Validation of a Mathematics Teaching Assessment Scale for K-12 Basic Education: A Confirmatory Factor Analysis Approach

Authors

  • Keith A. Madrilejos Jose V. Palma Senior High School, Quezon City, Philippines

DOI:

https://doi.org/10.69569/jip.2024.0081

Keywords:

Mathematics teaching assessment, 21st-century skills, Content validity, Reliability test, Construct validity

Abstract

Mathematics teaching in the K-12 Basic Education Curriculum encourages educators to adopt student-centered approaches and emphasize the development of 21st-century skills. Assessing the pedagogical practices of mathematics teachers using a specific tool validated through quantitative approaches is essential to ensure the effectiveness and quality of mathematics instruction. While previous research has focused on instrument validation in various areas, including self-efficacy of math teachers, mathematics teachers’ anxiety, and online education, existing classroom observation tools have limitations, particularly in assessing public school teachers' performance specifically intended for mathematics teachers. This study aimed to validate a mathematics teaching assessment scale. The scale, constructed based on the Department of Education's classroom observation tool, initially comprised 22 items across four constructs: Mastery of the K-12 Mathematics, Teaching Methodologies, ICT Integration, and Assessment of Learning. The scale was validated through content validation, reliability testing, inter-item correlation, confirmatory factor analysis (CFA), convergent validity, and discriminant validity. A total of 687 mathematics teachers from four public schools in each of the five municipalities of the National Capital Region participated. Content validity was established by eight experts using the Scale Content Validity Index and Item-Content Validity Index, with indices exceeding 0.833, indicating validity. Each construct demonstrated desirable reliability indices based on Cronbach's alpha and composite reliability coefficients. Confirmatory Factor Analysis removed six indicators, resulting in a final scale of 16 items across four constructs. The validated instrument can effectively evaluate mathematics teachers' classroom teaching, focusing on 21st-century skills and student-centered approaches.

Downloads

Download data is not yet available.

References

15-Day Capacity Development Program on Data Analysis (2021). Sponsored by STAR Training Center. Title of the Topic: Factor Analysis. Speaker: Dr. Carlo P. Magno.

Adamson, K., & Prion, S. (2013). Reliability: Measuring Internal Consistency Using Cronbach's α. Clinical Simulation in Nursing. 9, 179-180, https://doi.org/10.1016/j.ecns.2012.12.001

Ali, S., & Maat, S. M. (2019). Exploring the 21st Century Teaching and Learning Practice among Mathematics Secondary School Teachers. International Journal of Academic Research in Progressive Education and Development, 8(2), 361–378. http://dx.doi.org/10.6007/IJARPED/v8-i2/5990

Alkharusi, B., Aldhafri, S., Al-Hosni, K., Al-Busaidi, S., Ambusaidi, A. & Alrajhi, M. (2017). Development and Validation of a Scale for Measuring Mathematics Teaching Self Efficacy for Teachers in the Sultanate of Oman. International Journal of Instruction, 10(3), 143-158. https://doi.org/10.12973/iji.2017.10310a

Arrieta, G.S. (2020). Assessment of the ICT Integration in Teaching Math and Science in High School: Basis for an ICT Integration Program. Jurnal Pendidikan MIPA. 21(1), 95-108. http://dx.doi.org/10.23960/jpmipa/v21i1.pp95-108

Artuz, J. & Roble, D. (2021). Developing Students’ Critical Thinking Skills in Mathematics Using Online-Process Oriented Guided Inquiry Learning (O-POGIL). American Journal of Educational Research. https://www.sciepub.com/EDUCATION/abstract/13518

Asmar, A., Arnellis, A., & Sriningsih, R. (2020). Implementation of the 21st Century Skills to High Order Thinking Students' Mathematical in Senior High School Padang. Journal of Physics: Conference Series. International Conference on Mathematics and Mathematics Education. Volume 1554, https://iopscience.iop.org/article/10.1088/1742-6596/1554/1/012080

Bal, A.P. (2023). Assessing the impact of differentiated instruction on mathematics achievement and attitudes of secondary school learners. South African Journal of Education. 43(1), 1-10. https://orcid.org/0000-0003-1695-9876

Baumert, J., & Kunter, M. (2013). The Effect of Content Knowledge and Pedagogical Content Knowledge on Instructional Quality and Student Achievement. https://link.springer.com/chapter/10.1007/978-1-4614-5149-5_9

