Research Article
BibTex RIS Cite

Reflective and reflexive beliefs of two pre-service secondary Mathematics teachers

Year 2016, Volume: 1 Issue: 1, 34 - 65, 08.08.2018

Abstract

The objective of this paper is to present two
preservice secondary mathematics teachers’ beliefs about teaching Geometric
Transformations (GTs) using Geometer’s Sketchpad (GSP). The study comprised of
series of five task-based interviews with each of two participants, who were
senior undergraduate preservice teachers, at a medium-sized public university
in the Rocky Mountain Region of the United States. I used radical
constructivist grounded theory (RCGT) as a theoretical frame to guide this
study process. The results of study include reflective and reflexive beliefs
about teaching GTs with GSP. These beliefs have been further explored as
pre-reflective, in-reflective, post-reflective, pre-reflexive, in-reflexive,
and post-reflexive beliefs of two preservice secondary mathematic teachers
about teaching GTs with GSP. Pedagogical implications of these belief
categories are widely discussed. 

References

  • Adams, R. S., Turns, J., & Atman, C. J. (2003). Educating effective engineering designers: The role of reflective practice. Design Studies, 24(3), 275-294.
  • Adler, S. A. (1993). Teacher education: Research as reflective practice. Teaching and Teacher Education, 9(2), 159-167.
  • Bailyn, L. (1977). Research as a cognitive process: Implications for data analysis. Quality and quantity, 11, 97-107.
  • Barrett, J. L., & Lanman, J. A. (2008). The science of religious beliefs. Religion, 38(2008), 109-124.
  • Belbase, S. (2015). Preservice secondary mathematics teachers’ beliefs about teaching geometric transformations using Geometer’s Sketchpad. Doctoral dissertation, University of Wyoming, Laramie, WY, USA.
  • Bergkamp, J. (2010). The paradox of emotionality and competence in multicultural competency training: A grounded theory. A doctoral dissertation, Antioch University, Seattle, WA, USA. Bouma, R. (1997). Process theology/John B. Cobb, Jr. The Boston Collaborative Encyclopedia of Modern Western Theology. Online retrieved from: http://people.bu.edu/wwildman/bce/mwt_themes_850_cobb.htm#Process Theology/John B. Cobb, Jr.
  • Bourdieu, P. (2001). Meditações pascalianas. Translated by Sergio Miceli. Rio de Janeiro: Bertrand Brasil. Original publication: Méditations pascaliennes. Paris: Éditions du Seuil, 1997.
  • Braude, S. E. (1995). First person plural: Multiple personality and the philosophy of mind. Lanham, MD: Rowman & Littlefield Publishers, Inc.
  • Bucciarelli, L. L. (1984). Reflective practice in engineering design. Design Studies, 5(3), 185-190.
  • Campbell, D. (2010). A theory of consciousness. Unpublished doctoral dissertation, The University of Arizona.
  • Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Thousand Oaks, CA: SAGE.
  • Chen, R. J. (2011). Preservice mathematics teachers’ ambiguous views of technology. School Science and Mathematics, 111(2), 56-67.
  • 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.
  • Davies, B., & Harre, R. (1990). Positioning: The discursive production of selves. Journal for the Theory of Social Behavior, 20, 43-63.
  • Dewey, J. (1933). How we think? Buffalo, NY: Prometheus Books.
  • Duffy, A. (2009). Guiding students through reflective practice – the preceptors’ experiences: A qualitative descriptive study. Nurse Education in Practice, 9(3), 166-175.
