Nacionalno preverjanje znanja iz matematike pri učencih s primanjkljaji na posameznih področjih učenja : magistrsko delo

Kverh, Gabrijela (author), Kavkler, Marija (mentor), Vogrinc, Janez (comentor)

Preizkusi znanja matematike Nacionalnega preverjanja znanja (NPZ), Programa mednarodne primerjave dosežkov učencev (PISA) in Mednarodne raziskave trendov znanja matematike in naravoslovja (TIMSS) postajajo za vse učence, posebno pa še za učence s posebnimi potrebami (PP) in za učence s primanjkljaji pri učenju matematike (PUM), vse zahtevnejši. NPZ kot oblika zunanjega preverjanja znanja, ki ima preverjene merske karakteristike, pokaže močne in šibke točke učenja in poučevanja, ustreznost učnih načrtov, usposobljenost učiteljev in kvaliteto učbenikov. Dosežki učencev s PUM so na zunanjem preverjanju znanja matematike na prvi ali celo pod prvo ravnjo matematične pismenosti, kljub temu da jim je v osnovnih šolah po odločbi o usmeritvi nudena dodatna strokovna pomoč in učna pomoč in imajo pri pisanju NPZ številne prilagoditve. Učenci s PUM večinoma ne dosegajo druge ravni matematične pismenosti, ki bi jim omogočila nadgrajevanje znanja in uspešno delovanje v vsakdanjem življenju. Praviloma so uspešni pri nalogah, ki imajo enostavna navodila, preverjajo enostavne vsebine in zahtevajo rutinske postopke. Nekateri učenci s PUM, ki slabše pomnijo aritmetična dejstva in postopke, pa lahko uspešno rešujejo zahtevnejše problemske naloge, ki zahtevajo oblikovanje konceptov, posploševanje, lastno raziskovanje, vendar so njihove rešitve pogosto netočne. Skupina učencev s posebnimi potrebami (PP), ki imajo odločbo o usmeritvi, predstavlja 8,8 % populacije devetošolcev. Z raziskavo ugotavljamo, da je znotraj skupine učencev s PP kar 28,3 % učencev, ki imajo PUM, poleg PUM pa lahko tudi druge motnje, kot so motnje branja in pisanja (MBP), motnje pozornosti in koncentracije (MPK), govorno-jezikovne motnje (GJM), dispraksijo (DIS). Med učenci s PUM se najpogosteje pojavljajo motnje branja in pisanja, saj je teh učencev več kot tistih, ki imajo samo PUM. Četrtina učencev s PUM ima motnje pozornosti in koncentracije. Dispraksija in govorno-jezikovne motnje se v skupini učencev s PUM pojavljajo manj pogosto. Izkazano znanje učencev s PUM je kljub prilagoditvam, ki so jih le-ti deležni pri NPZ iz matematike (MAT) in slovenščine (SLO), pomembno nižje od znanja vrstnikov tako pri NPZ iz SLO kot tudi pri NPZ iz MAT na vseh taksonomskih ravneh. Povprečni rezultat na preizkusu NPZ iz MAT je pri teh učencih nižji tudi od povprečnega rezultata, ki so ga dosegli učenci iz skupine učencev s PP. Na osnovi primanjkljajev, ki jih imajo učenci s PUM, smo oblikovali šest skupin. Najštevilčnejšo skupino so predstavljali učenci, ki imajo samo PUM, v drugo skupino smo uvrstili učence, ki imajo poleg PUM tudi MBP, v tretjo učence, ki imajo poleg PUM tudi MPK, v četrto učence, ki so imeli poleg PUM oba primanjkljaja, tako MBP kot MPK, v peto učence, ki so imeli poleg PUM tudi DIS, in v šesto učence s PUM in GJM. Skupine učencev, ki smo jih oblikovali na osnovi njihovih primanjkljajev, so glede na dosežke pri NPZ iz MAT zelo heterogene, zato smo statistično pomembne razlike