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. In all seven partner universities from seven countries, project participants teach mathematics or statistics and seek to innovate in their practice. This improves opportunities for students to learn mathematics. The partners are members of national and international consortia, through which practices are shared and innovations discussed, analysed, challenged and critiqued. Some have experience of mathematical unit and task design and blended learning approaches using IT and digital media. Some have experience of providing workshops and seminars to induct new teachers into effective teaching practices. Some are familiar with inquiry-based practices, having used them in their own developmental activity with their students. All partners are passionately committed to innovation and creativity in enhancing teaching practices for the benefit of students who learn mathematics conceptually, relationally and applicably. We will draw on our experiences and commitment to a) Communicate sound inquiry-based principles of teaching and learning of mathematics; b) Develop our own teaching, and that of our colleagues, through communities of inquiry in local settings; c) Design inquiry-based tasks and mathematical units using digital media for blended learning in providing resources for mathematics teaching and learning; d) Design induction workshops and seminars introducing teachers to inquiry-based practices in teaching and learning; e) Extend the model of inquiry-based learning to modelling activities which enable students to engage with real problems in industry and science. f) Design evaluator procedures and integrate evaluation into the activity itself, in order to gain a realistic view of what the project is achieving. The methodology will be developmental and inquiry-based. We employ a model of inquiry in three layers: 1) Inquiry in mathematics between teachers and students using specially designed inquiry-based tasks; 2) Inquiry into innovative approaches to teaching mathematics with reflective (critical) analyses of teaching practice and its impact on students’ conceptual understanding. 3) Inquiry as a developmental approach to improving practice in the other two layers, taking an objective approach to gathering and analysing data from the observed activity as well as feeding back what is learned to the ongoing practices. We expect to engage teachers of mathematics in our institutions and countries in inquiry-based teaching; to create a digital body of inquiry-based mathematics teaching materials for use across Europe, optimised for bot