om det inte är dyskalkyli – vad är det då

277 Pages·2006·1.2 MB·Swedish

OM DET INTE ÄR DYSKALKYLI –
VAD ÄR DET DÅ?
En multimetodstudie av eleven i matematikproblem
ur ett longitudinellt perspektiv

Gunnar Sjöberg

Doktorsavhandling i Pedagogiskt arbete Nr 7
Provuppgifterna på omslaget är hämtad från det nationella provet i
matematik i årskurs 5 våren 1999.

© Gunnar Sjöberg 2006
ISSN 1650-8858.
ISBN 91-7264-047-2
Tryck: Arkitektkopia AB, UMEÅ.

Distribution: Institutionen för matematik, teknik och naturvetenskap,
Umeå universitet, 901 87 UMEÅ. Tel. [phone].
E-post: [email protected]
Sjöberg, Gunnar, 2006: Om det inte är dyskalkyli – vad är det då? En multimetodstudie
av eleven i matematikproblem ur ett longitudinellt perspektiv. (If it isn’t dyscalculia – then
what is it? A multi-method study of the pupil with mathematics problems from a longitudinal
perspective), Monograph. Language: Swedish, with a summary in English,

Department of Mathematics Technology and Science Education, Umeå
University, 901 87 Umeå, Sweden.

ISBN 91-7264-047-2 ISSN 1650-8858.

Abstract
One of the big problems of the Swedish nine-year compulsory school is the
large number of pupils who fail to achieve a satisfactory standard in
mathematics. One explanation that has been increasingly considered over the
last ten years is that the pupils have dyscalculia. Some research suggests that 6
per cent of compulsory school pupils suffer from this dysfunction, which
would in that case make it one of the Swedish school’s greatest teaching
problems.
The purpose of this thesis is to examine this problem area from two aspects.
First of all by examining the concept of dyscalculia by means of a review of the
literature from 1992 onwards. The second perspective has as its starting point a
case study where the purpose was to give a detailed picture of the pupil with
mathematics problems. The latter part of the study was carried out over a six-
year period when 200 pupils, 13 of them with particular mathematics problems,
were studied in detail.
A point of departure for the study was provided by a large database where as
much information as possible was collected about pupils from Year 5 of the
nine-year compulsory school to Year 2 of the three-year upper secondary
school. The pupils were asked to fill in regular questionnaires and classroom
observations were made of roughly 100 mathematics lessons, 40 of which were
recorded on video. Finally there were in-depth interviews of the 13 pupils on
two occasions, the final one being during Year 2 of the upper secondary
school.
The review of the research showed a series of dubious and indistinct
circumstances surrounding the dyscalculia concept, and also ambiguity with
regard to the diagnosis of dyscalculia. The conclusion of the review was that
the concept of dyscalculia ought at present to be used with great caution, or
perhaps not at all. Admittedly the review does not provide grounds for totally
dismissing the dyscalculia concept, but as long as it remains impossible to
determine the concept unambiguously, and I have not been able to do this in
the course of this study, there are no good scientific grounds for using the term
dyscalculia in practice.
The empirical study shows the complexity of the problem area. Both the causes
suggested by the pupils as the origin of the problem and the measures that
helped them to obtain their mathematics grades form a complex pattern. The
low work input of the pupils during mathematics lessons, an unsettled working
environment, large classes, problems of stress and anxiety prior to tests, and
obstructive gender patterns are among the causes suggested by the pupils as
explanations of the occurrence of the mathematics problems. Good teachers,
in other words teachers who can explain, set limits and give encouragement,
were a significant factor in reversing the downward trend. Positive experiences
of school changes, where the pupil felt that he or she could start again from the
beginning, were also mentioned as significant by several pupils. Collaboration
with fellow-pupils and the fact that the pupils themselves decided to get to
grips with the problems were other important reasons for the change. The
prospects of students with specific problems in mathematics nevertheless being
able to leave compulsory school with satisfactory grades appear, however, from
the results of this study, to be bright. All the pupils left the compulsory school
with satisfactory mathematics grades and also completed mathematics studies
at upper secondary school, despite major problems in the subject at
intermediate school (age 10-13) stage.
The study indicates the need for research closer to the actual practical situation
and to the importance of emphasizing good examples in practice. As the
students themselves emphasize discrete communication between them as
significant in the subject of mathematics, this is also an important area for
future research.

Key words: Mathematics learning, learning problems in mathematics, maths
anxiety, dyscalculia, special education, sociocultural theory, pupils’ work input,
school research, communication, gender.

