The Effect of Cognitive Development Programme (Turkish Maths/ Math Modules) on the Development of Mathematics Skills of Primary School Students

Abstract

This study was conducted to determine the effects of the Turkish Maths (Math Modules) cognitive development programme based on the PASS Theory on the mathematics skills of first grade students. In the study, unequal groups pretest-posttest experimental design, one of the quasi-experimental designs, was used. The study group consisted of 39 typically developing students attending 1st grade. The measurement tools to determine the effectiveness were the calculation performance test (De Vos, 1992; Olkun et al., 2013) and the number sense test for kindergarten and primary school students (Palabıyık & Tertemiz, 2021) developed for the first grade. To ensure social validity, semi-structured interviews were conducted with the class teacher of the experimental group and 9 parents. The quantitative data obtained were analysed manually through SPSS 27.00 package programme, and the social validity data were analysed manually through content analysis. As a result of the intervention; according to the Mann-Whitney U test results of the experimental group students and the control group students; it was determined that there was a significant difference between the scores obtained from the calculation performance test (U=99.00, p= .015 <.05) and the number sense test (U=20.50, p= .001 <.05). According to the social validity findings, each interviewee stated that the programme was beneficial for the children and the differences were observable. In line with the quantitative results and social validity findings, it is thought that the Turkish Maths (Math Modules) cognitive development programme is effective on first grade students in improving their mathematics skills.

Keywords

• The PASS theory
• Turkish Maths
• Math Modules
• mathematics skills
• quasi-experimental design.

References

1. Agodini, R., & Harris, B. (2010). An experimental evaluation of four elementary school math curricula. Journal of Research on Educational Effectiveness, 3(3), 199-253. https://doi.org/10.1080/19345741003770693
2. Aktan, O., & Akkutay, Ü. (2014). Preschool education in OECD countries and Türkiye. Asian Journal of Instruction (E-AJI), 2(1), 64-79.
3. Aydın, A., Selvitopu, A., & Kaya, M. (2018). Investments in education and PISA 2015 results: A comparative analysis. İlköğretim Online, 17(3), 1283-1301. https://doi.org/10.17051/ilkonline.2018.466346
4. Bachman, H. J., Votruba-Drzal, E., El Nokali, N. E., & Castle Heatly, M. (2015). Opportunities for learning maths in elementary school: Implications for SES disparities in procedural and conceptual maths skills. American Educational Research Journal, 52(5), 894-923. https://doi.org/10.3102/0002831215594877
5. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills:
6. Constructing adaptive expertise studies (pp. 1-20). Lawrence Erlbaum Associates.
7. Bodovski, K., & Farkas, G. (2007). Mathematics growth in early elementary school: The roles of beginning knowledge, student engagement, and instruction. The Elementary School Journal, 108(2), 115-130.
8. Byrnes, J. P., & Wasik, B. A. (2009). Factors predictive of mathematics achievement in kindergarten, first and third grades: An opportunity-propensity analysis. Contemporary Educational Psychology, 34(2), 167-183. https://doi.org/10.1016/j.cedpsych.2009.01.002

