Research Article

Conceptual and Procedural Knowledge of Students of Nepal in Algebra: A Mixed Method Study

Netra Kumar Manandhar 1 * , Binod Prasad Pant 1 , Shiva Datta Dawadi 2
More Detail
1 Department of STEAM Education, Kathmandu University, Lalitpur, NEPAL2 Tribhuvan University, Gorkha Campus, Gorkha, NEPAL* Corresponding Author
Contemporary Mathematics and Science Education, 3(1), 2022, ep22005, https://doi.org/10.30935/conmaths/11723
Published: 09 February 2022
OPEN ACCESS   1270 Views   1242 Downloads
Download Full Text (PDF)

ABSTRACT

Mathematical knowledge has been defined in several ways in the literature of mathematics education. Procedural knowledge (PK) and conceptual knowledge (CK) or both types of knowledge are the emphasis of knowledge construction. This is a research-based paper extracted from a dissertation of MEd in mathematics education of the first author under the supervision of the remaining two authors. In this context, this explanatory mixed method research study was carried out to find students’ level of PK and CK in algebra and explore why students develop such knowledge. In the quantitative part, the survey was conducted among 360 students of grade eight of 9 public schools of Kathmandu Metropolitan City. The study revealed that students have a lower level of CK (x̅ =8.56) but a higher level of PK (y̅ =14.05) out of 20 and a moderate positive correlation (r=+0.559, p<0.05) between PK and CK. The regression equation was: CK=3.716+0.345(PK). Similarly, PK was dependent, but CK was independent upon the gender of the respondents. In the qualitative part, a two-phase interview was conducted with six participants followed by a group discussion with four mathematics teachers teaching at the same level. This phase concluded that students are weak in reasoning, critical thinking, representational knowledge and comparing algebraic quantities. The reason is because students seemed to be forced/encouraged to develop procedural fluency because of teachers’ methods of teaching which oftentimes neglect the progressive pedagogical approaches. The research is useful for everyone who is working on educational reform to emphasize meaningful learning.

CITATION (APA)

Manandhar, N. K., Pant, B. P., & Dawadi, S. D. (2022). Conceptual and Procedural Knowledge of Students of Nepal in Algebra: A Mixed Method Study. Contemporary Mathematics and Science Education, 3(1), ep22005. https://doi.org/10.30935/conmaths/11723

