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Problemlösning i matematik : en studie av påverkansfaktorer i årskurserna 4-9. Bilaga 2 : elevernas lösningar av de olika problemen

Möllehed, Ebbe LU (2001) In Studia psychologica et paedagogica
Abstract
The purpose of this study is to identify the factors influencing pupils when they individually solve problems in mathematics in grades 4-9 in the compulsory school (ages: 10-16 years). The method that has been used is an analyses of the solutions of 25 problems given to each grade. Some of the problems were the same in all grades and about 100 pupils participated in each grade. Through an examination of the errors made by the pupils it has been possible to extract some abilities, which I have called factors, influencing problem solving. The factors have been indirectly described through categories of errors, made by the pupils. 16 factors have been identified, 9 factors belong to the cognitive development, 6 to the mathematical learning in... (More)
The purpose of this study is to identify the factors influencing pupils when they individually solve problems in mathematics in grades 4-9 in the compulsory school (ages: 10-16 years). The method that has been used is an analyses of the solutions of 25 problems given to each grade. Some of the problems were the same in all grades and about 100 pupils participated in each grade. Through an examination of the errors made by the pupils it has been possible to extract some abilities, which I have called factors, influencing problem solving. The factors have been indirectly described through categories of errors, made by the pupils. 16 factors have been identified, 9 factors belong to the cognitive development, 6 to the mathematical learning in school and one to an individual feature of carelessness. As a result of the extracted factors a model of problemsolving was built including all factors. Of all errors made by the pupils in all problems the cognitive factors contributed with about 60 %, the mathematical factors with 25 % and the individual factor with 15 %. This was valid in all grades. Comparisons between grades show that there is a great distribution of the pupils´ ability in problem solving. On an average 25 % of all pupils in grades 4 and 5 are able to solve a problem which 25 % of all pupils in grade 9 do not manage to work out. Comparisons between girls and boys have also been made concerning the proportion of correct answers in all problems. In grades 4 and 5 there are small differences but in grades 6-9 the boys have about 20 % more correct answers than the girls. (Less)
Abstract (Swedish)
Popular Abstract in Swedish

Syftet med studien är att bestämma de faktorer som påverkar eleverna då de löser matematiska problem i årskurserna 4-9 i grundskolan. Metoden, som använts, består i en analys av lösningarna till 25 problem, som getts i var och en av årskurserna. Några av problemen har varit desamma i alla årskurserna och ungefär 100 elever har deltagit i varje årskurs. Genom att undersöka de fel, som eleverna gjort, har det varit möjligt att bestämma ett antal förmågor, som jag kallat faktorer, vilka påverkar problemlösningen. Faktorerna har indirekt beskrivits genom kategorier av fel, som eleverna gjort. 16 faktorer har bestämts: 9 faktorer tillhör elevens kognitiva utveckling, 6 den matematiska inlärningen i... (More)
Popular Abstract in Swedish