  • Eacott, S. (2013). Research as a political activity: The fallacy of data speaking for themselves. Leadership and Policy Quarterly, 2(4), 223-235. Edwards, A. (1999). Reflective practice in sport management. Sport Management Review, 2(1), 67-81. Emmerich, N. (2014). Bourdieu’s collective enterprise of inculcation: The moral socialization and ethical enculturation of medical students. British Journal of Sociology of Education. DOI: 10.1080/01425692.2014.886939
  • Engel, P. (2000). Introduction: The varieties of beliefs and acceptance. In P. Engel (Ed.), Believing and accepting (pp. 1-30). Dordrecht, The Netherlands: Kluwer Academic Publishers
  • 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). Germany: Springer Spektrum.
  • Ertmer, P. A. (2006). Teacher pedagogical beliefs and classroom technology use: A critical link. Online reseource 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
  • Fletcher, S. (1997). Modeling reflective practice for preservice teachers: The role of teacher educators. Teaching and Teacher Education, 13(2), 237-243.
  • 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). Chesapeake, VA: AACE.
  • 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). Online available from: http://www.sfb882.uni-bielefeld.de/
  • 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.
  • Groarke, S. (2014). Managed lives: Psychoanalysis, inner security, and the social order. New York, NY: Routledge.
  • Hall, R. (2008). Applied social research: Planning, designing, and conducting real-world research. Sydney, Australia: Palgrave Macmillan.
  • Harford, J., & MacRuairc, G. (2008). Engaging student teachers in meaningful reflective practice. Teaching and Teacher Education, 24(7), 1884-1892.
  • Hargreaves, J. (2004). So how do you feel about that? Assessing reflective practice. Nurse Education Today, 24(3), 196-201.
  • Hertz, R. (Ed.). (1997). Reflexivity and voice. Thousand Oaks, CA: SAGE.
  • Hunter, J. (2015). Technology integration and high possibility classrooms: Building from TPACK. New York, NY: Routledge.
  • Jansen, A. (2008). An investigation of relationships between seventh-grade students’ beliefs and their participation during mathematics discussions in two classrooms. Mathematics Thinking and Learning, 10, 68-100.
  • Jarvis, P. (1992). Reflective practice and nursing. Nurse Education Today, 12(3), 174-181.
  • Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9, 187-211. Jovchelovitch, S. (1996). In defense of representation. Journal for the Theory of Social Behavior, 26, 121-136.
  • Kwanvig, J. (2013). Perspectivalism and reflective ascent. In D. Christensen & J. Lackey (Eds.), The epistemology of disagreement: New essays (pp. 223-242). Oxford, U.K.: Oxford University Press.
  • Layder, D. (1998). Sociological practice: Linking theory and social research. London, U. K.: SAGE.
  • Leikin, R., & Zazkis, R. (2010). Teachers’ opportunities to learn mathematics through teaching. In R. Leikin & R. Zazkis (Eds.), Learning through teaching mathematics: Development of teachers’ knowledge and expertise in practice (pp. 3-21). New York, NY: Springer.
  • 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
  • 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.
  • Lizardo, O., & Strand, M. (2011). Beyond ‘world images’: Beliefs as embodied action in the world. Paper presented at the annual meeting of the American Sociological Association Annual Meeting, Caesar’s Palace, Las Vegas, NV.
