Studies reveal a variation in the effects on education outcome from various social, political, and economical factors. The constant change makes it challenging to collect relevant data, and yet estimate a precise model which would still be applicable after a period of time. The PISA report of 2012 revealed that the Swedish students’ knowledge had dropped for the first time below the average for the OECD countries, starting a large debate regarding the explanations of the result. This paper empirically investigates, with the use of two-way fixed effects, the impact on the outcome variable average grade by the continuous variables per-pupil spending, educated teachers, amount of students per teacher, foreign students, and educated parents over the years from 2002 to 2013. The data used showed a presence of multicollinearity and heteroscedasticity, and robust standard errors were produced. The results show a negative coefficient effect on the education outcome by the per-pupil spending -0.00269 (0.001), and a positive coefficient effect by educated teachers 0.00066 (0.012) and educated parents 3.16903 (0.423). The continuous variables amount of students per teacher and foreign students were statistically insignificant. A yearly effect was present where the statistically significant values ranged from 0.11699:0.27475. A large share of the outcome proved to follow previous studies, whereas the deviants could partly be explained by structural changes in the Swedish schools, and grade inflation. The subjective nature of the outcome variable was however questioned as the schools’ themselves graded and reported the results. The paper provides a modern analysis of patterns for the Swedish students, municipalities, and interested to further investigate the underlying structure and problems.

Följande analys är baserad på en undersökning med 14 informanter och ämnar synliggöra vad svensklärare fokuserar på i sina bedömningar av elevtexter i svenskämnet i Stockholms gymnasieskolor. Resultatet visar att texternas kommunikativa kvaliteter och språkfunktion ges störst utrymme och mindre fokus ligger på språkformella aspekter. Det framkommer också att avancerade texter får mer precis bedömning medan sämre textkompositioner får mer generell. I uppsatsens analysavsnitt belyses dessa aspekter samt bedömningen av dem, hur de preciseras och formativt fungerar för elevens skriftspråksutveckling utifrån Lev Vygotskys teorier. Därefter diskuteras hur bedömningspraktiken påverkar undervisningen och vilka eventuella konsekvenser sådana tekniker kan förväntas ge. / The following analysis is based on a survey of 14 respondents and intends to make visible what Swedish teachers in the subject of Swedish focus on in their assessments of student texts, in Stockholm's upper high schools. The result shows that the communicative qualities of the texts and language functions are emphasized while the textual form, its linguistic correctness aspects, are given less focus. It also emerges that the advanced texts get more precise assessment, while poorer text compositions may be critiqued more generally. The essay’s analytical chapter confronts how these aspects are practiced, specified and utilized according to formative assessments based on Lev Vygotsky's theories. Then follows a discussion on how assessment practices affects teaching and what consequences one may expect from such an assessment culture.

Es ist eine weit verbreitete Wahrnehmung, dass der Übergang zwischen der Mathematik der gymnasialen Oberstufe und der Mathematik an der Universität für Studierende problematisch sein kann. Besondere Verständnisschwierigkeiten in Bereich der lineare Algebra (lA) bereiten den Studierenden die verschiedenen Herangehensweisen auf diesen beiden Ebenen. Dies lässt sich auf die strukturell-axiomatischer Herangehensweisen an die lA an der Universität, im Gegensatz zu ihrer arithmetisch-geometrischen Darstellung in der Schule, zurückführen. Dies bedingt ebenfalls Unterschiede im prozeduralen und konzeptuellen Verständnis. Ziel dieser Arbeit ist es, zu untersuchen, wie Schüler konzeptuelles Verständnis, Bezug nehmend auf die Theorien von concept definition/image in Verbindung mit multiplen Modi der Beschreibung und des Denkens von Konzepten wie Bilinearität z.B. Skalarprodukt und Multilinearität z.B. Determinanten gewinnen können. Um dies zu erreichen wurde eine substanzielle Lehr-Lernumgebung unter Verwendung einer dynamischen Geometriesoftware (DGS) entwickelt. Die Lerneinheit wurde an einem Berliner Gymnasium eingesetzt und dabei ein vollständiger design-based research Zyklus durchlaufen und eine multiple-level Datenanalyse durchgeführt. Die Ergebnisse