Enhancing the Conceptual, Procedural and Flexible Procedural Knowledge of Pre-Service Mathematics Teachers in Algebra

Wasiu Ismaila Otun(1*), Adetunji Abiola Olaoye(2)

(1) Department of Science & Technology Education, Faculty of Education, Lagos State University, Ojo, NIGERIA
(2) Department of Science & Technology Education, Faculty of Education, Lagos State University, Ojo, NIGERIA
(*) Corresponding Author


The study investigated the effects of Solve-Reflect-Pose Strategy (SRP) on pre-service mathematics teachers’ algebraic knowledge for teaching in Nigeria. A pre-test-post-test quasi experimental design was employed. Intact classes were used and in all, 182 pre-service mathematics teachers’ participated in the study (92 in the experimental group taught with the SRP and 90 in the control group taught using the Modified Conventional Method (MCM). One research instrument manipulated at three levels namely: Conceptual Knowledge Test (CKT), Procedural Knowledge Test (PKT) and Flexible Procedural Knowledge Test (FPKT), was used for the quantitative data and interview protocol for qualitative data. The two research questions formulated were analysed using descriptive statistics while independent sample t-test was used to analyse the two hypotheses. Results showed that there were statistically significant differences in the mean post-test achievement scores on conceptual knowledge test, procedural knowledge test and flexible procedural knowledge test between pre-service teachers exposed to the SRP and those exposed to the MCM, all in favour of the SRP group. Based on the results, SRP should be adopted as an instructional strategy and efforts should be made to integrate the philosophy of SRP into the pre-service teachers’ curriculum at the teacher-preparation institutions.


Solve-Reflect-Pose Strategy, Algebraic Knowledge for Teaching, Conceptual Knowledge, Procedural Knowledge, Flexible Procedural Knowledge

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Abramovich, S. (2015). Mathematical problem posing as a link between algorithmic thinking and conceptual knowledge. The Teaching of Mathematics, XVIII(2), 45–60.

Ajai, J. T., & Imoko, I. L. (2015). Gender difference in mathematics achievement and retention scores: A case of problem-based learning method. International Journal of Research in Education and Scxience (IJRES), 1(1), 45–50.

Aké, L. P., Godino, J. D., Gonzato, M., & Wilhelmi, M. R. (2013). Proto-algebraic levels of mathematical thinking. In Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education-PME (pp. 1–8). Kiel, Germany: Leibniz.

Akinsola, M. K. (2013). Helping Teacher Tame Underachievement in Mathematics: The Attitude Dimension. Ibadan, Nigeria: University of Ibadan.

Applebaum, M., & Leikin, R. (2007). Looking back at the beginning : Critical thinking in solving unrealistic problems. The Mathematics Enthusiast, 4(2), 258–265.

Asante, K. O. (2014). Sex Differences in Mathematics Performance among Senior High Students in. https://doi.org/10.4314/gab.v8i2.61947

Azuka, B. F., Jekayinfa, O., Durojaiye, D., & Okwuoza, S. O. (2013). Difficulty Levels of Topics in the New Senior Secondary School Mathematics Curriculum as Perceived by Mathematics Teachers of Federal Unity Schools in Nigeria. Journal of Education and Practice, 4(17), 23–30.

Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching. American Educator, 29, 14–22.

Barwell, R. (2005). Ambiguity in the Mathematics Classroom. Language and Education, 19(2), 118–126.

Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., … Tsai, Y.-M. (2010). Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal, 47(1), 133–180. https://doi.org/10.3102/0002831209345157

Boonen, A. J. H., Schoot, M. Van Der, Wesel, F. Van, Vries, M. H. De, & Jolles, J. (2013). What underlies successful word problem solving ? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271–279. https://doi.org/10.1016/j.cedpsych.2013.05.001

Cai, J., & Knuth, E. (2011). Early algebraization. A global dialogue from multiple perspectives. Berlin: Springer-Verlag.

Carraher, D. W. (2007). Early algebra and algebraic reasoning. Second handbook of research on mathematics teaching and learning.

Dooren, W. Van, Verschaffel, L., & Onghena, P. (2015). The Impact of Preservice Teachers ’ Content Knowledge on Their Evaluation of Students ’ Strategies for Solving Arithmetic and Algebra Word Problems. Journal for Research in Mathematics Education, 33(5), 319–351.

Filloy, E., Puig, L., & Rojano, T. (2008). Educational algebra. A theoretical and empirical approach. New York: Springer.

Gasco, J., & Villarroel, J. D. (2012). Algebraic problem solving and learning strategies in compulsory secondary education. Procedia - Social and Behavioral Sciences, 46, 612–616. https://doi.org/10.1016/j.sbspro.2012.05.172

Godino, J. D., Gonzato, M., & Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar . Implicaciones. Enseñanza de Las Ciencias, 32(1), 199–219.

