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preservice mathematics teachers beliefs technology integration radical constructivist grounded theory rcgt actional beliefs geometers sketchpad gsp geometric transformations

Preservice Secondary Mathematics Teachers’ Actional Beliefs about Teaching Geometric Transformations with Geometer’s Sketchpad

Shashidhar Belbase , Ram Krishna Panthi , Bishnu Khanal , Mukunda Prakash Kshetree , Bed Raj Acharya

Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they a.

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Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.

Keywords: Preservice mathematics teachers' beliefs, technology integration, radical constructivist grounded theory (RCGT), actional beliefs, Geometer's Sketchpad (GSP), geometric transformations.

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References

Andrini, B. (1991). Cooperative learning and mathematics: A multi-structured approach. Kagan Cooperative Learning Publishing.

Belbase, S. (2020). Early undergraduate Emirati female students’ beliefs about learning mathematics using technology. European Journal of Educational Research, 9(3), 1235-1255. https://doi.org/10.12973/eu.jer.9.3.1235

Belbase, S. (2018). Objectual beliefs of two preservice mathematics teachers about teaching geometric transformations with Geometer’s Sketchpad. International Journal for Research in Mathematics Education, 8(1), 38-59.

Belbase, S. (2017). Attitudinal and cognitive beliefs of two preservice secondary mathematics teachers. International Journal of Research in Education and Science, 3(2), 306-327.

Belbase, S. (2016). Reflective and reflexive beliefs of two preservice secondary mathematics teachers. European Journal of Educational and Social Sciences, 1(1), 34-65.

Belbase, S. (2015). Preservice secondary mathematics teachers’ beliefs about teaching geometric transformations using Geometer’s Sketchpad [Unpublished doctoral dissertation]. The University of Wyoming.

Belbase, S. (2014, July 28). Radical constructivist grounded theory: A hybrid epistemology [Paper presentation]. Research Symposium, University of Wyoming, Laramie, WY.

Belbase, S. (2013). Beliefs about teaching geometric transformations with geometers’ Sketchpad: A reflexive abstraction. Journal of Education and Research, 3(2), 15-38. https://doi.org/10.3126/jer.v3i2.8396

Badri, M. A., Mohaidat, J., & Rashedi, A. A. (2013). Technology readiness of school teachers: An empirical study of measurement and segmentation. Industrial Engineering & Management, 2(4), 1-10. https://doi.org/10.4172/2169-0316.1000117

Bailyn, L. (1977). Research as a cognitive process: Implications for data analysis. Quality and quantity, 11, 97-107.

Baloche, L. & Brody, C. M. (2017). Cooperative learning: Exploring challenges, crafting innovations. Journal of Education for Teaching, 43(3), 274-283. https://doi.org/10.1080/02607476.2017.1319513

Bergkamp, J. (2010). The paradox of emotionality and competence in multicultural competency training: A grounded theory [Unpublished doctoral dissertation]. Antioch University.

Blackwell, C. K., Lauricella, A. R., Wartella, E., & Robb, M. (2013). Adoption and use of technology in early education: The interplay of extrinsic barriers and teacher attitudes. Computers & Education, 69, 310–319.

Bloom, B. S. (Ed.). (1964). Taxonomy of educational objectives: The classification of educational goals, by a committee of college and university examiners. Longmans, Green.

Boehm, K. W. (1997). Experiences with The Geometer’s Sketchpad in the classroom. In J. R. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching, and research (pp. 71-73). The Mathematical Association of America.

Bossé, M. J., & Adu-Gyamfi, K. (2011). Stop teaching and lets students learn geometry. Mathematics Teacher, 105(4), 293-297.

Brumbaugh, D. (1997). Moving triangles. In J. R. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching, and research (pp. 69-70). The Mathematical Association of America.

