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Abstract

To measure the procedural and conceptual knowledge of functions and to clarify the relationship between them in the context of mathematics education in Morocco, a structural equation modeling (SEM) analysis was used. In addition, correlation tests between students’ grades at their Mathematical Analysis Assessments and their procedural and conceptual knowledge of functions scores were established to investigate whether students' grades mainly reflect their performance on procedural knowledge or conceptual knowledge. The sample consisted of 337 high school Moroccan students. The study findings indicated that a large group of participants scored high in procedural tasks but low in conceptual tasks. Besides, the participants’ grades in their exams correlate much more strongly with the estimated procedural knowledge scores than the estimated conceptual knowledge scores. On the other hand, the confirmatory factor analysis of the SEM confirmed the reliability, validity, and fitness of the measurement model, whereas the path analysis of the SEM supports the genetic view causal relationship that procedural knowledge of functions is necessary but not sufficient condition for conceptual knowledge. These results provide a theoretical foundation for improving mathematics education by working on the content of the assessments, the teachers’ teaching approaches, and the students’ learning strategies.

Keywords

Assessments Conceptual Knowledge Functions Genetic View Procedural Knowledge

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Qetrani, S., & Achtaich, N. (2022). Evaluation of procedural and conceptual knowledge of mathematical functions: A case study from Morocco. Journal on Mathematics Education, 13(2), 211–238. https://doi.org/10.22342/jme.v13i2.pp211-238
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References

