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- Pettersson, Annika, 1966-
(author)
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Grafisk och algebraisk representation : Gymnasieelevers förståelse av linjära funktioner
- 2016
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Licentiate thesis (other academic/artistic)abstract
- This thesis concerns upper secondary students’ understanding of algebraic and graphic representation of linear functions. Components of the students’ concept images, so-called ‘concept elements’, were studied as a way to capture their understanding. Four aspects affect the graphical view of a linear function, namely the parameter k, the parameter m, the scale of the coordinate axes and the domain of the function. Concerning the scale of the coordinate axis, there is a need to distinguish between two kinds of slope. When the scale of x-axis is changed, the k-value of the function, the so-called analytic slope, is constant but the visual slope changes. The tasks were designed so that three aspects were held constant in each task and one was varied. The study is qualitative and consists of two sub- studies. In the first, six students worked with two tasks involving the parameters k and m in the dynamic software GeoGebra. In the second, eight students were interviewed about a task concerning functions with different domains. Both studies also involved a task concerning the aspect of slope in a non-homogeneous coordinate system (a system with different scales on the axes). The results indicate three main findings: Firstly, students displayed difficulties in distinguishing between analytic and visual slope. Secondly, the word ‘start value’ can lead to conceptual problems when there is no visible intercept between the graphical representation of the function and the y-axis. Thirdly, the students displayed almost no concept elements in relation to the domain of a function.
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| 2. |
- Szabo, Attila, 1965-
(author)
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Matematiska förmågors interaktion och det matematiska minnets roll vid lösning av matematiska problem
- 2013
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Licentiate thesis (other academic/artistic)abstract
- The thesis deals with the interaction of mathematical abilities and the mathematical memory's role in problem-solving. To examine those phenomena, I analyzed the expression of mathematical abilities for high achieving students from upper secondary school. The study shows that the mathematical memory accounts for a relatively small proportion of time of the problem-solving process and that the mathematical memory emerges mainly during the initial phase of the process. Although the mathematical memory accounts for a small percentage of the time of the problem-solving process, the mathematical memory has a decisive role for the choice of problem-solving methods, because the students choose their solution methods in the initial phase of their problem-solving activity. The study shows that the choice of problem-solving method has significant consequences for the students' problem-solving activity; if the chosen methods did not lead to the desired outcome, so the students found it very difficult to change their initially chosen problem-solving methods. The study also shows that students who use general problem-solving methods perform better than students who use numerical methods.
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| 3. |
- Sandow, Erika, 1978-
(author)
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On the road : Social aspects of commuting long distances to work
- 2011
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Doctoral thesis (other academic/artistic)abstract
- With its point of departure of increasing numbers of people being engaged in commuting, the aim of this thesis is to reveal prerequisites for and consequences of long-distance commuting in Sweden for the individual and his or her partner. Special attention has been given to prerequisites for long-distance commuting in sparsely populated areas, and to social consequences related to long-distance commuting in terms of gender differences in commuting patterns, earnings and separation. The thesis is based on four empirical studies, presented in different papers. Two studies draw on individual longitudinal register data on all Swedish long-distance commuters living with a partner. The other two focus on commuting behaviour in sparsely populated areas, one based on individual register data and the other on a survey. Long-distance commuting (>30 kilometres) has become an increasingly common mobility strategy among Swedish workers and their households. Results from the thesis show that 11 percent of Swedish workers are long-distance commuters and about half of them live in a relationship. Among these couples many are families with children, indicating the importance of social ties in households’ decisions on where to work and live. Most long-distance commuters are men, and it is also likely that long-distance commuters have a high education level and are employed in the private sector. For the majority, long-distance commuting gives higher earnings; however, men benefit economically more than women do. As long-distance commuting reduces available family time, the non-commuting spouse often takes on a larger share of household commitments. The thesis shows that men’s long-distance commuting may therefore serve to reproduce and reinforce traditional gender roles on the labour market and within households. On the other hand, women’s long-distance commuting can lead to more equalitarian relationships on the labour market and within households. For the majority of couples it seems as if long-distance commuting becomes more than a temporary mobility strategy, while for some couples it does not work out very well. Separation rates are found to be higher among long-distance commuters compared to other couples; especially the first years of commuting seem to be the most challenging. It is suggested that coping strategies are important to make the consequences of long-distance commuting easier to handle and adjust to in the daily life puzzle. For those unable to handle these consequences, long-distance commuting is not a sustainable mobility strategy and can even end a relationship. The extent of long-distance commuting is low in sparsely populated areas, and those who do long-distance commute are mainly men. Most people work and live within the same locality and do not accept longer commuting times than do those in densely populated areas. In this thesis it is argued that facilitating car commuting in the more sparsely populated areas of Sweden can be more economically and socially sustainable, for the individual commuters as well as for society, than encouraging commuting by public transportation.
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| 4. |
- Sidenvall, Johan, 1974-
(author)
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Att lära sig resonera : om elevers möjligheter att lära sig matematiska resonemang
- 2015
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Licentiate thesis (other academic/artistic)abstract
- Students only learn what they get the opportunity to learn. This means, for example, that students do not develop their reasoning- and problem solving competence unless teaching especially focuses on developing these competencies. Despite the fact that it has for the last 20 years been pointed out the need for a reform-oriented mathematics education, research still shows that in Sweden, as well as internationally, an over-emphasis are placed on rote learning and procedures, at the cost of promoting conceptual understanding. Mathematical understanding can be separated into procedural and conceptual understanding, where conceptual understanding can be connected to a reform oriented mathematics education. By developing a reasoning competence conceptual understanding can also be developed. This thesis, which deals with students’ opportunities to learn to reason mathematically, includes three studies (with data from Swedish upper secondary school, year ten and mathematics textbooks from twelve countries). These opportunities have been studied based on a textbook analysis and by studying students' work with textbook tasks during normal classroom work. Students’ opportunities to learn to reason mathematically have also been studied by examining the relationship between students' reasoning and their beliefs. An analytical framework (Lithner, 2008) has been used to categorise and analyse reasoning used in solving tasks and required to solve tasks.Results support previous research in that teaching and mathematics textbooks are not necessarily in harmony with reform-oriented mathematics teaching. And that students indicated beliefs of insecurity, personal- and subject expectations as well as intrinsic- and extrinsic motivation connects to not using mathematical reasoning when solving non-routine tasks. Most commonly students used other strategies than mathematical reasoning when solving textbook tasks. One common way to solve tasks was to be guided, in particular by another student. The results also showed that the students primarily worked with the simpler tasks in the textbook. These simpler tasks required mathematical reasoning more rarely than the more difficult tasks. The results also showed a negative relationship between a belief of insecurity and the use of mathematical reasoning. Furthermore, the results show that the distributions of tasks that require mathematical reasoning are relatively similar in the examined textbooks across five continents.Based on the results it is argued for a teaching based on sociomathematical norms that leads to an inquiry based teaching and textbooks that are more in harmony with a reform-oriented mathematics education.
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