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Characterization of students formal-proof construction in mathematics learning Syamsuri Syamsuri; Purwanto Purwanto; Subanji Subanji; Santi Irawati
Communications in Science and Technology Vol 1 No 2 (2016)
Publisher : Komunitas Ilmuwan dan Profesional Muslim Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21924/cst.1.2.2016.2

Abstract

Formal proof is a deductive process beginning from some explicitly quantified definitions and other mathematical properties to get a conclusion. Characteristics of student formal-proof construction are required to identify the appropriate treatment can be determined. The purpose of this study was to describe the characteristics of the construction of formal-proof based overview of the proof structure and conceptual understanding that the student possessed. The data used in this article were obtained from the 3-step processes: students are asked to write down the proof of proving-question, they are asked about the knowledge required in constructing proof using questionnaire, and then they are interviewed. The results showed that formal-proof construction could be modeled by the Quadrant-Model. First Quadrant describes correct construction of formal-proof, Second Quadrant describes insufficiencies concept in construction formal-proof, Third Quadrant indicates insufficiencies concept and proof-structure in construction formal-proof and Fourth Quadrant describes incorrect proof-structure in construction of formal-proof. This model could give consideration on how to help students who are in Quadrant II, III, and IV to be able to construct a formal proof like Quadrant I.
Visuoalphanumeric Representations In Pattern Generalization Khomsatun Ni'mah; Purwanto Purwanto; Edy Bambang Irawan; Erry Hidayanto
Pancaran Pendidikan Vol 6, No 4 (2017)
Publisher : The Faculty of Teacher Training and Education The University of Jember Jember, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/pancaran.v6i4.119

Abstract

This study aims to describe how generalization process to 192 children in middle school at grade 7 in solving problems of patterns. Processing of the data in this study uses qualitative data analysis techniques. The analyzed data is the data obtained through direct observation technique, documentation, and interviews. This study based on research studies Rivera (2011) which resulted in a five – representations in pattern generalization, namely: verbal, visual, numeric, verbal alphanumeric, and visuoalpanumeric. Visuoalphanumeric representation can be interpreted that the ability of students in determining the general formula of n th pattern symbolically (algebraically) by manipulating the image (visually). Based on the analysis of the data in this study found there are a unique phenomenon that appeared namely visuoalphanumeric representation in pattern generalization process that is the childrens able to related rule of pattern on conjecturing process to another context of patterns problem through two ways, which are visually and symbolically.