Overcoming the obstacle of poor knowledge in proving geometry tasks

Magajna, Zlatan (author)

Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves several processes, the most salient being visual observation and deductive argumentation. These two processes are interwoven, but often poor observation hinders deductive argumentation. In the present article, we consider the possibility of overcoming the obstacle of a student’s poor observation by making use of computer-aided observation with appropriate software. We present the results of two small-scale research projects, both of which indicate that students are able to work out considerably more deductions if computer-aided observation is used. Not all students use computer-aided observation effectively in proving tasks: some find an exhaustive computer-provided list of properties confusing and are not able to choose the properties that are relevant to the task.

• Language: English
• Keywords: didactic use of computer, educational software, geometry, computer-aided observation, dynamic geometry, OK geometry, proof
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2013
• Number of pages: Str. 99-116
• Numbering: Vol. 3, no. 4
• PID: 20.500.12556/RUL-79211
• UDC: 37.091.3:514
• ISSN on article: 1855-9719
• DOI: 10.26529/cepsj.225
• COBISS.SI-ID: 9934409

Copyright

Podatek o licenci CC BY 4.0 je naveden na pristajalni strani članka (glej zgoraj izvorni URL). (Datum opombe: 20. 8. 2025)

• Publication date in RUL: 30.12.2015

Record is a part of a journal

• Title: CEPS journal : Center for Educational Policy Studies journal = revija Centra za študij edukacijskih strategij
• Publisher: Založba Univerze v Ljubljani = University of Ljubljana Press
• ISSN: 1855-9719
• COBISS.SI-ID: 252707584

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Title: Premagovanje ovire šibkega znanja pri geometrijskih dokazovalnih nalogah

Abstract

Pri dokazovanju v šolski geometriji ne gre le za dokazovanje resničnosti trditve. Pri pouku matematike je bistvo dokazovanja prepričljiva razlaga, zakaj je neka trditev resnična. Učenci doživljajo dokazovanje kot zahtevno; zahteven se jim zdi že pojem dokaza. Dokazovanje trditev o ravninski geometriji vključuje več procesov, najizrazitejša pa sta vizualno opazovanje in deduktivno argumentiranje. Ta procesa sta prepletena, pri čemer pa šibko opazovanje pogosto ovira deduktivno argumentacijo. V članku preučujemo možnost premagovanja ovire učenčevega šibkega opazovanja z uporabo računalniško podprtega opazovanja z ustrezno programsko opremo. Predstavljamo izsledke dveh manjših raziskav. Obe pokažeta, da učenci ob uporabi računalniško podprtega opazovanja oblikujejo bistveno več deduktivnih sklepov kot sicer. Vendar pa niso vsi učenci ob uporabi računalniško podprtega opazovanja učinkoviti: nekatere zmede izčrpen nabor lastnosti, ki jih opazi računalniški program, in niso zmožni med lastnostmi izbrati tistih, ki so pomembne za nalogo.

• Keywords: pouk, matematika, geometrija, učne metode, dokazovanje, didaktična uporaba računalnika, didaktična programska oprema, računalniško podprto opazovanje, dinamična geometrija, OK Geometry, dokaz