ISSN: 2222-6990
Open access
The objective of this research was to determine the validity of Students’ Mathematical Process Rubric (ProM3) using Many-Facet Rasch Model (MFRM). The data were gathered from 7 raters marking 188 scripts of Form 1 students from a number of boarding schools in the middle and northern zone of Malaysia. ProM3 Rubric was used to analyse students’ responses in problem solving and reflective writing tasks for 29 criteria, that is in five dimensions of the mathematical process, namely connection, representation, communication, reasoning and problem solving. MFRM was used to analyse the data to look into three facets; student ability, rater severity and item difficulty. The findings indicated that the accurate index measuring students’ ability facet was between -3.48 until 4.71 logit, raters’ severity facet between -0.59 until 0.74 logit, and items/criteria’s difficulty facet at -2.38 (problem identifying) until 1.45 (quantitative reasoning) logit. The high validity and reliability construct based on MFRM signified that the model can measure the accuracy of each facet score.
Adnan, M., & Jalil, N. S. (2016). Keupayaan Murid Cemerlang Akademik Tingkatan Empat dalam Menyelesaikan Masalah Algebra Bukan Rutin. Jurnal Pendidikan Sains & Matematik Malaysia, 6(1), 58–67.
Akdemir, E. (2018). Investigating the Reflective Thinking Skills of Students for Problem Solving. Online Submission, 1(November), 774–780. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=ED595226&site=ehost-live
Arter, J., & McTighe, J. (2001). Scoring Rubrics in the Classroom: Using Performance Criteria for Assessing and Improving Student Performance (T. R. Guskey & R. J. Marzano, eds.). California: Corwin Press.
Ayllon, M., Gomez, I., & Ballesta-Claver, J. (2016). Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving. Propositos y Representaciones, 4(1), 169–218. Retrieved from
https://eric.ed.gov/?id=EJ1126306%0Ahttp://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ1126306&site=ehost-live
Bond, T. G., & Fox, C. M. (2015). Applying the Rasch Model: Fundamental Measurement in the Human Sciences (Third). New York: Routledge Taylor and Francis Group.
Boud, D., Keogh, R., & Walker, D. (1985). Reflection: Turning Experience into Learning. In Learning. https://doi.org/10.1145/1734263.1734380
Branch, R. M. (2009). Instructional Design: The ADDIE Approach. New York: Springer Science + Bussiness Media.
Brookhart, S. M. (2010). General Principles for Assessing Higher-Order Thinking. In How to Assess Higher-Order Thinking Skills in Your Classroom (pp. 17–38). Retrieved from http://www.ascd.org/publications/books/109111/chapters/General_Principles_for_Assessing_Higher-Order_Thinking.aspx
Bruner, J. (1960). The Process of Education. New York: Vintage.
Carson, J. (2007). A Problem With Problem Solving?: Teaching Thinking Without Teaching Knowledge. The Mathematics Educator, 17(2), 7–14.
Costa, A. L. (2004). Habits of Mind. Current Surgery, 61(1), 101–103. https://doi.org/10.1016/j.cursur.2003.09.009
Costa, A. L., & Kallick, B. (2008). Learning and Leading with Habits of Mind: 16 Essential Characteristics for Success. Alexandria: Association for Supervision and Curriculum Development.
Dollah, M. U., Saad, N. S., Abdullah, M. F. N., & Yusof, Q. (2016). Penerapan Nilai Rasionalisme dan Objektivisme dalam Pengajaran Guru Matematik Sekolah Rendah. Jurnal Pendidikan Sains & Matematik Malaysia, 6(2), 85–108.
Dumas, D., Alexander, P. A., & Grossnickle, E. M. (2018). Relational Reasoning and Its Manifestations in the Educational Context?: a Systematic Review of the Literature. Educational Psychologist Review, 25(3), 391–427.
Eckes, T. (2015). Introduction to Many- Facet Rasch Measurement?: Analyzing and Evaluating Rater Mediated Assessment (2nd ed.). https://doi.org/10.3726/978-3-653-04844-5
Edelen, D., & Bush, S. B. (2020). A Cross-Cultural Approach for Communication in the Mathematics Classroom and Beyond. Southeastern Regional Association of Teacher Educators, 29(2). Retrieved from https://eric.ed.gov/?id=EJ1268308
Fuson, K. C., Kalchman, M., & Bransford, J. D. (2005). Mathematical Understanding: An Introduction. In How Students Learn: History, Mathematics, and Science in the Classroom (pp. 215–256). https://doi.org/10.17226/10126
Ghazi, S. R. (2014). Formal Operational Stage of Piaget’ s Cognitive Development Theory?: An Implication in Learning Mathematics. 17(2), 71–85.
Jonassen, D. H. (2004). Learning to Solve Problems?; An Instructional Design Guide. San Francisco: Pfeiffer.
Kadir, J., & Parman, M. S. (2013). Mathematical Communication Skills of Junior Secondary School Students in Coastal Area. Jurnal Teknologi, 2, 77–83.
Klerlein, J., & Hervey, S. (2000). Mathematics as a Complex Problem-Solving Activity?: Retrieved from https://www.generationready.com/mathematics-as-a-complex-problem-solving-activity/
Kolb, A. Y., & Kolb, D. A. (2012). Experiential Learning Theory. In Encyclopedia of the Sciences of Learning. https://doi.org/10.1007/978-1-4419-1428-6_227
Krawec, J. L. (2010). Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability. University of Miami.
Lantz, H. B. (2004). Rubrics for Assessing Student Achievement in Science Grades K-12. California: Corwin Press.
