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	<title>Peningkatan Lapisan Pemahaman Konsep Luas Bangun Datar Mahasiswa melalui Model Pembelajaran PRAKTAK | Sagala | Jurnal Didaktik Matematika</title>
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			<meta name="keywords" content="the layers of understanding, conceptual understanding of the area of plane geometry, the increase of layers of understanding, PRAKTAK learning model" />
	
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	<meta name="DC.Creator.PersonalName" content="Viktor Sagala"/>
	<meta name="DC.Creator.PersonalName" content="Ahmad Hatip"/>
	<meta name="DC.Date.created" scheme="ISO8601" content="2018-10-01"/>
	<meta name="DC.Date.dateSubmitted" scheme="ISO8601" content="2018-09-24"/>
	<meta name="DC.Date.issued" scheme="ISO8601" content="2018-09-28"/>
	<meta name="DC.Date.modified" scheme="ISO8601" content="2018-10-01"/>
	<meta name="DC.Description" xml:lang="en" content="   The objective of this study was to describe the increase in the prospective student teachers’ conceptual understanding of the area of plane geometry by applying the practicum-axiomatic learning model (PRAKTAK). The PRAKTAK learning model is a combination of practicum and axiomatic methods in learning of proving the area of plane geometry. The evaluation was carried out using a modified Pirie-Kieren model of the layers of concept understanding hypothesized in 1994 and developed by cognitive psychology experts from 2002 to 2017. The research subjects were third-semester students of the Mathematics Study Program at FKIP Unitomo Surabaya. A set of questions is administered to the subjects after participating in learning using the PRAKTAK model, followed by an interview. The data of worksheets and interview transcripts were analyzed qualitatively. The results showed that before the implementation of PRAKTAK learning model, the understanding layer of subjects satisfied the first to fourth layers, namely primitive knowing, image making, having images and property noticing. After the implementation of PRAKTAK learning model, the understanding layer of the subjects increased, fulfilling the fifth and half of the sixth layer, namely formalizing and observing. Thus, the subjects met the semi observing layer. The PRAKTAK model can be applied in a geometry learning, and the modified Pirie-Kieren understanding model can be employed as an alternative evaluation tool.   "/>
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	<meta name="DC.Identifier" content="11898"/>
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				<meta name="DC.Title" content="Peningkatan Lapisan Pemahaman Konsep Luas Bangun Datar Mahasiswa melalui Model Pembelajaran PRAKTAK"/>
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        <meta name="citation_author" content="Viktor Sagala"/>
        <meta name="citation_author_institution" content="Universitas Dr. Soetomo Surabaya"/>
        <meta name="citation_author" content="Ahmad Hatip"/>
        <meta name="citation_author_institution" content="Universitas Dr. Soetomo Surabaya"/>
<meta name="citation_title" content="Peningkatan Lapisan Pemahaman Konsep Luas Bangun Datar Mahasiswa melalui Model Pembelajaran PRAKTAK"/>

				<meta name="citation_date" content="2018/10/01"/>
	
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		<em>Viktor Sagala</em>
								<br />Universitas Dr. Soetomo Surabaya		<br />Indonesia	</p>

	<p>Program Studi Pendidikan Matematika<br />Fakultas Keguruan dan Ilmu Pendidikan Universitas Dr. Soetomo<br />Surabaya</p>
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		<em>Ahmad Hatip</em>
								<br />Universitas Dr. Soetomo Surabaya		<br />Indonesia	</p>