der Untersuchung zeigen nicht nur, dass eine Erweiterung der Vorstellungen der Schüler, eine Entwicklung multipler Denkmodi und ein Gewinn tieferen konzeptuellen Verständnisses in der lA erfolgreich vermittelt werden können, sondern geben auch Einblicke in ein mögliches theoretisches Modell, mit dessen Hilfe sich diese Prozesse weiter untersuchen lassen. Weiterhin werden die interaktiven Lehr-Lernmaterialien für die weitere Verwendung im Rahmen von Lehre und Forschung zur Verfügung gestellt. Es öffnen sich neue Forschungsfragen hinsichtlich lokalen Axiomatisierens in der lA der gymnasialen Oberstufe, welches auf einer Integration geometrischer, algebraischer und axiomatischer Denkmodi, unterstützt durch DGS, basieren könnte. / A common perception among researchers in mathematics education is that the transition between secondary- and tertiary level of mathematics may be problematic for the students. In particular, the exact and abstract nature of the theory of Linear algebra versus its arithmetic-geometric presentation in school appears to be difficult for the novice students. The application of properties for defining concepts at university in contrast to their usage for describing concepts in school points out a possible occurrence of obstacles for learning and discrepancies in procedural and conceptual understanding. The aim of this study is to examine how could upper-high school students develop a conceptual understanding based on concept definition and concept image in connection to multiple modes of description and thinking about concepts such as bi-linearity exemplified by the dot product of vectors and multi-linearity exemplified by determinants. In order to achieve this, I have created a specific teaching/ learning sequence in a dynamic geometry environment (DGE), then implemented it and evaluated it in a high school in Berlin, following a complete cycle of design-based research and conducting a multiple-level data analysis. The findings of the study show not only that widening students' concept images, developing multiple modes of thinking and gaining deeper conceptual understanding can successfully be mediated by dynamic geometries, but also give insights into an eventual theoretical model of how can they be further examined. Moreover, the study promotes authorized open-source interactive teaching/ learning materials for further sustainable practice and research. It opens new research questions about revisiting axiomatic approaches on local levels in upper high-school Linear algebra which may base on the integration of all three modes of description and thinking geometric, algebraic and abstract possibly facilitated by DGE. / Честа перцепција кај многумина истражувачи во областа на математичкото образование е дека транзицијата помеѓу средното и високото образование по математика може да биде проблематична за студентите. Егзакноста и апстрактноста на теоријата по Линеарна алгебра наспроти нејзината аритметичко-геометриска презентација во средното гимназиско образование се покажува како особено тешка за студентите. Примена на својствата на математичките поими за нивно дефинирање на универзитетско ниво наспроти нивното употреба за опишување на претходно дефинирани поими на училишно ниво, укажува на можна појава на тешкотии при нивното изучување и несовпаѓање на процедуралното и концептуалното разбирање на истите. Целта на оваа студија е да истражи како средношколците би можеле да развијат концептуално разбирање на поимите врз основа на концепт дефиниција и концепт слика во врска со мулти-моди на мислење, конкретно за поими како билинеарност, пр. скаларен производ на вектори, и мултилинеарност, пр. детерминанти. За да ја постигнам оваа цел, креирав наставна содржина поддржана од еден динамичен геометриски систем (ДГС) и следејќи целосен циклус на т.н. design-based research и спрoведувајќи мулти-анализа на податоци, истата ја имплементирав и евалуирав во едно средно училиште во Берлин. Резултатите од студијата укажуваат не само на фактот дека проширувањето на концепт сликите на учениците, развојот на мулти-моди на мислење и стекнувањето на длабоко концептуално разбирање на поимите можат да бидат успешно посредувани од ДГС туку овозможија и увид во еден теоретски модел за тоа коко тие можат понатаму да се истражуваат. Уште повеќе, студијата промовира авторизирани open-source интерактивни материјали за предавање и учење на содржините кои може да служат за понатамошни одржливи истражувања и развој. Студијата отвора нови истражувачки прашања за средношколската Линеарна алгебра која може да се базира на интеграција на сите три моди на мислење, геометриски, алгебарски и апстрактен, поддржан од ДГС.