Abstract
This study is part of broader research focused on the SIMPLE Approach, a constructivist intervention that integrates the bar model method with metacognitive scaffolding to enhance word problem-solving skills in Kosovo's lower secondary classrooms. It specifically examines the fidelity of implementation and teachers' perceptions of this approach. The study aims to fill a research gap in design-based intervention studies, which recognise the critical role of teachers but provide limited insight into their actual work and how faithfully they implement interventions. To address this gap, the study explored two areas: (1) the fidelity of three teachers' implementation of the SIMPLE Approach and (2) the teachers' perceptions of its usefulness. Data collected from classroom observations, teacher diaries, and interviews revealed varying levels of fidelity, which improved over time. Teacher 1 exhibited the lowest fidelity, struggling with the bar model method and limiting group work. In contrast, Teacher 3 demonstrated the highest fidelity, successfully incorporating all aspects of the SIMPLE Approach and promoting active pupil engagement. Regarding their perceptions, all three teachers maintained positive attitudes towards the SIMPLE Approach from the outset and appreciated its benefits by the end of the intervention. Although the generalisability of the findings is limited, they suggest that the SIMPLE Approach holds promise. However, the study highlights the need for comprehensive teacher training and ongoing support, especially when introducing new methods, to ensure effective implementation and high fidelity.
References
Altun, S., Yaba¸s, D., & Bal-Nayman, H. (2021). Teachers’ experiences on instructional design-based professional development: A narrative inquiry. International Electronic Journal of Elementary Education, 14(1), 35–50. https://doi.org/10.26822/iejee.2021.227
Anderson, T., & Shattuck, J. (2012). Design-based research: A decade of progress in education research? Educational Researcher, 41(1), 16–25. https://doi.org/10.3102/0013189X11428813
Arndt, H., & Rose, H. (2023). Capturing life as it is truly lived? Improving diary data in educational research. International Journal of Research & Method in Education, 46(2), 175–186. https://doi.org/10.1080/1743727X.2022.2094360
Baysal, E., & Sevinc, S. (2021). The role of the Singapore bar model in reducing students’ errors on algebra word problems. International Journal of Mathematical Education in Science and Technology, 53(2), 289–310. https://doi.org/10.1080/0020739X.2021.1944683
Berisha, V., Tha¸ci, X., Jashari, H., & Klinaku, S. (2013). Assessment of mathematics textbooks’ potential in terms of students’ motivation and comprehension. Journal of Education and Practice, 4(28), 33–37.
Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001
Brousseau, G. (1997). Theory of the Didactical Situations in Mathematics. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2
Brown, B., Friesen, S., Beck, J., & Roberts, V. (2020). Supporting new teachers as designers of learning. Education Sciences, 10(8), 207. https://doi.org/10.3390/educsci10080207
Carroll, C., Patterson, M., Wood, S., Booth, A., Rick, J., & Balain, S. (2007). A conceptual framework for implementation fidelity. Implementation Science, 2(1), Nu. 40. https://doi.org/10.1186/1748-5908-2-40
Century, J., Rudnick, M., & Freeman, C. (2010). A framework for measuring fidelity of implementation: A foundation for shared language and accumulation of knowledge. American Journal of Evaluation, 31(2), 199–218.
Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomised trial. Journal for Research in Mathematics Education, 42(2), 127–166.
