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Type :article
Subject :QA Mathematics
ISSN :2222-6990
Main Author :Siti Eshah Mokshein
Additional Authors :Normarina Abd Rahman
Hishamuddin Ahmad
Title :Validity and reliability of Students Mathematical Process Rubric (Prom3) based on many-Facet Rasch Model (MRFM).
Place of Production :Tanjong Malim
Publisher :Fakulti Pembangunan Manusia
Year of Publication :2021
Corporate Name :Universiti Pendidikan Sultan Idris

Abstract : Universiti Pendidikan Sultan Idris
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. Keywords: Mathematical Process, Problem Solving, Rater, Many-Facet Rasch Model (MFRM), Rubric Validation, Performance Assessment, Alternative Assessment

References

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).


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