	<p>Pendidikan Matematika FKIP Universitas Dr. Soetomo</p>
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	<a href="http://www.jurnal.unsyiah.ac.id/DM/issue/view/September%202018" target="_parent">Vol 5, No 2 (2018)</a> &gt;	<a href="http://www.jurnal.unsyiah.ac.id/DM/article/view/11898/0" class="current" target="_parent">Sagala</a>
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	<div id="articleTitle"><h3>Peningkatan Lapisan Pemahaman Konsep Luas Bangun Datar Mahasiswa melalui Model Pembelajaran PRAKTAK</h3></div>
	<div id="authorString"><em>Viktor Sagala, Ahmad Hatip</em></div>
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		<h4>Abstract</h4>
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		<div><p><em>The objective of this study was to describe the increase in the prospective student teachers’ conceptual understanding of the area of plane geometry by applying the practicum-axiomatic learning model (PRAKTAK). The PRAKTAK learning model is a combination of practicum and axiomatic methods in learning of proving the area of plane geometry. The evaluation was carried out using a modified Pirie-Kieren model of the layers of concept understanding hypothesized in 1994 and developed by cognitive psychology experts from 2002 to 2017. The research subjects were third-semester students of the Mathematics Study Program at FKIP Unitomo Surabaya. A set of questions is administered to the subjects after participating in learning using the PRAKTAK model, followed by an interview. The data of worksheets and interview transcripts were analyzed qualitatively. The results showed that before the implementation of PRAKTAK learning model, the understanding layer of subjects satisfied the first to fourth layers, namely primitive knowing, image making, having images and property noticing. After the implementation of PRAKTAK learning model, the understanding layer of the subjects increased, fulfilling the fifth and half of the sixth layer, namely formalizing and observing. Thus, the subjects met the semi observing layer. The PRAKTAK model can be applied in a geometry learning, and the modified Pirie-Kieren understanding model can be employed as an alternative evaluation tool.</em></p></div>
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		<h4>Keywords</h4>
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		<div>the layers of understanding, conceptual understanding of the area of plane geometry, the increase of layers of understanding, PRAKTAK learning model</div>
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		<h4>References</h4>
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							<p>Droujkova, M. (2005). Tables and Young Children’s Algebraic and Multiplicative Reasoning. International Group for the Psychology of M Athematics Education, 309.</p>
							<p>Dubinsky, E., &amp; McDonald, M. A. (2001). APOS: A Constructivist Theory of Learning in Undergraduate Mathematics Education Research. In The Teaching and Learning of Mathematics at University Level (pp. 275–282). Springer.</p>
							<p>Jones, B.F., &amp; Knuth, R. . (1991). What does Research Say about Mathematics? Retrieved October 8, 2018, from http://www.ncrl.org/sdrs/areas/stw_esys/2math.html</p>
							<p>Manu, S. S. (2005). Language Switching and Mathematical Understanding in Tongan Classrooms: An Investigation. Direction: Journal of Educational Studies, 27(2), 47–70.</p>
							<p>Martin, L. C. (2008). Folding Back and the Dynamical Growth of Mathematical Understanding: Elaborating the Pirie–Kieren Theory. The Journal of Mathematical Behavior, 27(1), 64–85.</p>
							<p>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. CBMS Issues in Mathematics Education, 12, 132–181.</p>
							<p>Moleong, J. L. (2010). Metode Penelitian Kualitatif (Edisi Revi). Bandung: PT Remaja Rosdakarya.</p>
							<p>Nur, M. (2011). Modul-Modul Keterampilan Proses Sains. Surabaya: Universitas Negeri Surabaya Pusat Sains dan Matematika Sekolah.</p>
							<p>Parameswaran, R. (2010). Expert Mathematics’ Approach to Understanding Definitions. Mathematics Educator, 20(1), 43–51.</p>
							<p>Pegg, J., &amp; Tall, D. (2005). The fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks. ZDM, 37(6), 468–475.</p>
							<p>Pirie, S., &amp; Kieren, T. (1994). Growth in Mathematical Undertsanding: How Can We Characterize It and How Can We Represent It? Educational Studies in Mathematics, 26, 165–190.</p>
							<p>Sagala, V. (2016). Profil Lapisan Pemahaman Konsep Turunan Fungsi dan Bentuk Folding Back Mahasiswa Calon Guru Berkemampuan Matematika Tinggi Berdasarkan Gender. MUST: Journal of Mathematics Education, Science and Technology, 1(2), 183–198.</p>
							<p>Sagala, V. (2017). Struktur Lapisan Pemahaman Konsep Turunan Fungsi Mahasiswa Calon Guru Matematika. Jurnal Didaktik Matematika, 4(2), 125–135.</p>
							<p>Tall, D. (1992). The Transition from Arithmetic to Algebra: Number Patterns, or Proceptual Programming. In New Directions in Algebra Education (pp. 213–231).</p>
							<p>Tall, D. (1999). Reflections on APOS theory in Elementary and Advanced Mathematical Thinking. In Proceedings of the 23 rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 148–155). ERIC.</p>
							<p>Walter, J. G., &amp; Gibbons, S. J. (2010). Student Problem-Solving Behaviors: Traversing the Pirie-Kieren Model for Growth of Mathematical Understanding. Thirteenth SIGMAA on Research in Undergraduate Mathematics Education Conference.</p>
							<p>Winaputra, U. S. (2001). Strategi Belajar Mengajar IPA. Jakarta: Universitas Terbuka.</p>
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		DOI: <a id="pub-id::doi" href="https://doi.org/10.24815/jdm.v5i2.11898">https://doi.org/10.24815/jdm.v5i2.11898</a>																				

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