American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2017, 5(3), 310-315
DOI: 10.12691/education-5-3-12
Open AccessArticle

Prospective Teachers’ Conceptual and Procedural Knowledge in Mathematics: The Case of Algebra

Habila Elisha Zuya1,

1Department of Science and Technology Education, Faculty of Education, University of Jos, Nigeria

Pub. Date: March 27, 2017

Cite this paper:
Habila Elisha Zuya. Prospective Teachers’ Conceptual and Procedural Knowledge in Mathematics: The Case of Algebra. American Journal of Educational Research. 2017; 5(3):310-315. doi: 10.12691/education-5-3-12

Abstract

The study investigated prospective mathematics teachers’ conceptual and procedural knowledge in algebra. Thirty six prospective teachers participated in the study. The independent variables of conceptual knowledge and procedural knowledge were investigated using quantitative methods. A 20-item instrument was used for collecting data. Descriptive and inferential statistics were used in analyzing the data collected. Specifically, the research questions were answered using the means and standard deviations, while the hypothesis was tested by conducting a paired t-test of difference. One of the findings of the study was the low performance of the respondents on conceptual knowledge test as against their performance on procedural knowledge test. The respondents differed significantly in their performances on conceptual and procedural knowledge, and the difference was in favor of procedural knowledge. It was recommended that teachers should give equal attention to both teaching of concepts and procedures in mathematics.

Keywords:
conceptual knowledge procedural knowledge algebra prospective teachers

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References:

[1]  Baroody, A. J. (2003). The development of adaptive expertise and flexibility: the integration of conceptual and procedural knowledge. Mahwah, NJ: Erlbaum.
 
[2]  Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38, 115-131.
 
[3]  Baykul, Y. (1999): Primary mathematics education. Ankara, Turkey, Ani Printing Press
 
[4]  Bryan, T. J. (2002). The conceptual knowledge of preservice secondary mathematics teachers: How well do they know the subject matter they will teach? Unpublished Doctoral Dissertation. The University of Texas at Austin, Austin TX.
 
[5]  Byrnes, J. P. & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777-786.
 
[6]  Canobi, K. H. (2004). Individual differences in children’s addition and subtraction knowledge. Cognitive Development, 19, 81-93.
 
[7]  Canobi, K. H., Reeve, R. A., & Pattison, P. E. (2003). Patterns of knowledge in children’s addition. Developmental Psychology, 39, 521-534.
 
[8]  Engelbrecht, J., Harding, A., & Potgieter, M. (2005). Undergraduate students' performance and confidence in procedural and conceptual mathematics. International journal of mathematical education in science and technology, 36(7): 701-712.
 
[9]  Faulkenberry, E. E. D. 2003. Secondary mathematics pre-service teachers’ conceptions of rational numbers. Unpublished Doctoral Dissertation, Oklahoma State University, Oklahoma.
 
[10]  Gelman, R., & Williams, E. M. (1998). Enabling constraints for cognitive development and learning: domain specificity and epigenesis. In D. Kuhn & R. S. Siegler (Eds), Handbook of Child Psychology: Cognition, Perception, and Language (5th edn, Vol. 2, pp. 575-630). New York: John Wiley.
 
[11]  Gilmore, C. K., & Bryant, P. (2006). Individual differences in children’s understanding of inversion and arithmetical skill. British Journal of Educational Psychology, 76, 309-331.
 
[12]  Gilmore, C. K., & Bryant, P. (2008). Can children construct inverse relations in arithmetic? Evidence for individual differences in the development of conceptual understanding and computational skill. British Journal of Developmental Psychology, 26, 301-316.
 
[13]  Haapasalo, L. & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. JMD—Journal for Mathematic-Didaktik, 21, 139-157.
 
[14]  Haapasalo, L. (2003). The Conflict between Conceptual and Procedural Knowledge: Should We Need to Understand in Order to be Able to Do, or vice versa? In L. Haapasalo & K. Sormunen (eds.) Towards Meaningful Mathematics and Science Education. Proceedings on the 19th Symposium of the Finnish Mathematics and Science Education Research Association. University of Joensuu. Bulletins of the Faculty of Education 86, pp. 1-20.
 
