Vloga narave koeficientov pri poenostavljanju algebrskih izrazov

magistrsko delo

Mojca Štembergar (Avtor), Alenka Lipovec (Mentor)

Povzetek

Magistrsko delo v ospredje postavlja težave, s katerimi se soočajo učenci pri poenostavljanju algebrskih izrazov. Temelje uspešnega poenostavljanja algebrskih izrazov postavljata ustrezno aritmetično predznanje ter sposobnost dojemanja algebrskega izraza kot proces in objekt (procept) s preklapljanjem med obema pogledoma. Na vzorcu 272 slovenskih osmošolcev smo preverjali, kakšno vlogo ima pri poenostavljanju algebrskih izrazov narava koeficientov členov. Ob tem nas je zanimalo, katere napake se pojavljajo pri poenostavljanju algebrskih izrazov. Sestavljen je bil preizkus znanja, v katerem so celoštevilske koeficiente algebrskih izrazov zamenjale decimalne številke in ulomki. Identifikaciji in štetju napak je sledila klasifikacija napak. Rezultati so pokazali, da so učenci najbolj uspešni pri poenostavljanju algebrskih izrazov s celoštevilskimi koeficienti, najmanj pa pri poenostavljanju algebrskih izrazov z ulomki. Pri poenostavljanju algebrskih izrazov se pojavljajo tako napake algebrske kot tudi aritmetične narave. Napake slovenskih osmošolcev se bistveno ne razlikujejo od napak, ki so jih zaznale raziskave v tujini, poleg tega sama narava koeficientov členov bistveno ne vpliva na vrsto napake. Napake so posledica nerazumevanja algebrske strukture, šibkega aritmetičnega predznanja, pa tudi vpliva novega znanja, ki se odraža v mešanju in napačni uporabi algebrskih pravil. Težave na algebrski in aritmetični ravni bi lahko omilili učni pristopi, ki bi dlje časa nudili ustrezno konkretno podporo predvsem tistim učencem, ki še niso dosegli formalne stopnje razvoja.

Ključne besede

matematika;poenostavljanje algebrskih izrazov;koeficienti;spremenljivke;napake učencev;magistrska dela;

Podatki

Jezik:	Slovenski jezik
Leto izida:	2016
Tipologija:	2.09 - Magistrsko delo
Organizacija:	UM FNM - Fakulteta za naravoslovje in matematiko
Založnik:	[M. Štembergar]
UDK:	37.091.3:512(043.2)
COBISS:	22502408
Št. ogledov:	1204
Št. prenosov:	109
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	The role of the coefficientb4s nature in simplifying algebraic expressions
Sekundarni povzetek:	The master's degree thesis exposes the problems faced by students in simplifying algebraic expressions. The basis of a successful algebraic expression simplification is provided by appropriate prior knowledge in arithmetics and the ability to perceive an algebraic expression as a process and concept (procept) with switching between two views when needed. The role of term's coefficient in the algebraic expression simplification was determined on a sample of 272 8th grade Slovenian elementary school students. Furthermore, we were interested in errors that occur in simplifying algebraic expressions. The test in which integer coefficients of algebraic expressions were replaced by decimal numbers and fractions was drawn up. Identification and count of errors were followed by error classification. Our results have shown that Slovenian students are most successful in simplifying algebraic expressions containing integer coefficients and least successful in simplifying algebraic expressions with fractions. In simplifying algebraic expressions both errors of algebraic and arithmetic nature occur. Errors of Slovenian students are not significantly different from errors detected by similar studies abroad. Moreover, the nature of term's coefficient does not substantially affect the nature of the error. Errors are the result of student's misunderstanding of algebraic structure, lack of appropriate prior knowledge in arithmetics as well as the impact of new acquired knowledge that reflects in messing up and misuse of algebraic rules. Problems on algebraic and arithmetic levels may be alleviated by teaching methods that provide adequate long-term practical support, particullary to those students who have not yet reached the formal stage of development.
Sekundarne ključne besede:	mathematics;simplifying algebraic expressions;coefficients;variables;student's errors;master theses;
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Magistrsko delo
Komentar na gradivo:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Strani:	IV, 108 str., [7] str. pril.
ID:	9137488