Journal of Innovations in Teaching and Learning
ISSN (Print): ISSN Pending ISSN (Online): 2945-4638 Website: https://www.sciepub.com/journal/jitl Editor-in-chief: Laila S. Lomibao
Open Access
Journal Browser
Go
Journal of Innovations in Teaching and Learning. 2023, 3(1), 54-59
DOI: 10.12691/jitl-3-1-10
Open AccessLiterature Review

Conceptual Understanding vs. Procedural Fluency: A Literature Review on the Mathematics Teachers Emphasis in Teaching of Rational Algebraic Expressions

Ezekiel O. Pelayo1, , Laila S. Lomibao1 and Rosie G. Tan1

1Department of Mathematics Education, University of Science and Technology of Southern Philippines, Cagayan de Oro City, Philippines

Pub. Date: October 09, 2023

Cite this paper:
Ezekiel O. Pelayo, Laila S. Lomibao and Rosie G. Tan. Conceptual Understanding vs. Procedural Fluency: A Literature Review on the Mathematics Teachers Emphasis in Teaching of Rational Algebraic Expressions. Journal of Innovations in Teaching and Learning. 2023; 3(1):54-59. doi: 10.12691/jitl-3-1-10

Abstract

This paper presents a review of published research articles related to teachers' conceptual understanding and procedural fluency in teaching rational algebraic expressions. The study reviewed practices in mathematics teachers emphasis in teaching rational algebraic expressions through content analysis. Findings revealed that mathematics teachers place a greater emphasis on conceptual understanding in teaching rational algebraic expressions than on developing procedural skills. Giving more emphasis on the conceptual understanding of rational algebraic expressions was essential than focusing on procedural fluency. It is suggested to consider some common strategies that were utilized by mathematics teachers to clear up misconceptions by students in simplifying rational algebraic expressions such as; probing, collaborative learning, differentiated learning. and small group instruction. Moreover, mathematics teachers are also encouraged to innovate strategies that they can utilize to help improve students’ learning of rational algebraic expressions.

Keywords:
rational algebraic expressions conceptual understanding procedural fluency

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Elbaz, F.L. (1983). Teacher thinking: A study of practical knowledge. London: Croom Helm.
 
[2]  Shulman, L.S. (1986). Paradigms and research programs in the study of teaching: A contemporary perspective. In M.C. Wittrock (Ed.), Handbook of research on teaching (pp. 3–36). New York: Macmillan.
 
[3]  Schon, D.A. (1983). The reflective practitioner: How professionals think in action. New York: Basic Books.
 
[4]  Baykul, Y. (1999): Primary mathematics education. Ankara, Turkey, Ani Printing Press.
 
[5]  Crooks, Noelle & Alibali, Martha. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review. 34. 10.1016/j.dr.2014.10.001.
 
[6]  Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative re-conceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38, 115-131.
 
[7]  McGehee, J. (1990). Prospective secondary teachers’ knowledge of the function concept. Unpublished Doctoral Dissertation, University of Texas.
 
[8]  Khashan, K.H. (2014). Conceptual and procedural knowledge of rational numbers for Riyadh elementary school teachers. Journal of Education and Human development, 3(4), 181-197.
 
[9]  Doyle, A. B., & Markiewicz, D. (2003). Associations between parenting style and attachment to mother in middle childhood and adolescence. International Journal of Behavioral Development, 27(2), 153–164., G. Donald (2007), Student Thinking, Available: http://www.math.tamu.edu/~snite/MisMath.pdf
 
[10]  Makonye JP, Hantibi N 2014. Exploration of Grade 9 learners’ errors on operations with directed numbers. Mediterranean Journal of Social Sciences, 5(20): 1564-1572.
 
[11]  Maphini, N.V. (2018). Implementing An Intentional Teaching Model to Investigate Grade 9 Learners’ Way of Working with Rational Algebraic Fractions. University of the Western Cape.
 
[12]  Kieran, C. (2007). Research on the learning and teaching of algebra. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 11–50). Sense.
 
[13]  Crooks, T. (2007, April). Key factors in the effectiveness of assessment for learning. Paper presented at the meeting of the American Educational Research Association, Chicago, IL.
 
[14]  Hirsh, H., Coen, M.H., Mozer, M.C., Hasha, R. and Flanagan, J.L, “Room service, AI-style,” IEEE intelligent systems, 14 (2). 8-19. Jul.2002.
 
[15]  Gough, D., Oliver, S., & Thomas, J. (2012). An introduction to systematic reviews. London: Sage.
 
[16]  Frykholm, J.A. (1999). The impact of reform: Challenges for mathematics teacher preparation. Journal of Mathematics Teacher Education, 2, 79–105.
 
[17]  Vula, E., & Kurshumlia, R. (2015).Mathematics Word Problem Solving Through Collaborative Action Research. Journal of Teacher Action Research, 1(2), 34-46.
 
[18]  Given, L. M. (2008). The Sage encyclopedia of qualitative research methods. Los Angeles, CA: Sage.
 
[19]  Ibrahim, Noorashikin Noor. 2003. Pedagogical content knowledge of mathematics teacher in algebra. Master of Education, Research Project. Bangi: Universiti Kebasngaan Malaysia.
 
