The Teaching and Assessment of Inquiry Competences

New competence-oriented learning goals can only be sustainably implemented if they are aligned with teaching and assessment goals. Within the fields of science, technology and mathematics education, one approach of competence-oriented teaching is based on the concept of inquiry-based education. Scientific inquiry in science, problem solving in mathematics, design processes in technology and innovation as a cross-curricular approach to teaching and learning that is emphasised as a key element of twenty-first-century skills allow students to engage in the thinking and working processes of scientists. By applying these approaches, teachers can address subject-specific as well as generic competences (e.g. investigation in science as a subject-specific competence vs. argumentation or communication as more generic competences). Since what is assessed strongly influences what is taught, changes in teaching need to be accompanied by changes in assessment in order to be sustainable. Teaching and learning goals need to be aligned, and assessment methods developed that allow for the assessment of competences related to scientific inquiry, mathematical problem solving or design and innovation processes. This chapter aims to provide a short overview about these inquiry-based approaches in the teaching and learning of science, technology, mathematics and innovation. Following a short introduction, the chapter consists of four subsections devoted to scientific inquiry, mathematical problem solving, design processes and innovation. Each subsection addresses three basic questions: (1) How is the construct defined and conceptualised? (2) How does teaching for inquiry change teaching? (3) What changes in assessment are necessary to assess inquiry competences