Knowledge of flexible mental computation of pre-service elementary mathematics teachers upon entry to university
This study sets out to determine the knowledge of flexible mental computation of pre-service elementary mathematics teachers when enrolling at university. Knowledge of the existing flexible mental computation skills of pre-service teachers could inform teacher educators’ preparation for teaching by determining the algorithms that pre-service teachers are unable to calculate. Such knowledge could also inform teacher educators as to why pre-service teachers are unable to calculate the algorithms. The study produced a domain-specific instrument in the form of a diagnostic test that teacher educators could adopt in their teaching to elicit pre-service teachers’ knowledge, a gap that this study aims to bridge. A diagnostic test comprising 21 items was administered by the researcher to 51 year-one pre-service teachers who agreed to participate in the study. Findings of the study indicate that the majority of the pre-service teachers who participated in the study have a limited understanding of the magnitude of numbers, of basic number facts, of the relationship between numbers and of the relationship between basic operations to calculate flexibly. The argument of the study is that teacher educators’ instruction would be relevant and successful if focused on the cognitive needs of pre-service teachers and the mathematical concepts that they are going to teach. Therefore, this study recommends that teacher educators establish pre-service teachers’ knowledge prior to instruction for relevance and for the success of teaching.
students’ confidence in their mathematics. International Journal of Mathematical Education in Science and Technology, 44(1), 70–83.
Bruner, J. (1977). The process of education: A landmark in educational theory. Cambridge: Harvard
Can, T. (2006, April 07). Constructivist education: What is constructivism? [Blog post]. Retrieved
Carpenter, F. (1974). The Skinner primer: Behind freedom and dignity. London: Collier Macmillan
Courtney-Clarke, M. & Wessels, H. (2014). Number sense of final year pre-service primary school
teachers. Pythagoras, 35(1).
Creswell, J.W. (2013). Qualitative inquiry and research design: Choosing among five approaches. Los
Creswell, J.W. (2015). A concise introduction to mixed methods research. Los Angeles: SAGE.
Given, L.M. (2008). The Sage encyclopedia of qualitative research methods. Los Angeles: SAGE.
Gresham, G. (2007). A study of mathematics anxiety in pre-service teachers. Early Childhood
Education Journal, 35(2), 181–188.
Hart, L.C., Oesterle, S., & Swars, S.L. (2013). The juxtaposition of instructor and student
perspectives on mathematics courses for elementary teachers. Edc Stud Math, 83, 429–451.
Hartnett, J. (2007). Categorisation of mental computation strategies to support teaching and to
encourage classroom dialogue. In J. Watson, & K. Beswick (Ed.), Proceedings 30th annual conference of the mathematics education research group of Australasia, Mathematics: Essential research, essential practice (pp. 345-352). Hobart, Tasmania: MERGA Incl.
Hein, G.E. (1991). Constructivist learning theory: The museum and the needs of people. CECA
(International Committee of Museum Educators) Conference (pp. 1–10). Jerusalem: Lesley College, Massachusetts USA.
Heirdsfield, A. (2002). The interview in mathematics education: The case of mental computation.
Annual Conference of the Australian Association for Research in Education (pp. 1-17). Brisbane: Australian Association for Research in Education.
Jakimovik, S. (2014). The mathematics education of pre-school teachers. Macedonia: Faculty of
Pedagogy "St. Kliment Ohridski".
Kasanda, C. (2005). Education in Africa: Post colonialism and globalisation in science and
mathematics education: The case of Namibia and Zambia. In M. Mostert & A.C. Kasanda (Eds.), Education in Namibia: A collection of essays (pp. 106–123). Windhoek: University of Namibia Publishers.
Kajander, A. (2010). Elementary mathematics teacher preparation in an era of reform: The
development and assessment of mathematics for teaching. Canadian Journal of Education , 33 (1), 228-255.
Kesicioğlu, O.S. (2015). The effects of an undergraduate programme of preschool teaching on
preservice teachers’ attitudes towards early mathematics education in Turkey: A longitudinal study. Early Child Development and Care, 185(1), 84–99.
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of
fundamental mathematics in China and the United States. New York: Routledge, Taylor and Francis Group.
McIntosh, A. (2004b). Developing computation. APMC, 9(4), 47–49.
Mcintosh, A., Reys, B.J., & Reys, R.E. (1992). A proposed framework for examining number sense.
For the Learning of Mathematics, 12(3), 2–8, 44.
Nambira, G., Kapenda, L., Tjipueja, G., & Sichombe, B. (2009). Performance of learners in
mathematics at upper primary phase in Okahandja district: Examining reasons for low performances. Okahandja: The National Institute for Educational Development.
National Council of Teachers of Mathematics (2000). Principles and standards for school
mathematics. Reston, VA: National Council of Teachers of Mathematics.
Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational
Review, 57(1), 1–21.
Star, J.R., & Stylianides, A.G. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181.
Tarasenkova, N.A. & Akulenko, I.A. (2013). Determination of students’ beliefs is one of the aspects
of competence oriented system of mathematics teachers’ methodical preparation. American Journal of Educational Research, 1(11), 477–483.
Thorndike, E.L. (1921). The psychology of learning. New York: Teachers College Columbia.
Van den Heuvel-Panhuizen, M. & Drijvers, P. (2014). Realistic mathematics education. In
S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 521–525). Utrecht: Springer Netherlands.
Vatilifa, N. (2014). Investigating the experiences of level 5-7 student teachers when teaching
fractions: A case study. In M. Schäfer, D. Samson, & B. Brown (Eds.), Namibia counts: Stories of mathematics education research in Namibia (pp. 123–137). Grahamstown: Education Department, Rhodes University.
Vygotsky, L. (1978). Mind and society: The development of higher psychological processes.
Cambridge: Harvard University Press.
Vygotsky, L.S. (1987). Thinking and speech. In R.W. Rieber & A.S.Carton (Eds.), The collected works of
L.S.Vygotsky (pp. 39–243). New York: Plenum Press.
Wang, F. & Hannafin, M.J. (2005). Design-based research and technology-enhanced learning
systems. Educational Technology Research and Development, 53(4), 5–23.
Whitacre, I. & Nickerson, S.D. (2006). Pedagogy that makes (number) sense: A classroom teaching
experiment around mental math. Proceedings of the 28th annual meeting of the North American chapter of the International group for the psychology of mathematics education (pp. 736–743). Mérida: Universidad Pedagógica Nacional.
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