  • Loughran, J. (2002). Effective reflective practice: In search of meaning in learning about teaching. Journal of Teacher Education, 63(1), 33-43.
  • Lowery, N. V. (2003). The fourth “R”: Reflection. The Mathematics Educator, 13(2), 23-31.
  • 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.
  • Mauther, N. S., & Doucet, A. (2003). Reflexive accounts and accounts of reflexivity in qualitative data analysis. Sociology, 37(3), 413-431.
  • Medeiros, E., & Capela, J. (2010). Processes of identity-building in the Zambesi Valley: Ethnic solidarity and the Zambesian ethos. In A. Keese (Ed.), Ethnicity and the long-term perspective: The African experience (pp. 35-66). Bern, Switzerland: International Academic Publishers.
  • 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.
  • Nozick, R. (1983). Philosophical explanations. Boston, MA: Harvard University Press.
  • 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.
  • Richard, M. (2013). Context and the attitudes: Meaning in context. Oxford, U. K.: Oxford University Press.
  • Rodwell, M. K. (1998). Social work constructivist research. New York, NY: Garland Publishing Inc. Romdenh-Romluc, R. (2007). Suppressed beliefs. Theoria, 58, 17-24.
  • Schön, D. A. (1983). The reflective practitioner. New York, NY: Basic Books.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 100-121.
  • Smitherman, S. E. (2006). Reflections on teaching a mathematics education course. Doctoral dissertation, Louisiana State University.
  • Sperber, D. (1997). Intuitive and reflective beliefs. Mind and Language, 12(1), 67-83.
  • 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.
  • Thompson, S., & Thompson, N. (2008). The critically reflective practitioner. New York, NY: Palgrave MacMillan.
  • Tremlin, T. (2006). Minds and gods: The cognitive foundations of religion. Oxford Scholarship Online. DOI: 10.1093/0195305345.001.0001
  • Van der Hart, O., Nijenhuis, E. R., & Steele, K. (2006). The haunted self: Structural dissociation and the treatment of chronic traumatization. New York, NY: W. W. Norton & Company, Inc.
  • Van Manen, M. (1991). The tact of teaching: The meaning of pedagogical thoughtfulness. Albany, NY: State University of New York Press.
  • von Glasersfeld, E. (1978). Radical constructivism and Piaget's concept of knowledge. Inn F. B. Murray (Ed.), The impact of Piagetian theory (pp. 109-122). Baltimore, MD: 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). Reston, VA: NCTM.
  • von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. New York, NY: Routledge Falmer.
  • 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. Doctoral dissertation, Queen Margaret University.
  • Whittock, T. (1997). Reflexive teaching, reflexive learning. Teaching in Higher Education, 2(2), 93-102. DOI: 10.1080/1356251970020201
  • Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). 150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring Teachers’ Thinking (pp. 104 – 124). London: Cassell.
  • Zimmermann, K. (2010). Gender knowledge under construction: The case of the European Union’s science and research policy. In B. Riegraft, B. Aulenbacher, Kirsch-Auwärter, & Müller (Eds.), Gender change in academia: Remapping the fields of work, knowledge, and politics from a gender perspective (pp. 173-188). Sabine Schöller, Germany: Springer Fachmedien.
Year 2016, Volume: 1 Issue: 1, 34 - 65, 08.08.2018