med skupinami potrdili le pri nalogah, ki preverjajo znanje računskih operacij in zaokroževanja, kjer statistično pomembno boljše rezultate dosegajo učenci, ki imajo poleg PUM tudi MPK, in učenci, ki imajo poleg PUM tudi GJM, najslabše pa učenci, ki imajo poleg PUM tudi MBP. Čeprav statistično pomembnih razlik pri ostalih testiranjih nismo mogli potrditi, se kaže tendenca, da najslabše rezultate pri nalogah I., II. in III. taksonomske ravni, pri večini nalog razdeljenih glede na vsebinska področja, kot so naloge računskih operacij in zaokroževanja, izrazov, uporabe formul, pretvarjanja količin, reševanja enačb in geometrijske naloge, pri nalogah, ki preverjajo znanje 5., 6., 7. in 8. razreda in pri nalogah, razdeljenih na območja zahtevnosti, dosegajo prav učenci, ki imajo poleg PUM tudi MBP. Učenci, ki imajo samo PUM, pa se uvrščajo takoj za njimi. Znanje MAT, ki so ga učenci, ki imajo samo PUM, izkazovali na NPZ iz MAT, ni na nobenem od omenjenih področij boljše od znanja učencev, ki imajo poleg PUM tudi druge omenjene primanjkljaje, kar kaže na napake pri diagnosticiranju učnih težav pri MAT. Med dosežki na NPZ iz SLO in MAT smo pri vseh skupinah učencev s PUM, ki so bile zajete v vzorec, ugotovili pozitivno zmerno povezanost. Motnje pozornosti in govorno-jezikovne motnje pomembno vplivajo na povezanost izkazanega znanja MAT in SLO, saj najmočnejšo povezanost rezultatov izkazujejo prav učenci, ki imajo PUM in MPK, in učenci, ki imajo PUM in GJM, kar je glede na naravo primanjkljajev teh dveh skupin učencev pričakovano. V skladu s pričakovanji smo ugotovili, da statistično pomembno boljše dosežke na NPZ iz MAT dosegajo učenci, ki imajo možnost uporabiti žepno računalo. Pri ostalih prilagoditvah statistično pomembnih razlik med učenci, ki so deležni prilagoditve, in tistimi, ki jih nimajo, nismo mogli potrditi. Žepno računalo omogoča učencem, ki imajo specifične aritmetične težave, da uspešneje izvajajo enostavne postopke računanja in pokažejo svoje znanje na višjih taksonomskih ravneh. Identificirali smo najpogostejše tipe napak pri aritmetičnih nalogah, reševanju enačb, geometrijskih nalogah in nalogah pretvarjanja količin, pri uporabi formul, pri reševanju in raziskovanju problemov in pri nalogah obdelave podatkov, ki jih učenci s PUM in drugimi omenjenimi primanjkljaji in motnjami delajo pri reševanju preizkusa NPZ iz MAT. Rečemo lahko, da večina teh učencev ne zna pisno deliti in zaokroževati števil, ne obvlada potenciranja in računanja z ulomki, ne zna reševati enačb, ne pozna sestavljenih formul, napake pa delajo tudi pri uporabi enostavnejših formul. Skoraj tretjina učencev ima težave z načrtovanjem ustrezne skice trikotnika, načrtovanjem kota ali višine, razlikovanjem polmera in premera. Učenci, ki smo jih zajeli v raziskavo, najslabše rešujejo naloge reševanja in raziskovanja problemov. Na osnovi primerjanja dosežkov učencev 6. in 9. razreda pri isti nalogi reševanja in raziskovanja problema lahko rečemo, da učenci, ki nimajo PUM, napredujejo v znanju reševanja in raziskovanja problemov iz 6. v 8. razred. Ta napredek je opazen samo pri manjšem številu učencev s PUM, ki izkazujejo specifične aritmetične težave in