REFERENCES

  1. Abd Rahman, Z. (2006). Mastery of algebraic concepts and attitudes towards algebra among secondary school students [Unpublished master of education project report]. Universiti Kebangsaan Malaysia.
  2. Barr, C., Doyle, M., Clifford, J., De Leo, T., & Dubeau, C. (2003). There is more to math: A framework for learning and math instruction. Waterloo Catholic District School Board.
  3. Brooks, J. A., & Freeman, J. B. (2018). Conceptual knowledge predicts the representational structure of facial emotion perception. Nature Human Behaviour, 2(8), 581-591. https://doi.org/10.1038/s41562-018-0376-6
  4. Byrnes, J. P., & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777-786. https://doi.org//10.1037/0012-1649.27.5.777
  5. Creswell, J. W. (2015). Research design: Qualitative, quantitative, and mixed method approaches. Pearson.
  6. Education Review Office (ERO). (2015). Report on national assessment of student achievement (NASA) 2013. The Author.
  7. Education Review Office (ERO). (2017). Report on national assessment of student achievement (NASA) 2017. The Author.
  8. Education Review Office (ERO). (2019). Report on national assessment of student achievement (NASA) 2018. The Author.
  9. Fuson, K. C., & Kwon, Y. (1992). Korean children’s understanding of multi-digit addition and subtraction. Child Development, 63(2), 491-506. https://doi.org/10.1111/j.1467-8624.1992.tb01642.x
  10. Ghazali, N. H., & Zakaria, E. (2011). Students’ procedural and conceptual understanding of mathematics. Australian Journal of Basic and Applied Science, 5(7), 684-691.
  11. Goodman, B., & Stivers, J. (2010). Project-based learning. Educational Psychology. https://www.fsmilitary.org/pdf/Project_Based_Learning.pdf
  12. Hecht, S. A. (1998). Toward an information-processing account of individual differences in fraction skills. Journal of Educational Psychology, 90(3), 545-559. https://doi.org/10.1037/0022- 0663.90.3.545
  13. Heemsoth, T., & Heinze, A. (2014). The impact of incorrect examples on learning fractions: A field experiment with 6th grade students. Instructional Science, 42(4), 639-657. https://doi.org/10.1007/s11251-013-9302-5
  14. Hiebert, J., & LeFevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Lawrence Erlbaum Associates, Inc.
  15. Klein, D. (2007). A quarter century of US ‘math wars’ and political partisanship. Journal of the British Society for the History of Mathematics, 22(1), 22-33. https://doi.org/10.1080/17498430601148762
  16. Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297-312.
  17. Lenz, K., Dreher, A., Holzäpfel, L., & Wittmann, G. (2020). Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions. British Journal of Educational Psychology, 90(3), 809-829. https://doi.org/10.1111/bjep.12333
  18. Luitel, B. C. (2009). Culture, worldview and transformative philosophy of mathematics education in Nepal: A cultural-philosophical inquiry [Unpublished doctoral dissertation]. Curtin University of Technology.
  19. McCormick, R. (1997). Conceptual and procedural knowledge. International Journal of Technology and Design Education, 7(1), 141-159. https://doi.org/10.1023/A:1008819912213
  20. Pant, B. P., Luitel, B. C., & Shrestha, I. M. (2020). Incorporating STEAM pedagogy in mathematics education. In Proceedings of Episteme 8 International Conference to Review Research in in Science, Technology and Mathematics Education, January 3-6, 2020 (pp. 319-326). Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai, India.
  21. Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions. Educational Studies in Mathematics, 79(1), 61-83. https://doi.org/10.1007/s10649-011-9338-x
  22. Rittle-Hohnson, B., & Siegler, R. S. (1998). The relations between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.), The development of mathematical skill (pp. 75-110). Phychology Press. https://doi.org/10.4324/9781315784755-6
  23. Rittle-Johnson, B. (2019). Iterative development of conceptual and procedural knowledge in mathematics learning and instruction. In J. Dunlosky, & K. Rawson (Eds.), The Cambridge handbook of cognition and education (pp. 124-147). Cambridge University Press. https://doi.org/10.1017/9781108235631.007
  24. Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175-189. https://doi.org/10.1037/0022-0663.91.1.175
  25. 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 University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014
  26. Rittle‐Johnson, B., Fyfe, E. R., & Loehr, A. M. (2016). Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson. British Journal of Educational Psychology, 86(4), 576-591. https://doi.org/10.1111/bjep.12124
  27. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93, 346-–362. https://doi.org/10.1037//0022-0663.93.2.346
  28. Ross, A. A. (2010). The effects of constructivist teaching approaches on middle school students’ algebraic understanding [Doctoral thesis]. Texas A & M University. https://core.ac.uk/download/pdf/147133472.pdf
  29. Shenton, A. K. (2004). Strategies for ensuring trustworthiness in qualitative research projects. Education for Information, 22(2), 63-75. https://doi.org/10.3233/EFI-2004-22201
  30. Star, J. R. (2005). Re-conceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 404-411. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.544.4487&rep=rep1&type=pdf
  31. Tian, J., & Siegler, R. S. (2017). Fractions learning in children with mathematics difficulties. Journal of Learning Disabilities, 50(6), 614-620. https://doi.org/10.1177/0022219416662032
  32. Viro, E., Lehtonen, D., Joutsenlahti, J., & Tahvanainen, V. (2020). Teachers’ perspectives on project-based learning in mathematics and science. European Journal of Science and Mathematics Education, 8(1), 12-31. https://doi.org/10.30935/scimath/9544
  33. Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. Falmer.
  34. Yilmaz, K. (2011). The cognitive perspective on learning: Its theoretical underpinnings and implications for classroom practices. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 84(5), 204-212. https://doi.org/10.1080/00098655.2011.568989
  35. Zuya, Z. H. (2017). Prospective teachers’ conceptual and procedural knowledge in mathematics: The case of algebra. American Journal of Educational Research, 5(3), 310-315. https://doi.org/10.12691/education-5-3-12