Buckareff, A. A. (2006). Compatibilism and doxastic control. Philosophia, 34, 143-152. http://doi.org/10.1007/s11406-006-9013-0

Cantürk-Günhan, B., & Özen, D. (2010). Geometer’s Sketchpad software for non-thesis graduate students: A case study in Turkey. In V. Durand-Guerrier,  S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education6 (pp. 1301-1309). Institut National De Recherche Pédagogique.

Cennamo, K. S., Ross, J. D., & Ertmer, P. A. (2010). Technology integration for meaningful classroom use: A standard-based approach. CENGAGE Learning.

Chai, C. S., Wong, B., & Teo, T. (2011). Singaporean preservice 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. SAGE.

Chen, R. J. (2011). Preservice mathematics teachers’ ambiguous views of technology. School Science and Mathematics, 111(2), 56-67.

Cleaves, W. P. (2008). Promoting mathematics accessibility through multiple representations: JIGSAWS. Mathematics Teaching in the Middle School, 13(8), 446-452.

Cole, K. A. (1999). Walking around: Getting more from informal assessment. Mathematics Teaching in the Middle School, 4(4), 224-227.

Common Core State Standards Initiative. (2010). Common core state standards for mathematics. http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf

Corbin, J. M., & Strauss, A. L. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). SAGE Publications, Inc.

Cowen, J. B. (2009). The influence of perceived usefulness, perceived ease of use, and subjective norm on the use of computed radiography systems: A pilot study. KNOWLEDGE BANK. https:// shorturl.at/fpzLP

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). 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). The Mathematical Association of America.

Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly, 13(3), 319-330.

Deng, F., Chai, C. S., Chin-Chung, T., & Min-Hsien, L. (2014). The relationships among Chinese practicing teachers' epistemic beliefs, pedagogical beliefs and their beliefs about the use of ICT. Journal of Educational Technology & Society, 17(2), 245–256.

Dickinson, D. (1994). Multiple technologies for multiple intelligences. In A. Ward (Ed.), Multimedia and learning: A school leader’s guide (pp. 42-47). National School Boards Association.

Erens, R., & Eichler, A. (2015). 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). Springer Spektrum.

Ertmer, P. A. (2006). Teacher pedagogical beliefs and classroom technology use: A critical link. Online 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(September 2012), 423-435. https://doi.org/10.1016/j.compedu.2012.02.001

Falk, A. E. (2004). Desire and Beliefs: Introduction to some recent philosophical debates. Hamilton Books.

Foley, J. A., & Ojeda, C. (2007). How do teacher beliefs influence technology use in the classroom? In R. Carlsen, K. McFerrin, J. Price, R. Weber, & D. A. Willis (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2007 (pp. 796-801). AACE.

Forgasz, H. J., Vale, C., & Ursini, S. (2010). Technology for mathematics education: Equity, access, and agency. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology- rethinking the terrain, The 17th ICMI Study (pp. 385-404). Springer.

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. PUB - Publikationen an der Universität Bielefeld. http:// shorturl.at/ghnMP

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). The Mathematical Association of America.

Gillies, R. M. (2016). Cooperative learning: Review of research and practice. Australian Journal of Teacher Education, 41(3), 39-54. http://doi.org/10.14221/ajte.2016v41n3.3

Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. 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). Lawrence Erlbaum Associates.

Güneş, E., & Bahçivan, E. (2017). A mixed research-based model for preservice science teachers' digital literacy: Responses to "which beliefs" and "how and why they interact" questions. Computers & Education, 118, 96–106. https://doi.org/10.1016/j.compedu.2017.11.012

Hall, R. (2008). Applied social research: Planning, designing, and conducting real-world research. Palgrave Macmillan.

Hertz, R. (Ed.). (1997). Reflexivity and voice. SAGE.

Hodges, T. E., & Conner, E. (2011). A teacher and a student describe how integrating technology into mathematics classroom redefined their roles. Mathematics Teacher, 104(6), 432-438.

Hunter, J. (2015). Technology integration and high possibility classrooms: Building from TPACK. Routledge.