imajo možnost uporabe žepnega računala, pri ostalih učencih pa ne. Učence, ki imajo samo PUM, smo razdelili v dve skupini glede na odstotek točk, ki so ga dosegli na preizkusu NPZ iz MAT. Poleg kvantitativnih razlik v izkazanem znanju smo med skupinama ugotovili tudi kvalitativne razlike. Razlike se pojavljajo tako v številu kot tudi v vrsti napak, ki jih delajo pri reševanju preizkusa NPZ iz MAT, vrsti in deležu nalog, ki se jih ne lotevajo. Učenci s PUM, ki imajo nižje dosežke, kažejo napake pri reševanju vseh nalog, medtem ko so učenci iz skupine PUM, ki imajo višje dosežke in imajo tudi v večjem deležu možnost uporabe žepnega računala, uspešneje rešujejo naloge višjih taksonomskih ravni in v manjšem deležu puščajo naloge nerešene. Struktura znanja MAT je pri teh dveh skupinah učencev različna. Vse ugotovitve, do katerih smo prišli pri raziskavi, so skladne z izsledki stroke. Zbrani podatki in izpeljane ugotovitve so veljavne ter pomembne za slovenski prostor, saj so bili podatki zbrani skoraj na celotni populaciji učencev s PUM, ki imajo samo PUM ali pa poleg PUM tudi MPB, MPK, GJM in DIS. Opozorili bi na previdnost pri interpretaciji dosežkov skupine učencev s PUM in DIS, ker so podatki za to skupino učencev zbrani na majhnem vzorcu. Kljub temu da po podatkih mednarodnih raziskav PISA in TIMSS slovenski osnovnošolci dosegajo relativno dobre rezultate, saj se uvrščajo od 9. do 14. mesta, in da preizkusa NPZ in TIMSS približno enako odražata matematično znanje naših osnovnošolcev, z nizkimi povprečnimi dosežki pri NPZ iz MAT v populaciji vseh osnovnošolcev, posebno pa še v skupini učencev s PUM, ne moremo biti zadovoljni. Premalo se zavedamo, da sta poučevanje in učenje MAT vzajemna procesa, ki temeljita na kvalitetni učni pripravi, poznavanju vsakega učenca in uporabi veččutnih in procesnodidaktičnih pristopov. Učenci s PUM so skupina učencev, ki po intelektualnih sposobnostih ne odstopajo od vrstnikov, a imajo številne primanjkljaje na matematičnih, kognitivnih in metakognitivnih področjih, ki vplivajo na usvajanje znanja vsa leta šolanja na vseh taksonomskih ravneh, na vseh matematičnih področjih, tako pri enostavnih nalogah kot pri zahtevnejših, zato so glede na možnost, da izkažejo matematično znanje, najbolj ranljiva skupina učencev. Ti učenci pri izkazovanju matematičnega znanja, pa tudi znanja slovenščine, ne morejo dosegati primerljivih rezultatov z vrstniki. Proceduralno znanje MAT pri učencih s PUM kaže zaostanek v razvoju, primanjkljaji pri deklarativnem znanju pa so globlji in kažejo na razvojno drugačnost. Načrtovana, premišljena uporaba prilagoditve pri NPZ, kot je uporaba žepnega računala, daje učencem s PUM možnost, da izkažejo matematično znanje reševanja in raziskovanja problemov, ki je osnova matematične pismenosti.

• Language: Slovenian
• Keywords: nacionalno preverjanje znanja, primanjkljaji pri učenju, motnje pozornosti in koncentracije, motnje na področju branja in pisanja, govorno-jezikovne motnje, dispraksija, prilagoditve pri NPZ
• Work type: Master's thesis
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Publisher: [G. Kverh Žgur]
• Year: 2016
• Number of pages: XIII, 146 str., [15] str. pril.