Abstract

References

  • Adams, R. S., Turns, J., & Atman, C. J. (2003). Educating effective engineering designers: The role of reflective practice. Design Studies, 24(3), 275-294.
  • Adler, S. A. (1993). Teacher education: Research as reflective practice. Teaching and Teacher Education, 9(2), 159-167.
  • Bailyn, L. (1977). Research as a cognitive process: Implications for data analysis. Quality and quantity, 11, 97-107.
  • Barrett, J. L., & Lanman, J. A. (2008). The science of religious beliefs. Religion, 38(2008), 109-124.
  • Belbase, S. (2015). Preservice secondary mathematics teachers’ beliefs about teaching geometric transformations using Geometer’s Sketchpad. Doctoral dissertation, University of Wyoming, Laramie, WY, USA.
  • Bergkamp, J. (2010). The paradox of emotionality and competence in multicultural competency training: A grounded theory. A doctoral dissertation, Antioch University, Seattle, WA, USA. Bouma, R. (1997). Process theology/John B. Cobb, Jr. The Boston Collaborative Encyclopedia of Modern Western Theology. Online retrieved from: http://people.bu.edu/wwildman/bce/mwt_themes_850_cobb.htm#Process Theology/John B. Cobb, Jr.
  • Bourdieu, P. (2001). Meditações pascalianas. Translated by Sergio Miceli. Rio de Janeiro: Bertrand Brasil. Original publication: Méditations pascaliennes. Paris: Éditions du Seuil, 1997.
  • Braude, S. E. (1995). First person plural: Multiple personality and the philosophy of mind. Lanham, MD: Rowman & Littlefield Publishers, Inc.
  • Bucciarelli, L. L. (1984). Reflective practice in engineering design. Design Studies, 5(3), 185-190.
  • Campbell, D. (2010). A theory of consciousness. Unpublished doctoral dissertation, The University of Arizona.
  • Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Thousand Oaks, CA: SAGE.
  • Chen, R. J. (2011). Preservice mathematics teachers’ ambiguous views of technology. School Science and Mathematics, 111(2), 56-67.
  • 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.
  • Davies, B., & Harre, R. (1990). Positioning: The discursive production of selves. Journal for the Theory of Social Behavior, 20, 43-63.
  • Dewey, J. (1933). How we think? Buffalo, NY: Prometheus Books.
  • Duffy, A. (2009). Guiding students through reflective practice – the preceptors’ experiences: A qualitative descriptive study. Nurse Education in Practice, 9(3), 166-175.
  • Eacott, S. (2013). Research as a political activity: The fallacy of data speaking for themselves. Leadership and Policy Quarterly, 2(4), 223-235. Edwards, A. (1999). Reflective practice in sport management. Sport Management Review, 2(1), 67-81. Emmerich, N. (2014). Bourdieu’s collective enterprise of inculcation: The moral socialization and ethical enculturation of medical students. British Journal of Sociology of Education. DOI: 10.1080/01425692.2014.886939
  • Engel, P. (2000). Introduction: The varieties of beliefs and acceptance. In P. Engel (Ed.), Believing and accepting (pp. 1-30). Dordrecht, The Netherlands: Kluwer Academic Publishers
  • 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). Germany: Springer Spektrum.
  • Ertmer, P. A. (2006). Teacher pedagogical beliefs and classroom technology use: A critical link. Online reseource 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
  • Fletcher, S. (1997). Modeling reflective practice for preservice teachers: The role of teacher educators. Teaching and Teacher Education, 13(2), 237-243.
  • 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). Chesapeake, VA: AACE.
  • 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). Online available from: http://www.sfb882.uni-bielefeld.de/
  • 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.
  • Groarke, S. (2014). Managed lives: Psychoanalysis, inner security, and the social order. New York, NY: Routledge.
  • Hall, R. (2008). Applied social research: Planning, designing, and conducting real-world research. Sydney, Australia: Palgrave Macmillan.
  • Harford, J., & MacRuairc, G. (2008). Engaging student teachers in meaningful reflective practice. Teaching and Teacher Education, 24(7), 1884-1892.
  • Hargreaves, J. (2004). So how do you feel about that? Assessing reflective practice. Nurse Education Today, 24(3), 196-201.
  • Hertz, R. (Ed.). (1997). Reflexivity and voice. Thousand Oaks, CA: SAGE.
  • Hunter, J. (2015). Technology integration and high possibility classrooms: Building from TPACK. New York, NY: Routledge.
  • Jansen, A. (2008). An investigation of relationships between seventh-grade students’ beliefs and their participation during mathematics discussions in two classrooms. Mathematics Thinking and Learning, 10, 68-100.
  • Jarvis, P. (1992). Reflective practice and nursing. Nurse Education Today, 12(3), 174-181.
  • Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9, 187-211. Jovchelovitch, S. (1996). In defense of representation. Journal for the Theory of Social Behavior, 26, 121-136.
  • Kwanvig, J. (2013). Perspectivalism and reflective ascent. In D. Christensen & J. Lackey (Eds.), The epistemology of disagreement: New essays (pp. 223-242). Oxford, U.K.: Oxford University Press.
  • Layder, D. (1998). Sociological practice: Linking theory and social research. London, U. K.: SAGE.
  • Leikin, R., & Zazkis, R. (2010). Teachers’ opportunities to learn mathematics through teaching. In R. Leikin & R. Zazkis (Eds.), Learning through teaching mathematics: Development of teachers’ knowledge and expertise in practice (pp. 3-21). New York, NY: Springer.
  • 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
  • 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.
  • Lizardo, O., & Strand, M. (2011). Beyond ‘world images’: Beliefs as embodied action in the world. Paper presented at the annual meeting of the American Sociological Association Annual Meeting, Caesar’s Palace, Las Vegas, NV.
  • Loughran, J. (2002). Effective reflective practice: In search of meaning in learning about teaching. Journal of Teacher Education, 63(1), 33-43.
  • Lowery, N. V. (2003). The fourth “R”: Reflection. The Mathematics Educator, 13(2), 23-31.
  • 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.
  • Mauther, N. S., & Doucet, A. (2003). Reflexive accounts and accounts of reflexivity in qualitative data analysis. Sociology, 37(3), 413-431.
  • Medeiros, E., & Capela, J. (2010). Processes of identity-building in the Zambesi Valley: Ethnic solidarity and the Zambesian ethos. In A. Keese (Ed.), Ethnicity and the long-term perspective: The African experience (pp. 35-66). Bern, Switzerland: International Academic Publishers.
  • 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.
  • Nozick, R. (1983). Philosophical explanations. Boston, MA: Harvard University Press.
  • 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.
  • Richard, M. (2013). Context and the attitudes: Meaning in context. Oxford, U. K.: Oxford University Press.
  • Rodwell, M. K. (1998). Social work constructivist research. New York, NY: Garland Publishing Inc. Romdenh-Romluc, R. (2007). Suppressed beliefs. Theoria, 58, 17-24.
  • Schön, D. A. (1983). The reflective practitioner. New York, NY: Basic Books.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 100-121.
  • Smitherman, S. E. (2006). Reflections on teaching a mathematics education course. Doctoral dissertation, Louisiana State University.
  • Sperber, D. (1997). Intuitive and reflective beliefs. Mind and Language, 12(1), 67-83.
  • 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.
  • Thompson, S., & Thompson, N. (2008). The critically reflective practitioner. New York, NY: Palgrave MacMillan.
  • Tremlin, T. (2006). Minds and gods: The cognitive foundations of religion. Oxford Scholarship Online. DOI: 10.1093/0195305345.001.0001
  • Van der Hart, O., Nijenhuis, E. R., & Steele, K. (2006). The haunted self: Structural dissociation and the treatment of chronic traumatization. New York, NY: W. W. Norton & Company, Inc.
  • Van Manen, M. (1991). The tact of teaching: The meaning of pedagogical thoughtfulness. Albany, NY: State University of New York Press.
  • von Glasersfeld, E. (1978). Radical constructivism and Piaget's concept of knowledge. Inn F. B. Murray (Ed.), The impact of Piagetian theory (pp. 109-122). Baltimore, MD: 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). Reston, VA: NCTM.
  • von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. New York, NY: Routledge Falmer.
  • 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. Doctoral dissertation, Queen Margaret University.
  • Whittock, T. (1997). Reflexive teaching, reflexive learning. Teaching in Higher Education, 2(2), 93-102. DOI: 10.1080/1356251970020201
  • Wilson, S. M., Shulman, L. S., & Richert, A. E. (1987). 150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring Teachers’ Thinking (pp. 104 – 124). London: Cassell.
  • Zimmermann, K. (2010). Gender knowledge under construction: The case of the European Union’s science and research policy. In B. Riegraft, B. Aulenbacher, Kirsch-Auwärter, & Müller (Eds.), Gender change in academia: Remapping the fields of work, knowledge, and politics from a gender perspective (pp. 173-188). Sabine Schöller, Germany: Springer Fachmedien.
There are 72 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Articles
Authors

Shashidhar Belbase This is me

Publication Date August 8, 2018
Published in Issue Year 2016 Volume: 1 Issue: 1

Cite

APA Belbase, S. (2018). Reflective and reflexive beliefs of two pre-service secondary Mathematics teachers. European Journal of Educational and Social Sciences, 1(1), 34-65.