[20]  Bryan, L., & Atwater, M. (2002), Teacher beliefs and cultural models: A challenge for science teacher preparation programs. Science Education, 86, 821-839.
 
[21]  Schoenfeld, A.H 2002. “Making mathematics work for all children: Issues of standards, testing, and equity”. Educational researcher, 31(1), 13-25.
 
[22]  Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge in mathematics. In R. Cohen Kadosh & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1102-1118). Oxford, UK: Oxford University Press.
 
[23]  Star, J.R. 2002. “Developing conceptual understanding and procedural skill in mathematics: An interactive process”. Journal of Educational psyhology, 93(2), 346-362.
 
[24]  Conley, D. T., & French, E. M. (2014). Student ownership of learning as a key component of college readiness. American Behavioral Scientist, 58(8), 1018–1034.
 
[25]  Canobi, K. H. (2009). Concept-procedure interactions in children's addition and subtraction. Journal of Experimental Child Psychology, 102, 131-149.
 
[26]  Eisenhart, Margaret & Borko, Hilda & Underhill, Robert & Brown, Catherine & Jones, Doug & Agard, Patricia. (1993). Conceptual Knowledge Falls through the Cracks: Complexities of Learning to Teach Mathematics for Understanding. Journal for Research in Mathematics Education. 24. 8. 10.2307/749384.
 
[27]  Tirosh, D. 2000. “Enhancing prospective teachers’ knowledge of children conceptions: The case of division of fractions” Journal for Research in Mathematics Education, 30(1), 5-25.
 
[28]  Torbeyns, J., Schneider, M, Xin, Z. & Siegler, R. S. 2015. Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents.Learning and Instruction,37, 5-13.
 
[29]  Star, J.R. 2002. “Developing conceptual understanding and procedural skill in mathematics: An interactive process”. Journal of Educational psyhology, 93(2), 346-362.
 
[30]  Leung, F., & Park, K. (2002). Competent students, competent teachers? International Journal of Educational Research, 37, 113-129.
 
[31]  Capraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27(2-3), 147-164.
 
[32]  Baidoo, J. (2019). Dealing with Grade 10 Learners’ Misconceptions and Errors When Simplifying Algebraic Fractions. University of Johannesburg, South Africa.
 
[33]  Thomas, C. 2010. Fraction competency and algebra success. Thesis Submitted in partial fulfilment of the Requirements for the degree of Master of Natural Sciences, Louisiana State University.
 
[34]  Baker, S., Gersten, R. & Lee, D.-S. 2002. A synthesis of empirical research on teaching mathematics to low-achieving students.The Elementary School Journal, 103, 51-73.
 
[35]  Ruhl J.B, Stephen M. Posner, and Taylor H. Ricketts, Engaging Policy in Science Writing: Patterns and Strategies, (2011) Available at: https://scholarship.law.vanderbilt.edu/faculty-publications/1107.
 
[36]  Figuaeras H, Males H, Otten S 2008. Algebra Students’ Simplification of Rational Expressions. Michigan: Michigan State University Press.
 
[37]  Ntuli, E. & Godfrey, A. Wearable technology: Improving mathematical classroom discourse using Pivot-head Eyeglasses. 2018. Association for the Advancement of Computing in Education (AACE), 1113-1118
 
[38]  Chen, X. 2013. Meta-teaching: Meaning and strategy.Africa Education Review, 10, S63- S74.
 
[39]  Martin-Stanley, B. L. & Martin-Stanley, C. R. 2007. Constructivism and technology: Strategies for increasing student learning outcomes. National Social Science Association. Retrieved on January, 25, 2012.
 
[40]  Vygotsky, L. S. 1978. The prehistory of written language. Mind in society: The development of higher psychological processes, 105-119.
 
[41]  Van Steenbrugge, H., Remillard, J., Valcke, M. & Desoete, A. 2015.Teaching fractions in elementary school: An observational study. the elementary school journal, 116, 49-75
 
[42]  Reed, J. G., & Baxter, P. M. (2004). The author/citation approach to searching. In J. G. Reed & P. M. Baxter, Library use: A handbook for psychology (pp. 75–80). American Psychological Association.
 
[43]  Tomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., Conover, L. A., & Reynolds, T. (2008). Differentiating instruction in response to student readiness, interest, and learning profile in academically diverse classrooms: A review of literature. Journal for the Education of the Gifted, 27(2-3), 119-145.
 
[44]  Tom, C. A. (2013). The differentiated classroom: Responding to the needs of all learners (2nd ed.). ASCD
 
[45]  Lane, M. (2008), Subsequent educational attainment in a US national sample. Journal of Psychiatric Research, 42, 708-716.
 
[46]  Kame’enui, E.J. (Eds.). (2004). Vocabulary instruction: Research to practice (pp. 14-17, 29-63, 160). New York: Guilford.
 
[47]  Vula, E., & Kurshumlia, R. (2015).Mathematics Word Problem Solving Through Collaborative Action Research. Journal of Teacher Action Research, 1(2), 34-46.
 
[48]  Serravallo, J. & Goldberg, G. (2010) Conferring with readers: Supporting each student’s growth and independence. Portsmouth, NH: Heinemann.