magistrsko delo
Blanka Mlakar (Author), Marija Kavkler (Mentor), Alenka Polak (Co-mentor)

Abstract

Rezultati raziskave TIMSS 2011 za Slovenijo ter vsakoletno nacionalno preverjanje znanja v OŠ pokažejo na najnižje matematične dosežke pri učencih v Pomurski regiji. Rezultati nacionalnega preverjanja znanja izpostavijo še dve pomembni dejstvi, in sicer da rezultati močno korelirajo s socialno-ekonomskimi dejavniki družine ter da učenci s posebnimi potrebami po učnih dosežkih pri matematiki pomembno zaostajajo za vrstniki. Slovenski osnovnošolski učitelji zaznavajo, da imajo učenci veliko težav z učenjem aritmetike, in sicer z učenjem poštevanke, z računskimi operacijami, ulomki, enačbami ter z izrazi s spremenljivkami. Učenci s primanjkljaji na področju učenja aritmetike (v nadaljevanju PPUA) imajo pogosto aritmetično proceduralne težave, slabše razvite zaznavne sposobnosti, šibko razvito konceptualno znanje, slabše pomnjenje, vizualno-prostorske težave, slabše razvite jezikovne sposobnosti, slabše razvite finomotorične sposobnosti in motnje pozornosti. Proceduralno znanje se čez leta šolanja nadgrajuje preko avtomatizacije aritmetičnih dejstev in postopkov z vajo in mehanično vadbo ali pa z neposrednim učenjem strategij. Veliko učencev s PPUA ima težave že pri avtomatizaciji osnovnih aritmetičnih postopkov, te težave se stopnjujejo v tretjem triletju, kjer morajo obvladati kompleksnejše aritmetične postopke, kot sta računanje z ulomki in drugimi racionalnimi števili ter reševanje enačb. Osnovni cilj dela z učenci s PPUA je razvoj takih metod in pristopov, ki vsaj kompenzirajo učne težave, če jih že popolnoma ne odpravijo. To poudarja tudi posodobljeni učni načrt za matematiko (2011), ki navaja, da je učencem s posebnimi potrebami treba prilagoditi učenje matematike, uporabiti drugačen didaktični pristop in tudi drugačen dostop do tehnologije kot preostalim učencem. Učencem s PPUA pri pouku pomagamo s pomočjo strategij dobre poučevalne prakse, direktnega poučevanja matematike, timskega poučevanja, kooperativnih (sodelovalnih) oblik učenja, verbalizacije reševanja nalog, prav tako pa tudi s pomočjo didaktičnih pripomočkov ter z učenjem metakognitivnih strategij. Domači in tuji avtorji priporočajo izvajanje dodatne strokovne pomoči (v nadaljevanju DSP) za učence s posebnimi potrebami znotraj razreda oz. oddelka, s strategijami sodelovalnega učenja in poučevanja, saj na ta način učenci s PPUA napredujejo na učnem področju ter postajajo bolj samozavestni, ra¬zvijajo socialne spretnosti in krepijo odnose z vrstniki. Temeljni namen naše raziskave je bil oblikovati, izvesti in analizirati trening za izboljšanje aritmetičnega proceduralnega znanja za skupino učencev s PPUA, ki je temeljil na izvajanju dodatne strokovne pomoči, na strategiji timskega poučevanja učiteljice matematike in izvajalke DSP ter vrstniškega sodelovalnega učenja. Učiteljica matematike je poučevala po metodah dobre poučevalne prakse z izbiro sistematičnih in kakovostnih strategij poučevanja ter z izvajalko DSP izvedla 20 do 25 ur timskega pouka v 7., 8. in 9. razredu, v katerih so bili vključeni učenci s PPUA. Izvajalka DSP je izvedla med 20 in 32 ur individualne in pomoči v paru v okviru DSP za vsakega učenca s PPUA, ob tem pa so bili ti učenci še vključeni v organizirano vrstniško sodelovalno učenje v obsegu 10 ur. Raziskava je primer multiple študije primera s strategijo kliničnega poučevanja. V vzorec je bilo vključenih 8 učencev s PPUA iz 7., 8. in 9. razreda in 39 učencev vrstnikov brez PPUA iz istih razredov. V raziskavi so bili uporabljeni različni merski instrumenti, s katerimi smo ugotavljali aritmetično proceduralno znanje ter usvojene učne cilje iz aritmetike v skladu z učnim načrtom. Numerične rezultate preizkusov smo predstavili tabelarično vključno s primerjavo rezultatov skupine učencev s PPUA in skupine učencev brez PPUA ter jih analizirali s pomočjo deskriptivne