[15]  Halford, G. S. (1993). Children’s Understanding: The Development of Mental Models. Hillsdale, NJ: Erlbaum.
 
[16]  Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102, 395-406.
 
[17]  Hallett, D., Nunes, T., Bryant, P., & Thorpe, C. M. (2012). Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology, 113 (2012) 469-486
 
[18]  Hiebert, J., & Lefevre, P. (1986). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis (pp. 1-27). Hillsdale, NJ: Erlbaum.
 
[19]  İşleyen, T., & Işık, A. (2003). Conceptual and procedural learning in mathematics. Journal of the Korea Society of Mathematical Education (Series D: Research in mathematical education), 7(2), 91-99
 
[20]  Karmiloff-Smith, A. (1992). Beyond Modularity: A Developmental Perspective on Cognitive Science. Cambridge, MA: MIT Press.
 
[21]  Kerslake, D. (1986). Fractions: Children’s strategies and errors: A report of the strategies and errors in Secondary Mathematics Project. Windsor, UK: NFER-Nelson.
 
[22]  Khashan, K.H. (2014). Conceptual and procedural knowledge of rational numbers for Riyadh elementatry school teachers. Journal of Education and Human development, 3(4), 181-197.
 
[23]  Kilpatrick, J., Swafford, J. O., & Findell, B. (2001). Adding it up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
 
[24]  Mabbott, D. J. & Bisanz, J. (2003). Developmental change and individual differences in children’s multiplication Child Development, 74, 1091-1107.
 
[25]  McGehee, J. (1990). Prospective secondary teachers’ knowledge of the function concept. Unpublished Doctoral Dissertation, University of Texas.
 
[26]  Nunes, T., Bryant, P., Barros, R., & Sylva, K. (2012). The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82, 136-156.
 
[27]  Resnick, L. B. & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in Instructional Psychology (Vol. 3, pp. 41-95). Hillsdale, NJ: Erlbaum.
 
[28]  Resnick, L. B. (1982). Syntax and Semantics in Learning to Subtract. In T. P. Carpenter, J. M. Moser & T. A. Romberg (Eds.), Addition & Subtraction: A Cognitive Perspective (pp. 136-155). Hillsdale, NJ: Lawrence Erlbaum Associates Pulishers.
 
[29]  Rittle-Johnson, B. & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: does one lead to the other? Journal of Educational Psychology, 91, 175-189.
 
[30]  Rittle-Johnson, B. & Schneider, M. (2012). Developing Conceptual and Procedural Knowledge of Mathematics. In R. Cohen Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition. Oxford University Press.
 
[31]  Rittle-Johnson, B., & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skills (pp. 75-110). London: Psychology Press.
 
[32]  Schneider, M., & Stern, E. (2010a). The developmental relations between conceptual and procdural knowledge: A multimethod approach. Developmental Psychology, 46, 178-192.
 
[33]  Siegler, R. S. & Stern, E. (1998). Conscious and unconscious strategy discoveries: a micro genetic analysis. Journal of Experimental Psychology: General, 127, 377-397.
 
[34]  Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404-411.
 
[35]  Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2014-4333). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website: http://whatworks.ed.gov.
 
[36]  Star, J. R. (2016). Small steps forward: Improving mathematics instruction incrementally. Phi Delta Kappan, 97, 58- 62.
 
[37]  Stump, S. L. (1996). Secondary mathematics teachers' knowledge of the concept of slope. Unpublished Doctoral dissertation, Illinois State University. DAI-A, 58(2): 408.
 
[38]  Zakaria, E., Yaakkob, M.J., Maat, S.M., & Adnan, M. (2010). Conceptual knowledge and mathematics achievement of matriculation students. Procedia-Social and Behavioral Sciences, 9, 1020-1024.
 
[39]  Zakaria, E. & Zaini, N. (2009). Conceptual and Procedural Knowledge of Rational Numbers in Trainee Teachers. European Journal of Social Sciences, 9(2): 202-217.
 
[40]  www.dictionary.com. Searched 2016.