Li, Y., & Schoenfeld, A. H. (2019). Problematizing Teaching and Learning Mathematics as Given in STEM Education. International Journal of STEM Education, 6(1). https://doi.org/10.1186/s40594-019-0197-9
Linacre, J. M. (2018). A User’s Guide to FACETS Rasch Model Computer Programs.
Linacre, J. M. (2019). Winsteps Help for Rasch Analysis 4.4.0.
Lunz, M. E. (1997). Performance Examinations: Technology for Analysis and Standard Setting. Annual Meeting of the National Council of Measurement in Education. https://doi.org/10.1158/1535-7163.mct-16-0142
Malaysian Education Ministry. (2016). Standard Curriculum for Secondary School?: Mathematics Form One. In Malaysian Education Ministry. Putrajaya.
Mcleod, S. (2017). Kolb-Learning Styles. Retrieved from www.simplypsychology.org/learning-kolb.html
Mcleod, S. (2018). Bruner’ s Three Modes of Representation. 1–5.
McNamara, T. F. (1996). Measuring Second Language Performance. London: Longman.
Moskal, B. M. (2003). Recommendations for Developing Classroom Performance Assessments and Scoring Rubrics. Practical Assessment, Research & Evaluation, 8(14), 1–5.
Myford, C. M., & Mislevy, R. J. (1995). Monitoring and Improving a Portfolio Assessment System. Princeton: Center for Performance Assessment Educational Testing Service.
Myford, C. M., & Wolfe, E. W. (2003). Detecting and Measuring Rater Effects Using Many-Facet Rasch Measurement?: Part I. Journal of Applied Measurement, 4(4), 386–422.
Noor, F. M., Zamri, S. N. A & Eu, L. K. (2016). Penaakulan Perkadaran Murid Tahun Lima dalam Topik Nisbah dan Kadaran. Jurnal Pendidikan Malaysia, 41(2), 99–105.
OECD. (2018). Pisa 2021 Mathematics Framework ( Draft ). Retrieved from https://pisa2021-maths.oecd.org/ca/index.html
Piaget, J. (2008). Intellectual Evolution from Adolescence to Adulthood 1. Human Development, 14, 40–47. https://doi.org/10.1159/000112531
Ponte, J. P. (2007). Investigations and Explorations in The Mathematics Classroom. ZDM - International Journal on Mathematics Education, 39(5–6), 419–430. https://doi.org/10.1007/s11858-007-0054-z
Rasiman, Prasetyowati, D., & Kartinah. (2020). Development of Learning Videos for Junior High School Math Subject to enhance Mathematical Reasoning. International Journal of Education and Practice, 8(1), 18–25. https://doi.org/10.18488/journal.61.2020.81.18.25
Rothstein, A., Rothstein, E., & Lauber, G. (2007). Write for Mathematics (2nd ed.). California, USA: Corwin Press.
Schoenfeld, A. H. (2013). Reflections on Problem Solving Theory and Practice. The Mathematics Enthusiast, 10(1).
Scusa, T. (2008). Five Processes of Mathematical Thinking (University of Nebraska-Lincoln). Retrieved from http://digitalcommons.unl.edu/mathmidsummative/38
Stergar, C. (2005). Performance Task, Checklist and Rubrics. Illinois: Pearson Education.
Sujadi, I., & Masamah, U. (2017). Mathematical Reflective Thinking Processesof Senior High School Students. 25, 115–126.
Sundstrom, T. (2014). Mathematical Reasoning?: Writing and Proof (1.1). California, USA: Creative Commons.
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014). Cognitive Components of a Mathematical Processing Network in 9-year-old Children. Developmental Science, 17(4), 506–524. https://doi.org/10.1111/desc.12144
Usta, N. (2020). Evaluation of Preservice Teachers’ Skills in Solving Non-Routine Mathematical Problems through Various Strategies. Asian Journal of Education and Training, 6(3), 362–383. https://doi.org/10.20448/journal.522.2020.63.362.383
Wen, T. K., Tajudin, N. M., & Masri, R. (2017). Pembinaan Item dalam Bidang Perkaitan bagi Mata Pelajaran Matematik Tingkatan Empat Berdasarkan Model Taksonomi Pemprosesan Maklumat. Jurnal Pendidikan Sains & Matematik Malaysia, 7(2), 1–18.
Wood, T. (2001). Teaching Differently?: Creating Opportunities for Learning Mathematics. Theory Into Practice, 40(2), 110–117. https://doi.org/10.1207/s15430421tip4002
Wright, B. D., & Linacre, J. M. (1989). Observations Are Always Ordinal; Measurements, However, Must Be Interval. Archives of Physical Medicine and Rehabilitation, 70(12), 857–860.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press Chicago.
Yee, C. S., Tze, W. J., & Abdullah, A. H. (2017). Pencapaian Matematik TIMSS 1999 , 2003 , 2007 , 2011 dan 2015?: Di Mana Kedudukan Malaysia Dalam Kalangan Negara Asia Tenggara?? Malaysian Journal of Higher Order Thinking Skills In Education, (December).
In-Text Citation: (Rahman et al., 2021)
To Cite this Article: Rahman, N. A., Mokshein, S. E., & Ahmad, H. (2021). Validity and Reliability of Students’ Mathematical Process Rubric (Prom3) based on many-Facet Rasch Model (MRFM). International Journal of Academic Research in Business and Social Science, 11(2), 1315-1331.
Copyright: © 2021 The Author(s)
Published by HRMARS (www.hrmars.com)
This article is published under the Creative Commons Attribution (CC BY 4.0) license. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this license may be seen at: http://creativecommons.org/licences/by/4.0/legalcode