statistike ali testiranja razlik med dosežki skupine učencev s PPUA in vrstnikov brez PPUA s t-preizkusom za neodvisne vzorce s pomočjo računalniškega programa SPSS. Kvalitativno pa smo interpretirali dosežene cilje iz učnega načrta učencev s PPUA, ter evalvirali izvajanje DSP, timskega pouka, sodelovanja s starši in sodelovalnega vrstniškega učenja. Analiza začetne ocene funkcioniranja skupine učencev s PPUA je pokazala, da so učenci od začetka osnovnošolskega izobraževanja izkazovali težave na področju razvoja številskih predstav, šibkejšega delovnega in semantičnega spomina, ki je oviral normalen priklic dejstev in postopkov, na področju predelovanja informacij (vizualno-spacialne primanjkljaje) ter konceptualnega znanja, ki se je izražalo v slabšem razumevanju pojmov in postopkov. Primerjava rezultatov pred in po treningu je pokazala, da so učenci s PPUA imeli v obeh primerih slabše razvito aritmetično proceduralno znanje, slabše avtomatizirana aritmetična dejstva in postopke, počasneje in manj fleksibilno so uporabljali aritmetična dejstva in postopke ter statistično manj natančno in redkeje so s pravilnimi strategijami reševali besedilne naloge, od skupine učencev brez PPUA. Največji razkorak v aritmetičnem proceduralnem znanju med skupinama smo opazili na področju številskih predstav, reševanja enačb in obvladovanja računskih operacij. Obe skupini učencev z in brez PPUA sta izboljšali svoje rezultate na področju avtomatizacije in fleksibilne uporabe aritmetičnih dejstev in postopkov, pri tem so učenci s PPUA povprečno veliko bolj napredovali od druge skupine, na področju reševanja besedilnih nalog pa smo minimalni napredek zasledili le pri skupini učencev s PPUA. Pet od osmih učencev s PPUA je po treningu popolnoma usvojilo 70 % ali več minimalnih standardov znanja, ostalih 30 % pa delno. Dva učenca nista niti delno usvojila vseh minimalnih standardov znanja. Učenci s PPUA so imeli največ težav z usvajanjem ciljev iz urejanja ulomkov, z računskimi operacijami z racionalnimi števili (še posebej neuspešni so bili v računski operaciji deljenja) in z reševanjem besedilnih nalog z racionalnimi števili in linearnimi enačbami. Rezultati analize izvajanja DSP, timskega poučevanja in vrstniškega sodelovalnega učenja so pokazali, da so učenci s PPUA bili z vso pomočjo zelo zadovoljni, da sta izvajalki timskega pouka največkrat izbrali alternativni tip timskega poučevanja in poučevanje v paru, redkeje pa pravo timsko poučevanje ter da ima timsko poučevanje veliko prednosti za učence in učitelje. Pričujoča raziskava je model obravnave učencev s PPUA, ki izkorišča vire, dosegljive v sistemu, kot jih predvideva model »odziv na obravnavo«. S pomočjo dobre poučevalne prakse učiteljice matematike pri pouku, intenzivne sistematične obravnave pri urah DSP, s timskim poučevanjem učiteljice matematike in izvajalke DSP, z drugo učno pomočjo (kot je dopolnilni pouk ter individualna in skupinska pomoč) in vrstniškim sodelovalnim učenjem so učenci dosegli napredek v aritmetičnem proceduralnem znanju. Ob tem pa se učenci s PPUA naučijo še samostojnosti, organiziranosti, krepijo čustveno stabilnost, dvigujejo samopodobo in izboljšujejo svoj položaj v družbi. Menimo, da je opisani trening primeren tudi za učence, ki imajo poleg specifičnih primanjkljajev na področju aritmetike še druge specifične težave, kot je pogosto disleksija, motnje pozornosti in koncentracije (pojav komorbidnosti) ter za učence s PPUA, ki prihajajo iz družin z nižjim socialno-ekonomskim statusom in nižjo izobrazbeno strukturo staršev. Izsledki te raziskave imajo veliko uporabno vrednost za pedagoško prakso na področju specialne in rehabilitacijske pedagogike in matematike. Izvedena celostna obravnava učencev s PPUA v tretjem triletju, je model intenzivnega treninga, ki ga v sodelovanju izvajajo specialni in rehabilitacijski pedagogi in učitelji matematike, pri tem pa še vključijo vrstnike.

