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algebraic reasoning cognitive system marzanos taxonomy matrix algebra

Development and use of Test Instruments to measure Algebraic Reasoning Based on Cognitive Systems in Marzano’s Taxonomy

Mochamad Abdul Basir , S.B. Waluya , Dwijanto , Isnarto

Algebraic reasoning involves representation, generalization, formalization of patterns and order in all aspects of mathematics. Hence, the focus of al.

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Algebraic reasoning involves representation, generalization, formalization of patterns and order in all aspects of mathematics. Hence, the focus of algebraic reasoning is on patterns, functions, and the ability to analyze situations with the help of symbols. The purpose of this study was to develop a test instrument to measure students' algebraic reasoning abilities based on cognitive systems in Marzano's taxonomy. The cognitive system in Marzano's taxonomy consists of four levels, including retrieval, comprehension, analysis, and knowledge utilization. According to the stage of cognitive development, students are at the level of knowledge utilization. At this level, students can make decisions, solve problems, generates and test hypotheses, as well as carry out investigations that are in line with indicators of algebraic reasoning abilities. The stages in developing the test instrument were based on three phases: preliminary investigation phase, prototyping phase, and assessment phase. The study obtains a set of valid and reliable algebraic reasoning test instruments for students based on the cognitive system in Marzano's taxonomy. Through the development of an algebraic reasoning test instrument based on Marzano's taxonomy, students can build' thinking habits so that active learning exercises occurs.

Keywords: Algebraic reasoning, cognitive system, Marzano’s taxonomy, Matrix algebra.

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References

Abdul, M., & Risqi, H. (2018). Cognitive load in working memory on trigonometry Learning. Unnes Journal of Mathematics Education, 7(2), 85–89. https://doi.org/10.15294/ujme.v7i2.25366

Basir, M., & Wijayanti, D. (2020). Strategies to provide scaffolding when teaching mathematical reasoning. In B. Santoso, H. P. Adi, H. Sulistyo, D. Wijayanti, C. Anwar, & A. F. Ogunbaado (Eds). Proceedings of the 1st International Conference on Islamic Civilization, ICIC 2020, Indonesia. European Alliance for Innovation (EAI).  https://doi.org/10.4108/eai.27-8-2020.2303266

Blanton, M. L., & Kaput, J. J. (2011). Functional thinking as a route into algebra in the elementary grades. ZDM-International Reviews on Mathematical Education, 37(1), 34-42. https://doi.org/10.1007/978-3-642-17735-4_2

Blech, C., Gaschler, R., & Bilalić, M. (2019). Why do people fail to see simple solutions? Using think-aloud protocols to uncover the mechanism behind the Einstellung (mental set) effect. Thinking and Reasoning, November. https://doi.org/10.1080/13546783.2019.1685001

Bolondi, G. (2021). What can we learn from large-scale surveys about our students learning of maths? AAPP Atti Della Accademia Peloritana Dei Pericolanti, Classe Di Scienze Fisiche, Matematiche e Naturali, 99, 1–9. https://doi.org/10.1478/AAPP.99S1A4

Bråting, K., & Kilhamn, C. (2021). Exploring the intersection of algebraic and computational thinking. Mathematical Thinking and Learning, 23(2), 170–185. https://doi.org/10.1080/10986065.2020.1779012

Cañadas, M. C., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about linear functional relationships. Journal of Mathematical Behavior, 41, 87–103. https://doi.org/10.1016/j.jmathb.2015.10.004

Colley, B. M., Bilics, A. R., & Lerch, C. M. (2012). Reflection: A Key Component to Thinking Critically. The Canadian Journal for the Scholarship of Teaching and Learning, 3(1). https://doi.org/10.5206/cjsotl-rcacea.2012.1.2

Driscoll, M. (1999). Developing algebraic habits of mind. Fostering Algebraic Thinking: A Guide for Teachers Grades 6–10, 1–8.

Eroğlu, D., & Tanişli, D. (2017). Zihnin cebirsel alişkanliklarinin sinif ortamina entegrasyonu [Integration of algebraic habits of mind into the classroom practice]. Elementary Education Online, 16(2), 566–583. https://doi.org/10.17051/ilkonline.2017.304717

Faragher, L., & Huijser, H. (2014). Exploring evidence of higher order thinking skills in the writing of first year undergraduates. The International Journal of the First Year in Higher Education, 5(2), 33-44. https://doi.org/10.5204/intjfyhe.v5i2.230

Irvine, J. (2020). Marzano’s new taxonomy as a framework for investigating student affect. Journal of Instructional Pedagogies, 24(June), 1–31.

Isnani, I., Waluya, S. B., Rochmad, R., Sukestiyarno, S., Suyitno, A., & Aminah, N. (2020). How is Reasoning Ability in Learning Real Analysis? In W. Strielkowski (Ed.), Proceeding of the International Conference on Agriculture, Social Sciences, Education, Technology and Health (ICASSETH 2019) (pp. 253–256). Atlantis Press. https://doi.org/10.2991/assehr.k.200402.059

Kaput, J. J., & Blanton, M. L. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446. https://bit.ly/3rjhmw5

Kusmaryono, I., Jupriyanto, & Kusumaningsih, W. (2021). Construction of students’ mathematical knowledge in the zone of proximal development and zone of potential construction. European Journal of Educational Research, 10(1), 341–351. https://doi.org/10.12973/eu-jer.10.1.341

Martin, G. (2009). Focus in high school mathematics: Reasoning and sense making. National Council of Teachers of Mathematics.

Martin, P. K., Schroeder, R. W., Olsen, D. H., Maloy, H., Boettcher, A., Ernst, N., & Okut, H. (2020). A systematic review and meta-analysis of the Test of Memory Malingering  in adults: Two decades of deception detection. Clinical Neuropsychologist, 34(1), 88–119. https://doi.org/10.1080/13854046.2019.1637027

Marzano, R. J., & Kendall, J. S. (2007). Praise for the second edition of the new taxonomy of educational objectives. Corwin Press.

Marzano, R. J., & Kendall, J. S. (2008). Designing & assessing educational objectives: applying the new taxonomy. Corwin Press.

Obara, S. (2019). Pre-service teachers exploring the role of pattern-based reasoning in the context of algebraic thinking. Eurasia Journal of Mathematics, Science and Technology Education, 15(11). https://doi.org/10.29333/ejmste/109262

Otten, M., van den Heuvel‐Panhuizen, M., Veldhuis, M., Boom, J., & Heinze, A. (2020). Are physical experiences with the balance model beneficial for students’ algebraic reasoning? An evaluation of two learning environments for linear equations. Education Sciences, 10(6), 1–23. https://doi.org/10.3390/educsci10060163

Plomp, T., & Nieveen, N. (Eds.). (2013). An intruduction to tducational design research. SLO - Netherlands Institute for Curriculum Development. https://bit.ly/3I9Ygi7

Pourdavood, B. R., McCarthy, K., & McCafferty, T. (2020). The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 7(3), 241–254. https://doi.org/10.30958/aje.7-3-1

Uygun, T., & Güner, P. (2019). Representation of algebraic reasoning in sets through argumentation. International Journal of Contemporary Educational Research, 6(2), 215 – 229. https://doi.org/10.33200/ijcer.557781

Wilkinson, L. C., Bailey, A. L., & Maher, C. A. (2018). Students’ mathematical reasoning, communication, and language representations: A video-narrative analysis. ECNU Review of Education, 1(3), 1–22. https://doi.org/10.30926/ecnuroe2018010301

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