Pre-service Teachers as Agents of Change in the Mathematics Classroom: A Case Study
Keywords:
pre-service teacher, agent of change, problem based learning, teaching through problem solving, teacher assumptionsAbstract
The pre-service teacher followed in this paper aimed to act as an agent of change during a time of reform in Irish post primary mathematics education. A teacher-researcher led action research project was conducted to depict the reality of the situation regarding the implementation of mathematical problem solving from a variety of perspectives – namely those of the pre-service teacher/teacher-researcher, the second-level students, and the other mathematics teachers in the school. A problem-based approach to teaching and learning was implemented by the teacher-researcher using Van de Walle’s teaching through problem solving framework. Following this intervention, participating students showed an improvement in engagement with mathematical problem solving and expressed positive opinions regarding the problem based approach to teaching and learning. Meanwhile, other mathematics teachers in the school expressed concerns relating to the reality of implementing problem solving in their classrooms, however these concerns were not issues faced by the author when implementing problem solving in the same setting. When these concerns were indirectly challenged by the pre-service teacher a change in conversation occurred.
References
Akkoc, H., Balkanlioglu, M. & Yesildere-Imrie, S. (2016). Exploring preservice mathematics teachers’ perception of mathematics teacher through communities of practice, Mathematics Teacher Education and Development, 18(1), 37-51.
Anderson, J. (2003). Teachers’ choice of tasks: A window into beliefs about the role of problem solving in learning mathematics. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics educations research: Innovation, networking, opportunity (Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia, pp. 72-80). Geelong, Australia: MERGA.
Anderson, J. (2008). Identifying problem solving in school mathematics: Students’ and teachers’ perspectives. In J. Vincent, J. Dowsey & R. Pierce (Eds.), Connected maths (Keynote presentation at the 45th annual conference of the Mathematics Association of Victoria, pp. 14-24). Melbourne, Australia: MAV.
Anderson, J., Sullivan, P. & White, P. (2004). The influence of perceived constraints on teachers’ problem-solving beliefs and practices. In I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, pp. 39-46). Geelong, Australia: MERGA.
Anderson, J. & White, P. (2004). Problem solving in learning and teaching mathematics. In B. Perry, G. Anthony & C. Diezmann (Eds.), Research in mathematics education in Australasia 2000-2003 (pp. 127-150). Queensland, Australia: Post Pressed.
Bailey, K.D. (1978). Methods of social research. Basingstoke, England: Collier-Macmillan.
Bay-Williams, J.M., & Meyer, M.R. (2005). Why not just tell students how to solve the problem? Mathematics Teaching in the Middle School, 10(7), 340–41.
Bay-Williams, J.M., & Martinie, S.L. (2009). Math and non-fiction: Grades 6-8. Sausalito, CA: Marilyn Burns Books.
Berger, K. (2006). The developing person through childhood and adolescence (7th ed.). New York: Worth.
Boaler, J. (1997). Experiencing school mathematics: Teaching styles, sex and setting. Buckingham, England: Open University Press.
Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62.
Boaler, J. & Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases to support teaching and learning. Portsmouth, NH: Heinemann.
Boud, D., & Feletti, G. (1999). The challenge of problem-based learning. London, England: Kogan Page Limited.
Braund, M. & Campbell, B. (2010). Learning to teach about ideas and evidence in science: The student teacher as change agent. Research in Science Education, 40(2), 203-222.
Brenner, M., Brown, J. & Canter, D. (1985). The research interview. London, England: Academic Press Inc.
Brookfield, S. (1995). Becoming a critically reflective teacher. San Francisco: Jossey-Bass.
Brownell, W.A. (1946). Introduction: Purpose and scope of the yearbook. In N.B. Henry (Ed.), Forty-fifth yearbook of the National Society for the Study of Education: Part 1. The measurement of understanding (pp. 1-6). Chicago: University of Chicago.
Buschman, L. (2004). Teaching Problem Solving in Mathematics. Teaching Children Mathematics, 10(6), 302–309.
Campbell, P.F. (1996). Empowering children and teachers in the elementary mathematics classrooms of urban schools. Urban Education, 30(4), 449-475.
Carpenter, T.P., Fennema, E., Peterson, P.L., Chiang, C.P. & Loef, M. (1989). Using knowledge of children’s mathematical thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531.
Cavanagh, M. (2006). Mathematics teachers and working mathematically: Responses to curriculum change. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, pp. 115-122). Adelaide, Australia: MERGA.
Cavanagh, M. & Prescott, A. (2007). Professional experience in learning to teach secondary mathematics: Incorporating pre-service teachers into a community of practice. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, pp. 182-191). Adelaide, Australia: MERGA.
Chapko, M. & Buchko, M. (2004). Math instruction for inquiring minds. Principal, 84, 30-33.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B. & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3-29.
Cohen, L., Manion, L. & Morrison, K. (2005). Research methods in education (5th ed.). London, England: Routledge.
Connor, P. & Lake, L. (1988). Managing organizational change. New York: Praeger.