Birgin, O. & Yılmaz, M. (2023). Development and Validation of a Scale to Assess the Frequency of Using Classroom Assessment Tools and Methods for Mathematics Teachers. International Journal of Educational Research and Innovation (IJERI). 20, 1-20. https://doi.org/10.46661/ijeri.8075

Branzuela, N., Namoco, S., Duero, J., & Walag, A.P. (2023). Descriptive Analysis of the National Achievement Test of Primary and Secondary Students in Misamis Oriental Philippines. Sci.Int.(Lahore). 35(6), 809-813. https://www.researchgate.net/publication/376613773_Descriptive_Analysis_of_the_NAtional_Achievement_Test_Performanc_eof_Primary_and_Secondary_Schools_Students_in_Misamis_Oriental_Philippines

Buckle, J. (2024). A Comprehensive Guide to 21st Century Skills. Panorama Education. https://www.panoramaed.com/blog/comprehensive-guide-21st-century-skills

Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows. Thousand Oaks, CA: Sage Publications. https://www.scirp.org/reference/referencespapers?referenceid=2264937

Calaguas, G. (2012). Teacher effectiveness scale in higher education: Development and psychometric properties. International Journal of Research Studies in Education, 2(2), 3-20. https://www.researchgate.net/publication/272696664_Teacher_effectiveness_scale_in_higher_education_Development_and_psychometric_properties

Cambridge University Press (2021). Chapter 5 - Confirmatory Factor Analysis, retrieved from: https://www.cambridge.org/core/books/abs/assessing-measurement-invariance-for-applied-research/confirmatory-factor-analysis/6244C89BBAC08AC1B33338076F15BEED

Capinding, A.T. (2023). Construction and Validation of Mathematical Satisfaction Questionnaire: An Exploratory and Confirmatory Factory Analysis. Problems of Education in the 21st Century. 81(3), 327-339. http://dx.doi.org/10.2139/ssrn.4507618

Casildo, N., Aguirre, M., Bonifacio, KL., Ayunar, G., Escarlos, G., & Wenceslao, R. (2023). A Decision Support System for Predicting Students’ Performance in the National Achievement Test (NAT) of Senior High School Students. ASSEHR 745, 178–190. https://www.atlantis-press.com/proceedings/icetech-22/125989114

Chigonga, B. (2020). Formative Assessment in Mathematics Education in the Twenty-First Century. Theorizing STEM Education in the 21st Century. https://www.intechopen.com/chapters/69139

Demosthenous E, Christou C, Pitta-Pantazi D. (2021) Mathematics Classroom Assessment: A Framework for Designing Assessment Tasks and Interpreting Students’ Responses. European Journal of Investigation in Health, Psychology and Education. 11(3), 1088-1106. https://doi.org/10.3390/ejihpe11030081

Department of Education (2019). Classroom Observation Tool, Philippine Professional Standards for Teachers

Department of Education. (2016). K-12 curriculum guide in Mathematics.

Department of Education. (2023). MATATAG curriculum for Mathematics.

DepEd order no. 8, s.2015. Policy Guidelines on Classroom Assessment for the K to 12 Basic Education Program

Engel, K., Moosbrugger, H., and Muller H. (2003). Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness Fit Measures. MRP-Online. 8, 23-74. https://www.researchgate.net/publication/251060246_Evaluating_the_Fit_of_Structural_Equation_Models_Tests_of_Significance_and_Descriptive_Goodness-of-Fit_Measures

Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272-299. https://doi.org/10.1037/1082-989X.4.3.272

Finster, M. & Feldman, J. (2019). Examining Construct Validity of a Child Health Interview Instrument. Westat, An Employee-Owned Research Corporation, 1600 Research Boulevard Rockville, Maryland 20850-3129 (301) pages 251-1500, https://files.eric.ed.gov/fulltext/ED599089.pdf

Fornell, C., & Larcker, D.F. (1981). Evaluating Structural Equation Models with Unobserved variables and Measurement error. JMR. Journal of Marketing Research, 18(1), 39. https://www.scirp.org/reference/ReferencesPapers?ReferenceID=1927929

