Our context is the teaching and learning of mathematics at university level in seven countries: the Czech Republic, Germany, Netherlands, Norway, Spain, Ukraine and the UK. Evidence shows that students’ learning is often of a procedural nature, so that students do not develop in-depth conceptual understandings through which they can relate mathematics to other disciplines and the world around them. Teaching using traditional forms and methods reinforces this status quo. We seek to improve teaching through inquiry-based approaches that allow students to achieve a more conceptually-based understanding of mathematics more appropriate for solving problems in engineering, science, labour market.

This should be achieved through

• clear principles of inquiry-based teaching-learning and associated models of practice;
• teaching innovation in which teachers engage in inquiry into their teaching practice and learn from critical reflection and feedback;
• observation and analysis of teaching events to provide evidence of outcomes for students;
• design of mathematical units and inquiry-based tasks for use by teachers and their students, whether on campus or at a distance;
• induction workshops and courses to introduce new or practising teachers to inquiry-based practices
• synthesis of models of inquiry-based practice that can be used to promote students’ conceptual learning of mathematics.

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