9. Büyüköztürk, Ş., Çakmak, E.K., Akgün, K.Ş., & Demirel, F. (2012). Scientific research methods (12th edition). Pegem A Publishing.
10. Cai, D., Ge, Y., Wang, L., & Leung, A. W. (2024). Improvement in math ability and cognitive processing in children with low attention: An intervention based on PASS theory. Journal of Intelligence, 12(9), 83. https://doi.org/10.3390/jintelligence12090083
11. Charles, R., Crown, W., Fennell, F. S., Caldwell, J. H., Cavanagh, M., Chancellor, D., et al. (2005). Scott Foresman-Addison Wesley mathematics. Grade 1. Glenview, IL: Pearson Scott Foresman.
12. Cinkılıç, H. (2009). Investigation of the effect of pre-school education on the school maturity of primary school 1st grade studentsMaster's degree, Selçuk University
13. Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1-29. https://doi.org/10.1177/016146811311500603
14. Clements, D. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(5), 270-275. https://doi.org/10.5951/TCM.7.5.0270
15. Clements, D. H. (2004). Major themes and recommendations. In D. H. Clements, J. Sarama, & A. M. Dibiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education. Erlbaum.
16. Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the building blocks project. Journal for Research in Mathematics Education, 38, 136-163. https://doi.org/10.2307/30034954
17. Clements, D.H., & Sarama, J. (2009). Learning and teaching early maths: The learning trajectories approach. New York, NY: Routledge.
18. Clements, D.H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333, 968-970. https://doi.org/10.1126/science.1204537
19. Cowan, R., Donlan, C., Shepherd, D.-L., Cole-Fletcher, R., Saxton, M., & Hurry, J. (2011). Basic calculation proficiency and mathematics achievement in elementary school children. Journal of Educational Psychology, 103(4), 786-803. https://doi.org/10.1037/a0024556
20. Creswell, W.J. (2017). Introduction to mixed methods research (1st edition). Pegem Academy.
21. Das, J. P. (2014). Math modules in English. University of Alberta. Fundation Centre JP Das.
22. Das, J. P., Naglieri J. A., & Kirby, J. R. (1994). Assessment of cognitive processes: the pass theory of intelligence. Allyn and Bacon A Division of Simon and Schuster Inc.
23. De Vos, T. (1992). Tempo test rekenen [Arithmetic tempo test]. Nijmegen, The Netherlands: Berkhout.
24. Deaño, M., Alfonso, S., Diniz, A. M., Iglesias-Sarmiento, V., & Das, J. P. (2023). Math modules training improves math achievement & associated cognitive processing. Psychology, 14, 1053-1069. https://doi.org/10.4236/psych.2023.146057
25. Ekici, Ş., & Ekici, E. (2024). Preschool education models in OECD countries and Türkiye comparison. Journal of Social Development, 2(2), 31-38. https://doi.org/10.5281/zenodo.15063331
26. Fuson, K. C. (2006). Math expressions. Grade 1. Boston: Houghton Mifflin.
27. Fuson, K. C. (2012). Children's counting and concepts of number. Springer Science & Business Media.
28. Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Developmental Psychology, 47(6), 1539- 1552.
29. Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38(4), 293-304. https://doi.org/10.1177/00222194050380040301
30. Ginsburg, H. P., & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29(4), 274-285. https://doi.org/10.1016/j.appdev.2008.04.008
31. Griffin, S. (1997). Number worlds: Grade one level. Number Worlds Alliance Inc.
32. Griffin, S. (1998). Number worlds: Grade two level. Number Worlds Alliance Inc.
33. Griffin, S. (2000). Number worlds: Preschool level. Number Worlds Alliance Inc.
34. Griffin, S. (2004). Building number sense with number worlds: A mathematics programme for young children. Early Childhood Research Quarterly, 19(1), 173-180. https://doi.org/10.1016/j.ecresq.2004.01.012
35. Griffin, S., & Case, R. (1995). Number worlds: Kindergarten level. Number Worlds Alliance Inc.
36. Guhl, P. (2019). The impact of early maths and numeracy skills on academic achievement in elementary school. [Master's thesis, Northwestern College]. https://nwcommons.nwciowa.edu/education_masters/155/
37. Hook, W., Bishop, W., & Hook, J. (2007). A quality maths curriculum in support of effective teaching for elementary schools. Educational Studies in Mathematics, 65, 125-148.
38. Jordan, N. C., & Hanich, L. B. (2003). Characteristics of children with moderate mathematics deficiencies: A longitudinal perspective. Learning Disabilities Research & Practice, 18(4), 213-221. https://doi.org/10.1111/1540-5826.00076
39. Jordan, N. C., Kaplan, D., Nabors Oláh, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153-175. https://doi.org/10.1111/j.1467-8624.2006.00862.x