• PID: 20.500.12556/RUL-85941
• UDC: 376: 37.091.26(043.2)
• COBISS.SI-ID: 11192137
• Publication date in RUL: 20.09.2017

Secondary language

• Language: English
• Title: National assesment in mathematics for pupils with specific leraning disabilities

Abstract

Exams in mathematics within the scope of National Assessment of Knowledge (NAK), Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) are becoming more and more demanding for all pupils, in particular for pupils with special needs (PP) and pupils with learning difficulties in mathematics (PUM). NAK as a form of external assessment of knowledge with verified measurement characteristics indicates strong and weak points of learning and teaching, adequacy of curricula, competence of teachers and quality of schoolbooks. Results of pupils with PUM achieved at the external assessment of knowledge are at the first or even below the first level of mathematical literacy, although, based on the decision of the placement of children with special needs, these pupils are provided additional professional and educational support in primary schools and they are entitled to several adaptations at sitting the NAK. Pupils with PUM mostly do not reach the second level of mathematical literacy that would enable them upgrading the knowledge and successful functioning in everyday life. They are usually more successful in completing the assignments with simple instructions and contents that require only routine procedures. Some pupils with PUM find it hard to remember arithmetic facts and procedures, but are successful in solving more demanding problem solving assignments that require concept formation, generalization and own research, however, their solutions are often incorrect. The group of pupils with special needs (PP) that have been approved special educational placement of children with special needs represents 8.8 % of the ninth graders. Our research proved that in the group of pupils with PP there are 28.3 % of pupils with PUM and even some other disabilities, such as reading and writing disabilities (MBP), disturbance in attention and concentration (MPK), speech and language disorders (GJM), or dyspraxia (DIS). Pupils with PUM that have also reading and writing disabilities outnumber the pupils with PUM only. A quarter of the pupils with PUM indicate also disturbance in attention and concentration. Dyspraxia and speech and language disorders are less common in the group of pupils with PUM. In spite of the adaptations that the pupils with PUM are entitled to at sitting the NAK in mathematics (MAT) and Slovene language (SLO), their knowledge is significantly lower than the knowledge of their peers in the NAK in Slovene language as well as the NAK in mathematics at all taxonomic levels. Average result of the NAK exam in mathematics of these pupils is also lower than the average result of the pupils with PP. Based on the learning difficulties of the pupils with PUM, six groups were formed. The largest group was the group of pupils with PUM only. In the second group were pupils with PUM and MBP, in the third group were pupils with PUM and MPK, in the fourth group were pupils with PUM, MBP and MPK, in the fifth group were pupils with PUM and DIS, and in the sixth group were pupils with PUM and GJM. The groups of pupils formed based on their learning difficulties are very heterogeneous as regards the results in the NAK in MAT. Therefore, statistically important differences between the groups were verified only in the assignments that test the knowledge of arithmetic operations and rounding where statistically significantly better results are achieved by the pupils that indicate MPK in addition to PUM, and the pupils that indicate GJM in addition to PUM, while the worst results are achieved by the pupils with MBP in addition to PUM. Although statistically significant differences in other tests could not have been verified, there is a tendency that the worst results in the assignments of the taxonomic levels I, II, and III, in most of the assignments divided as to their contents, such as arithmetic operations and rounding, expressions, use of formulas, quantity conversion, solving equations and geometry, in the assignments for testing the knowledge in 5th, 6th, 7th and 8th grade, and in the assignments divided as to the difficulty level are achieved by the pupils with MBP in addition to PUM and followed by the pupils with PUM only. Knowledge of MAT demonstrated in the NAK in MAT by the pupils with PUM only is worse than the knowledge of the pupils with other learning disabilities in addition to PUM in any of the aforementioned areas, which indicates errors in diagnosing learning difficulties in MAT. The results of NAK in SLJ and MAT of all groups of pupils with PUM included in the sample indicated moderate positive correlation. Disturbance in attention, and speech and language disorders have a significant impact on the correlation of the indicated knowledge of MAT and SLO as the strongest correlation