Razlike u matematičkom postignuću učenika četvrtog razreda osnovne škole u Srbiji i Sloveniji

This paper presents the findings that are parts of a larger international project studying the achievements in mathematics and science for students in primary and lower secondary education. Specifically, we focused on the study of differences in mathematics achievement for Serbian and Slovenian fourth-graders. The study used a sample of 7,861 fourth-grade students from Serbia (N = 3,736) and Slovenia (N = 4,125). The results showed that Serbian students had higher overall achievement and scored higher in both the number content and the knowing cognitive domains, whereas Slovenian students scored higher on the geometry content and the data content domains, also having a higher balance among achievements for both content and cognitive domains. It was also found that Slovenian students had higher self-confidence in learning mathematics. Because there were no other significant differences between Serbia and Slovenia with respect to two other contextual variables and the correlations among these three contextual variables, the explanations of the achievement differences were based upon the consideration of various aspects of curriculum, teaching practice, and teachers' professional development in Serbia and Slovenia. The paper raises the question of educational implications of these findings and the possible directions of improving the quality of mathematics teaching.U radu su izloženi nalazi koji predstavljaju deo obimnog međunarodnog projekta proučavanja postignuća učenika osnovnih škola u oblasti matematike i prirodnih nauka (TIMSS 2011). Konkretnije, usmerili smo se na proučavanje razlika u matematičkom postignuću srpskih i slovenačkih učenika četvrtog razreda osnovne škole. Istraživanje je sprovedeno na uzorku od 7,861 učenika četvrtog razreda osnovne škole iz Srbije (N=3,736) i Slovenije (N=4,125). Rezultati istraživanja pokazuju da učenici iz Srbije imaju viši nivo ukupnog postignuća i više skorove u sadržinskom domenu Broj i kognitivnom domenu Znanje, dok učenici iz Slovenije imaju više skorove u sadržinskim domenima Geometrija i Podaci, kao i veći balans između postignuća u sadržinskim i kognitivnim domenima. Takođe, utvrđeno je da slovenački učenici imaju viši nivo samopouzdanja u učenju matematike u odnosu na učenike iz Srbije. S obzirom na to da nisu utvrđene značajnije razlike i korelacije po pitanju drugih kontekstualnih varijabli u Srbiji i Sloveniji, objašnjenje razlika u matematičkom postignuću učenika bazirano je na razmatranju različitih aspekata kurikuluma, nastavne prakse i profesionalnog usavršavanja nastavnika. U radu se postavlja pitanje obrazovnih implikacija dobijenih nalaza i mogućih pravaca unapređivanja kvaliteta nastave matematike

GRUPIRANJE UČENIKA PREMA SPOSOBNOSTIMA I USPJEH UČENIKA NA DRŽAVNOJ MATURI

The first part of the article deals with the characteristics of ability grouping and its impact on pupils’ learning outcomes, the importance of teaching differentiation and individualization as well as their advantages and limitations. The second part of the article presents the results of a study that attempted to examine the organizational characteristics of ability grouping in Slovenian and Mathematics in Slovenian primary schools, call attention to the role of the sociocultural environment when dividing pupils into levels and analyze the performance of ability-grouped pupils, on the one hand, and pupils from heterogeneous groups, on the other, on the National Assessment of Knowledge. The research comprised 1,454 ninth-grade pupils from 41 Slovenian primary schools. The study has shown that approximately three-quarters of schools implement ability education; the majority offer classes at three and the rest at two difficulty levels. Pupils’ school grades and socio-cultural background play an important role in the ranking of pupils into levels. The results showed a medium-to-high grade statistical correlation between pupils’ levels in Mathematics and Slovenian language, on the one hand, and their mother’s and father’s education and their average grades for Slovenian and Mathematics in the 7th , 8 th and 9th grades, on the other hand. This result indicates that social background significantly influences pupils’ learning performance. In addition, the study has shown that ability grouping can be effective only if teachers adjust both the teaching methods and learning materials to the pupils at each individual level.Prvi dio članka opisuje značajke grupiranja učenika prema sposobnostima i učinak grupiranja na ishode učenja, važnost diferencijacije i individualizacije nastave, kao i njihove prednosti i ograničenja. Drugi dio članka prikazuje rezultate istraživanja kojim su se pokušale ispitati organizacijske značajke grupiranja prema sposobnostima u Slovenskom jeziku i Matematici u slovenskim osnovnim školama, skrenuti pozornost na ulogu društvenokulturnog okruženja na podjelu učenika prema sposobnostima i analizirati uspjeh na državnoj maturi učenika grupiranih prema sposobnostima s jedne strane i učenika iz heterogenih skupina s druge strane. Istraživanjem je obuhvaćeno 1,454 učenika devetih razreda iz 41 slovenske osnovne škole. Rezultati su pokazali da se u otprilike tri četvrtine škola provodi obrazovanje prema sposobnostima; većina škola nudi nastavu diferenciranu prema tri, a ostale prema dvije razine težine. Ocjene učenika i društveno-kulturno okruženje imaju značajnu ulogu u rangiranju učenika prema razinama. Rezultati su pokazali srednju do visoku statističku korelaciju između učeničkih razina u Matematici i Slovenskom jeziku s jedne strane te obrazovanja njihovih majki i očeva kao i njihove prosječne ocjene iz Slovenskog jezika i Matematike u 7., 8. i 9. razredu s druge strane. Dobiveni rezultati pokazuju da društveno okruženje značajno utječe na uspješnost učenja kod učenika. Osim toga, istraživanje je pokazalo da grupiranje prema sposobnostima može biti djelotvorno samo ako učitelji usklade metode poučavanja i učenja, kao i materijale prema svakoj individualnoj razini učenika

