Meanings, Dimensions, and Categories of Mathematics Teacher Beliefs: A Navigation through the Literature

Shashidhar Belbase

Abstract


This paper aimed to discuss the meanings, dimensions, and categories of teacher beliefs about teaching and learning mathematics. I reviewed the relevant literature about teacher beliefs in general, beliefs about mathematics, and beliefs about mathematics teaching and learning in particular. Based on the review of the literature, I outlined the meanings of teacher beliefs and conceptualized three dimensions of teacher beliefs – affective dimension, cognitive dimension, and pedagogical dimension. Then, I discussed three viewpoints to observe teacher beliefs – relational, institutional, and praxis lenses. I utilized these lenses to categorize belief constructs into three classes of beliefs about mathematics, teaching mathematics, and learning mathematics. These classes’ included-instrumentalist, constructivist, and integral beliefs. I addressed the pedagogical implications of these categorical beliefs in the end.

Keywords


constructivist beliefs; dimension of beliefs; integral beliefs; instrumental beliefs; teacher beliefs

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References


Aguirre, J. M. (2009). Teacher domain-specific beliefs and their impact on mathematics education reform. In J. Maas & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 45-58). Rotterdam: Sense Publisher.

Alexander, P. A., & Sinatra, G. M. (2007). First steps: Scholar’s promising movements into a nascent field of inquiry. In S. Vosniadou, A. Baltas, & X. Vamvakoussi (Eds.), Reframing the conceptual change approach in learning and instruction (pp. 221–236). Oxford: Elsevier.

Anderson, J. (1996). Some teachers’ beliefs and perceptions of problem solving. In P. C. Clarkson (Ed.), Technology of mathematics education (pp. 30-37). Melbourne: MERGA.

Audi, R. (1988). Belief, justification, and knowledge: An introduction to epistemology. Belmont: Wadsworth Publishing Company.

Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs: Prentice Hall.

Battista, M. T. (1994). Teacher beliefs and the reform movement in mathematics education. Phi Delta Kappan, 75(6), 462-470.

Belbase, S. (2013a). A unified theory of mind-brain relationship: Is it possible? Open Journal of Philosophy, 3(4), 443-450.

Belbase, S. (2013b). Beliefs about teaching geometric transformations with geometers’ Sketchpad: A reflexive abstraction. Journal of Education and Research, 3(2), 15-38.

Belbase, S. (2015). Preservice secondary mathematics teachers’ beliefs about teaching geometric transformations using Geometer’s Sketchpad. Dissertation. Laramie: University of Wyoming.

Bendixen, L. D., Schraw, G., & Dunkle, M. E. (1998). Epistemic beliefs and moral reasoning. Journal of Psychology, 13, 187–200.

Beswick, K. (2007). Teachers’ beliefs that matter in secondary mathematics classrooms. Educational Studies in Mathematics, 65, 95-120.

Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127-147.

Blömeke, S., Hsieh, F. J., Kaiser, G., & Schmidt, W. H. (Eds.). (2014). International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn TEDS-M Results. New York: Springer.

Bodur, H. O., Brinberg, D., & Coupey, E. (2000). Belief, affect, and attitude: Alternate models of the determinants of attitude. Journal of Consumer Psychology, 9(1), 17-28.

Boyd, P., & Ash, A. (2018). Mastery mathematics: Changing teacher beliefs around in-class grouping and mind set. Teaching and Teacher Education, 75, 214-223.

Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. New York: Springer.

Brosnan, P. A., Edwards, T., & Erickson, D. (1996). An exploration of change in teachers’ beliefs and practices during implementation of mathematics standards. Focus on Learning Problems in Mathematics, 18(4), 35-53.

Brown, A. B., & Baird, J. (1993). Inside the teacher: Knowledge, beliefs, and attitudes. In P. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 245-259). New York: Macmillian.

Cain, T. (2011). Teacher’s classroom-based action research. International Journal of Research & Method in Education, 34(1), 3-16.

Cano, F., & Cardelle-Elawar, M. (2008). Family environment, epistemological beliefs, learning strategies, and academic performance: A path analysis. In M. S. Khine (Ed.), Knowing, knowledge, and beliefs: Epistemological studies across diverse cultures (pp. 219-240). New York: Springer.

Chandler, M., Boyes, M., & Ball. L. (1990). Relativism and stations of epistemic doubt. Journal of Experimental Child Psychology, 50, 370–395.