Keywords

aritmetično proceduralno znanje;timsko poučevanje;dodatna strokovna pomoč;vrstniško sodelovalno učenje;primary education;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL PEF - Faculty of Education
Publisher: [B. Mlakar]
UDC: 376:373.3(043.2)
COBISS: 11176265 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Treatment of students with severe specific learning disabilities in arithmetic in the third term of elementary school
Secondary abstract: The results of the TIMSS 2011 research for Slovenia and the results of the annual National Assessment of Knowledge examinations in the nine-year primary education programme show the lowest mathematics achievement of pupils in Pomurje region. The results of the National Assessment of Knowledge examinations highlight two important facts. Firstly, that the results are strongly correlated with socio-economic factors of families and secondly, that the achievements in mathematics of children with special educational needs, significantly fall behind their peers. Slovenian primary school teachers have observed that pupils have a lot of problems with learning arithmetic, which means learning basic arithmetic operations, fractions, equations and expressions with variables. Pupils with learning disabilities in arithmetic (hereinafter referred to as LDA) often have arithmetic procedural problems, underdeveloped cognitive skills, weakly developed conceptual knowledge, poor memory, visual-spatial intelligence problems, poorly developed language skills, less well developed fine motor skills and attention-deficit disorders. Procedural knowledge is built throughout the years of education by automation of arithmetic facts and procedures, with exercise and mechanical drill or by direct learning strategies. Many pupils with LDA have problems with the automation of basic arithmetic operations, which are intensified in the last three-year period of elementary school, when they have to cope with complex arithmetic operations such as calculating with fractions and other rational numbers, as well as solving equations. The main purpose of working with pupils with LDA is to develop such methods and approaches that would compensate their learning difficulties if not completely eliminate them. This is also emphasized by the updated Maths curriculum, which states that the teaching methods and approaches of learning mathematics for pupils with special educational needs should be adapted accordingly. Teachers should use a different teaching approach and a different access to the technology as for the rest of the pupils. In the classroom we can help pupils with LDA by using the strategies of good teaching practice, the direct teaching approach of mathematics and cooperative (collaborative) learning forms of teaching and learning. This encourages pupils to involve in active learning, verbalization of problem solving, use of teaching aids and metacognition. Domestic and foreign authors recommend the implementation of the additional professional assistance for children with special needs within the class, using strategies of cooperative learning and teaching, as these pupils with LDA gain in the learning field, becoming more confident, while they develop social skills and strengthen relationships with their peers. The central aim of the research was to design, implement and analyse a training to improve the arithmetic procedural knowledge for a group of pupils with LDA, which was based on the implementation of the additional professional assistance, on the strategy of team teaching of the Maths teacher and the additional professional assistant, as well as on peer collaborative learning. The Maths teacher was teaching according to the methods of good teaching practices and together with the additional professional assistant, at least 20 lessons of team teaching in the 7th, 8th and 9th class were carried out, in which pupils with LDA were involved as well. The additional professional assistant carried out 20 or more individual assistance lessons, as well as assistance in pairs for each pupil with LDA, while these pupils were still involved in organized peer collaborative learning in the range of 10 lessons. The research is an example of a multiple case study with clinical teaching strategy. The sample included 8 pupils with LDA from the 7th, 8th and 9th grade and 39 peers without LDA from the same classes. In the research, a variety of measurement instruments were used to investigate arithmetic skills and the acquired learning objectives of arithmetic in accordance with the curriculum. Numerical results of the tests were presented in a tabular form including a comparison of