Mapping the Layers of Understanding: An Analysis of Mathematical Comprehension in Literacy Questions using the Pirie-Kieren Theory
), Yohanes Ovaritus Jagom(2), Kristoforus Djawa Djong(3), Meryani Lakapu(4), Wilridus Beda Nuba Dosinaeng(5), Samuel Igo Leton(6), Patrisius Batarius(7), Natalia Magdalena Rafu Mamulak(8), Ilda Guterres(9)
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Country:
(1) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(2) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(3) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(4) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(5) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(6) Department of Mathematics Education, Widya Mandira Catholic University, Indonesia
(7) Department of Computer Science, Widya Mandira Catholic University, Indonesia
(8) Department of Computer Science, Widya Mandira Catholic University, Indonesia
(9) Department of Mathematics Education, Universidade Oriental Timor-Lorosa’e, Timor-Leste
Corresponding Author
The Pirie-Kieren theory provides a dynamic framework that explains how mathematical understanding develops in layers, starting from initial introduction to reflection through eight layers of understanding. The eight layers of understanding are Primitive Knowing, Image Making, Image Having, Property Noticing, Formalizing, Observing, Structuring, and Inventising. This study aims to analyze students' mathematical understanding in solving literacy problems based on Pirie-Kieren's theory. This study is a qualitative descriptive study, involving 15 tenth-grade students at SMA Negeri 2 Kupang Barat, Indonesia. The research instruments used were literacy tests and interviews. In-depth interviews were conducted with student representatives who had reached each layer of understanding. Student representatives were selected based on purposive sampling. Data analysis in this study was carried out in four stages, namely data reduction, data presentation, conclusion drawing, and triangulation. The literacy test data were analyzed based on Pirie-Kieren's eight layers of understanding. The eight layers of understanding are. The results show that 73.33% of students reached the image having a layer of understanding, 13.33% reached the formalizing layer, 6.67% reached the image-making layer, and 6.67% reached only the primitive knowing layer. No students reached the observing, structuring, or inventing layers. The dominance of students in the image, having a level of understanding, shows that most students have only reached the initial stage. These results indicate that students' mathematical understanding of literacy questions remains at a basic level and has not developed into a reflective understanding.
Keywords: mathematical literacy, literacy questions, mathematical understanding, Pirie Kieren theory.
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