Ihde, D. (2000). This is not a text, or, do we read images? In M. T. Carroll & E. Tafoya (Eds.), Phenomenological approaches to popular culture (pp. 65-75). Bowling Green State University Popular Press.

Inan, F. A., & Lowther, D. L. (2010). Laptops in the K-12 classrooms: Exploring factors impacting instructional use. Computers & Education, 55(3), 937–944.

Jääskelä, P., Häkkinen, P., & Rasku-Puttonen, H. (2017). Teacher beliefs regarding learning, pedagogy, and the use of technology in higher education. Journal of Research on Technology in Education, 49(3-4), 198–211. http://doi.org/10.1080/15391523.2017.1343691

Johnson, D. W., & Johnson, R. T. (1990). Using cooperative learning in math. In N. Davidson (Ed.), Cooperative learning in mathematics: A handbook for teachers (pp. 103-125). Addison-Wesley.

Karagiorgi, Y. (2005). Throwing light into the black box of implementation: ICT in Cyprus elementary schools. Educational Media International, 42(1), pp. 19-32.

Keren-Kolb, E. & Fishman, B. (2006). Using drawings to draw out a preservice teacher’s beliefs about technology integration. American Educational Research Association.

Key Curriculum Press. (2009). The research base for the Geometer’s Sketchpad – executive summary. The Author.

Knowles, M. S. (1975). Self-directed learning. Association Press.

Kuntze, S., & Dreher, A. (2015). PCK and awareness of affective aspects reflected in teachers’ views about learning opportunities – a conflict? In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions (pp. 295-318). Springer.

Lao, J. R., & Young, J. (2020). Resistance to belief change: Limits of learning. Routledge.

Layder, D. (1998). Sociological practice: Linking theory and social research. SAGE.

Leatham, K. R. (2002). Preservice secondary mathematics teachers’ beliefs about teaching with technology [Unpublished doctoral dissertation]. The University of Georgia.

Leatham, K. R. (2007). Preservice secondary mathematics teachers’ beliefs about the nature of technology in the classroom. Canadian Journal of Science, Mathematics, and Technology Education, 7(2-3), 183-207.

Lichtenstein, B. B. (2000). The matrix of complexity: A multi-disciplinary approach for studying emergence in coevolution. http://www.hsdinstitute.org/learn-more/library/articles/MatrixOfComplexity.pdf

Lin, C. Y. (2008). Beliefs about using technology in the mathematics classroom: Interviews with preservice elementary teachers. Eurasian Journal of Mathematics, Science, & Technology Education, 4(2), 135-142.

Liu, S. H. (2011). Factors related to pedagogical beliefs of teachers and technology integration. Computers & Education, 56(4), 1012–1022. http://doi.org/10.1016/j.compedu.2010.12.001

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). Abo Akademi.

Manouchehri, A., Enderson, M. C., & Pugnucco, L. A. (1998). Exploring geometry with technology. Mathematics Teaching in the Middle School, 3(6), 436-442.

Martin, E., Prosser, M., Trigwell, K., Ramsden, P. & Benjamin, J. (2000). What university teachers teach and how they teach it. Instructional Science, 28(5), 387-412.

Merriam, S. B. (2002). Andragogy and self-directed learning: Pillars of adult learning theory. New Directions for Adult and Continuing Education, 2001(89), 3-14. https://doi.org/10.1002/ace.3

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. https://doi.org/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.

Morrow, J. (1997). Dynamic visualization from middle school through college. In J. R. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching, and research (pp. 33-46). The Mathematical Association of America.

Muller, K. O. (2010). How technology can promote the learning of proof. Mathematics Teacher, 103(6), 437-441.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. The Author.

National Council of Teachers of Mathematics. (2011). Technology in teaching and learning of mathematics: A position of the National Council of Teachers of Mathematics. NCTM.

Ng, W., Nicholas, H., & Williams, A. (2010). School experience influences on preservice teachers’ evolving beliefs about effective teaching. Teaching and Teacher Education, 26(2010), 278-289.

