Development and Validation of Year Five Geometrical Measurement Skills Instrument (GMSI)

Siti Nur Annisa Mohd Nasser, Lim Hooi Lian


Geometrical measurement is one of the most difficult fields in primary school mathematics and regularly found to be an area of weaknesses. The factors affecting the low understanding is due to the lack of valid and reliable assessment instruments. Thus, this study aimed to develop and validate a Geometrical Measurement Skill Instrument (GMSI) to assess Year Five National school pupils’ geometrical measurement skills in geometrical measurement. GMSI was developed by applying the SOLO Taxonomy and was constructed in the super item format which consisted of 24 items altogether. This study applied a survey approach to assess 132 Year Five pupils’ geometrical measurement skills. The content validity was examined using the Content Validity Index (CVI) analysis. For the construct validity, data were obtained and analyzed using the Rasch analysis. From the CVI analysis, the results showed that GMSI could be used for the pilot study. Results for the construct validity indicated that GMSI fulfilled the psychometric properties and is valid and reliable. Hence, the results could help teachers and pupils to diagnose the strength and weaknesses of geometrical measurement and help them to plan systematic remedy to improve teaching and learning.


Measurement Skills; Geometrical Measurement; Spatial Skills; Numerical Skills; SOLO Model


K. Fuson, D. Clements, and S. B. Kazez, Geometry, Spatial Reasoning, and Measurement. National Council of Teachers of Mathematics, 2010, 2010.

E. M. Kim, J. Haberstroh, S. Peters, H. Howell, and L. Nabors Oláh, “A Learning Progression for Geometrical Measurement in One, Two, and Three Dimensions,” ETS Res. Rep. Ser., vol. 2017, no. 1, pp. 1–26, 2017, doi: 10.1002/ets2.12189.

L. Outhred and D. McPhail, “A framework for teaching early measurement. In J. Bana, & A. Chapman (Eds.),” in Mathematics education beyond 2000, no. July, Perth: Mathematics Education Research Group of Australasia Incorporated, 2000, pp. 487–494.

M. Vasilyeva, L. H. Ludlow, B. M. Casey, and C. S. Onge, “Examination of the psychometric properties of the measurement skills assessment,” Educ. Psychol. Meas., vol. 69, no. 1, pp. 106–130, 2009, doi: 10.1177/0013164408318774.

T. Crites, B. J. Dougherty, H. Slovin, and K. Karp, “Geometric Measurement,” in Putting Essential Understanding into Practice: Geometry, 6-8, National Council of Teachers of Mathematics, 2018, pp. 11–34.

I. V. . Mullis, M. O. Martin, E. J. Gonzalez, and S. J. Chrostowski, “TIMSS 2003 International Mathematics Report,” 2004.

W. Wartono, J. R. Batlolona, and A. Putirulan, “Cognitive Conflict Strategy and Simulation Practicum to Overcome Student Misconception on Light Topics,” J. Educ. Learn., vol. 12, no. 4, pp. 747–756, 2018, doi: 10.11591/edulearn.v12i4.10433.

T. Laurens, F. A. Batlolona, J. R. Batlolona, and M. Leasa, “How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement?,” Eurasia J. Math. Sci. Technol. Educ., vol. 14, no. 2, pp. 569–578, 2018, doi: 10.12973/ejmste/76959.

S. Y. Chog, T. J. Wong, and A. Halim, “Pencapaian Matematik TIMSS 1999 , 2003 , 2007 , 2011 dan 2015 : Di Mana Kedudukan Malaysia Dalam Kalangan Negara Asia Tenggara ?,” Malaysian J. High. Order Think. Ski. Educ., vol. 2, no. 23, pp. 54–108, 2018.

Malaysian Examination Syndicate, “Kupasan Mutu Jawapan UPSR Matematik 015/025/035,” Putrajaya, 2017.

Malaysian Examination Syndicate, “Kupasan Mutu Jawapan UPSR Matematik 015/025/035,” Putrajaya, 2013.

Malaysian Examination Syndicate, “Kupasan Mutu Jawapan UPSR Matematik 015/025/035,” Putrajaya, 2014.

Malaysian Examination Syndicate, “Kupasan Mutu Jawapan UPSR Matematik 015/025/035,” Putrajaya, 2012.

Malaysian Examination Syndicate, “Kupasan Mutu Jawapan UPSR Matematik 015/025/035,” Putrajaya, 2010.