Cooper, T. (1986). Problem solving. Queensland: Mathematics Education, Brisbane College of Advanced Education.
Curriculum Development Council & The Hong Kong Examinations and Assessment Authority (2007). Mathematics Curriculum and Assessment Guide (Secondary 4-6).
Davis, R.B. (1992). Understanding “understanding”. Journal of Mathematical Behaviour, 11, 225-241.
Dewey, J. (1929). The quest for certainty. New York: Minton, Balch & Co.
Diggs, V. (2009). Ask—think—create: The process of inquiry. Lnowledge Quest, 37, 30-33.
Dweck, C.S. (2007). The perils and promises of praise. Educational Leadership, 65(2), 34-39.
Erikson, E. H. (1963). Childhood and society (2nd ed.). New York: Norton.
Fullan, M. (1993). The professional teacher: Why teachers must become change agents. Educational Leadership, 50(6), 1-13.
Fullan, M. (1999). Change forces: The sequel. Philadelphia, PA: Falmer.
Fuson, K.C. & Briars, D.J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21, 180-206.
Fuson, K.C., Smith, S.T. & Lo Cicero, A. (1997). Supporting Latino first graders’ ten-structured thinking in urban classrooms. Journal for Research in Mathematics Education, 28(6), 738-766.
Hadaway, W. (1993). Mathematical problem solving In. P.S. Wilson (Ed.), Research ideas for the classroom: High school mathematics. New York: MacMillan.
Hiebert, J. & Carpenter, T.P. (1992). Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.
Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A. & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12-21.
Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A. & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
Hunt, J. McV. (1961). Intelligence and experience. New York: Ronald.
Ingvarson, L., Beavis, A., Bishop, A., Peck, R. & Elsworth, G. (2004). Investigation of effective mathematics teaching and learning in Australian secondary schools. Melbourne: Australian Council for Education Research.
Jeffes, J., Jones, E., Wilson, M., Lamont, E., Straw, S., Wheater, R. & Dawson, A. (2013). Research into the impact of Project Maths on student achievement, learning and motivation: final report. Slough, England: NFER.
Jick, T. (1979). Mixing qualitative and quantitative methods: Triangulation in action. Administrative Science Quarterly, 24(4), 602-611.
Kamii, C. & Joseph, L.L. (1989). Young children continue to reinvent arithmetic. New York: Teachers College.
Kaplinsky, R. (2013, September 6). How Much Does a 100x100 In-N-Out Cheeseburger Cost? Retrieved from http://robertkaplinsky.com/work/in-n-out-100-x-100/.
Kemmis, S. & McTaggart, R. (1992). The action research planner (3rd ed.). Victoria, Australia: Deakin University Press.
Kohn, A. (1993). Punished by rewards: The trouble with gold stars, incentive plans, A’s, praise, and other bribes. Boston: Houghton Mifflin.
Lane, C., Faulkner, F. & Smith, A. (2016). A CPD Programme for ‘out-of-field’ mathematics teachers in Ireland: Programme outline and initial evaluations by participants. Paper presented at the Science and Mathematics Education Conference, Dublin, Ireland.
Lappan, G. & Briars, D. (1995). How should mathematics be taught? In I.M. Carl (Ed.), Prospects for school mathematics (pp. 115-156). Reston, VA: NCTM.
Lappan, G., & Even, R. (1989). Learning to teach: Constructing meaningful understanding of mathematical content (Craft Paper 89-3). East Lansing, MI: Michigan State University.
Lave, J. & Wenger, E. (1991) Situated Learning: Legitimate Peripheral Participation. New York: Cambridge University Press.
Lewin, K. (1948). Resolving social conflicts. New York: Harper and Row.
Lortie, D. (1975). Schoolteacher: A sociological study. Chicago: University of Chicago Press.
Lovitt, C. (2000). Investigations: A central focus for mathematics. Australian Primary Mathematics Classroom, 5(4), 8–11.
Lyons, M., Lynch, K., Close, S., Sheeran, E., & Boland, P. (2003). Inside classrooms: A study of teaching and learning. Dublin: Institute of Public Administration.
Marcovitz, D. (1997). Technology and change in schools: The roles of student teachers. Paper presented at the eighth international conference of the Society for Information Technology and Teacher Education (SITE), Orlando, FL.
Martinez, M. (1998). What is problem solving? The Phi Delta Kappan, 79(8), 605-609.
Milch, D. (2006, April 20). Television’s greatest writer [Video file]. Retrieved from http://techtv.mit.edu/videos/16086-television-s-great-writer-david-milch-mit-communications-forum.
Murray, F. & Stotko, E. (2004). The student teacher as an agent of instructional reform: Effects of student teachers on supervising teachers. Action in Teacher Education (Association of Teacher Educators), 26(3), 73-81.
Murray, H., Olivier, A. & Human, P. (1992). The development of young students’ division strategies. In W. Geeslin & K. Graham (Eds.), Proceedings of the sixteenth PME Conference, Vol. 2 (pp. 152-159). Durham, NH: University of New Hampshire.