Obara, S. (2010). Students’ investigation of a view tube. Mathematics Teacher, 104(2), 127-132.

O’Neal, L J., Gibson, P., & Cotton, S. R. (2017). Elementary school teachers’ beliefs about the role of technology in 21st-Century teaching and learning. Computers in the Schools, 34(3), 1-15. https://doi.org/10.1080/07380569.2017.1347443

Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332. http://doi.org/10.3102/00346543062003307

Peker, M., & Ulu, M. (2020). The effect of preservice mathematics teachers’ beliefs about mathematics teaching-learning on their mathematics teaching anxiety. International Journal of Instruction, 11(3), 249-264. https://doi.org/10.12973/iji.2018.11318a

Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 257-318). Information Age Publishing.

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). Routledge.

Polly, D. (Ed.). (2015). Cases on technology integration in mathematics education. Information Science Reference.

Rodwell, M. K. (1998). Social work constructivist research. Garland Publishing Inc.

Santucci, L. C. (2011). Recreating history with Archimedes and Pi: Students use modern technology to investigate historical perspectives and calculate an approximation of π. Mathematics Teacher, 105(4), 298-303.

Siegel, L. M., Dickinson, G., Hooper, E. J., & Daniels, M. (2008). Teaching algebra and geometry concepts by modeling telescope optics. Mathematics Teacher, 101(7), 490-497.

Steffe, L. P. (2002). The constructivist teaching experiment: Illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177 – 194). 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). Erlbaum.

Strauss, A. L., & Corbin, J. M. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). SAGE Publications, Inc.

Suurtamm, C., Thompson, D. R., Kim, R. Y., Moreno, L. D., Sayac, N., Schukajlow, S., Silver, E. Ufer, S. & Vos, P. (2016). Assessment in mathematics education: Large scale assessment and classroom assessment. Springer Nature.

Teo, T., Chai, C. S., Hung, D., & Lee, C. B. (2008). Beliefs about teaching and uses of technology among preservice teachers. Asia-Pacific Journal of Teacher Education, 36(2), 163-174.

Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). NCTM.

Tondeur, J., Hermans, R., van Braak, J., & Valcke, M. (2008). Exploring the link between teachers’ educational belief profiles and different types of computer use in the classroom. Computers in Human Behavior, 24(6), 2541–2553.

Tough, A. (1971). The adult’s learning projects: A fresh approach to theory and practice in adult learning. Ontario Institute for Studies in Education.

von Glasersfeld, E. (1978). Radical constructivism and Piaget's concept of knowledge. In F. B. Murray (Ed.), The impact of Piagetian theory (pp. 109-122). University Park Press.

von Glasersfeld, E. (1990). An exposition of constructivism: Why some like it radical. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (pp. 19-29). NCTM.

von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. Routledge Falmer.

Wachira, P., & Keengwe, J. (2011). Technology integration barriers: Urban school mathematics teachers’ perspective. Journal of Science Education and Technology, 20(1), 17-25. https://doi.rog/10.1007/s10956-010-9230-y

Warfield, H. A. (2013). The therapeutic value of pilgrimage: A grounded theory study North Carolina State University [Unpublished doctoral dissertation]. North Carolina State University.

Welsh, R. (2009). International barriers to small business development: A study of independent retailers from the Edinburgh South Asian Community [Unpublished doctoral dissertation]. Queen Margaret University.

Wilson, M., & Cooney, T. J. (2002). Mathematics teacher change and development: The role of beliefs. In G.C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 127-148). Kluwer Academic Publisher.

Wyatt, K. W., Lawrence, A., & Foletta, G. M. (1997). Geometry activities for middle school students with The Geometer’s Sketchpad. Key Curriculum Press.

Yurekli, B., Stein, M. K., Correni, R., & Kisa, Z. (2020). Teaching mathematics for conceptual understanding: Teachers’ beliefs and practices and the role of constraints. Journal for Research in Mathematics Education, 51(2), 234-247. http://doi.org/10.5951/jresematheduc-2020-0021

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