Browsing by Subject "mathematics"

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  • Lappas, Stefanos (Helsingin yliopisto, 2022)
    Rubio de Francia’s extrapolation theorem constitutes a powerful result in the theory of weighted norm inequalities, which is a subarea of Harmonic Analysis. It allows one to deduce an inequality (often but not necessarily: the boundedness of an operator) on all weighted Lp spaces with a range of p, by checking it just for one exponent p (but all relevant weights). The main goal of this dissertation is to show analogous methods for extrapolation of compactness. The dissertation consists of an introductory part and three research articles. Our frameworks are the weighted Lebesgue and weighted Morrey spaces. In the first article we provide extrapolation of compactness for linear operators on weighted Lebesgue spaces. Several generalizations of this result such as off-diagonal and limited range extrapolation of compactness are proved as well. In the second article a bilinear extension of the main result of the first article is considered. In addition, we discuss more general results which deal with multilinear operators. The final article extends the first one to the setting of weighted Morrey spaces. Regarding the applications of all articles, in a relatively soft way, our methods recover several recent results and also give some new ones about compactness of commutators of linear and bilinear singular integrals, fractional integrals and multipliers on weighted spaces.
  • Lindqvist, Jessica (Helsingin yliopisto, 2020)
    Homework is a part of the day-to-day activities in most schools. The use and benefits of homework is undergoing debate. Existing research in the field is limited and sometimes conflicting. The Finnish curriculum does not require homework to be used in teaching. Thus, it is the teacher who decides if, how and what kind of homework the pupils shall be assigned. Mathematics is a subject where homework is commonly used. It is therefore relevant to study how teachers think about homework within this particular subject and how the homework in use relates to the (social)constructivist view on learning that the current curriculum is largely based on. The aim of this study was to examine what kind of homework in mathematics primary school teachers assign and how they argue either in favor of or against homework in mathematics education. Focus was on effects that develop mathematics performance. In addition, the teachers’ views on the importance of parental involvement relating to homework in mathematics was studied. A questionnaire was sent to primary school teachers in three Swedish-speaking schools in the metropolitan area of Finland. The questionnaire included both multiple-choice and open-ended questions. 19 teachers responded. Both quantitative and qualitative data analysis was performed. A deductive methodological approach was applied. The study showed that the teachers view learning in a social-constructive manner. The type of homework assigned does not, however, reflect this. Focus is on repetitive mechanical assignments to be performed individually. For instance, assignments including problem-solving are in limited use, although many believe that such assignments, along with repetitive ones, support learning in mathematics. Homework that these teachers assign does not to any large extent require being done outside of school. This leads to the relevant question whether homework is used due to the insufficiency of time in school. Most of the teachers argued for the use of homework in mathematics by reference to the importance of repetition. A majority viewed parental involvement as important. Despite the fact that the curriculum stresses equality, only three respondents reflected upon the risk that parental involvement might lead to inequality. Homework club at school was most commonly viewed as the remedy against the absence of support at home. Most teachers showed an unproblematic attitude towards the use of homework in mathematics education.
  • Hannula, Sandra (Helsingin yliopisto, 2019)
    Research shows that motivation is an important part of mathematics learning. Without motivation to learn math, learning outcomes would be significantly worse. The purpose of the study is to find out what the motivation factors are during the mathematics lessons for grades five and six. Since previous studies also show that the teacher has a central role in creating and maintaining the motivation for mathematics, the teacher's significance for the motivation is also examined in this study. In the survey, 28 pupils from grade five and 24 pupils from grade six participated. In total, 52 pupils from three different schools in Itä-uusimaa participated. The material was collected during the spring of 2019. The survey is mainly quantitative where the material was collected through a questionnaire. The questionnaire consisted of two open questions, which were analyzed through qualitative content analysis. According to the results, the students were motivated during the mathematics lessons, they perceived mathematics as important and useful. The biggest motivating factor was the teacher's activity, where the students mentioned that a good mathematics teacher is kind, happy and helpful and has good subject and educational skills. A student with high internal goal orientation experiences the mathematics lessons as meaningful. High internal goal orientation was also associated with high values of one's own mathematical skills. The differences between the sexes and the grades were small.