40. Kıldan, A. O. (2010). In the context of pre-school education; "Quality in education services". Journal of Süleyman Demirel University Faculty of Economics and Administrative Sciences, 15(2), 111-130.
41. Kroesbergen, E. H., Van Luit, J. E., Naglieri, J. A., Taddei, S., & Franchi, E. (2010). PASS processes and early mathematics skills in Dutch and Italian kindergarteners. Journal of Psychoeducational Assessment, 28(6), 585-593. https://doi.org/10.1177/0734282909356054
42. Larson, N. (2004). Saxon Maths 1. Harcourt Achieve.
43. Lehrl, S., Kluczniok, K., & Rossbach, H. G. (2016). Longer-term associations of preschool education: The predictive role of preschool quality for the development of mathematical skills through elementary school. Early Childhood Research Quarterly, 36, 475-488. https://doi.org/10.1016/j.ecresq.2016.01.013
44. McIntosh, A., Reys, B. J., & Reys, R. E. (2005). A proposed framework for examining basic number sense. In Subject learning in the primary curriculum (pp. 209-221). Routledge.
45. Memisevic, H., Biscevic, I., & Pasalic, A. (2018). Predictors of maths achievement in the elementary school students grades 1-3. Acta Neuropsychologica, 16, 249-258.
46. Mix, K. S., Levine, S. C., Cheng, Y. L., Young, C., Hambrick, D. Z., Ping, R., & Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206- 1227. https://doi.org/10.1037/xge0000182
47. Naglieri, J. A., & Gottling, S. H. (1995). A study of planning and mathematics instruction for students with learning disabilities. Psychological Reports, 76(3_suppl), 1343-1354. https://doi.org/10.2466/pr0.1995.76.3c.1343
48. Nelson, P. M., Parker, D. C., & Zaslofsky, A. F. (2016). The relative value of growth in growth in maths fact skills across late elementary and middle school. Assessment for Effective Intervention, 41(3), 184-192. https://doi.org/10.1177/1534508416634613
49. Newton, K. J., Lange, K., & Booth, J. L. (2020). Mathematical flexibility: Aspects of a continuum and the role of prior knowledge. The Journal of Experimental Education, 88(4), 503-515. https://doi.org/10.1080/00220973.2019.1586629
50. Olkun, S. (2012). Number sense: What is it? Why is it important? How does it develop? [Number sense: what is it, why is it important? how we develop it?]. Journal of Educator Teacher, 10, 6.
51. Olkun, S., Can, D., & Yesilpinar, M. (2013). Computational performance test: Validity and reliability study. XII. National Classroom Teacher Education Symposium. Adnan Menderes University Faculty of Education, Aydın.
52. Pagani, L. S., Larocque, D., Tremblay, R. E., & Lapointe, P. (2004). The impact of junior kindergarten on maths skills in elementary school. Canadian Journal of School Psychology, 19(1-2), 117-136. https://doi.org/10.1177/082957350401900106
53. Palabıyık, E., & Tertemiz, N. (2021). Development of number sense tests for kindergarten and primary school students: Validity and reliability study. Journal of Ufuk University Institute of Social Sciences, 10(20), 27-57.
54. Pomalato, S. W. D., Ismail, R., Harefa, A. O., Imawan, O. R., Ningsi, B. A., & Wulandari, D. (2021). Instrument test development of mathematics skill on elementary school. Turkish Journal of Computer and Mathematics Education, 12(6), 2447-2455.
55. Russell, S. J., Economopoulos, K., Mokros, J., Kliman, M., Wright, T., Clements, D. H., et al. (2006). Investigations in number, data, and space: Grade 1. Pearson Scott Foresman.
56. Sarı, M. H., & Ekici, G. (2018). Determination of affective variables affecting mathematics achievement and arithmetic performance of 4th grade primary school students. OPUS International Journal of Society Researches, 8(15), 1562-1594. https://doi.org/10.26466/opus.451025
57. Thyer, B. A. (2012). Quasi-experimental research designs. Oxford University Press.
58. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics. Pearson.
59. Wang, A. H. (2010). Optimising early mathematics experiences for children from low-income families: A study on opportunity to learn mathematics. Early Childhood Education Journal, 37, 295-302. https://doi.org/10.1007/s10643-009-0353-9
60. Warrick, P. D. (1989). Investigation of the PASS model (planning, attention, simultaneous, successive) of cognitive processing and mathematics achievementDoctoral dissertation, The Ohio State University.
61. Yang, D. C., Li, M. N., & Lin, C. I. (2008). A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6, 789-807.
62. Yee, L. P. (2010). Designing a mathematics curriculum. Indonesian Mathematical Society Journal on Mathematics Education, 1(1), 1-10.