G. Tan Sisman and M. Aksu, “A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume,” Int. J. Sci. Math. Educ., vol. 14, no. 7, pp. 1293–1319, 2016, doi: 10.1007/s10763-015-9642-5.

D. Clements, “Learning and Teaching Measurement (2003 Yearbook),” Natl. Counc. Teach. Math., Dec. 2003.

J. Hannighofer, M. van den Heuvel-Panhuizen, S. Weirich, and A. Robitzsch, “Revealing German primary school students’ achievement in measurement,” ZDM - Int. J. Math. Educ., vol. 43, no. 5, pp. 651–665, 2011, doi: 10.1007/s11858-011-0357-y.

M. Vasilyeva, B. M. Casey, E. Dearing, and C. M. Ganley, “Measurement skills in low-income elementary school students: Exploring the nature of gender differences,” Cogn. Instr., vol. 27, no. 4, pp. 401–428, 2009, doi: 10.1080/07370000903221809.

D. H. Clements and M. T. Battista, “Geometry and Spatial Reasoning,” in Handbook of research on mathematics teaching and learning (pp., New York: Macmillan, 1992, pp. 420–464.

V. Tůmová and N. Vondrová, “Links between Success in Non-measurement and Calculation Tasks in Area and Volume Measurement and Pupils’ Problems,” Sci. Educ., vol. 8, no. 2, pp. 100–129, 2017.

M. T. Battista, The Development of Geometric and Spatial Thinking. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age, 2007.

H.-M. E. Huang and K. G. Witz, “Children’s Conceptions of Area Measurement and Their Strategies for Solving Area Measurement Problems,” J. Curric. Teach., vol. 2, no. 1, pp. 10–26, 2012, doi: 10.5430/jct.v2n1p10.

M. Battista, “Cognition-based assessment and teaching of geometric measurement,” Build. students’ Reason., pp. 258–292, 2012.

H.-M. E. Huang and K. G. Witz, “Developing children’s conceptual understanding of area measurement: A curriculum and teaching experiment,” Learn. Instr., vol. 21, no. 1, pp. 1–13, 2011, doi: 10.1016/j.learninstruc.2009.09.002.

B. M. Casey, E. Dearing, M. Vasilyeva, C. M. Ganley, and M. Tine, “Spatial and Numerical Predictors of Measurement Performance: The Moderating Effects of Community Income and Gender,” J. Educ. Psychol., vol. 103, no. 2, pp. 296–311, 2011, doi: 10.1037/a0022516.

W. Y. Hwang, S. W. D. Purba, Y. F. Liu, Y. Y. Zhang, and N. S. Chen, “An Investigation of the Effects of Measuring Authentic Contexts on Geometry Learning Achievement,” IEEE Trans. Learn. Technol., vol. 12, no. 3, pp. 291–302, 2019, doi: 10.1109/TLT.2018.2853750.

M. T. Battista, M. L. Winer, and L. M. Frazee, “How Spatial Reasoning and Numerical Reasoning Are Related in Geometric Measurement,” pp. 355–362, 2017.

N. S. Newcombe, J. L. Booth, and E. A. Gunderson, “Spatial Skills, Reasoning, and Mathematics,” Cambridge Handb. Cogn. Educ., pp. 100–123, 2019, doi: 10.1017/9781108235631.006.

R. Lehrer, L. Jaslow, and C. L. Curtis, “Developing an understanding of measurement in the elementary grades,” in Learning and teaching measurement, vol. Yearbook, D. H. Clements and G. W. Bright, Eds. Reston, Va: National Council of Teachers of Mathematics, 2003, pp. 100–121.

J. Biggs and K. F. Collis, Evaluating the Quality of Learning: The SOLO Taxonomy (Structure of the Observed Learning Outcome), vol. 1, no. 4. 1982.

J. Hattie and G. T. L. Brown, “Assessment Tools for Teaching and Learning Technical Report #43: Cognitive processes in asTTle: The SOLO taxonomy,” Univ. Auckl., no. August 2004, 2004, [Online]. Available:

L. R. Gay, G. E. Mills, and P. AirAsian, “Survey Research,” in Educational Research Competencies for Analysis and Applications, 9th ed., Pearson Education, Inc, 2012, pp. 175–191.

K. Kelley, B. Clark, V. Brown, and J. Sitzia, “Good practice in the conduct and reporting of survey research,” Int. J. Qual. Heal. Care 2003, vol. 15, no. 3, pp. 261–266, 2003.