  1. Abouhanifa, S., & Benkenz, N. (2018). Praxéologies enseignantes à l’égard du développement de la pensée algébrique chez les élèves du collège. 32. Retrieved from https://cifem2018.sciencesconf.org/data/pages/Didactique_TIC_Innovation_pedagogique.pdf
  2. Arend, B. D. (2007). Course assessment practices and student learning strategies in online courses. Online Learning Journal, 11(4), 3-17. http://dx.doi.org/10.24059/olj.v11i4.1712
  3. Benmansour, N. (1999). Motivational orientations, self-efficacy, anxiety, and strategy use in learning high school mathematics in Morocco. Retrieved from https://www.um.edu.mt/library/oar/handle/123456789/18779
  4. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606. https://doi.org/10.1037/0033-2909.88.3.588
  5. Bourqia, R., El Asmai, H., & Benbigua, A. (2018). Moroccan student results in mathematics and science in an international context. Retrieved from https://www.csefrs.ma/wp-content/uploads/2018/06/TIMSS-Version-Fr-26-05-2018.pdf
  6. Boutin, G. (2000). Le béhaviorisme et le constructivisme ou la guerre des paradigmes. 37–40. Retrieved from https://www.erudit.org/fr/revues/qf/2000-n119-qf1196762/56026ac.pdf
  7. Braine, M. D. S. (1988). Pinker S., Language learnability and language development. Journal of Child Language, 15(1), 189–199. https://doi.org/10.1017/S0305000900012137
  8. Bransford, J., Brown, A. L., & Cocking, R. (1999). How People Learn: Mind, Brain, Experience and School. Retrieved from http://www.csun.edu/~SB4310/How%20People%20Learn.pdf
  9. Breidenbach, D., Dubinsky, E., Hawks, J., & Devilyna, N. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247–285. https://doi.org/10.1007/BF02309532
  10. Browne, M. W., & Cudeck, R. (1989). Single sample cross-validation indices for covariance structures. Multivariate Behavioral Research, 24(4), 445-455. https://doi.org/10.1207/s15327906mbr2404_4
  11. Bryk, A. S., Sebring, P. B., Allensworth, E., Luppescu, S., & Easton, J. Q. (2010). Organizing schools for improvement: Lessons from Chicago. University of Chicago Press. Retrieved from https://press.uchicago.edu/Misc/Chicago/078007.html
  12. Byrne, B. M. (1998). Structural equation modeling with Lisrel, Prelis, and Simplis: Basic concepts, applications, and programming. Psychology Press. https://doi.org/10.4324/9780203774762
  13. 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
  14. Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87–103. https://doi.org/10.1207/s15326985ep2302_2
  15. CSEFRS. (2014). Mise en œuvre de la Charte nationale d’éducation et de formation: Acquis, déficits et défis. Conseil Supérieur de l’Éducation, de la Formation et de la Recherche Scientifique. Retrieved from https://www.csefrs.ma/publications/charte-nationale-deducation-et-de-formation/?lang=fr
  16. CSEFRS. (2016). Programme National d’Évaluation des Acquis des élèves. Conseil Supérieur de l’Éducation, de la Formation et de la Recherche Scientifique. Retrieved from https://www.csefrs.ma/publications/programme-national-devaluation-des-acquis-des-eleves/?lang=fr
  17. CSEFRS. (2021). Programme national d’évaluation des Acquis des élèves de la 6ème année primaire et 3ème année secondaire collégiale – PNEA 2019. Conseil Supérieur de l’Éducation, de la Formation et de la Recherche Scientifique. Retrieved from: https://www.csefrs.ma/publications/programme-national-devaluation-des-acquis-des-eleves-de-la-6eme-annee-primaire-et-3eme-annee-secondaire-collegiale-pnea-2019/?lang=fr
  18. Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159-199. https://doi.org/10.3102/00346543053002159
  19. Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 95–126). Springer Netherlands. https://doi.org/10.1007/0-306-47203-1_7
  20. Duval, R. (1993). 1993 Annales de didactique et de sciences cognitives. V. 5. P. 37-65. Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Retrieved from https://publimath.univ-irem.fr/biblio/IST93004.htm
  21. El Asame, M., & Wakrim, M. (2018). Towards a competency model: A review of the literature and the competency standards. Education and Information Technologies, 23(1), 225–236. https://doi.org/10.1007/s10639-017-9596-z
  22. El Faddouli, N., El Falaki, B., Idrissi, M. K., & Bennani, S. (2011). Adaptive assessment in learning system. Retrieved from https://www.researchgate.net/profile/Brahim-El-Falaki/publication/303376522_ADAPTIVE_ASSESSMENT_IN_LEARNING_SYSTEM/links/5aabeee3458515baa3b98895/ADAPTIVE-ASSESSMENT-IN-LEARNING-SYSTEM.pdf
  23. Eronen, L., & Haapasalo, L. (2010). Making Mathematics through Progressive Technology. 12. Retrieved from http://www.elisanet.fi/medusa/cas/Eronen&Haapasalo.pdf
  24. Gelman, R., & Williams, E. M. (1998). Enabling constraints for cognitive development and learning: Domain specificity and epigenesis. Handbook of Child Psychology: Volume 2: Cognition, Perception, and Language, 575–630. Retrieved from https://www.researchgate.net/publication/232508159_Enabling_constraints_for_cognitive_development_and_learning_Domain_specificity_and_epigenesis
  25. Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal Für Mathematik-Didaktik, 21(2), 139–157. https://doi.org/10.1007/BF03338914
  26. Hair, William C, Barry J. Babin, & Rolph E. Anderson. (2010). Multivariate Data Analysis: Global Edition, 7th Edition. Pearson. Retrieved from https://www.pearson.com/uk/educators/higher-education-educators/program/Hair-Multivariate-Data-Analysis-Global-Edition-7th-Edition/PGM916641.html
  27. Halford, G. S. (2014). Children’s understanding: The development of mental models. Psychology Press. https://doi.org/10.4324/9781315801803
  28. Hamouchi, A., Errougui, I., & Boulaassass, B. (2012). L’enseignement au Maroc, de l’approche par objectifs à l’approche par compétences: Points de vue des enseignantes et enseignants. Etudier. Retrieved from https://www.etudier.com/dissertations/l%E2%80%99Enseignement-Au-Maroc-De-l%E2%80%99Approche-Par/55516493.html
  29. Heibert, J., & Lefevre, P. (1986). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. In Conceptual and Procedural Knowledge. Routledge https://doi.org/10.4324/9780203063538
  30. Heibert, J., & Wearne, D. (1986). Procedures Over Concepts: The Acquisition of Decimal Number Knowledge. In Conceptual and Procedural Knowledge. Routledge. Retrieved from https://psycnet.apa.org/record/1986-98511-008
