Overcoming the obstacle of poor knowledge in proving geometry tasks

Abstract

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.

Keywords

didactic use of computer;educational software;geometry;computer-aided observation;dynamic geometry;OK geometry;proof;

Data

Language:	English
Year of publishing:	2013
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
Publisher:	Pedagoška fakulteta Univerze
UDC:	37.091.3:514
COBISS:	9934409
ISSN:	1855-9719
Parent publication:	CEPS journal
Views:	1735
Downloads:	401
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Premagovanje ovire šibkega znanja pri geometrijskih dokazovalnih nalogah
Secondary 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.
Secondary keywords:	pouk;matematika;geometrija;učne metode;dokazovanje;geometry;didactic use of computer;educational software;didaktična uporaba računalnika;didaktična programska oprema;
URN:	URN:NBN:SI
Type (COBISS):	Article
Pages:	str. 99-116
Volume:	ǂVol. ǂ3
Issue:	ǂno. ǂ4
Chronology:	2013
DOI:	10.26529/cepsj.225
ID:	9106916