The Impact of Differentiation Model in Mathematics on Learner Achievements Obtained from the External and Internal Assessment of Knowledge/Utjecaj diferencijacijskog modela u nastavi matematike na postignuća učenika s obzirom na vanjsko i unutarnje vredno

Abstract

Abstract

We present a study in which we consider  whether the learners, who had mathematics instruction in the 9th grade of primary school in heterogeneous groups, significantly differed in their mathematics achievements measured by using the external and internal assessment of knowledge from the learners in homogeneous groups. No statistically significant differences in the average achievements were found in the external assessment. On the contrary, in the internal assessment of knowledge the learners in homogenous groups on average had significantly higher achievements in comparison to the learners in heterogeneous groups. The analysis of covariance performed in homogenous and heterogeneous ability groups showed that the learners, who were placed in the lower or middle third after the initial examination in their school, in the final external examination progressed relatively better in heterogeneous groups. The learners who were placed in the upper third in their school according to their mathematics achievements showed no differences in this regard. The internal assessment of knowledge displayed that the learners who were placed in the middle or upper third in their school after the initial external examination, in the final examination progressed relatively better in homogenous groups. The learners who were placed in the lower third after the initial external examination in their school showed no differences in this regard.

Key words: grouping of pupils; individualization and differentiation; internal assessment of knowledge; external assessment of knowledge; mathematics.

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Sažetak

Predstavljamo istraživanje u kojem razmatramo  razlikuju li se značajno učenici koji su imali nastavu matematike u devetom razredu osnovne škole u heterogenim grupama po svojim postignućima, određenim vanjskim i internim vrednovanjem znanja, od učenika u homogenim grupama. Pri vanjskom vrednovanju nisu zabilježene statistički značajne razlike u slučaju prosječnih postignuća. No, interno je vrednovanje znanja učenika u homogenim grupama u prosjeku ukazalo na statistički značajno veća postignuća u usporedbi s učenicima u heterogenim grupama. Analiza kovarijance provedena po razinama za učenike u homogenim i heterogenim grupama pokazala je da su učenici koji su, poslije inicijalnog vrednovanja u svojim školama, našli mjesto u donjoj ili srednjoj trećini, relativno bolje napredovali u heterogenim grupama pri finalnom vanjskom vrednovanju. Učenici koji su se, prema uspjehu iz matematike, našli u gornjoj trećini u svojim školama, nisu pokazali nikakve razlike u tome smislu. Interno je vrednovanje znanja pokazalo da su učenici koji su se u svojim školama, poslije inicijalnog vanjskog vrednovanja, našli u srednjoj ili gornjoj trećini pri finalnom vrednovanju, relativno bolje napredovali u homogenim grupama. Učenici koji su pripadali donjoj trećini poslije inicijalnog vanjskog vrednovanja u svojim školama, nisu pokazali nikakve razlike u tome pogledu.

Ključne riječi: podjela učenika u grupe; individualizacija i diferencijacija; unutarnje vrednovanje znanja; vanjsko vrednovanje znanja; matematika