Utjecaj diferencijacijskog modela u nastavi matematike na postignuća učenika s obzirom na vanjsko i unutarnje vrednovanje znanja

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.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

The process-didactic approach to teaching the mathematical topic of “measuring” in primary schools

Merjenje je pomembna matematična vsebina v osnovni šoli. Z namenom, da bi pri učencih dosegli kakovostno znanje o merjenju, smo za pouk matematike razvili procesnodidaktični pristop ter ga evalvirali z vidika učinkov kakovosti znanja učencev. Na osnovi teoretskega poznavanja miselnega razvoja otrok, vključno z novejšimi spoznanji o otrokovem mišljenju, ter poznavanja socialne kognicije, učenja in poučevanja smo izdelali procesnodidaktični pristop za poučevanje matematike (merjenja v osnovni šoli), ki posebno pozornost namenja izkustvenemu učenju, refleksiji, razvijanju miselnih navad, postavljanju primernih spodbud s strani učitelja, kognitivnemu oz. socialno-kognitivnemu konfliktu. Na vzorcu 137 učencev četrtega razreda iz slovenskih osnovnih šol smo izvedli empirično raziskavo. V eksperimentalno skupino je bilo vključenih 67 učencev, v kontrolno skupino pa 70 učencev. V eksperimentalni skupini je pouk potekal po procesnodidaktičnem pristopu, v kontrolni skupini je imel pouk značilnosti transmisijskega pristopa. S teoretično zasnovo testov, ki smo jih priredili kot merski instrument, smo ob izbranih vsebinah o merjenju količin v četrtem razredu osnovne šole testirali znanja na različnih taksonomskih ravneh. Evalvacija rezultatov glede kakovosti izkazanega znanja učencev je pokazala, da med eksperimentalno in kontrolno skupino obstajajo statistično pomembne razlike v znanju merjenja količin v korist eksperimentalne skupine.Measuring belongs to the science of mathemats in primary schools. In order to improve knowledge about measuring, we created a process-didactic approach for mathematical instruction and evaluated it by determining the quality of knowledge that the pupils gained. Based on our theoretical knowledge about the mental development of children, including new findings on children’s thinking and our knowledge of social cognition and learning and teaching, we prepared a process-didactic approach for teaching mathematics (measuring in Primary Schools). The process-didactic approach particularly focuses on experiential learning, reflection, the development of mental habits, setting adequate incentives on the part of teachers, cognitive conflict and socio-cognitive conflict. We carried out an empirical research on a sample of 137 pupils from the fourth grade of Slovenian primary schools. The experimental group included 67 pupils and the control group 70 pupils. The process for the experimental group was conducted according to the process-didactic approach, and the control group was conducted using the transmission approach. Using theoretically conceived tests, which were modified to function as a measuring instrument, we tested the knowledge of the pupils at different taxonomic levels by carefully selecting the contents of the measuring quantities. The evaluation the of results, regarding the quality of pupil-knowledge, shows that there are statistically significant differences in the knowledge of measuring quantities between the experimental and the control group in favour of the experimental group