Churchill, D. (2006). Teachers’ private theories and their design of technology-based learning. British Journal of Educational Technology, 37(4), 559-576.

Day, R. (1996). Case studies of preservice secondary mathematics teachers’ beliefs: Emerging and evolving themes. Mathematics Education Research Journal, 8(1), 5-22.

Dede, Y., & Uysal, F. (2012). Examining Turkish preservice elementary teachers’ beliefs about the nature and the teaching of mathematics. International Journal of Humanities and Social Science, 2(12), 125-135.

Dengate, B., & Lerman, S. (1995). Learning theory in mathematics education: Using the wide angle lens and not just the microscope. Mathematics Education Research Journal, 7(1), 26-36.

Dionne, J. J. (1984). The perception of mathematics among elementary school teachers. In J. M. Moser (Ed.), Proceedings of 6th conference of the North American Chapter of the International Group of the Psychology of Mathematics Education (pp. 223-228). Madison: University of Wisconsin.

Dunn, M. L. (2002). Theories of learning. In Learning and Teaching Briefing Papers Series, Headington: Oxford Brookes University.

Eichler, A., & Erens, R. (2015). Domain-specific belief systems of secondary mathematics teachers. In B. Pepin, B. Roesken-Winter (eds.), From beliefs to dynamic affect systems in mathematics education, Advances in Mathematics Education (pp. 179-200). New York: Springer.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–254). New York: The Falmer Press.

Ernest, P. (1991). The philosophy of mathematics education. New York: Routledge Falmer.

Ernest, P. (1995). The one and many. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 459-486). Hillsdale: Lawrence Erlbaum.

Ernest, P. (2015). Postmodern mathematics. In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematics Education (pp. 605-608). Seoul: Springer International Publishing.

Farrell, T. S. C. (2013). Reflective practice in ESL teacher development groups. London: Palgrave Macmillan.

Feit, N. (2008). Belief about the self: A defense of the property theory of content. Oxford: Oxford University Press.

Felbrich, A., Kaiser, G., & Schmotz, C. (2014). The cultural dimension of beliefs: An investigation of future primary teachers’ epistemological beliefs concerning nature of mathematics in 15 countries. In S. Blömeke et al. (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn: TEDS-M results (pp. 209-229). New York: Springer.

Fenstermacher, G. (1979). A philosophical consideration of recent research on teacher effectiveness. In L. S. Shulman (Ed.), Review of research in education (Vol. 6, pp. 157-185). Itasca: Peacock.

Fisher, P. O. (1992). Beliefs about and attitudes toward mathematics and mathematics teaching held by prospective elementary teachers at the University of Nebraska-Lincoln. Dissertation. Lincoln: University of Nebraska-Lincoln.

Fives, H., & Buehl, M. M. (2012). Spring cleaning for the messy construct of teacher beliefs: What are they? Which have been examined? What can they tell us? In K. R. Harris, S. Graham & T. Urdan (Eds.), APA Educational Psychology Handbook (Vol. 2, pp. 471-499). Washington DC: APA.

Furinghetti, F., & Morselli, F. (2009). Every unsuccessful problem solver is unsuccessful in his or her own way: Affective and cognitive factors in proving. Educational Studies in Mathematics, 70, 71-90.

Furenghetti, F., & Morselli, F. (2011). Beliefs and beyond: Hows and whys in the teaching of proof. ZDM Mathematics Education, 43, 587-599.

Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. C. Leder, E. Pehkonen, & G. Tӧrner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 39-58). Dordrecht: Kluwer Academic Publishers.

Garcia, G. (2009). The role of pedagogical beliefs in teachers’ integration of technology in the classroom. Mansfield: University of Connecticut.

Giroux, H. A. (1992). Border crossing: Cultural workers and the politics of education. New York: Routledge.

Goldin, G. A. (2002). Affect, meta-affect, and mathematical beliefs structures. In G. C. Leder, E. Pehkonen, & G. Tӧrner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 59-72). Dordrecht: Kluwer Academic Publishers.

Goldin, G., Rösken, B., & Törner, G. (2009). Beliefs- no longer a hidden variable in mathematics teaching and learning process. In J. Maas & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 1-18). Rotterdam: Sense Publisher.

Goss, M., Powers, R., & Hauk, S. (2013). Identifying change in secondary mathematics teachers’ pedagogical content knowledge. Proceedings for the 16th conference on Research in Undergraduate Mathematics Education. Denver: SIGMAA.