Gebremedhin, M.A., & Fenta, A.A. (2015). Assessing Teachers’ Perception on Integrating ICT in Teaching Learning Process: The Case of Adwa College. Journal of Education and Practice. 6(4), 114-124. https://eric.ed.gov/?id=EJ1083759

George, M.P. (2021). Mathematics Teachers’ Pedagogical Content Knowledge and its Relation to Student Achievement. Walden University, College of Education. https://scholarworks.waldenu.edu/cgi/viewcontent.cgi?article=12664&context=dissertations

Ghavifekr, S. & Rosdy, W.A.W. (2015). Teaching and learning with technology: Effectiveness of ICT integration in schools. International Journal of Research in Education and Science (IJRES), 1(2), 175-191. https://files.eric.ed.gov/fulltext/EJ1105224.pdf

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2009). Multivariate data analysis (7th ed.). Prentice-Hall. https://www.drnishikantjha.com/papersCollection/Multivariate%20Data%20Analysis.pdf

Hawker, G.A., Davis, A.M., French, M.R., Cibere, J., Jordan, M.D., March, M.B., Suarez-Almazor, M., Katz, J.M., & Dieppe, P. (2008). Development and Preliminary Psychometric Testing of a New OA Pain Measure – an OARSI/OMERACT Initiative. Osteoarthritis Research Society International, 16, 409-414. https://pubmed.ncbi.nlm.nih.gov/18381179/

Ismail, S. N., Muhammad, S., Omar, M. N., Shanmugam, S. K. S., & Rajoo, M. (2022). The practice of critical thinking skills in teaching mathematics: Teachers’ perception and readiness. Malaysian Journal of Learning and Instruction, 19(1), 1-30. https://doi.org/10.32890/mjli2022.19.1

Jislan, F., Jani, S. H. M., Shahid, S. A. M., Thomas, M., Francis, P., & Francis, P. (2018). Using Teaching Effectiveness Scale as Measurement for Quality Teaching. International Journal of Academic Research in Business and Social Sciences, 8(9), 1394–1404. http://dx.doi.org/10.6007/IJARBSS/v8-i9/4704

Joaquin, N.B., Lumbre, A.P., & Monterola, S.C. (2023). Relationship between Mathematics Teachers’ Teaching Styles and Students’ Achievement in Mathematics. Athens Journal of Sciences, 10(1), 9-30. https://doi.org/10.30958/ajs.10-1-1

Kaya, D., & Keşan, C. (2023). The Connection of Mathematics with Real-Life Situations: Preservice Elementary Mathematics Teachers' Perceptions of Creating and Evaluating Story Problems. 12. 118-135. https://doi.org/10.55020/iojpe.1135191

Keiler, L.S. (2018). Teachers’ roles and identities in student-centered classrooms. IJ STEM Ed 5, 34. https://doi.org/10.1186/s40594-018-0131-6

Kock, N. (2020). Using indicator correlation fit indices in PLS-SEM: Selecting the algorithm with the best fit. Data Analysis Perspectives Journal, 1(4), 1-4. https://scriptwarp.com/dapj/2020_DAPJ_1_4/Kock_2020_DAPJ_1_4_XsCorrMatrixIndices.pdf

Lal Kumar, A.C., Dinesh Kumar, A., & Vasuki, M. (2024). A Study on Teaching Effectiveness of Mathematics Teachers, International Journal of Scientific Research and Modern Education, International Peer Reviewed - Refereed Research Journal, 9(1), 33- 37, https://www.researchgate.net/publication/378595477_A_STUDY_ON_TEACHING_EFFECTIVENESS_OF_MATHEMATICS_TEACHERS

Lazarides, R., Watt, H., & Richardson, P. (2020). Teachers' classroom management self-efficacy, perceived classroom management, and teaching contexts from beginning until mid-career. Learning and Instruction. Volume 69. https://doi.org/10.1016/j.learninstruc.2020.101346

Lesia, M.P., Aigbavboa, C.O. & Thwala, W.D. (2024). Factors influencing residential location choice in South Africa: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). J Hous and the Built Environ, 39, 133–160. https://doi.org/10.1007/s10901-023-10070-w

Lynn, MR. (1986). Determination and quantification of content validity. Nursing Research. 35(6), 381–385, https://www.scirp.org/reference/referencespapers?referenceid=2044975

Lucero, L., Hernandez, N., Grageda, C., & Semilla, J. (2024). Development and Validation of Classroom Observation Tool for Pre-Service Teachers based on Career Stage 1 of the Professional Standard for Teachers. 12(1), 194-203. https://www.russianlawjournal.org/index.php/journal/article/view/3642/2328

Mananghaya, A. K. (2020). It's Not Complicated: Analysis of Data from A Single, Two, or More Populations. University of the Philippines Los Baños, Institute of Statistics. Webinar Title: One-STAT at a time Session 1. YouTube.

