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In educational contexts, assessments may be designed to target students, preservice teachers, or teachers, either as individuals or as representatives of a group, and for a multitude of purposes. One key aim of assessment in mathematics education is to provide evidence that can be used to make decisions about or improve mathematics education, which then raises questions about which aspects of mathematical competence should be assessed-as well as how and for what purpose. This review paper addresses three related themes: (1) issues related to the assessment process and to the development of assessments that can validly assess mathematical competence in all its complexity; (2) issues related to educational policy and policy-making based on assessment data, in particular the reciprocal relationship between assessment and policy; and (3) issues related to equity, such as gender issues or the achievement gap between majority and minority students. Awareness of the relation between assessment, teaching, and learning is shown throughout the paper. Strong relationships between the three focus areas are found, that impact assessment validity and call for further development of assessment practices in mathematics education.

In this chapter, central ideas of Mixed Methods Research are presented in which qualitative and quantitative research methods are combined or integrated. In addition to the explanation of common Mixed Methods terminology, the chapter provides an overview of the most important aspects that must be reflected in the planning and conduction of a mixed-methodological research project. On the basis of considerations on the nature of the research object and specific conditions of mathematics education research, methodological aspects of the research question, research design and data analysis are described. The chapter concludes with considerations on the challenges of Mixed Methods, as well as recommendations on the step-by-step approach to a Mixed Methods Research project.

Zusammenfassung Pädagogisches und fachdidaktisches Wissen gelten als zentrale kognitive Elemente professioneller Kompetenz von Lehrkräften. Der Erwerb entsprechenden Wissens soll daher möglichst schon im Lehramtsstudium erfolgen. Wie allerdings pädagogisches Wissen und fachdidaktisches Wissen zueinander in Verbindung stehen bzw. voneinander abgegrenzt werden können, ist konzeptionell wie empirisch noch weitgehend ungeklärt. Vor diesem Hintergrund bearbeitet der vorliegende Beitrag mithilfe standardisierter Wissenstests und auf der Basis von 889

Contrary to the opinion that formative and summative assessment approaches are not compatible, this article presents a theoretically grounded way in which different forms of assessment can be combined and integrated in university mathematics teacher education. Two mixed-assessment approaches are demonstrated through the analysis of a case study involving a practice-based seminar accompanying a school internship. First, a formative eportfolio assessment was combined with a summative panel survey to assess the learning opportunities of mathematics pre-service teachers. Second, the formative eportfolio approach was integrated with a summative oral course examination to make statements about the learning processes and learning outcomes of the pre-service teachers. Our analyses conclude that combining and integrating the two forms of assessment present the possibility of evaluating different aspects of the pre-service teachers' perceptions of opportunities to learn. Benefits, validation aspects and limitations of the two approaches of combining and integrating assessment forms are discussed.

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In education, the ‘Nordic model’ refers to the similarities and shared aims of the education systems developed in the five Nordic countries—Denmark, Finland, Iceland, Sweden and Norway—after World War II. Traditionally, there have always been many similarities and links between the Nordic countries through their historical connections and geographical proximity. The common experience of solidarity and political oppression during World War II also created the basis for a common political orientation in the postwar period, which was also reflected in the education systems during the development of the countries’ economies and their establishment of welfare states. At the same time, this very process has been strongly supported by social-democratic governance in these countries in the 1960s and 1970s (Blossing, Imsen, & Moos, 2014). The model is based on a concept of Education for All, where equity, equal opportunities and inclusion are consistently cited as the goal of schooling and orientation (Blossing et al., 2014; Telhaug, Mediås, & Aasen, 2006). This corresponds to the egalitarian idea of a classless society, which is characterised by individual democratic participation, solidarity and mutual respect and appreciation for all. This idea was manifested in, for example, major reallocations of economic resources through the tax systems and free schooling for all, which arose out of the principle that parents’ lack of economic resources should not prevent children from obtaining a good quality education. The equalisation of structural inequalities and creation of equity was—and still is—the task of the education system in the Nordic countries. Worldwide, especially within the Nordic countries, the view is being shared that the education system should be fair and provide access and opportunities for further education, regardless of where someone lives, the status of the parental home, where someone comes from, what ethnic background someone has, what age or gender someone is, what skills one has or whether someone has physical disabilities (Blossing et al., 2014; Quaiser-Pohl, 2013). Some special features of the Nordic system are therefore deeply embedded in the school culture in the countries, for example, through the fact that access to free and public local schools and adapted education is statutory, which is in contrast to many other countries, even other European ones (further developed and discussed in Chap. 10.1007/978-3-030-61648-9_2). The Nordic model is widely considered a good example of educational systems that provide equal learning opportunities for all students. Achieving equity, here meaning the creation of fairness, is expressed concretely in political measures to distribute resources equally and strengthen the equality of marginalised groups by removing the barriers to seize educational opportunities, for example, when mixed-ability comprehensive schools are created or the educational system is made inclusive regarding students with special needs (UNESCO, 1994; Wiborg, 2009). Equality is roughly connoted with ‘sameness in treatment’ (Espinoza, 2007), while equity takes further in consideration also the question of how well the requirements of individual needs are met. Thus, the goal of equity is always linked to the concept of justice, provided that an equality of opportunities is created. If, however, one looks at individual educational policy decisions on the creation of educational justice in isolation, one must weigh which concept of equity or equality is present in each case. For example, it is not enough to formally grant equal rights in the education system to disadvantaged groups, but something must also be done actively to ensure that marginalised groups can use and realise this equality. The complexity of the terms becomes even greater when one considers that to achieve equality, measures can be taken that presuppose an unequal distribution of resources or unequal treatment and, therefore, are not fair e.g., when resources are bundled especially for disadvantaged groups and these are given preferential treatment (will be further developed and discussed in Chap. 10.1007/978-3-030-61648-9_2). Thus, equality and equity rely on each other and are in a field of tension comprising multiple ideas (Espinoza, 2007).