results of both groups, pupils with LDA and pupils without LDA. The results were analysed using descriptive statistics or by testing the differences between the achievements of pupils with LDA and peers without LDA by t-test for independent samples, respectively. The achievements of pupils with LDA on set objectives of the curriculum were qualitatively interpreted. Furthermore, the implementation of additional professional assistance, team teaching, cooperation with parents and collaborative peer learning was evaluated. It is evident from the results of the initial diagnostic assessment that the group of pupils with LDA showed from the beginning of their education process difficulties of a weak representation of numbers and a poor working and semantic memory, which has hindered the normal retrieval of facts and processes. Additionally, visual-spatial deficits and poorly developed conceptual knowledge was present, which was reflected in a feeble understanding of the concepts and procedures. Comparing the results before and after training, demonstrated that pupils with LDA had in both cases worse arithmetic skills and less well automated arithmetical facts and procedures. They were slower and less flexible using arithmetical facts and procedures, and they were statistically less precise and they used the appropriate strategies for solving the arithmetic word problems less frequently. Representation of numbers, solving equations and arithmetic operations are the fields of arithmetic procedural knowledge, where the most evident differences between the groups before training were observed. Both groups of pupils have improved their results in the field of automation and flexible use of arithmetic facts and procedures; in average, the group with LDA has achieved higher progress than the other group. In the testing of arithmetic word problems only the pupils with LDA achieved a minimum progress. Five of eight pupils with LDA assimilated 70% or more minimum standards of knowledge after the training. Two pupils failed to assimilate the minimum standards entirely. Pupils with LDA mostly had difficulties with assimilating the objectives of the editing fractions, of arithmetic operations with rational numbers (the biggest setbacks were in arithmetic operations of division) and solving text tasks with rational numbers and equations. The results of the analysis of the implementation of additional professional assistance, team teaching and peer collaborative learning showed that pupils with LDA appreciated the assistance and the support of the training. The results also showed that the teachers in the collaborative lessons often chose an alternative teaching style or a pair teaching style, while an actual team teaching style had been used rarely. Another conclusion was that the team teaching methods have many benefits for pupils and teachers as well. The present study is a model of treatment of children with LDA exploiting the resources available in the system, as foreseen by the model "respond to treatment". With the strategies of good teaching practices of the Maths teacher in the classroom, intensive systematic treatment in the additional professional assistance lessons, team teaching of the Maths teacher and additional professional assistant and with other teaching lessons (such as remedial classes and individual and group support) and peer collaborative learning, pupils improve procedural knowledge in arithmetic. At the same time, pupils with LDA learn about independence, organization, they strengthen emotional stability, raise self-esteem and improve their position in society. We believe that the described training is also suitable for pupils who have beside specific deficits in arithmetic also other specific learning disabilities, as is dyslexia and disorders of attention and concentration (the phenomenon of co-morbidity), and for pupils with LDA who come from families with lower socio-economic status and lower educational levels of parents. The results of this research have a great practical value for the pedagogical practice in the field of special and rehabilitation pedagogy and mathematics. Conducted comprehensive treatment of pupils with LDA in the third period of elementary school is a model of intensive training by the cooperation between the special and rehabilitation educators and teachers of mathematics, while it included peers.
Secondary keywords: learning difficulty;arithmetic;učne težave;aritmetika;osnovnošolski pouk;
File type: application/pdf
Type (COBISS): Master's thesis
Thesis comment: Univ. Ljubljana, Pedagoška fak., Specialna in rehabilitacijska pedagogika
Pages: XIII, 239 str.
ID: 9171269