Our context is the teaching and learning of mathematics at university level in seven countries: the Czech Republic, Germany, Netherlands, Norway, Spain, the UK and Ukraine. Evidence shows that students’ learning is often of a procedural nature: students do not develop in-depth conceptual understandings through which they can relate mathematics to other disciplines and the world around them. Traditional forms of teaching reinforce 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, and in the labour market. This should be achieved through • clear principles of inquiry-based teaching-learning and associated models of practice; • teaching innovation in which lecturers 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 lecturers and their students in face to face or blended learning settings; • induction workshops and other meetings to professionalize lecturers to apply and promote inquiry-based teaching and learning in face to face and blended learning settings; • synthesis of models of inquiry-based practice that can be used to promote students’ conceptual of mathematics in STEM education. In all partner universities, project participants teach mathematics or statistics and seek to innovate in their practice. 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 lecturers 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 lecturers 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 lecturers 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 mathematics lecturers 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 both advantaged and disadvantaged learners; to recognise issues and problems which challenge teaching and learning and address them through collaborative inquiry-based exploration; as more lecturers and students are engaged in inquiry-based teaching-learning, we expect to see, locally, a change in lecturers' and students' recognition of alternative ways of teaching and learning mathematics this change of learning culture will become transnational when outcomes are disseminated, practices shared and principles communicated. Disseminating our results and good practice, we contribute to the modernisation of education at universities and to the improvement of professional competences of university lecturers and students across Europe thus addressing the initiative of The European Commission to “improve the interaction between research and teaching ensuring that teaching is based on state-of-the art knowledge and adequately recognised and that graduates have strong analytical and problem-solving skills."
PLATINUM stands for Partnership in Learning and Teaching IN University Mathematics. Partners are from 8 universities in 7 countries in the EU. Each university team consists of academics who teach mathematics or statistics. They are experts in these subjects. Just a few were mathematics educators who had training in didactics and pedagogy, the substance of expertise in teaching and learning (TL). The main aim of PLATINUM has been to improve learning and teaching of mathematics/statistics for the benefit of our students. In order to do this, we have focused on our own knowledge and expertise, shared experiences, studied theory and the wider literature, developed our TL practice and become more deeply aware of a range of relevant factors. Over the three years of the project, every member of each partner team has contributed, learned and developed their practice. Our chief theoretical perspective has been that of Inquiry-Based Learning and Teaching in Mathematics (IBME). This is based on belief and experience, and associated knowledge, that students learn mathematics more effectively when they engage deeply themselves, asking their own mathematical questions and exploring their own mathematical ideas while guided and informed by their teachers. This is in contrast with common approaches to teaching and learning mathematics in which teachers present rules, procedures, formulae and standard solutions which students (try to) commit to memory, possibly without a deep understanding of the concepts involved. Our approach to IBME has been through a theoretical model in three layers: a) inquiry-based mathematical learning and teaching with students; b) teachers’ inquiry into their own teaching practice through communities of inquiry with their colleagues c) critical alignment in developing their own practice while aligning with common practices in their professional community. This model has provided a framework for all activities within PLATINUM. It was new to many of our colleagues. Those familiar with the model presented and explained it as part of LT workshops. Each partner had to make sense of the model in their own context with their own professional team and with their own students. Communities of Inquiry, exploring together, designing activities (including tasks and teaching units), were essential to understanding and use of the model. We agreed to write narratives from our experience that would be a vehicle for sharing experience and developing practice across partnership teams. Through working together in PLATINUM, we came to know each other, to learn about colleagues’ expertise and experience, to gain insight into national expertise and the contexts which supported it. From working within our model/framework, we came to develop our own meanings for the theoretical terminology and explore these in our own practice. Each partnership team developed according to their original context, their own expertise, their relating of theory to everyday events, expanding their own visions and practices, comparing experience with other teams, building on the expertise of others. Over time we came to know each other’s strengths and learning needs, to respect our differential growth within PLATINUM, to form teams with different responsibilities. So, for example, one team had oversight of the development of tasks and teaching units; another took responsibility for professional development; yet another focused on mathematical modelling as a process for connecting with users of mathematics: engineers, scientists and technologists. These two sorts of teams formed the warp and weft (using a weaving metaphor) of our activity and development. The substance of this growth involved a developing sense of the meaning of inquiry in all its facets related to our knowledge and practice. We came to ‘know’ inquiry, not only as a theoretical idea but as ‘finger-tip’ knowledge in our actions and speech as we worked with students or with each other. This knowledge is built on experience from day to day in our design of teaching and its practice. It is the basis of where we are today as we continue with what we have learned over the three years. It is not finished of course; we continue in the style we have developed over these years; inquiry, in its several manifestations, has become a normal part of our practice. In our initial proposal to Erasmus+, we promised to produce a book in which each partner would write a case study to present aspects of their activity and learning over the years in PLATINUM. This book is now written and published, presenting all aspects of PLATINUM to our readers who can become informed and learn from our experiences. On our PLATINUM website we present a wealth of inquiry-based ideas and practical materials that interested practitioners may use in their own teaching and develop themselves along Platinum lines.