Innehållsförteckning

FÖRORD................................................................................................7
1. INLEDNING.....................................................................................9
Eleven och forskningsområdet.......................................................................10
Min väg till forskningsområdet.......................................................................14
Forskningsområdet........................................................................................17
2. SYFTE...............................................................................................23
Avhandlingens avgränsningar, disposition samt begreppsprecision.................24
Arbetets begränsningar..............................................................................24
Avhandlingens disposition........................................................................25
Begreppsprecisering..................................................................................26
3. TEORETISKA PERSPEKTIV.......................................................27
Sociokulturellt perspektiv...............................................................................27
Genusperspektiv............................................................................................32
Kategoriskt eller relationellt perspektiv...........................................................36
4. METOD............................................................................................43
Distinktionen kvalitativ – kvantitativ forskning..............................................44
En induktiv etnografisk fallstudie med ett longitudinellt perspektiv................46
Influenser av grounded theory i projektet.......................................................49
GENOMFÖRANDE....................................................................................55
Fas ett: den grundläggande empiriinsamlingen...........................................55
De nationella proven som urvalsinstrument..........................................56
Årskurs 5-proven läsåret 1998-1999.................................................59
Första urvalssteget: kommun och skolområden....................................60
Fas två: fördjupad studie...........................................................................62
Andra urvalssteget: fyra högstadieskolor...............................................62
Projektskolor...................................................................................65
Tredje urvalssteget: eleven i problem....................................................68
Videoinspelningar och det fortsatta arbetet......................................70
Fas tre: analys och reflektion.....................................................................71
DATAINSAMLINGSMETODER...............................................................72
Databas.....................................................................................................72
Enkäter.....................................................................................................73
Klassrumsobservationer............................................................................75
Intervjuer och återkopplingsmöten............................................................77
Forskningsetiska överväganden.................................................................80
ANALYS AV EMPIRIN...............................................................................82
Databas (elevdokumentation och enkäter).................................................83
Klassrumsobservationer............................................................................84
Intervjuer och sammanställning av analysen..............................................86
5. RESULTAT......................................................................................91
FORSKNINGSÖVERSIKT AV DYSKALKYLIBEGREPPET...................92
Begreppet dyskalkyli..................................................................................93
Forskningsresultat om dyskalkyli...............................................................99
Central forskning om dyskalkyli..............................................................103
Hur diagnostiseras eleven i matematikproblem........................................104
Diskrepanskriteriet och IQ-begreppet.....................................................107
Alternativa förklaringar till inlärningsproblem i matematik......................108
Dyskalkyli – en huvudförklaring till problemen.......................................110
TRETTON ELEVER I MATEMATIKPROBLEM....................................113
Eleverna i matematikproblem – ingen homogen grupp............................113
Möt Statister...........................................................................................114
Stabila hemförhållanden och rik fritid.................................................115
Skolan viktig men tråkig och ointressant.............................................116
Matten inget favoritämne...................................................................119
Möt Fighters...........................................................................................122
Socialt oroligt.....................................................................................122
Tydliga visioner men låga ambitioner..................................................125
Låg arbetsinsats på matematiklektionerna...........................................128
Möt Kepselever.......................................................................................129
Praktiska killar med stabila hemförhållanden......................................130
Uppvaknande i matematik..................................................................131
Möt Askungen........................................................................................134
Att tappa greppet...............................................................................134
Engagerande och stöttande hemförhållanden.....................................135
En lyckad nystart................................................................................136
Matten är inte längre så viktig.............................................................138
Varför fick eleverna problem?.................................................................140
Arbetsinsats och tidsanvändning........................................................140
Stress och provångest.........................................................................147
Skillnader mellan 13-gruppen och jämförelsegruppen....................151
Provräkningar................................................................................152
De nationella proven.....................................................................157
Negativa möten med lärare.................................................................161
Elevernas undervisningsmiljö.............................................................164
Brist på arbetsro............................................................................164
Gruppstorlek.................................................................................168
Lektionslängd och innehåll.................................................................172
Kommunikationsmönster under matematiklektionen..........................176
Vändningen............................................................................................183
Studieresultaten..................................................................................183
Vad bidrog till vändningen i matematik?.............................................185
Eleven som hjälplärare – eleven som samarbetspartner.......................186
Att byta från mellanstadiet till högstadiet – ett sätt att börja om..........192
Att själv ta tag i problemet..................................................................193
Den stöttande läraren.........................................................................194
Tjejer och killar i matematikproblem.......................................................199
Genusaspekter som framträtt ur empirin............................................205
Att inte förlora ansiktet..................................................................205
Killars dominans – tjejers undfallenhet..........................................206
Tapetblommor - tjejer som knappt syns och hörs..........................213
Tjejer som sub-teachers.................................................................214
Mammans roll för eleven i problem...............................................216
6. SAMMANFATTANDE ANALYS OCH DISKUSSION............221
Huvudresultat..............................................................................................222
Rätten att beteckna eleven i matematikproblem.......................................222
Eleven i matematikproblem.....................................................................224
Orsaker till elevernas matematikproblem.................................................225
Vändningar.............................................................................................227
Genusaspekter och eleven i matematikproblem.......................................230
Metoddiskussion och resultatens värde........................................................231
Kvaliteter i framställningen som helhet...................................................233
Kvaliteter hos resultaten..........................................................................235
Validitetskriterier.....................................................................................236
Didaktiska implikationer..............................................................................239
Till sist.........................................................................................................240
SUMMARY.........................................................................................241
REFERENSER..................................................................................249
Bilaga 1.......................................................................................................271