Algebraic Thinking Ability Test (ATAT) measuring 7th grade students using Rasch Measurement Model

Authors

  • Hasniza Ibrahim Kulliyyah of Education, International Islamic University Malaysia (IIUM), Malaysia
  • Madihah Khalid Kulliyyah of Education, International Islamic University Malaysia (IIUM), Malaysia
  • Noor Lide Abu Kassim Kulliyyah of Education, International Islamic University Malaysia (IIUM), Malaysia
  • Norshahira Isa Kulliyyah of Education, International Islamic University Malaysia (IIUM), Malaysia

DOI:

https://doi.org/10.37134/jpsmm.vol13.2.9.2023

Keywords:

Algebraic Thinking, Rasch Analysis, Malaysian 13-Year-Old, 7th Grade Students

Abstract

Algebraic ability is crucial for students to master; however, studies have shown that many students struggle with learning algebra. In the Malaysian context, there is a lack of specific instruments to measure the algebraic ability of 13-year-old or 7th grade students. This study aims to develop a valid and reliable instrument to measure the algebraic thinking ability of 7th grade students in Malaysia. The Algebraic Thinking Ability Test (ATAT) assessment utilized the Winsteps Rasch Measurement Model. Fifteen main question items were selected, each further divided into subsections and treated as individual items, resulting in a total of twenty-seven items. These items were adapted and modified from the Form One or 7th grade Mathematics Textbook and TIMSS Mathematics questions. Each item had a different rating scale; thus, the Partial Credit Model (Group 0) was applied for analysis. The newly developed instrument was administered to 93 students from government schools in Selangor, Malaysia. The results indicated that the Algebra Test adequately described students' ability in algebra; however, the students' ability was found to be exceptionally low in this study. In other words, the respondents demonstrated lower capability as a group than the item difficulty. Overall, this research contributes to the development of a reliable and valid instrument to measure the algebraic ability of 7th grade students in Malaysia. The findings highlight the need for targeted interventions and support to improve students' algebraic thinking skills in the Malaysian education system.

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References

Alsaeed, M. S. (2017). Using the internet in teaching algebra to middle school students: A study of teacher perspectives and attitudes. Contemporary Issues in Education Research (CIER), 10(2), 121-136.

Andrich, D. A. (2013). The legacies of R. A. Fisher and K. Pearson in the application of the Polytomous Rasch model for assessing the empirical ordering of categories. Educational and Psychological Measurement, 73(4), 553-580. doi:10.1177/0013164413477107

Andrich, D., Sheridan, B., Lyne, A. & Luo, G. (2000). RUMM: A windows-based item analysis program employing Rasch unidimensional measurement models. Perth: Murdoch University.

Ayber, G., & Tanışlı, D. (2017). An analysis of middle school mathematics textbooks from the perspective of fostering algebraic thinking through generalization. Educational Sciences: Theory & Practice, 17(6).

Azizan, N. H., Mahmud, Z., Rambli, A.(2020). Rasch Rating Scale Item Estimates using Maximum Likelihood Approach: Effects of Sample Size on the Accuracy and Bias of the Estimates. International Journal of Advanced Science and Technology Vol. 29, No. 4s, pp. 2526 - 2531

Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd), Lawrence Erlbaum, Mahwah, New Jersey

Bond, T., & Fox, C. (2015). Applying the Rasch model, fundamental measurement in the human sciences (Third ed.). New York, NY: Routledge.

Bond, T., & Fox, C. (2015). Applying the Rasch model, fundamental measurement in the human sciences (Third ed.). New York, NY: Routledge.

Booth, J. L., Barbieri, C., Eyer, F., & Paré-Blagoev, E. J. (2014). Persistent and pernicious errors in algebraic problem solving. The Journal of Problem Solving, 7(1), 3.

