edinburgh South Asian Community. A doctoral dissertation, Queen Margaret University.
Willig, C. (2014). Interpretation and analysis. In U. Flick (Ed.), The SAGE handbook of qualitative data analysis (pp. 136-150). Los Angeles, CA: Sage Publications, Inc.
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