The participation on work life and society, the opportunity of personal fulfillment and the solving of everyday tasks depend – among others – on peoples’ proficiencies in mathematics (European Commission, 2011; OECD, 2014a). These proficiencies assist people in making well-founded judgements and decisions and to behave appropriately in different situations (OECD, 2016). PISA (Programme for International Student Assessment), as well as other international studies, measures these proficiencies by focusing on the students’ achievement. Furthermore, according to the determinations of school achievement, theoretical frameworks and researches consider the development of students’ achievement as an interplay between factors on different levels (e.g. Guthrie, Wigfield & You, 2012; Hooper, Mullis & Martin, 2014; OECD, 2014a). Pointing out one of these theoretical frameworks, Schrader and Helmke (2015) developed a model to explain this interplay between individual and other determinants of school achievement. Within this model two different types of determinants are focused: individual motivational determinants – focusing also on emotional aspects like interest – and individual cognitive determinants which comprise self-concept and self-efficacy. These determinants are assumed to have an impact on the learning activities of students which influence the students’ school achievement at the output level. However, motivational and cognitive determinants are mainly influenced by the students’ background, family and school related factors. On the individual level findings reveal a significant effect of students’ attitudes towards mathematic achievement (Chen, Yeh & Hwang, 2013; Henderlong Corpus & Wormington, 2014; OECD, 2013). Analyses of students’ attitudes influencing the mathematic achievement offer more detailed insights into the determination of mathematic achievement and constitute the starting point for the presented research based on PISA 2012, using the data from two European countries (Germany and Denmark). In the international comparison of PISA 2012, which focus was on mathematic achievement, Germany (514 points) and Denmark (500 points) belong to the top fifteen performing countries worldwide and perform better than the OECD-average (494).

International researches have been conducted to portray the effect which different attitude variables have on mathematic achievement (Eccles, Adler & Meece, 1984; Marsh & Martin, 2011; OECD, 2013; Vecchione, Aessandri & Marsicano, 2014). In conclusion, most of these research findings reveal a considerable effect of emotional and motivational variables such as self-concept and self-efficacy towards mathematic achievement for Germany, Denmark and other countries. Apart from students’ attitudes as a relevant factor concerning mathematic achievement, findings from PISA 2012 outline differences in the mathematic achievement by controlling gender as well as the social and immigrant background: Both in Germany and in Denmark boys outperform girls and students with lower socio-economic status or with an immigration background achieve lower mathematic competences (OECD, 2013). Considering these findings, this paper focuses on a common consideration of these attitude variables by using a classification method. Against this backdrop, we focus the following research questions:

1. Can different types of students in Germany and Denmark be identified according to their attitudes towards mathematics?
2. How do different attitudes towards mathematics relate to mathematic achievement?
3. To what extent do the identified types of students relate to the mathematic achievement controlling for students’ background variables?

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