Grant, C. E. (1984). A study of the relationship between secondary mathematics teachers’ beliefs about teaching-learning process and their observed classroom behaviors. Dissertation. Grand Forks: University of North Dakota.

Green, T. (1971). The activities of teaching. New York: McGraw-Hill.

Grundy, S. (1987). Curriculum: Product or praxis? New York: Falmer Press.

Habermas, J. (1972). Knowledge and human interests (2nd ed.). London: Heinemann.

Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47-57.

Hart, L. E. (1989). Describing the affective domain: Saying what we mean. In D. B. McLeod & V. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 33-45). New York: Springer-Verlag.

Hashweh, M. Z. (1996). Effects of science teachers’ epistemological beliefs in teaching. Journal of Research in Science Teaching, 33(1), 47-63.

Hermans, C. A. M. (2002). Ultimate meaning as silence: The monologic and polyphonic Author-God in religious communication. In C. A. M. Hermans, G. Immink, A. de Jong & J. van der Lans (Eds.), Social constructionism and theology (pp. 113-146). Boston: Brill.

Hermans, R., van Braak, J., & Van Keer, H. (2008). Development of the beliefs about primary education scale: Distinguishing a developmental and transmissive dimension. Teaching and Teacher Education, 24(1), 127-139.

Herppich, S., & Wittwer, J. (2018). Preservice teachers’ beliefs about students’ mathematical knowledge structure as a foundation for formative assessments. Teaching and Teacher Education, 76, 242-254.

Hersh, R. (1979). Some proposals for reviewing the philosophy of mathematics. Advances in Mathematics, 31, 31-50.

Hull Jr, R. E. (1979). On pedagogical caring. Educational theory, 29(3), 237-243.

Idris, N. (2006). Teaching and learning of mathematics: Making sense and developing cognitive abilities. Negara: Utusan Publications.

Jones, D. L. (1991). A study of the beliefs systems of two beginning middle school mathematics teachers. Dissertation. Athens: University of Georgia.

Kagan, D. M. (1992). Implications of research on teacher beliefs. Educational Psychologist, 27(1), 65-90.

Kalaja, P., Barcelos, A. M. F., Aro, M., & Ruohotie-Lehty, M. (2015). Beliefs, agency, and identity in foreign language learning and teaching. New York: Palgrave Macmillan.

Kardash, C. M., & Howell, K. L. (2000). Effects of epistemological beliefs and topic-specific beliefs on undergraduates cognitive and strategic processing of dual-positional text. Journal of Educational Psychology, 92(3), 524-535.

Kim, R., & Albert, L. R. (2015). Mathematics teaching and learning: South Korean elementary teachers’ mathematical knowledge for teaching. New York: Springer.

Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development. Eaglewood Cliffs: Prentice-Hall.

Kuhs, T. M., & Ball, D. L. (1986). Approaches to teaching mathematics: Mapping the domains of knowledge, skills, and dispositions. East Lansing: Michigan State University, Center for Teacher Education.

Kuntze, S., & Friesen, M. (2018). The role of mathematics teachers’ views for their competence of analyzing classroom situations. In B. Rott et al. (Eds.), Views and beliefs in mathematics education (pp. 183-194). Switzerland: Springer.

Lampert, M., & Ball, D. L. (1998). Teaching multimedia and mathematics: Investigations of real practice. New York: Teachers College, Columbia University.

Leatham, K. R. (2002). Preservice secondary mathematics teachers’ beliefs about teaching with technology. Dissertation. Athens: University of Georgia.

Leder, G. C., Pehkonen, E., & Törner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education. Dordrecht: Kluwer Academic Publisher.

Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod & V. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 75-88). New York: Springer-Verlag.

Liljedahl, P. (2018a). Relationship between proxies for learning and mathematically related beliefs. In H. Palmer & J. Skott (Eds.), Students’ and teachers’ values, attitudes, feelings, and beliefs in mathematics classrooms (pp. 1-11). Switzerland: Springer.

Liljedahl, P. (2018b). Affect as a system: The case of Sara. In B. Rott et al. (Eds.), Views and beliefs in mathematics education (pp. 21-32). Switzerland: Springer.