Mathematics Teachers Association of the Philippines (n.d.). Cooperative Learning in the Teaching of Mathematics, prepared by Sr. Iluminada C. Coronel

Mattan S., Ben-Shachar, Dominique, M., Daniel, L., Indrajeet, P., Brenton, W., Remi, T., & Wagonner, P. (n.d.). Interpret of CFA / SEM Indices of Goodness of Fit. effectsize. Retrieved from: https://easystats.github.io/effectsize/reference/interpret_gfi.html

Mohd Arof, K., Ismail, S., & Saleh, A.L. (2018). Contractor’s Performance Appraisal System in the Malaysian Construction Industry: Current Practice, Perception and Understanding. International Journal of Engineering & Technology. https://www.researchgate.net/publication/326698967_Contractor's_Performance_Appraisal_System_in_the_Malaysian_Construction_Industry_Current_Practice_Perception_and_Understanding

Motseki, P. & Kakoma, L. (2023). The influence of different teaching and learning strategies in mathematics - a case study. The Independent Journal of Teaching and Learning. 18(1), 98-117. https://doi.org/10.17159/ijtl.v18i1.17174

Myers, N., Ahn, S., & Jin, Y. (2011). Sample Size and Power Estimates for a Confirmatory Factor Analytic Model in Exercise and Sport: A Monte Carlo Approach. Research Quarterly for Exercise and Sport, American Alliance for Health, Physical Education, Recreation and Dance, 82(3), 412–423, https://pubmed.ncbi.nlm.nih.gov/21957699/

National Council of Teachers of Mathematics (2020). NCTM 2020 Standards for Mathematics Teacher Preparation. https://www.nctm.org/Standards-and-Positions/CAEP-Standards/

Nieto, J.L., Garrido, S., Dominguez-Lara, S., Levican, K., & Chacaltana, M. (2023). Psychometric properties of the Teachers’ Sense of Efficacy Scale in a sample of Chilean public-school teachers. Frontiers in Psychology, Volume 14, https://doi.org/10.3389/fpsyg.2023.1272548

Nunnally, J.C., & Bernstein, I.H. (1994). Psychometric Theory. New York. NY: McGraw-Hill

Oswald, F., Donnellan, B., Ozkok, O., Zyphur, M., Barsky A., & Theilacker, M. (2019). Modeling Measurement as a Sequential Process: Autoregressive Confirmatory Factor Analysis (AR-CFA). Frontiers of Psychology. 10| https://doi.org/10.3389/fpsyg.2019.02108

Patnode, L.H., & Lee, H. (2021). Differentiated Instruction to Teach Mathematics: Through the Lens of Responsive Teaching. Mathematics Teacher Education and Development. 23(3), 6-25, https://eric.ed.gov/?id=EJ1320720

Philippine Association of Researchers and Statistical Software Users (PARSSU). (2022). Confirmatory Factor Analysis and Structural Equation Modeling using SPSS AMOS: Statistical Tools for Theory-Testing Research, Topic 3. Presented by Prof. Johnny T. Amora.

Philippine Star (2024, January 23). Delays in testing leave DepEd in the dark about student progress. Authored by Cristina Chi. https://www.philstar.com/headlines/2024/01/23/2327932/delays-testing-leave-deped-dark-about-student-progress

Podkhodova, N., Snegurova, V., Stefanova, N., Triapitsyna, A., & Pisareva, S. (2020). Assessment of Mathematics Teachers’ Professional Competence. Journal on Mathematics Education, 11(3), 477-500. http://doi.org/10.22342/jme.11.3.11848.477-500

Price, P.C., Jhangiani, R., & Chiang, I.C. (2015). Complex Correlational Designs. Research Methods in Psychology – 2nd Edition. https://opentextbc.ca/researchmethods/chapter/complex-correlational-designs/

