Prendergast, M. and Johnson, P. and Fitzmaurice, O. and Liston, M. and O'Keeffe, L. and O'Meara, N.
(2014)
*Mathematical thinking: Challenging prospective teachers to do more than 'talk the talk'.*
International Journal of Mathematical Education in Science and Technology, 45 (5).
pp. 635-647.
ISSN 0020739X (ISSN)

## Abstract

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme. © 2013 © 2013 Taylor & Francis.

Item Type: | Article |
---|---|

Additional Information: | Cited By :1; Export Date: 23 February 2015; Correspondence Address: Prendergast, M.; School of Hospitality Management and Tourism, Dublin Institute of Technology, Dublin, Ireland; email: Mark.Prendergast@dit.ie; References: (2005) Review of mathematics in post-primary education, , National Council for Curriculum and Assessment, Dublin,: Department of Education and Science, The Stationary Office; (2008) Statement on raising national mathematical achievement, , Expert Group on Future Skills Needs (EGFSN), Dublin,: EGFSN; (2006) Review of mathematics in post-primary education, pp. 11-20. , National Council for Curriculum and Assessment, Irish Mathematics Society Bulletin; Conway, P., Sloane, C., International trends in post-primary mathematics education (2005) National Council for Curriculum and Assessment; Brown, S., Cooney, T., Jones, D., Mathematics teacher education (1990) Handbook of research on teacher education, , In:, In:, In: Houston R, editorsHaberman M, editorsSikula J, editors New York (NY),: Macmillan; Cobb, P., Wood, T., Yacke, E., McNeal, B., Characteristics of classroom mathematics traditions: an interactional analysis (1992) Am Educ Res J, 29, pp. 573-604; Dossey, J.A., The nature of mathematics: its role and influence (1992) Handbook of research on mathematics teaching and learning, pp. 39-48. , In: Grouws DA, editors New York (NY),: Macmillan; Backhouse, J., Haggarty, L., Pirie, S., Stratton, J., (1992) Improving the learning of mathematics, , London,: Cassell; Lyons, M., Lynch, K., Close, S., Sheerin, E., Boland, P., (2003) Inside classrooms - the teaching and learning of mathematics in the social context, , Dublin,: Institute of Public Administration; Askey, R., Good intentions are not enough. 1999, , http://www.math.wisc.edu/~askey/ask-gian.pdf, Available from; Smith, A., (2004) Making mathematics count - the report of Professor Adrian Smith's inquiry into post-14 mathematics education, , The Stationary Office Limited; Hill, H.C., Rowan, B., Ball, D.L., Effects of teachers' mathematical knowledge for teaching on student achievement (2005) Am Educ Res J, 42, pp. 371-406; (2008) Foundations for success: The final report of the National Mathematics Advisory Panel, , National Mathematics Advisory Panel, Washington, DC),: US Department of Education; Kulm, G., (2008) Teacher knowledge and practice in middle grades mathematics, , Rotterdam,: Sense Publishers; Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress (2010) Am Educ Res J, 47, pp. 133-180; Ball, D.L., The mathematical understandings that prospective teachers bring to teacher education (1990) Elem Sch J, 90, pp. 449-466; Ma, L., (1999) Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States, , Mahwah, NJ),: Erlbaum; (2003) Mathematical proficiency for all students: Towards a strategic development programme in mathematics education, , RAND Mathematics Study Panel, Santa Monica, CA,: RAND Corporation; Brown, C.A., Borko, H., Becoming a mathematics teacher in impact (1992) Handbook of research on mathematics teaching and learning, pp. 209-239. , In: Grouws DA, editors New York (NY),: Macmillan; Li, Y., Kulm, G., Knowledge and confidence of preservice mathematics teachers: the case of fraction division (2008) ZDM Math Educ, 40, pp. 833-843; Blanco, L., The mathematical education of primary teachers in Spain (2003) Int J Math Teach Learn, , http://www.cimt.plymouth.ac.uk/journal/blanco1.pdf, Available from; Handal, B., Teachers' mathematical beliefs: a review (2003) Math Educ, 13, pp. 47-57; Lortie, D., (1975) Schoolteacher: A