Process Approach to Learning and Teaching Mathematics

In the research, a quasi-experimental model was applied and the experimental group received the process approach to learning and teaching mathematics, which builds on the cognitive-constructivist findings of educational profession about learning and teaching mathematics. In the control group, the transmission approach prevailed. In the research, the question was answered of what impact the implementation of the process approach to learning and teaching mathematics has on the learner’s knowledge, which can be tested and assessed. Students in the experimental group (EG) performed significantly better in basic and conceptual knowledge, in solving simple mathematical problems, and in complex knowledge than those in the control group. Results of the research have also shown that there are statistically significant correlations between individual areas of mathematical knowledge. The correlations between the areas of knowledge are from medium high to high, indicating that conceptual knowledge correlates significantly with solving simple mathematical problems and with complex knowledge

Stajališta nastavnika o oblicima pomoći za učenike s poteškoćama u učenju

The article presents the types of help provided for pupils with learning disabilities in mathematics in Slovenian primary schools. We have carried out research into the implementation of different types of help in reference to the Working Concept: Learning Disabilities in Primary Schools, assuming that schools provide individual support work plans for pupils with learning disabilities. A questionnaire was used to assess the implementation of assistance provided to pupils with learning disabilities during lessons and out of regular mathematics instruction as well as the satisfaction of teachers with the efficiency of different forms of assistance for pupils with learning disabilities in mathematics. Respondents were asked to evaluate through different assessment scales the frequency of the implementation of various forms of assistance in and out of classes (1-never, 2-rarely, 3-often, 4-always), as well as their satisfaction with the effectiveness of types of assistance provided for pupils with learning disabilities in mathematics through different assessment scales (1-not satisfied with efficiency at all, 2-barely satisfied with efficiency, 3- neither satisfied nor dissatisfied with efficiency, 4-quite satisfied with efficiency, 5-very satisfied with efficiency). The results of the empirical study have shown that teachers most often choose remedial classes, assistance to pupils within extended stay and additional individual assistance out of regular instruction; and during regular classes they tend to adapt their delivery of the syllabus, they adapt the knowledge consolidation models and they adapt the application of adequate learning tools. As regards the teaching process, teachers’ highest assessment is given to the satisfaction of effective adaptation of the knowledge consolidation model and to the promotion of the use of effective teaching materials.Ovaj rad prikazuje oblike pomoći za učenike s poteškoćama u učenju matematike u osnovnim školama u Sloveniji. Provedeno istraživanje vezano je uz primjenu različitih vrsta potpore po preporuci Radnog koncepta: Poteškoće u učenju u osnovnim školama, uz pretpostavku da škole nude podršku putem individualnih planova rada za učenike s poteškoćama u učenju. Kako bi procijenili primjenu pomoći koja se nudi učenicima s poteškoćama u učenju za vrijeme sata i nakon redovite nastave matematike koristili smo se upitnikom kao i za procjenu zadovoljstva nastavnika s učinkovitošću različitih oblika pomoći za učenike s poteškoćama u učenju matematike. Od ispitanika se tražila procjena putem različitih skala: mjerenje učestalosti implementacije različitih oblika pomoći za vrijeme i izvan nastave (od : 1 – nikada, 2 – rijetko, 3 – često, 4 – uvijek), kao i procjena učinkovitosti s određenim oblicima pomoći za učenike s poteškoćama u učenju matematike kroz skalu procjene (od: 1 – nezadovoljan s učinkovitošću, 2 – jedva zadovoljan s učinkovitošću, 3 – osrednje zadovoljan s učinkovitošću, 4 – dosta zadovoljan s učinkovitošću, 5 – vrlo zadovoljan s učinkovitošću. Rezultati empirijskog istraživanja pokazali su da se nastavnici najčešće koriste dopunskom nastavom, pomažu učenicima u produženom boravku i dodatno im individualno pomoći izvan redovite nastave; za vrijeme redovite nastave uglavnom prilagođavaju izvedbeni plan rada, prilagođavaju model konsolidacije znanja te prilagođavaju primjenu prikladnih alata za učenje. Vezano uz proces poučavanja najviša ocjena dana je zadovoljstvu s učinkovitim prilagođavanjem modela konsolidacije znanja te poticanju korištenja materijala za učinkovito poučavanje

Processes of learning with regard to students\u27 learning difficulties in mathematics