L. A. Miller and R. L. Lovler, Foundations of psychological testing: A practical approach. Carlifonia: Sage Publications, 2018.

M. E. @ E. B. M. Matore, “Pembinaan Instrumen Kecerdasan Menghadapi Cabaran (Ikbar) Bagi Pelajar Politeknik Menggunakan Model Rasch,” Universiti Sains Malaysia, 2015.

A. L. Adibah, “Pembanglinan Instrumen Penilaian Akhlak Pelajar di Institusi Pengajian Ttnggi Awam,” Universiti Teknologi Malaysia, 2013.

H. Azman, “Instrumen Penilaian Pembimbing dalam Pelaksanaan Pembelajaran Berasaskan Kerja Pelajar di Industri,” Universiti Teknologi Malaysia, 2012.

T. G. Bond and C. M. Fox, Applying the Rasch Model, 3rd ed. New York: Routledge, 2015.

J. S. Grant and L. L. Davis, “Selection and use of content experts for instrument development,” Res. Nurs. Health, vol. 20, no. 3, pp. 269–274, 1997, doi: 10.1002/(sici)1098-240x(199706)20:3<269::aid-nur9>;2-3.

Mary R. Lynn, “Determination and Quantificatiom of Content Validity,” Journal of Experimental Psychology: General, vol. 136, no. 1. pp. 382–386, 1986, doi: 10.1161/CIRCULATIONAHA.112.092098.

M. F. M. Marzuki, N. A. Yaacob, and N. M. Yaacob, “Translation, cross-cultural adaptation, and validation of the Malay version of the system usability scale questionnaire for the assessment of mobile apps,” J. Med. Internet Res., vol. 20, no. 5, pp. 1–7, 2018, doi: 10.2196/10308.

M. M. Ozair, K. A. Baharuddin, S. A. Mohamed, W. Esa, and M. S. B. Yusoff, “Development and Validation of the Knowledge and Clinical Reasoning of Acute Asthma Management in Emergency Department (K-CRAMED),” Educ. Med. J., vol. 9, no. 2, pp. 1–17, 2017, doi: 10.21315/eimj2017.9.2.1.

M. S. B. Yusoff, “ABC of Content Validation and Content Validity Index Calculation,” Educ. Med. J., vol. 11, no. 2, pp. 49–54, 2019, doi: 10.21315/eimj2019.11.2.6.

D. F. Polit and C. T. Beck, “The Content Validity Index: Are You Sure You Know What’s Being Reported? Critique and Recommendations,” Res. Nurs. Health, vol. 29, pp. 489–497, 2006, doi: 10.1002/nur.

J. M. Linacre, “Data Variance Explained by Rasch Measures,” Trans. Rasch Meas. SIG Am. Educ. Res. Assoc., vol. 20, no. 1, 2006.

W. P. Fisher, “Rating scale instrument quality criteria,” Rasch Meas. Trans., vol. 21, no. 1, p. 1095, 2007.

K. J. Conrad, K. M. Conrad, M. L. Dennis, B. B. Riley, and R. Funk, “Validation of the Substance Problem Scale (SPS) to the Rasch Measurement Model, GAIN Methods Report . (1.1 ed.),” Chicago, IL, 2011.

J. M. Linacre, Winsteps Rasch measurement computer program User’s Guide. Beaverton, Oregon, 2020.

J. M. Linacre, “Help for Winsteps Rasch Measurement and Rasch Analysis Software:Largest residual correlations for items,” 2012.

W. J. Boone, J. R. Staver, and M. S. Yale, Rasch analysis in the human sciences. Netherlands: Springer, 2014.

J. M. Linacre, “Reasonable mean-square fit values,” Rasch Meas. Trans., vol. 8, no. 3, p. 370, 1994.

J. M. Linacre, “Fit diagnosis: Infit outfit mean-square standardized,” Help Winsteps Rasch Meas. Softw., 2014.

J. M. Linacre, “Reliability and separation of measures,” 2020.

K. Cipora, P. A. Schroeder, and H.-C. Nuerk, “On the Multitude of Mathematics Skills: Spatial-Numerical Associations and Geometry Skill?,” in Visualizing Mathematics. Research in Mathematics Education, Springer, Cham, 2018, pp. 361–370.

D. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge, 2014.



  • There are currently no refbacks.

Copyright (c) 2021 Institute of Advanced Engineering and Science

International Journal of Evaluation and Research in Education (IJERE)
p-ISSN: 2252-8822, e-ISSN: 2620-5440

View IJERE Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.