Combs, K. M., Buckley, P. R., Lain, M. A., Drewelow, K. M., Urano, G., & Kerns, S. E. U. (2022). Influence of classroom-level factors on implementation fidelity during scale-up of evidence-based interventions. Prevention Science, 23(1), 969–981. https://doi.org/10.1007/s11121-022-01375-3
Cooper, J. L., Sidney, P. G., & Alibali, M.W. (2018). Who benefits from diagrams and illustrations in math problems? Ability and attitudes matter. Applied Cognitive Psychology, 32(1), 24–38. https://doi.org/10.1002/acp.3371
Crawford, L., Carpenter, D. M., Wilson, M. T., Schmeister, M., & McDonald, M. (2012). Testing the relation between fidelity of implementation and student outcomes in math. Assessment for Effective Intervention, 37(4), 224–235. https://doi.org/10.1177/1534508411436111
Creswell, J.W., Hanson, W. E., Clark Plano, V. L., & Morales, A. (2007). Qualitative research designs: Selection and implementation. The Counseling Psychologist, 35(2), 236–264. https://doi.org/10.1177/0011000006287390
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6(348), 22–34. https://doi.org/10.3389/fpsyg.2015.00348
Design-Based Research Collective (DBRC) (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8. https://doi.org/10.3102/0013189X032001005
Ford, C., McNally, D., & Ford, K. (2017). Using design-based research in higher education innovation. Online Learning, 21(3). https://doi.org/10.24059/olj.v21i3.1232
Freeman-Green, S. M., O’Brien, C., Wood, C. L., & Hitt, S. B. (2015). Effects of the SOLVE strategy on the mathematical problem-solving skills of secondary students with learning disabilities. Disabilities Research and Practice, 30(2), 76–90. https://doi.org/10.1111/ldrp.12054
Gani, M. A., Tengah, K. A., & Said, H. (2019). Bar model as an intervention in solving word problems involving percentages. International Journal on Emerging Mathematics Education, 3(1), 69–76. https://doi.org/10.12928/ijeme.v3i1.11093
Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). What the United States can learn from Singapore’s world class mathematics system (and what Singapore can learn from the United States): An exploratory study. American Institutes for Research. http://files.eric.ed.gov/fulltext/ED491632.pdf
Hembree, R. (1992). Experiments and relational studies in problem-solving: A meta-analysis. Journal for Research in Mathematics Education, 23(3), 242–273. https://doi.org/10.2307/749120
Ho, S. Y., & Lowrie, T. (2014). The model method: Pupils’ performance and its effectiveness. The Journal of Mathematical Behavior, 35, 87–100. https://doi.org/10.1016/j.jmathb.2014.06.002
Ismajli, H., & Krasniqi, B. (2022). Constructivist instruction practices in Kosovo primary education: The field of languages and communication curriculum. Journal of Social Studies Education Research, 13(1), 259–281.
Kaur, B. (2018). The why, what and how of the ‘Model’ method: A tool for representing and visualising relationships when solving whole number arithmetic word problems. ZDM Mathematics Education, 51(1), 151–168. https://doi.org/10.1007/s11858-018-1000-y
Kho, T. H. (1987). Mathematical models for solving arithmetic problems. In Proceedings of the 4th Southeast Asian Conference on Mathematics Education (ICMI-SEAMS) (pp.345–351). Singapore.
Mcnamara, O., Jaworski, B., Rowland, T., Hodgen, J., & Prestage, S. (2002). Developing mathematics teaching and teachers: A research monograph. British Society for Research into Learning Mathematics BSRLM.
Ministry of Education, Science and Technology (MEST). (2016). Curriculum Framework for Pre-university Education in the Republic of Kosovo.
Morin, L. L., Watson, S. M. R., Hester, P., & Raver, S. (2017). The use of a bar model drawing to teach word problem solving to pupils with mathematics difficulties. Learning Disability Quarterly, 40(2), 91–104. https://doi.org/10.1177/0731948717690116
Morina, Q. (2023). The impact of the SIMPLE strategy on word problem solving — a case study. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 3620–3621). Alfréd Rényi Institute of Mathematics and ERME.
Morina, Q., & Vondrová, N. (2021). Block model approach and its effect on word problem solving: A case study. In J. Novotná & H. Moraová (Eds.), International Symposium Elementary Mathematics Teaching, Proceedings (pp. 31–320). Charles University, Faculty of Education.