Davadas, S. D., & Lay, Y. F. (2018). Factors affecting students’ attitude toward mathematics: A structural equation modeling approach. Eurasia J. of Mathematics, Science, and Technology Education, 14(1), 517–528. doi: 10.12973/ejmste/80356.

Egodawatte, G., & Stoilescu, D. (2015). Grade 11 Students' Interconnected Use of Conceptual Knowledge, Procedural Skills, and Strategic Competence in Algebra: A Mixed Method Study of Error Analysis. European Journal of Science and Mathematics Education, 3(3), 289-305.

Fey, J. T., & Smith, D. A. (2017). Algebra as part of an integrated high school curriculum. In And the rest is just algebra (pp. 119-129). Springer, Cham.

Ganesen, P., Osman, S., Abu, M. S., & Kumar, J. A. (2020). The relationship between learning styles and achievement of solving algebraic problems among lower secondary school students. International Journal of Advanced Science and Technology, 29(95), 2563-2574.

HasibuanF., & DasariD. (2020). Algebraic Thinking Ability of class 7 SMP on Material Algebraic Form. International Conference on Elementary Education, 2(1), 791-802. Retrieved from http://proceedings.upi.edu/index.php/icee/article/view/688

Hock, T. T., Yunus, A. S. M., Tarmizi, R. A., & Ayub, A. F. M. (2015). Understanding Primary School teachers' perspectives of teaching and learning in geometry: Shapes and Spaces. In 2015 International Conference on Research and Education in Mathematics (ICREM7) (pp. 154-159). IEEE.

Ibrahim, H., Isa, N., & Embong, Z. (2023). Investigating Creative Problem-Solving in Learning Mathematics Through Cyclical Action Research. Journal of Islamic, Social, Economics and Development (JISED), 8 (56), 638 – 651.

Isa, N., & Ibrahim, H. (2023). The relationship between students’ mathematics attitude and their mathematical thinking. Journal of Islamic, Social, Economics and Development (JISED), 8 (56), 664 – 680.

Jahudin, J., & Siew, N. M. (2023). An Algebraic Thinking Skill Test In Problem-Solving For Seventh Graders.

Problems of Education in the 21st Century, 81(2), 223.

Jupri, A., Drijvers, P. H. M., & den Heuvel-Panhuizen, V. (2016). An instrumentation theory view on students’ use of an applet for algebraic substitution. International Journal for Technology in Mathematics Education, 23(2), 63-80.

Kanbir, S., Clements, M. K., & Ellerton, N. F. (2018). Research Design and Methodology. In Using Design Research and History to Tackle a Fundamental Problem with School Algebra (pp. 115-140). Springer, Cham.

Kaput, J. J. (1998). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. The Journal of Mathematical Behavior, 17(2), 265-281.

Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, NJ: Lawrence Erlbaum Associates.

Karabatsos, G. (2000). A critique of Rasch residual fit statistics. Journal of Applied Measurement, 1:152-176.

Khali, Z. K., & Rosli, R. (2021). Topic analysis of Algebraic Expressions and Algebraic Formulae in Form 1 and Form 2 Mathematics Textbooks.Jurnal Pendidikan Sains Dan Matematik Malaysia, 11(2), 26-38. https://doi.org/10.37134/jpsmm.vol11.2.3.2021.

Khalid, M. (2017). Fostering problem solving and performance assessment among Malaysian mathematics teachers. Sains Humanika, 9(1-2).

Khalid, M., Yakop, F. H., & Ibrahim, H. (2020). Year 7 Students' Interpretation of Letters and Symbols in Solving Routine Algebraic Problems. The Qualitative Report, 25(11), 4167-4181.

Kuppusamy, S., & Musa, M. (2021). Investigating International School Secondary students’Attitude towards Mathematics.Jurnal Pendidikan Sains Dan Matematik Malaysia,11(2), 122-130. https://doi.org/10.37134/jpsmm.vol11.2.10.2021.

Linacre, J. (1994). Many-Facet Rasch measurement. Chicago: MESA Press.

