Development of Four-Tier Diagnostic Test (FTDT) To Assess Readiness of Incoming Grade 11 Students in General Mathematics

Readiness in General Mathematics is a critical factor in ensuring students’ successful transition from Junior High School to Senior High School. However, traditional assessments often focus solely on the correctness of answers and fail to identify students’ reasoning, confidence, and misconceptions. This study aimed to develop a Four-Tier Diagnostic Test (FTDT) integrated with the Certainty of Response Index (CRI) to assess the readiness of incoming Grade 11 students in General Mathematics. Specifically, it sought to establish the psychometric properties of the instrument and analyze students’ readiness through multidimensional diagnostic classifications.
A descriptive-developmental research design was employed involving 100 Grade 10 students from Dr. Apolonio M. Lirio National High School. The instrument underwent expert validation and pilot testing. Data were analyzed using the Content Validity Index (CVI), Rasch Model, Readiness Index (RI), and frequency and percentage distribution.
Results showed that the FTDT demonstrated good content validity, with an S-CVI/Ave of 0.81. Rasch analysis revealed high person reliability for both the knowledge tier (0.883) and reasoning tier (0.884), indicating that the instrument could effectively differentiate students according to readiness levels. The Readiness Index revealed that 55% of students exhibited low readiness, 42% demonstrated moderate readiness, and only 3% achieved high readiness. Furthermore, the FTDT-CRI classification identified misconceptions, false negative responses, false positive responses, and lack of knowledge, highlighting significant gaps in prerequisite competencies.
The findings suggest that the FTDT integrated with CRI is a valid and reliable diagnostic instrument for assessing readiness in General Mathematics. The instrument provides a comprehensive assessment of students’ knowledge, reasoning, and confidence, which may assist teachers in identifying learning gaps and designing targeted instructional interventions and bridging programs

Diagnostic assessment, Certainty of Response Index, Four-Tier Diagnostic Test, General Mathematics readiness, Rasch Model, Readiness Index

1. Aksoy, G. (2024). Development of a four-tier diagnostic test to identify misconceptions in chemistry. Journal of Chemical Education Research, 101(2), 345–356. [Google Scholar] [Crossref]

2. Aristiawan, A., et al. (2025). Development of a four-tier diagnostic test in algebra to identify students’ misconceptions. International Journal of Mathematics Education, 18(1), 45–60. [Google Scholar] [Crossref]

3. Bernardo, A. B. I. (2002). Language and mathematical problem solving among bilinguals. The Journal of Psychology, 136(3), 283–297. [Google Scholar] [Crossref]

4. Bernardo, A. B. I., & Ismail, R. (2020). Mathematics achievement and higher-order thinking skills of Filipino students. Asia Pacific Education Review, 21(3), 417–429. [Google Scholar] [Crossref]

5. Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7–74. [Google Scholar] [Crossref]

6. Bond, T. G., & Fox, C. M. (2015). Applying the Rasch model: Fundamental measurement in the human sciences (3rd ed.). Routledge. [Google Scholar] [Crossref]

7. Boone, W. J., Staver, J. R., & Yale, M. S. (2014). Rasch analysis in the human sciences. Springer. [Google Scholar] [Crossref]

8. Brookhart, S. M. (2013). How to create and use rubrics for formative assessment and grading. ASCD. [Google Scholar] [Crossref]

9. Bujang, M. A., et al. (2024). Sample size guidelines for pilot studies. Malaysian Journal of Medical Sciences, 31(1), 1–10. [Google Scholar] [Crossref]

10. Caleon, I. S., & Subramaniam, R. (2010). Development and application of a multi-tier diagnostic test. International Journal of Science Education, 32(7), 939–961. [Google Scholar] [Crossref]

11. Capuno, R., et al. (2021). Confidence and problem-solving performance in mathematics. International Journal of Educational Research, 105, 101714. [Google Scholar] [Crossref]

12. Carlson, M. P., et al. (2010). The calculus concept readiness (CCR) instrument. International Journal of Mathematical Education in Science and Technology, 41(7), 833–855. [Google Scholar] [Crossref]

13. Chen, Y., et al. (2014). Sample size requirements for Rasch model stability. Educational Measurement: Issues and Practice, 33(4), 14–24. [Google Scholar] [Crossref]

14. Chi, M. T. H. (2005). Commonsense conceptions of emergent processes. Journal of the Learning Sciences, 14(2), 161–199. [Google Scholar] [Crossref]

15. Chick, H. L. (2004). Cognitive aspects of algebraic understanding. In K. Stacey et al. (Eds.), The future of the teaching and learning of algebra (pp. 12–29). Springer. [Google Scholar] [Crossref]

16. Department of Education. (2016). Senior high school curriculum guide. DepEd. [Google Scholar] [Crossref]

17. Desstya, A., et al. (2025). Validity of four-tier diagnostic tests. Journal of Educational Assessment, 19(2), 112–125. [Google Scholar] [Crossref]