of results is indicated by the pupils with PUM and MPK, and the pupils with PUM and GJM, which is expected due to the nature of the learning disabilities of these two groups of pupils. As expected, we have established that statistically significantly better results in NAK in MAT are achieved by the pupils that are allowed to use a calculator. We were unable to verify statistically significant differences between the pupils entitled to the adaptations and the pupils not entitled to the adaptations. Calculator enables pupils with specific arithmetic issues to carry out simple calculation procedures more effectively and to manage to demonstrate their knowledge at a higher taxonomic level. We have identified the most common types of errors in arithmetic operations, solving equations, geometry, quantity conversion, use of formulas, solving and research of problems, and data processing assignments made by the pupils with PUM and other aforementioned learning disabilities at sitting the NAK in MAT. We can conclude that most of these pupils is unable to divide by using written method, to round the numbers, lacks knowledge in involution and calculation with fractions, cannot solve equations, is not familiar with combined formulas and makes errors also in using simpler formulas. Almost one third of pupils have issues with making a sketch of triangle, projection of an angle or height, and distinguishing between radius and diameter. Results of the pupils included in the research are the worst in terms of solving the assignments of solving and researching of problems. Based on the comparison of the achievements of sixth graders and ninth graders in the same assignment of solving and researching a problem, we can conclude that pupils without PUM make progress in the knowledge of solving and researching of problems from the sixth to the eighth grade. This progress is noticed only with a smaller number of pupils with PUM that indicate specific arithmetic issues and are allowed to use the calculator, and not with the other pupils. Pupils with PUM only were divided into two groups based on the percentage of points reached during the NAK in MAT. In addition to quantitative differences in knowledge of the two groups, we have detected also qualitative differences. They are reflected in the number as well as in the type of errors made during the NAK in MAT, and the type and percentage of assignments that they do not tackle. The pupils with PUM that have achieved lower results made errors in all assignments, while the pupils with PUM that have achieved higher results and the majority of which is allowed to use the calculator are more successful in solving the assignments of higher taxonomic levels and leave less assignments completely empty or intact. The structure of knowledge of MAT is different in these two groups of pupils. All conclusions reached during this research are consistent with the findings of the profession. Collected data and conclusions made are valid and important for Slovenia as a whole as the data were collected by taking into account the entire population of pupils with PUM only or with MPB, MPK, GJM or DIS in addition to PUM. Attention must be paid in the interpretation of the achievements of the group of pupils with PUM and DIS as the data for this group of pupils was collected on a small sample. According to international research by PISA and TIMSS, Slovene primary school pupils achieve relatively good results as they rank from 9th to 14th place. Similarly, NAK and TIMSS exams reflect good mathematical knowledge of our primary school pupils. However, we cannot be satisfied with low average results in MAT in the population of all primary school pupils, in particular in the group of pupils with PUM. Teachers and special pedagogues are insufficiently qualified and engaged to provide the pupils the opportunity to acquire a high quality conceptual, declarative, procedural and problem knowledge, knowledge organization and integration, and remembering. We are insufficiently aware of the fact that teaching and learning of MAT are reciprocal processes based on a quality lesson plan, knowing of each individual pupil and the use of multi-sensory and process-didactic approaches. A group of pupils with PUM is a group of pupils that does not deviate from their peers in terms of their intellectual capabilities, but it is the most vulnerable group of pupils in terms of the opportunity to demonstrate the mathematical knowledge. Different cognitive and metacognitive disabilities and disabilities in acquiring mathematical knowledge prevent these pupils from achieving the results comparable to the results of their peers. Adaptations of NAK, such as planned and reasonable use of a calculator, give them the opportunity to prove their mathematical knowledge at higher taxonomic levels, which they are often unable to prove due to the problems they have with the calculation.

• Keywords: learning difficulty, mathematics, assessment, učne težave, vrednotenje