sociological study, , Chicago (IL),: University of Chicago Press; Pajares, M.F., Teachers' beliefs and educational research: cleaning up a messy construct (1992) Rev Educ Res, 62, pp. 307-332; Tillema, H.H., Changing the professional knowledge and beliefs of teachers: a training study (1995) Learn Instruction, 5, pp. 291-318; Kennedy, M., (1991) An agenda for research on teacher learning. National Centre for Research on Teacher Learning Special Report, , East Lansing (MI),: Michigan State University; Feiman-Nemser, S., McDiarmid, G.W., Melnick, S.L., Parker, M., (1989) Changing beginning teachers' conceptions: A description of an introductory teacher education course, , East Lansing (MI),: National Centre for Research on Teacher Education; Hart, L.C., Preservice teachers' beliefs and practice after participating in an integrated content/methods course (2002) Sch Sci Math, 102, pp. 4-14; Ball, D.L., Unlearning to teach mathematics (1998) Learn Math, 8, pp. 40-48; O'Meara, N., (2011) Improving mathematics teaching at second level through the design of a model of teacher knowledge and an intervention aimed at developing teachers' knowledge [dissertation], , University of Limerick; Toumasis, C., Problems in training secondary mathematics teachers: the Greek experience (1992) Int J Math Educ Sci Technol, 23, pp. 287-299; Liston, M., Whose fault is it anyway? The truth about the mathematical knowledge of prospective secondary school teachers and the role of mathematics teacher educators (2012), 12th International Congress on Mathematics Education, Seoul, KoreaRichardson, V., Constructivist teaching and teacher education: theory and practice (1997) Constructivist teacher education: Building new understandings, pp. 3-14. , In: Richardson V, editors Washington, DC),: Falmer Press; Abdal-Haqq, I., (1998) Constructivism in teacher education: Considerations for those who would link practice to theory, , Washington, DC),: ERIC Clearinghouse on Teaching and Teacher Education; Mayer, R.E., Should there be a three-strikes rule against pure discovery learning? (2004) Am Psychol, 59, pp. 14-19; Fahlberg-Stojanovska, L., Stojanovski, V., GeoGebra - freedom to explore and learn (2009) Teach Math Appl, 28 (2), pp. 69-76; Halpin, R., A model of constructivist learning practice: computer literacy integrated to elementary mathematics and science teacher education (1999) J Res Comput Educ, 32, pp. 128-138; Boaler, J., When do girls prefer football to fashion? An analysis of female underachievement in relation to 'realistic' mathematic contexts (1994) Br Educ Res J, 20, pp. 551-564; Burton, L., The teaching of mathematics to young children using a problem solving approach (1980) Educ Stud Math, 11, pp. 43-58; Schoenfeld, A.H., When good teaching leads to bad results: the disasters of 'well-taught' mathematics courses (1988) Educ Psychol, 23, pp. 145-166; Niemi, D., Assessing conceptual understanding in mathematics: representations, problem solutions, justifications, and explanations (1996) J Educ Res, 89 (6), pp. 351-363; Skemp, R.R., Relational understanding and instructional understanding (1976) Math Teach, 77 (1), pp. 20-26; Usiskin, Z., What does it mean to 'understand' some mathematics? Paper presented at: 12th International Congress on Mathematics Education (ICME-12); 2012 Jul 8-15, Seoul, KoreaLandis, J.R., Koch, G.G., The measurement of observer agreement for categorical data (1977) Biometrics, 33, pp. 159-174; Artzt, A.F., Sultan, A., Curcio, F.R., Gurl, T., A capstone mathematics course for prospective secondary mathematics teachers (2012) J Math Teach Educ, 15, pp. 251-262 |

Uncontrolled Keywords: | mathematical thinking; pedagogical beliefs; prospective mathematics teachers; relational understanding; teacher education |

Depositing User: | National Forum |

Date Deposited: | 10 Dec 2015 21:24 |

Last Modified: | 10 Dec 2015 21:28 |

URI: | http://eprints.teachingandlearning.ie/id/eprint/3549 |

### Actions (login required)

View Item |

### Downloads

Downloads per month over past year