Liljedahl, P., Rolka, K., & Rösken, B. (2007). Affecting affect: The re-education of preservice teachers’ beliefs about mathematics and mathematics learning and teaching. In M. Strutchens & W. Martin (Eds.), 69th NCTM yearbook – The learning of mathematics (pp. 319–330). Reston: National Council of Teachers of Mathematics.

Lo, W. Y., & Anderson, J. (2010). Beyond the curriculum: The mathematical beliefs of pre-service primary teachers in Hong Kong. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 657–644). Fremantle: MERGA.

Manderfeld, K., & Siller, H. S. (2018). Evaluation of an approach of professional role reflection in mathematics education. In B. Rott et al. (Eds.), Views and beliefs in mathematics education (pp. 103 – 113). Switzerland: Springer.

Martino, P. D., & Zan, R. (2011). Attitude toward mathematics: A bridge between beliefs and emotions. ZDM Mathematics Education, 43, 471-482.

McAlpine, L., Eriks-Brophy, A., & Crago, M. (1996). Teaching beliefs in Mohawk classrooms: Issues of language and culture. Anthropology & Education Quarterly, 27(3), 390-413.

McLeod, D. B. (1988). Affective issues in mathematical problem solving: Some theoretical considerations. Journal of Research in Mathematics Education, 19, 134-141.

Nagata, A. L. (2004). Promoting self-reflexivity in intercultural education. Journal of Intercultural Communication, 8, 139-167.

Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317–328.

Nkhwalume, A. A. (2013). The plausibility of a postmodern pedagogy of mathematics in the African context. Mathematical Theory and Modeling, 3(5), 112-117.

Nunez, I. (2009). Activity theory in mathematics education. Proceedings of the British society for research into learning mathematics, 29(2), 53-57.

Linnebo, O. (2009). Platonism in the philosophy of mathematics. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Stanford: Metaphysics Research Lab, Stanford University.

Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-322.

Palmer, H. (2018). How to understand changes in Novice mathematics’ talk about good mathematics teaching? In B. Rott et al. (Eds.), Views and beliefs in mathematics education (pp. 127-136). Switzerland: Springer.

Part, I. (2009). An empirical study on beliefs of pre-service teachers. In J. Maas & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: New research results (pp. 131-142). Rotterdam: Sense Publisher.

Pepin, B., & Roesken-Winter, B. (Eds.). (2015). From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions. New York: Springer.

Perkkilä, P. (2003). Primary school teachers' mathematics beliefs and teaching practices. Proceedings of the Third Conference of the European Society for Research in Mathematics Education. Bellaria: University of Pisa.

Perry, B., Howard, P., & Tracey, D. (1999). Head mathematics teachers’ beliefs about the learning and teaching of Mathematics. Mathematics Education Research Journal, 11, 39–57.

Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. F. (1989). Teachers' pedagogical content beliefs in mathematics. Cognition and Instruction, 6(1), 1-40.

Polya, G. (1957). How to solve it (2nd ed.). London: Penguin Books.

Prawat, R. (1992). Teachers’ beliefs about teaching and learning: A constructivist perspective. American Journal of Education, 100, 354-395.

Purnomo, Y. W., Suryadi, D., & Darwis, S. (2016). Examining preservice elementary school teacher beliefs and instructional practices in mathematics class. International Electronic Journal of Elementary Education, 8(4), 629-642.

Qian, G., & Alvermann, D. (1995). Role of epistemological beliefs and learned helplessness in secondary school students’ learning science concepts from text. Journal of Educational Psychology, 87(2), 282–292.

Quinn, R. J. (1998a). The influence of mathematics methods course on preservice teachers’ pedagogical beliefs concerning manipulatives. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 71(4), 236-238.

Quinn, R. J. (1998b). Technology: Preservice teachers’ beliefs and the influence of a mathematics methods course. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 71(6), 375-377.

Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), The handbook of research in teacher education (pp. 102-119). New York: Macmillan.

Richardson, V. (2003). Preservice teachers’ beliefs. In J. Raths & A. C. McAninch (Eds.), Teacher beliefs and classroom performance: The impact of teacher education (pp.1-22). Greenwich: Information Age Publishing.

Rokeach, M. (1968). Beliefs, attitudes and values. San Francisco: Jossey-Bass.

Roth, W. -M., & Lee, Y.-J. (2007). “Vygotsky’s neglected legacy”: Cultural-historical activity theory. Review of Educational Research, 77(2), 186-232.

Savasci-Acikalin, F. (2009). Teacher beliefs and practices in science education. Asia-Pacific Forum on Science Learning and Teaching, 10(1).