18. Duncan, G. J., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. [Google Scholar] [Crossref]

19. Engzell, P., Frey, A., & Verhagen, M. D. (2021). Learning loss due to school closures during the COVID-19 pandemic. Proceedings of the National Academy of Sciences, 118(17), e2022376118. [Google Scholar] [Crossref]

20. Fadhilatullathifi, N., et al. (2020). Application of four-tier diagnostic tests in calculus. Journal of Mathematics Education, 11(3), 567–580. [Google Scholar] [Crossref]

21. Gurel, D. K., Eryilmaz, A., & McDermott, L. C. (2015). A review and comparison of diagnostic instruments. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 989–1008. [Google Scholar] [Crossref]

22. Habiddin, & Page, E. M. (2019). Development of four-tier diagnostic test instruments. Journal of Science Education, 20(3), 45–55. [Google Scholar] [Crossref]

23. Hasan, S., Bagayoko, D., & Kelley, E. L. (1999). Misconceptions and the certainty of response index (CRI). Physics Education, 34(5), 294–299. [Google Scholar] [Crossref]

24. Harjono, A., et al. (2021). Development of diagnostic tests in science education. Journal of Science Education, 12(4), 455–470. [Google Scholar] [Crossref]

25. Hwang, G. J., et al. (2021). Enhancing students’ problem-solving ability in mathematics. Computers & Education, 168, 104209. [Google Scholar] [Crossref]

26. Istiyono, E., et al. (2023). Development of four-tier diagnostic tests in physics education. Journal of Physics Education Research, 19(1), 010101. [Google Scholar] [Crossref]

27. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. [Google Scholar] [Crossref]

28. Kiray, S. A., & Simsek, U. (2021). The effect of diagnostic tests on conceptual understanding. International Journal of Science Education, 43(8), 1325–1342. [Google Scholar] [Crossref]

29. Kuhfeld, M., et al. (2020). Projecting the potential impact of COVID-19 school closures. Educational Researcher, 49(8), 549–565. [Google Scholar] [Crossref]

30. Linacre, J. M. (1994). Sample size and item calibration stability. Rasch Measurement Transactions, 7(4), 328. [Google Scholar] [Crossref]

31. Mamolo, L. (2017). Development of an achievement test in General Mathematics. Visayas State University. [Google Scholar] [Crossref]

32. Mejias, S. (2019). Early assessment and intervention in mathematics readiness. Journal of Educational Psychology, 111(5), 789–802. [Google Scholar] [Crossref]

33. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM. [Google Scholar] [Crossref]

34. Niss, M., & Højgaard, T. (2021). Competencies and mathematical learning. Springer. [Google Scholar] [Crossref]

35. Organisation for Economic Co-operation and Development. (2019). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. [Google Scholar] [Crossref]

36. Orale, R., & Uy, M. (2018). Algebra misconceptions among Filipino students. Asia Pacific Journal of Education, 38(2), 217–233. [Google Scholar] [Crossref]

37. Piaget, J. (1952). The origins of intelligence in children. International Universities Press. [Google Scholar] [Crossref]

38. Polit, D. F., & Beck, C. T. (2006). The content validity index. Research in Nursing & Health, 29(5), 489–497. [Google Scholar] [Crossref]

39. Polit, D. F., Beck, C. T., & Owen, S. V. (2007). Is the CVI an acceptable indicator? Research in Nursing & Health, 30(4), 459–467. [Google Scholar] [Crossref]

40. Rahmatiah, R., & Nurhayati, N. (2022). Confidence-based assessment in mathematics learning. Journal of Mathematics Education, 13(1), 45–58. [Google Scholar] [Crossref]

41. Tall, D. (1993). Advanced mathematical thinking. Kluwer Academic Publishers. [Google Scholar] [Crossref]

42. UNESCO. (2019). Global education monitoring report 2019: Migration, displacement and education. UNESCO. [Google Scholar] [Crossref]

43. Villegas, F. (2020). Developmental research design in education. Philippine Journal of Education, 99(1), 12–20. [Google Scholar] [Crossref]

44. Villegas, J. H. (2021). Designing project-based formative assessment in Science 10 in a modular distance learning modality (Master’s thesis, Laguna State Polytechnic University, San Pablo City Campus). [Google Scholar] [Crossref]

45. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. [Google Scholar] [Crossref]

46. Widodo, A., et al. (2023). Improving diagnostic assessment using CRI. Journal of Educational Evaluation, 17(2), 89–102. [Google Scholar] [Crossref]

47. Wright, B. D., & Stone, M. H. (1979). Best test design. Mesa Press. [Google Scholar] [Crossref]

48. Yusoff, M. S. B. (2019). ABC of content validation. Education in Medicine Journal, 11(2), 49–54. [Google Scholar] [Crossref]

49. Zakaria, E., & Zainal, M. (2020). Validity of diagnostic tests in mathematics education. International Journal of Instruction, 13(3), 67–82. [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples