Analysis of Students' Mathematical Understanding using the Pirie-Kieren Lens


(1) Universitas Muhammadiyah Gresik, Indonesia
(2) Universitas Muhammadiyah Gresik, Indonesia
(3) Universitas Muhammadiyah Gresik, Indonesia


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Copyright (c) 2023 Irwani Zawawi, Syaiful Huda, Irma Surya Afriani
Creating a learning environment that supports students' understanding is an important notion in mathematics education (Carpenter & Lehrer, 1999). In this case, it is necessary to have a flow in the learning process. Learning trajectory will help teachers apply models, teaching material strategies and appropriate assessments according to students' thinking stages. The flow of student learning in the development of symbols and their meaning in mathematics can be done through technology and information (Bakker et al., 2003). The purpose of this study is to analyze the understanding of mathematical concepts in high school students using the Pirie-Kieren theory lens. Based on the results of the analysis of student worksheets for groups with visual, auditory, and kinesthetic learning styles, they have fulfilled the layer of Piere-Kieren understanding up to the stage/organizing layer. The difference in the results of the worksheets of the students in the three groups of learning styles can be seen in their process of finding ways to arrange the candies/boxes equally.Creating a learning environment that supports students' understanding is an important notion in mathematics education (Carpenter & Lehrer, 1999). In this case, it is necessary to have a flow in the learning process. Learning trajectory will help teachers apply models, teaching material strategies and appropriate assessments according to students' thinking stages. The flow of student learning in the development of symbols and their meaning in mathematics can be done through technology and information (Bakker et al., 2003). The purpose of this study is to analyze the understanding of mathematical concepts in high school students using the Pirie-Kieren theory lens. Based on the results of the analysis of student worksheets for groups with visual, auditory, and kinesthetic learning styles, they have fulfilled the layer of Piere-Kieren understanding up to the stage/organizing layer. The difference in the results of the worksheets of the students in the three groups of learning styles can be seen in their process of finding ways to arrange the candies/boxes equally.
Keywords: mathematics learning, Piere-Kieren theory, high school students.
Ainsworth, S. E., Bibby, P. A., & Wood, D. J. (1998). Analysing the costs and benefits of multi-representational learning environments. In P. R. H. P. A. B. & T. de J. (Eds. ). M. W. van Someren (Ed.), Learning with multiple representations (pp.120–134). Oxford: Elsevier Science Ltd.
Ainsworth, S. (1999). The functions of multiple representations. www.elsevier.com/ locate/compedu
Bakker, A., Doorman, M., & Drijvers, P. (2003). Design research on IT Design research on how IT may support the development of symbols and meaning in mathematics education.
Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers’ beliefs. Journal of Mathematical Behavior, 23(2), 135–167.
Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema, & T. A. Romberg (Eds.). Mathematics Classrooms That Promote Understanding, 19–32.
Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2006). Learning mathematics in elementary and middle Schools. (4th ed.). N.J.: Merrill/Prentice Hall.
Chuang- Yih Chen. (2002). A hypothetical learning trajectory of arguing statements about
geometric figures.
Clements, D. H., & Sarama, J. (2020). Learning and teaching early math: the learning trajectories approach (3rd ed.). Routledge. .
Delice, A., & Sevimli, E. (2010). Ogretmen adaylarinin coklu temsil kullanma becerilerinin problem cozme basarilari yonuyle incelenmesi: Belirli integral ornegi. Educational Sciences: Theory & Practice, 10(1), 111–149.
Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. In Educational Studies in Mathematics (Vol. 61, Issues 1–2, pp. 103– 131).
Duval, R. (2017). Understanding the mathematical way of thinking - The registers of semiotic representations. In Understanding the Mathematical Way of Thinking - The Registers of Semiotic Representations. Springer International Publishing.
Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105–121.
Flores, R., Koontz, E., Inan, F. A., & Alagic, M. (2015). Multiple representation instruction first versus traditional algorithmic instruction first: Impact in middle school mathematics classrooms. Educational Studies in Mathematics, 89(2), 267– 281.
Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving “Ability to use multiple representations in Functions and Geometry: The Transition from Middle to High school”-Research Promotion Foundation View project.
Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. In Educational Psychology (Vol. 24, Issue 5, pp. 645–657).
Goldin, G. A. (1987). Cognitive representational systems for mathematical problem solving. In Problems of representation in the teaching and learning of mathematics (pp. 125–145). Hillsdale, NJ: Lawrence Erlbaum Associates. oldin, Gerald A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In Theory of Mathematical learning (1st ed., pp.397–430). Routledge.
Gravemeijer, K., & Cobb, P. (2006). “Design Research from a Learning Perpective. Routledge.
Hiebert, J. (1988). Theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19(3), 333–355.
Kaput, J. J. (1998). Direct all correspondence to. Jmb Journal Of Mathematical Behavior, 17(2), 265–261.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. Problems of Representation in the Teaching and Learning of Mathematics, 21, 33–40.
Meel, D. E. (2003). Models and theories of mathematical understanding: Comparing Pirie and Kieren’s model of the growth of mathematical understanding and APOS theory. USA: American Mathematical Society., 12, 132–182.
Ng, S. F., & Lee, K. (2009). The model method: singapore children’s tool for representing and solving algebraic word. In Source: Journal for Research in Mathematics Education (Vol. 40, Issue 3).
Presmeg, N. C., & Balderas-Cañas, P. E. (2001). Visualization and affect in nonroutine problem solving. Mathematical Thinking and Learning, 3(4), 289–313.
Salkind, G. M. (2007). Mathematical presentation. http://mason.gmu.edu/~gsalkind/portfolio/products/857LitReview.pdf
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.
Van de Walle, J. A. (2007). Elementary and middle school mathematics: teaching developmentally (6th ed.). Johns Hopkins University.
Yin, R. K. (2014). Case study research: Design and methods (applied social research methods) (p. 46). Thousand Oaks, CA: Sage publications.
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