Sayers, J., & Adrews, P. (2018). Developing and trailing a simple-to-use instrument for surveying teacher education students’ mathematics-related beliefs. In H. Palmer & J Skott (Eds.), Students’ and teachers’ values, attitudes, feelings, and beliefs in mathematics classrooms (pp. 77-88). Switzerland: Springer.

Schmidt, W. H., & Kennedy, M. M. (1990). Teachers’ and teacher candidates’ beliefs about subject matter and about teaching responsibilities. East Lansing: Michigan State University.

Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 334-370). New York: Macmillan.

Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational implications. New York: Routledge.

Schommer, M., Crouse, A., & Rhodes, N. (1992). Epistemological beliefs and mathematical text comprehension: Believing it is simple does not make it so. Journal of Educational Psychology, 6, 39–42.

Schwier, R. A., & Misanchuk, E. R. (1993). Interactive multimedia instruction. New Jersey: Educational Technology Publications.

Shahvarani, A., & Savizi, B. (2007). Analyzing some Iranian-High School teachers’ beliefs on mathematics, mathematics learning, and mathematics teaching. Journal of Environmental & Science Education, 2(2), 54-59.

Silver, E. A. (2003). Border crossing: Relating research and practice in mathematics education. Journal for Research in Mathematics Education, 34, 182–184.

Sinatra, G. M. (2005). The “warming trend” in conceptual change research: The legacy of Paul Pintrich. Educational Psychologist, 40, 107–115.

Skemp, R. R. (1971). The psychology of learning mathematics. Harmondsworth Middlesex: Penguin Books.

Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26(3), 9-15.

Skott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamics affect systems in mathematics education: Exploring a mosaic of relationships and interactions (pp. 3-23). New York: Springer.

Smitherman, S. E. (2006). Reflections on teaching a mathematics education course. Dissertation. Baton Rouge: Louisiana State University.

Spezio, M. L., & Adolphs, R. (2010). Emotion, cognition, and beliefs: Findings from cognitive neuroscience. In T. Bayne & J. Fernandez (Eds.), Delusion and self-deception (pp. 86-106). New York: Taylor & Francis Group.

Spillane, J. P., Hopkins, M., & Sweet, T. M. (2017). School district educational infrastructure and change at scale: Teacher peer interactions and their beliefs about mathematics instruction. American Educational Research Journal, 55(3), 532-571.

Steffe, L. P., & Gale, J. (1995). Constructivism in education. Hillsdale: Lawrence Erlbaum.

Steffe, L. P., & Kieren, T. (1994). Radical constructivism and mathematics education. Journal for Research in Mathematics Education, 25(6), 711-733.

Stinson, D. W., & Bullock, E. C. (2015). Critical postmodern methodology in mathematics education research: Promoting another way of thinking and looking. Athens: Georgia State University.

Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213-226.

Stonewater, J. K., & Oprea, J. M. (1988). An analysis of in-service teachers’ mathematical beliefs: A cognitive development perspective. In M. J. Behr, C. B. Lacampagne, & M. M. Wheeler (Eds.), Proceedings of the 10th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 356–363). DeKalb: Northern University.

Streibel, M. J. (1991). Instructional design and human practice: What can we learn from Habermas’s theory of technical and practical human interests? Proceedings of selected research presentations at the annual convention of the Association for Educational Communications and Technology. Bloomington: AECT.

Taylor, E., Taylor, P. C., Karnovsky, S., Aly, A., & Taylor, N. (2017). “Beyond Bali”: A transformative education approach for developing community resilience to violent extremism. Asia Pacific Journal of Education, 37(2), 193-204.

Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.

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

Tillema, H. H. (1995). Changing the professional knowledge and beliefs of teachers: A training study. Learning and Instruction, 5(4), 291–318.

Törner, G. (1998). Self-estimating teachers’ views on mathematics teaching- modifying Dionne’s approach. In S. Berenson, K. Dawkins, M. Blandon, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 628-634). Columbus: International Group for the Psychology of Mathematics Education.

Tracey, D., Perry, B., & Howard, P. (1998). Teacher beliefs about the learning and teaching of mathematics: Some comparisons. Adelaide: Mathematics Education Research Group of Australasia.

Van Zoest, L., Jones, G. A., & Thornton, C. A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program. Mathematics Education Research Journal, 6(1), 37–55.