Nelson, M. C., Cordray, D. S., Hulleman, C. S., Darrow, C. L., & Sommer, E. C. (2012). A procedure for assessing intervention fidelity in experiments testing educational and behavioral interventions. The Journal of Behavioral Health Services & Research, 39(4), 374–396. https://doi.org/10.1007/s11414-012-9295-x
O’Donnell, C. L. (2008). Defining, conceptualizing, and measuring fidelity of implementation and its relationship to outcomes in K-12 curriculum intervention research. Review of Educational Research, 78(1), 33–84. https://doi.org/10.3102/0034654307313793
Osman, S., Che Yang, C. N. A., Abu, M. S., Ismail, N., Jambari, H., & Kumar, J. A. (2018). Enhancing pupils’ mathematical problem-solving skills through bar model visualisation technique. International Electronic Journal of Mathematics Education, 13(3), 273–279. https://doi.org/10.12973/iejme/3919
Özkubat, U., Karabulut, A., & Serhat, U. A. (2021). Investigating the effectiveness of STAR strategy in math problem-solving. International Journal of Progressive Education, 17(2), 83–100. https://doi.org/10.29329/ijpe.2021.332.6
Pantziara, M., Gagatsis, A., & Elia, I. (2009). Using diagrams as tools for the solution of nonroutine mathematical problems. Educational Studies in Mathematics, 72, 39–60. https://doi.org/10.1007/s10649-009-9181-5
Pearce, D. L., Bruun, F., Skinner, K., & Lopez-Mohler, C. (2013). What teachers say about student difficulties solving mathematical word problems in grades 2–5. International Electronic Journal of Mathematics Education, 8(1), 3–19.
Perry, J., Lundie, D., & Golder, G. (2018). Metacognition in schools: What does the literature suggest about the effectiveness of teaching metacognition in schools? Educational Review, 71(4), 483–500. https://doi.org/10.1080/00131911.2018.1441127
Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton University Press.
Pongsakdi, N., Kajamies, A., Veermans, K., Lertola, K., Vauras, M., & Lehtinen, E. (2020). What makes mathematical word problem solving challenging? Exploring the roles of word problem characteristics, text comprehension, and arithmetic skills. ZDM Mathematics Education, 52(1), 33–44. https://doi.org/10.1007/s11858-019-01118-9
Rutakumwa, R., Mugisha, J. O., Bernays, S., Kabunga, E., Tumwekwase, G., Mbonye, M., & Seeley, J. (2020). Conducting in-depth interviews with and without voice recorders: a comparative analysis. Qualitative Research, 20(5), 565–581. https://doi.org/10.1177/1468794119884806
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205
Sterner, H. (2019). Teachers as actors in educational design research: What is behind the generalised formula? LUMAT: International Journal on Math, Science and Technology Education, 7(3), 6–27. https://doi.org/10.31129/LUMAT.7.3.403
Teong, S. K. (2003). The effect of metacognitive training on mathematical word-problem solving. Journal of Computer Assisted Learning, 19(1), 46–55. https://doi.org/10.1046/j.0266-4909.2003.00005.x
Ventistas, G., Ventista, O. M., & Tsani, P. (2024). The impact of realistic mathematics education on secondary school students’ problem-solving skills: A comparative evaluation study. Research in Mathematics Education, advance online placement. https://doi.org/10.1080/14794802.2024.2306633
Verschaffel, L., Schukajlow, S., Star, J., & Dooren, V.W. (2020). Word problems in mathematics education: A survey. ZDM Mathematics Education, 52(1), 1–16. https://doi.org/10.1007/s11858-020-01130-4
Windschitl, M. (2002). Framing constructivism in practice as the negotiation of dilemmas: An analysis of the conceptual, pedagogical, cultural, and political challenges facing teachers. Review of Educational Research, 72(2), 131–175. https://doi.org/10.3102/00346543072002131
Yi, J. (2008). The use of diaries as a qualitative research method to investigate teachers’ perception and use of rating schemes. Journal of Pan-Pacific Association of Applied Linguistics, 12(1), 1–10.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of the published work (See The Effect of Open Access).