National Academy of Sciences, National Academy of Engineering, and Institute of Medicine (2007). Rising above the gathering storm: Energizing and employing America for a brighter economic future. Washington, DC: National Academies Press.
National Council for Curriculum and Assessment (NCCA) (2008). Developing Post-Primary Mathematics Education. Dublin: Government of Ireland Publications.
National Council for Curriculum and Assessment (NCCA) (2011). Mathematics Syllabus Foundation, Ordinary & Higher Level For examination from 2016. Dublin: Government of Ireland Publications.
National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices.
National Research Council (2012). Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century. Washington, DC: National Academies Press.
Ní Ríordáin, M. & Hannigan, A. (2011). Who teaches mathematics at second-level in Ireland? Irish Educational Studies, 30(3), 289-304.
Noffke, S.E. & Zeichner, K.M. (1987). Action research and teacher thinking. Paper presented at the annual meeting of the American Educational Research Association, Washington, DC.
OECD (2017). Education at a Glance 2017: OECD Indicators. Paris: OECD Publishing.
Oldham, E. (2001). The culture of mathematics education in Ireland: keeping the faith? Irish Educational Studies, 20, 266-277.
O’Meara, N. & Prendergast, M. (2017). Time in Mathematics Education (TiME): A National Study Analysing the Time Allocated to Mathematics at Second Level in Ireland, Dublin: Trinity Long Room Hub.
Ontario (2005). The Ontario curriculum, grades 9 and 10 Mathematics. Toronto: Ontario Ministry of Education.
O’Sullivan, M. (2003). Learning to teach physical education. In S.J. Silverman & C.D. Ennis (Eds.), Student learning in physical education: Applying research to enhance instruction (2nd ed., pp. 275-294). Champaign, IL: Human Kinetics.
Peterson, J. (2004). Math and non-fiction: Grades K-2. Sausalito, CA: Math Solutions Publications.
Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, USA: Princeton University Press.
Price, J. & Valli, L. (2005). Preservice teachers becoming agents of change: pedagogical implications for action research. Journal of Teacher Education, 56(1), 57-72
Rigelman, N. (2007). Fostering Mathematical Thinking and Problem Solving: The Teacher’s Role. Teaching Children Mathematics, 13(6), 308-314.
Rowan, T.E. & Bourne, B. (1994). Thinking like mathematicians: Putting the K-4 standards into practice. Portsmouth, NH: Heinemann.
Schoenfeld, A.H. (1985). Mathematical problem solving. Florida, USA: Academic Press.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
Schroeder, T.L. & Lester, F.K., Jr. (1989). Developing understanding in mathematics via problem solving. In P.R. Trafton (Ed.), New directions for elementary school mathematics (pp. 31-42). Reston, VA: NCTM.
Schwarz, S.L. (1996). Hidden messages in teacher talk: Praise and empowerment. Teaching Children Mathematics, 2(7), 396-401.
Sheffield, S. & Gallagher, K. (2004). Math and nonfiction: Grades 3-5. Sausalito, CA: Math Solutions Publications.
Shiel, G. & Kelleher, C. (2017). An Evaluation of the Impact of Project Maths on the Performance of Students in Junior Cycle. Dublin: Educational Research Centre.
Silver, E.A. & Stein, M.K. (1996). The QUASAR project: The “revolution of the possible” in mathematics instructional reform in urban middle schools. Urban Education, 30(4), 476-521.
Szetela, W. & Nicol, C. (1992). Evaluating Problem Solving in Mathematics. Educational Leadership, 49(8), 42-45.
TED (2010, May 13). Dan Meyer: Math class needs a makeover [Video file]. Retrieved from https://www.youtube.com/watch?v=NWUFjb8w9Ps.
Tomlinson, P. (1999). Conscious reflection and implicit learning in teacher preparation: Implications for a balanced approach. Oxford Review of Education, 25(4), 533-544.
Travers, K.J. (1967). A test of pupil preference for problem-solving situations in junior high school mathematics. Journal of Experimental Education, 35, 9-18.
Van de Walle, J. (2004). Elementary & Middle School Mathematics. Boston: Allyn & Bacon.
Vygotsky, L.S. (1978). Mind in society: The development of higher mental process. Cambridge, MA: Harvard University Press.
Wallace, A.H. (2007). Anticipating student responses to improve problem solving. Mathematics Teaching in the Middle School, 12(9), 504-511.
Weinburgh, M., Smith, L. & Smith, K. (1997). Preparing preservice teachers to use technology in teaching math and science. Techtrends, 42(5), 43-45.
Wood, T., Cobb, P., Yackel, E. & Dillon, D. (1993). Rethinking elementary school mathematics: Insights and issues. Journal for Research in Mathematics Education Monograph No. 6. Reston, VA: NCTM.
Woods, D.R. (2000). An evidence-based strategy for problem solving. Journal of Engineering Education, 89, 443-459.
Woolfolk, A., Hughes, M. & Walkup, V. (2008). Psychology in Education. Essex, England: Pearson Education Limited.
