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

Sammanfattning: 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.