V uvodu pišemo o procesih učenja matematike: o razvoju matematičnih pojmov, o številskih in prostorskih predstavah, o branju in razumevanju besedila idr. Osrednji del prispevka namenjamo raziskavi, s katero smo ugotovili, da se opredeljevanje procesov učenja, ki so povezani z učnimi težavami učencev pri matematiki, statistično značilno ne razlikuje med učitelji razrednega pouka in učitelji matematike. Oboji kot procese učenja, pri katerih se najpogosteje pojavljajo učne težave pri učenju matematike, izpostavljajo razvoj številskih predstav, razvoj matematičnih pojmov, logično sklepanje ter branje in razumevanje besedila. Vsi procesi učenja, ki so jih učitelji ocenili kot procese učenja, ki najbolj ovirajo učenje, imajo dokaj izenačene povprečne ocene glede stopnje zahtevnosti, in sicer od 2,6 do 2,8, kar je zelo blizu oceni zelo otežuje učenje.In the introduction, we write about the process of learning mathematics: the development of mathematical concepts, numerical and spatial imagery on reading and understanding of texts, etc. The central part of the paper is devoted to the study, in which we find that identifying the learning processes associated with learning difficulties of students in mathematics, is not statistically significantly different between primary school teachers and teachers of mathematics. Both groups expose the development of numerical concepts, logical reasoning, and reading and understanding the text as the ones with which difficulties in learning mathematics appear the most frequently. All the processes of learning that the teachers assessed as the ones that represent the greatest barriers to learning have a fairly uniform average estimates of the degree of complexity, ranging from 2.6 to 2.8, which is very close to the estimate makes learning very difficult

Teaching strategies for helping students with difficulties in learning mathematics

Na šolsko uspešnost učenca vplivajo različni dejavniki: kognitivni, socialni in emocionalni dejavniki, domače okolje, šolsko okolje idr. Pomembno vlogo pri šolskih dejavnikih imajo tako organizacija pouka kot učiteljeva ravnanja pri poučevanju. S perspektive učencev z učnimi težavami so odločitve učiteljev tesno povezane s poznavanjem vzrokov in značilnosti učnih težav ter z metodičnim znanjem za poučevanje učencev z učnimi težavami. V prvem delu članka opredelimo splošne in specifične učne težave učencev pri matematiki, vzroke zanje ter ukrepe pomoči. V drugem delu so prikazani rezultati raziskave, katere osnovni namen je bil proučiti vsebine, pri katerih imajo učenci učne težave pri matematiki, zadovoljstvo učiteljev z učinkovitostjo različnih oblik pomoči učencem z učnimi težavami pri matematiki ter usposobljenost učiteljev za izvajanje oblik pomoči. Rezultati raziskave so pokazali, da največ učiteljev zaznava učne težave pri poštevanki, seštevanju in odštevanju s prehodom, pri količinah/merskih enotah/pretvarjanju, pri reševanju matematičnih problemov ter pri besedilnih nalogah. Z učinkovitostjo različnih oblik pomoči so učitelji srednje zadovoljni. Največje zadovoljstvo z učinkovitostjo oblik pomoči so učitelji izrazili pri tistih pristopih, pri katerih se tudi čutijo najbolj usposobljeni, to je pri uporabi ustreznih učnih pripomočkov ter pri prilagajanju utrjevanja znanja.Pupils’ performance in school is influenced by various elements, such as cognitive, social, and emotional factors, home environment, school environment, etc. As regards school, the organisation of education and teachers’ conduct in teaching play an important role. From the perspective of pupils with learning difficulties, teachers’ decisions are closely linked with their knowledge of learning difficulties and the causes of the latter as well as with the methodical knowledge they need so as to be able to teach pupils with learning difficulties. The first part of the article introduces general and specific learning disabilities of pupils in mathematics, along with the causes for learning disabilities and the means to helping pupils. The second part of the article summarises the results of a survey, the main purpose of which was to examine which were those mathematics topics that tended to cause most learning difficulties. The survey also focused on the satisfaction of teachers with the efficiency of the methodical ways of helping those pupils, and on the qualification of teachers to deliver different kinds of assistance. The results of the survey indicated that most teachers noticed learning disabilities occurring in multiplication, addition and subtraction over tenths, in quantities/measure units/conversion of units, and in solving mathematic problems and textual exercises. The teachers were fairly satisfied with the efficiency of the methodical ways of assistance. They expressed most satisfaction with those approaches which they felt they were most qualified for, i.e. the use of different didactic props and adapting the ways of reinforcing knowledge with pupils who had learning disabilities