  31. Hiebert, J. (Ed.). (1986). Conceptual and Procedural Knowledge: The Case of Mathematics. Routledge. https://doi.org/10.4324/9780203063538
  32. Hirtt, P. N. (2009). L’approche par compétences: Une mystification pédagogique. Retrieved from http://sauvonsluniversite.com/IMG/pdf/APC_Mystification.pdf
  33. Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence: An essay on the construction of formal operational structures. Routledge. https://doi.org/10.4324/9781315009674
  34. Janvier, C. (1978). The interpretation of complex cartesian graphs representing situations: Studies and teaching experiments. Ph.D. Dissertation. Nottingham University. Retrieved from https://flm-journal.org/Articles/342368A19260FACE7BC364ED38AD7.pdf
  35. Lauritzen, P. (2012). Conceptual and Procedural Knowledge of Mathematical Functions. 172. Retrieved from https://erepo.uef.fi/bitstream/handle/123456789/11481/urn_isbn_978-952-61-0893-3.pdf?sequence=1&isAllowed=y
  36. Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349–371. https://doi.org/10.1007/s10649-006-9071-z
  37. Ma, L. (2020). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (3rd ed.). Routledge. https://doi.org/10.4324/9781003009443
  38. Mawfik, N., Hijazi, R., Lakramti, A., & Mensouri, L. (2003). Réformes et tendances de l’enseignement des mathématiques au Maroc. 6. Retrieved from http://emf.unige.ch/files/4814/5459/5222/EMF2003_GT4_Mawfik.pdf
  39. MNEPS. (2007). Programmes du secondaire qualifiant. Ministry of National Education Preschool and Sports, Morocco. https://www.men.gov.ma/Fr/Pages/Programmes-qualifiant.aspx
  40. Muhtadi, D., Wahyudin, Kartasasmita, B. G., & Prahmana, R. C. I. (2017). The integration of technology in teaching mathematics. Journal of Physics: Conference Series, 943(1), 012020. https://doi.org/10.1088/1742-6596/943/1/012020
  41. Nesher, P. (1986). Are mathematical understanding and algorithmic performance related? For the Learning of Mathematics, 6(3), 2–9. Retrieved from https://www.jstor.org/stable/pdf/40247817.pdf?acceptTC=true
  42. OECD. (2018). pisa for development assessment and analytical framework: reading, mathematics and science. OECD. https://doi.org/10.1787/9789264305274-en
  43. Ourahay, M. (2021). Effets de l’évaluation sommative sur la pratique pédagogique des enseignants cas de l’enseignement des mathématiques au baccalauréat. Revue Marocaine de l’Évaluation et de la Recherche Educative, 5, 406–419. https://doi.org/10.48423/IMIST.PRSM/rmere-v0i5.25635
  44. Piaget, J. (1977). The development of thought: Equilibration of cognitive structures. (Trans A. Rosin). viii, 213. https://doi.org/10.3102/0013189X007011018
  45. Polya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Retrieved from https://books.google.co.ma/books?id=z_hsbu9kyQQC
  46. Rice, M. F., & Carter, R. A. (2016). Online teacher work to support self-regulation of learning in students with disabilities at a fully online state virtual school. Online Learning, 20(4), 118–135. http://dx.doi.org/10.24059/olj.v20i4.1054
  47. Rico, L. (1997). Los organizadores del currículo de matemáticas (L. Rico, E. Castro, E. Castro, M. Coriat, A. Marín, L. Puig, M. Sierra, & M. M. Socas, Eds.; pp. 39–59). ice - Horsori. http://funes.uniandes.edu.co/522/
  48. Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds to support mathematical problem solving. Cognition and Instruction, 23(3), 313–349. https://doi.org/10.1207/s1532690xci2303_1
  49. 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(2), 346–362. https://doi.org/10.1037/0022-0663.93.2.346
  50. Sáenz, C. (2009). The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). Educational Studies in Mathematics, 71(2), 123–143. https://doi.org/10.1007/s10649-008-9167-8
  51. Saoudi, K., Chroqui, R., & Okar, C. (2020). Student achievement in Moroccan student achievement in Moroccan educational reforms: A significant gap between aspired outcomes and current practices. Interchange, 51(2), 117–136. https://doi.org/10.1007/s10780-019-09380-2
  52. Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental Psychology, 47(6), 1525–1538. https://doi.org/10.1037/a0024997
  53. Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178–192. https://doi.org/10.1037/a0016701
  54. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36. https://doi.org/10.1007/BF00302715
  55. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
  56. Siegler, R. S., & Stern, E. (1998). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127(4), 377–397. https://doi.org/10.1037/0096-3445.127.4.377
  57. Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9–15. https://doi.org/10.5951/AT.26.3.0009
  58. Skinner, B. F. 1904-1990 (Burrhus F. (1968). La Révolution scientifique de l’enseignement /. https://eduq.info/xmlui/handle/11515/12202
  59. Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565–579. https://doi.org/10.1016/j.learninstruc.2007.09.018
  60. Tamani, S., Amad, Z., Abouhanifa, S., El-Khouzai, E., & Radid, M. (2021). Analysis on the actions of a continuous distance training session for teachers and its impact on their actual practices. International Journal of Interactive Mobile Technologies (IJIM), 15, 119. https://doi.org/10.3991/ijim.v15i17.22411
  61. Tambwe, M. A. (2019). Challenges facing the implementation of a Competency-Based Education and Training (CBET) system in Tanzanian technical institutions. In J. L. P. Lugalla & J. M. Ngwaru (Eds.), Education in Tanzania in the Era of Globalisation: Challenges and Opportunities (pp. 242–255). Mkuki na Nyota Publishers. https://doi.org/10.2307/j.ctvh8r02h.24
  62. Vandenberg, R. J. (2006). Introduction: Statistical and methodological myths and urban legends: Where, pray tell, did they get this idea? Organizational Research Methods, 9(2), 194–201. https://doi.org/10.1177/1094428105285506
  63. Velde, C. (1999). An alternative conception of competence: Implications for vocational education. Journal of Vocational Education & Training, 51(3), 437–447. https://doi.org/10.1080/13636829900200087
  64. Zucker, B. (1984). The relation between understanding and algorithmic knowledge in decimals. Unpublished Master Thesis. The University of Haifa.