Rakes, C.R., Stites, M.L., Ronau, R.N., Bush, S.B., Fisher, M.H., Safi, F., Desai, S., Schmidt, A., Andreasen, J.B., & Saderholm, J. (2022). Teaching Mathematics with Technology: TPACK and Effective Teaching Practices. Educ. Sci. 12, 133. https://doi.org/10.3390/ educsci12020133

Röschel A, & Wagner C, D, M. (2021). Examination of validity, reliability, and interpretability of a self-reported questionnaire on Occupational Balance in Informal Caregivers (OBI-Care) - A Rasch analysis. PLoS One. 16(12), 261-315. https://pubmed.ncbi.nlm.nih.gov/34941966/

Sachdeva, S., & Eggen, P.O. (2021). Learners’ Critical Thinking About Learning Mathematics. International Electronic Journal of Mathematics Education. 16(3), 6-44. https://doi.org/10.29333/iejme/11003

Shahzad, S., & Mehmood, N. (2019). Development of Teaching Effectiveness Scale for University Teachers. Journal of Research in Social Sciences, 7(2), 2305-6533. https://www.researchgate.net/publication/336145557_Development_of_Teaching_Effectiveness_Scale_for_University_Teachers

Shun, S., Beck, S., Pett, M., & Berry, P. (2006). Psychometric Testing of Three Chinese Fatigue Instruments in Taiwan. Journal of Pain and Symptom Management. 32, 155-167. https://pubmed.ncbi.nlm.nih.gov/16877183/

Streiner, D., & Norman, G. (1991). Health Measurement Scales: A Practical Guide to Their Development and Use. Oxford University Press.

Taber, K.S. (2018). The use of Cronbach’s alpha when developing and reporting research instruments in science education. Research in Science Education, 48, 1273-1296. https://doi.org/10.1007/s11165-016-9602-2

Tavakol M, & Wetzel A. (2020). Factor Analysis: a means for theory and instrument development in support of construct validity. Int J Med Educ. 11, 245-247. https://pubmed.ncbi.nlm.nih.gov/33170146/

Teaching at UNSW, Sydney (2023). Giving Assessment Feedback. https://www.teaching.unsw.edu.au/assessment-feedback

Türel, Y., Özdemir, T., & Elmali, F. (2017). Teachers’ ICT Skills Scale (TICTS): Reliability and Validity. Cukurova University Faculty of Education Journal. 46, 503-516. https://dergipark.org.tr/tr/download/article-file/358165

WGU. (2020). What is Constructivism? https://www.wgu.edu/blog/what-constructivism2005.html#:~:text=Constructivism%20is%20based%20on%20the,new%20things%20that%20they%20learn

White M. (2021). Sample size in quantitative instrument validation studies: A systematic review of articles published in Scopus, Heliyon. 8(12), 122-143. https://pubmed.ncbi.nlm.nih.gov/36568672/

Ximénez C. (2016). Recovery of Weak Factor Loadings When Adding the Mean Structure in Confirmatory Factor Analysis: A Simulation Study. Frontiers of Psychology. 6, 1943. https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2015.01943/full

Yanuari, N. & Turmudi, T. (2023). Critical thinking in mathematics education: A bibliometric Analysis. International Journal of Trends in Mathematics Education Research. 6(2), pages 191-197. https://doi.org/10.33122/ijtmer.v6i2.241

Yin, M., Cronen, S., Condelli, L., & Ogut, B. (2022). Teacher Effectiveness in Adult Education: The Relationship Between Teacher Characteristics and Student Test Gains and Transitions into Postsecondary Education. Adult Education Quarterly. 72(3), 262–283, https://journals.sagepub.com/doi/abs/10.1177/07417136211044515

Yusoff, M.S. (2019). ABC of Content Validation and Content Validity Index Calculation. Education in Medicine Journal. 11. 49-54. https://doi.org/10.21315/eimj2019.11.2.6

Downloads

Published

2024-04-16

How to Cite

Madrilejos , K. (2024). Validation of a Mathematics Teaching Assessment Scale for K-12 Basic Education: A Confirmatory Factor Analysis Approach. Journal of Interdisciplinary Perspectives, 2(6), 6–20. https://doi.org/10.69569/jip.2024.0081