Syftet med studien är att bestämma de faktorer som påverkar eleverna då de löser matematiska problem i årskurserna 4-9 i grundskolan. Metoden, som använts, består i en analys av lösningarna till 25 problem, som getts i var och en av årskurserna. Några av problemen har varit desamma i alla årskurserna och ungefär 100 elever har deltagit i varje årskurs. Genom att undersöka de fel, som eleverna gjort, har det varit möjligt att bestämma ett antal förmågor, som jag kallat faktorer, vilka påverkar problemlösningen. Faktorerna har indirekt beskrivits genom kategorier av fel, som eleverna gjort. 16 faktorer har bestämts: 9 faktorer tillhör elevens kognitiva utveckling, 6 den matematiska inlärningen i skolan och en faktor får tillskrivas ett personligt drag av slarv. Som ett resultat av de bestämda faktorerna har en modell för problemlösningen konstruerats, vilken innehåller alla faktorerna. Av alla fel, som gjorts av eleverna i alla faktorerna, har de kognitiva faktorerna bidragit med cirka 60 %, de matematiska med 25 % och den individuella faktorn med 15 %. Detta gäller i alla årskurserna. Som en följd av undersökningens uppläggning har vissa jämförelser gjorts: 1. Jämförelse mellan årskurserna visade att det är en stor spridning av elevernas problemlösningsförmåga. I medeltal kan 25 % av eleverna i årskurserna 4 och 5 lösa ett problem, som 25 % av eleverna i årskurs 9 misslyckas med. Det är endast 5 uppgifter som är gemensamma för alla årskurserna och som jämförelsen bygger på. Resultatet får närmast ses som en tendens och behöver kompletteras med nya och mer omfattande studier. 2. Jämförelse mellan problemlösningsförmågan hos flickor och pojkar har också gjorts med avseende på antalet korrekta svar i alla problemen. I årskurserna 4 och 5 är skillnaderna små men i årskurserna 6-9 har pojkarna omkring 20 % fler korrekta svar än flickorna. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Björkqvist, Ole, Åbo Akademi, Institutionen för lärarutbildning, Vasa
organization
alternative title
Problemsolving in mathematics. A study of factors influencing problemsolving in grades 4-9.
publishing date
type
Thesis
publication status
published
subject
keywords
age differences, Ability, cognitive ability, gender differences, grades 4-9, mathematics, Pedagogy and didactics, problem solving, Pedagogik, didaktik, Matematik
in
Studia psychologica et paedagogica
pages
200 pages
publisher
Tomas Hallström, Lärarhögskolan, S- 200 45 Malmö, Sweden , tel.: 040-6658365,
defense location
Lärarhögskolan, Malmö, sal E 126.
defense date
2001-09-24 10:15:00
external identifiers
  • other:ISRN: LUSDAG/ (SAPP-1082) 1-200 (2001)
ISSN
0346-5926
ISBN
91-88810-20-8
language
Swedish
LU publication?
yes
id
947e2c5b-416b-4a29-a286-04702d95e907 (old id 27772)
date added to LUP
2016-04-01 15:48:08
date last changed
2025-04-04 14:56:27
@phdthesis{947e2c5b-416b-4a29-a286-04702d95e907,
  abstract     = {{The purpose of this study is to identify the factors influencing pupils when they individually solve problems in mathematics in grades 4-9 in the compulsory school (ages: 10-16 years). The method that has been used is an analyses of the solutions of 25 problems given to each grade. Some of the problems were the same in all grades and about 100 pupils participated in each grade. Through an examination of the errors made by the pupils it has been possible to extract some abilities, which I have called factors, influencing problem solving. The factors have been indirectly described through categories of errors, made by the pupils. 16 factors have been identified, 9 factors belong to the cognitive development, 6 to the mathematical learning in school and one to an individual feature of carelessness. As a result of the extracted factors a model of problemsolving was built including all factors. Of all errors made by the pupils in all problems the cognitive factors contributed with about 60 %, the mathematical factors with 25 % and the individual factor with 15 %. This was valid in all grades. Comparisons between grades show that there is a great distribution of the pupils´ ability in problem solving. On an average 25 % of all pupils in grades 4 and 5 are able to solve a problem which 25 % of all pupils in grade 9 do not manage to work out. Comparisons between girls and boys have also been made concerning the proportion of correct answers in all problems. In grades 4 and 5 there are small differences but in grades 6-9 the boys have about 20 % more correct answers than the girls.}},
  author       = {{Möllehed, Ebbe}},
  isbn         = {{91-88810-20-8}},
  issn         = {{0346-5926}},
  keywords     = {{age differences; Ability; cognitive ability; gender differences; grades 4-9; mathematics; Pedagogy and didactics; problem solving; Pedagogik; didaktik; Matematik}},
  language     = {{swe}},
  publisher    = {{Tomas Hallström, Lärarhögskolan, S- 200 45 Malmö, Sweden , tel.: 040-6658365,}},
  school       = {{Lund University}},
  series       = {{Studia psychologica et paedagogica}},
  title        = {{Problemlösning i matematik : en studie av påverkansfaktorer i årskurserna 4-9. Bilaga 2 : elevernas lösningar av de olika problemen}},
  year         = {{2001}},
}