Heaton, J. (2000). Secondary analysis of qualitative data: A review of the literature. York: Social Policy Research Unit (SPRU), University of York.

Hydea, J. (2009). Gender, culture, and mathematics performances. Retrieved from http/tctvido.madison.com/uw/gender

Iji, C. O., & Uka, N. K. (2012). Influence Teachers Qualifications on Students Mathematics Scores and Interest. ABACUS: Journal of Mathematical Association of Nigeria, 37(1), 38–48.

Kastberg, S., Sanchez, W. B., Edenfield, K., Tyminski, A., Stump, S., Sanchez, W., … Stump, S. (2012). What is the Content of Methods ? Building an Understanding of Frameworks for Mathematics Methods Courses. In Proceedings for the Thirty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 1259–1267). Kalamazo, Michigan: Western Michigan University.

Khng, K. H., & Lee, K. (2009). Inhibiting interference from prior knowledge : Arithmetic intrusions in algebra word problem solving Inhibiting interference from prior knowledge : Arithmetic intrusions in algebra word problem solving ☆. Learning and Individual Differences, 19(2), 262–268. https://doi.org/10.1016/j.lindif.2009.01.004

Kieran, C. (2007). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan.

Latterell, C. M. (2008). IUMPST: The Journal. Vol 1 (Content Knowledge), May 2008. The Journal, 1(May), 1–13.

Maciejewski, W., & Star, J. R. (2016). Research in Mathematics Education Developing flexible procedural knowledge in undergraduate calculus. Research in Mathematics Education, 18(13), 229–316. https://doi.org/10.1080/14794802.2016.1148626

Nathan, M. J., & Koedinger, K. R. (2000). Teachers ’ and Researchers ’ Beliefs About the Development. Journal For Research in Mathematics Education, 31(2), 168–190.

Ogunkunle, L. A. (2007). Effects of gender on mathematics achievement of students in constructivist and non-constructivists groups in secondary school. ABACUS, Journal of Mathematical Association of Nigeria, 32(1), 41–50.

Otun, W. I. (2017). Effects of solve-reflect-pose strategy on pre-service mathematics teachers’ algebraic knowledge for teaching and problem posing skills. Lagos State University.

Perie, M., Moran, R., & Lutkus, A. D. (2005). NAEP 2004 Trends in Academic Progress: Three Decades of Student Performance in Reading and Mathematics. U. S. Department of Education, Institute of Education Sciences, National Center for Education Statistics. Washington, DC: Government Printing Office. Retrieved from http://nces.ed.gov/ pubsearch/pubsinfo.asp?pubid=2005464

Rittle-Johnson, B., & Schneider, M. (2015). Developing Conceptual and Procedural Knowledge of Mathematics. In In R. C. Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1102–1118). Oxford: Oxford University Press.

Rittle-johnson, B., Schneider, M., & Star, J. R. (2015). Not a One-Way Street : Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics. Educational Psychology Review, 27(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x

Rittle-johnson, B., & Star, J. R. (2009). Compared to what ? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529–554. https://doi.org/10.1037/a0014224

Rittle-johnson, B., Star, J. R., & Durkin, K. (2012). Developing procedural flexibility : Are novices prepared to learn from comparing procedures ? British Journal of Educational Psychology, 82(3), 436–455. https://doi.org/10.1111/j.2044-8279.2011.02037.x

S., K., Tyminski, A., & Sanchez, W. (2013). Reframing research on methods courses.

Salman, M. F. (2008). Analysis of errors committed in word problems involving simultaneous linear equations by Nigerian secondary school students. Ilorin Journal of Education, 2L, 126–155.

Schneider, M., & Stem, E. (2010). The Developmental Relations Between Conceptual and Procedural Knowledge : A Multimethod Approach. Developmental Psychology, 46(1), 178–192.

Schoenfeld, A. H. (2007). The Complexities of Assessing Teacher Knowledge. Measurement : Interdisciplinary Research and Perspectives, 5(2), 198 – 204. https://doi.org/10.1080/15366360701492880

Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Refor. Harvard Folucational Review, 57, 1–22.

Yuretich, R. F. (2004). Encouraging Critical Thinking: Measuring Skills in Large Introductory Science Classes. Journal of College Science Teaching, 33(3), 40–45.

Zuya, E. H. (2015). Mathematics Teachers ’ Ability to Investigate Students ’ Thinking Processes Mathematics Teachers ’ Ability to Investigate Students ’ Thinking Processes About Some Algebraic Concepts. Journal of Education and Practice, 5(25), 117–213.

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