Linacre, J. (2007). Facets Rasch measurement computer program (Version 3.62). Chicago: Winsteps.

Linacre, J. M. (2002). What do infit and outfit, mean-square and standardized mean? Rasch Measurement Transactions, 16(2), 1.

Linacre, J. M. (2002a). Optimizing rating scale category effectiveness. Journal of Applied Measurement, 3(1), 85- 106.

Linacre, J. M. (2002b). What do infit and outfit, mean-square and standardized mean? Rasch Measurement Transactions, 16(2), 1.

Linacre, J. M. (2003). Data variance: Explained, modeled and empirical. Rasch Meas Trans, 17(3), 942-943. Linacre, J. M. (2011). Rasch measures and unidimensionality. Rasch Measurement Transactions, 24(4), 1310. Linacre, J. M. (2012). Winsteps Rasch Tutorial 2. Retrieved from www.winsteps.com/a/winsteps-tutorial-2.pdf Linacre, J. M. (2016) Winsteps® Rasch measurement computer program. Winsteps.com, Beaverton

Linacre, J. M. (2016). DIF - DPF - bias - interactions concepts. Winsteps Help. Retrieved from http://www.winsteps.com/winman/difconcepts.htm

Ministry of Education (MOE) (2013). Malaysia Educational Blueprint Annual Report 2013. Ministry of Education: Putrajaya.

Ministry of Education Malaysia (MOE) (2019). https://www.moe.gov.my/muat-turun/penerbitan-dan- jurnal/terbitan/buku-informasi/2722-quick-facts-2019/file

Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International Results in Mathematics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/

Musa, M., Khalid, S. N., Rahmat, F., Mohamed, N. A., & Mat, N. A. A. (2022). Integration of STEM in the Field of Statistics and Probability in Form Two Mathematics KSSM.Jurnal Pendidikan Sains Dan Matematik Malaysia,12(1), 116-130. https://doi.org/10.37134/jpsmm.vol12.1.10.2022

Mustaffa, N. B., Ismail, Z. B., Said, M. N. H. B. M., & Tasir, Z. B. (2017). A Review on the Development of Algebraic Thinking Through Technology. Advanced Science Letters, 23(4), 2951-2953.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all.

Reston, VA: National Council of Teachers of Mathematics.

OECD (2010), PISA 2009 Results: Learning Trends: Changes in Student Performance Since 2000 (Volume V), PISA, OECD Publishing.

OECD (2017). PISA 2015 Collaborative Problem Solving: https://www.oecd.org/pisa/pisaproducts/Draft%20PISA%202015%20Collaborative%20Problem%20So lving%20Framework%20.pdf

PISA, O. (2012). Results in focus 2014-02-17. http://www,oecd. org/pisa/keyfindings/pisa-2012-results- overview,pdf.

Prendergast, M., & O’Donoghue, J. (2014). ‘Students enjoyed and talked about the classes in the corridors’: pedagogical framework promoting interest in algebra. International Journal of Mathematical Education in Science and Technology, 45(6), 795-812.

Ralston, N. (2013). The development and validation of a diagnostic assessment of algebraic thinking skills for students in the elementary grades (Doctoral dissertation).

Rasch, G. (1960). Probabilistic models for some intelligence and achievement tests. Copenhagen: Danish Institute for Educational Research.

Rasch, G. (1980). Probabilistic models for some intelligence and achievement tests. (Expanded ed.). Chicago, IL: University of Chicago Press.

Remillard, J. T., Baker, J. Y., Steele, M. D., Hoe, N. D., & Traynor, A. (2017). Universal Algebra I policy, access, and inequality: Findings from a national survey. Education Policy Analysis Archives,25(101).

Remillard, J. T., Baker, J. Y., Steele, M. D., Hoe, N. D., & Traynor, A. (2017). Universal Algebra I policy, access, and inequality: Findings from a national survey. Education Policy Analysis Archives, 25(101).

Sabah, S., Hammouri, H., & Akour, M. (2013). Validation of A Scale of Attitudes Toward Science Across Countries Using Rasch Model: Findings From TIMSS. Journal of Baltic Science Education, 12(5).

Saleh, S., & Rahman, M. A. A. (2016). A Study of Students' Achievement in Algebra: Considering the Effect of Gender and Types of Schools. European Journal of STEM Education, 1(1), 19-26.

Saundarajan, K., Osman, S., Kumar, J., Daud, M., Abu, M. & Pairan, M. (2020). Learning Algebra using Augmented Reality: A Preliminary Investigation on the Application of Photomath for Lower Secondary Education. International Journal of Emerging Technologies in Learning (iJET), 15(16), 123-133. Kassel, Germany: International Journal of Emerging Technology in Learning. Retrieved September 6, 2023 from https://www.learntechlib.org/p/217953/.

Seng, E. L. K. (2014). Investigating Teachers' Views of Student-Centred Learning Approach. International Education Studies, 7(7), 143-148.

Smith EV Jr (2002) Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. J Appl Meas. 2002; 3(2):205-31.

Star, J. R., Caronongan, P., Foegen, A. M., Furgeson, J., Keating, B., Larson, M. R., ... & Zbiek, R. M. (2015).

Teachingstrategies for improving algebra knowledge in middle and high school students.

Suwito, A., Yuwono, I., Parta, I. N., Irawati, S., &Oktavianingtyas, E. (2016). Solving Geometric Problems by UsingAlgebraic Representation for Junior High School Level 3 in Van Hiele at Geometric Thinking Level. International Education Studies, 9(10), 27-33.

Wang, X. (2015). The literature review of algebra learning: Focusing on the contributions to students’ difficulties.

Creative Education, 6(2). 10.4236/ce.2015.62013

Welder, R. M. (2012). Improving algebra preparation: Implications from research on student misconceptions and difficulties. School Science and Mathematics, 112(4), 255–264.

WINSTEPS. (2012). Rasch Software. Retrieved fromhttp://www.winsteps.com/winsteps.htm Witzel, B. (2016). Students with math difficulties and the arithmetic to algebra gap. In B. S.

Wright, B. D. & Stone M. H. (1979). Best Test Design, p.98 - "random uncertainty of less than .3 logits," referencing MESA Memo 19: Best Test and Self-Tailored Testing. Also .3 logits in Solving Measurement Problems with the Rasch Model. Journal of Educational Measurement 14 (2) pp. 97-116, Summer 1977 (and MESA Memo 42)

Wright, B. D., & Linacre, J. M. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370.

Wright, B. D., & Masters, G. N. (1982). Rating scale analysis, Rasch measurement. Chicago, IL: MESA Press. Ying, C. L., Osman, S., Kurniati, D., Masykuri, E. S., Kumar, J. A., & Hanri, C. (2020). Difficulties that Students

Face when Learning Algebraic Problem-Solving. Universal Journal of Educational Research, 8(11), 5405-5413.

Zaipul Bahari, F. A., & Saleh, S. (2023). Content Validation Procedure: Development of Problem-solving Skills Test (PSST): Prosedur Pengesahan Kandungan: Pembangunan Ujian Kemahiran Penyelesaian Masalah (PSST).Jurnal Pendidikan Sains Dan Matematik Malaysia,13(1), 1–9. https://doi.org/10.37134/jpsmm.vol13.1.1.2023.

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Published

2023-11-14

How to Cite

Ibrahim, H., Khalid, M., Abu Kassim, N. L., & Isa, N. (2023). Algebraic Thinking Ability Test (ATAT) measuring 7th grade students using Rasch Measurement Model. Jurnal Pendidikan Sains Dan Matematik Malaysia, 13(2), 96–111. https://doi.org/10.37134/jpsmm.vol13.2.9.2023

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