Inquiry in University Mathematics Teaching and Learning: The Platinum Project
Inquiry in University Mathematics Teaching and Learning: The Platinum Project
Contributor(s): Inés Gómez-Chacón (Editor), Reinhard Hochmuth (Editor), Barbara Jaworski (Editor), Josef Rebenda (Editor), Johanna Ruge (Editor), Stephanie Thomas (Editor)
Subject(s): Logic, Higher Education , Educational Psychology, Individual Psychology, Personality Psychology, Behaviorism, Methodology and research technology, Pedagogy
Published by: Masarykova univerzita nakladatelství
Keywords: Mathematics teaching and learning; PLATINUM project; IBME activities; spidercharts; creating teaching units; ICT use; student inquiry; thinking mathematically;
Summary/Abstract: The book presents developmental outcomes from an EU Erasmus+ project involving eight partner universities in seven countries in Europe. Its focus is the development of mathematics teaching and learning at university level to enhance the learning of mathematics by university students. Its theoretical focus is inquiry-based teaching and learning. It bases all activity on a three-layer model of inquiry: (1) Inquiry in mathematics and in the learning of mathematics in lecture, tutorial, seminar or workshop, involving students and teachers; (2) Inquiry in mathematics teaching involving teachers exploring and developing their own practices in teaching mathematics; (3) Inquiry as a research process, analysing data from layers (1) and (2) to advance knowledge inthe field. As required by the Erasmus+ programme, it defines Intellectual Outputs (IOs) that will develop in the project. PLATINUM has six IOs: The Inquiry-based developmental model; Inquiry communities in mathematics learning and teaching; Design of mathematics tasks and teaching units; Inquiry-based professional development activity; Modelling as an inquiry process; Evalutation of inquiry activity with students. The project has developed Inquiry Communities, in each of the partner groups, in which mathematicians and educators work together in supportive collegial ways to promote inquiry processes in mathematics learning and teaching. Through involving students in inquiry activities, PLATINUM aims to encourage students` own in-depth engagement with mathematics, so that they develop conceptual understandings which go beyond memorisation and the use of procedures. Indeed the eight partners together have formed an inquiry community, working together to achieve PLATINUM goals within the specific environments of their own institutions and cultures. Together we learn from what we are able to achieve with respect to both common goals and diverse environments, bringing a richness of experience and learning to this important area of education. Inquiry communities enable participants to address the tensions and issues that emerge in developmental processes and to recognise the critical nature of the developmental process. Through engaging in inquiry-based development, partners are enabled and motivated to design activities for their peers, and for newcomers to university teaching of mathematics, to encourage their participation in new forms of teaching, design of teaching, and activities for students. Such professional development design is an important outcome of PLATINUM. One important area of inquiry-based activity is that of “modelling” in mathematics. Partners have worked together across the project to investigate the nature of modelling activities and their use with students. Overall, the project evaluates its activity in these various parts to gain insights to the sucess of inquiry based teaching, learning and development as well as the issues and tensions that are faced in putting into practice its aims and goals.
- E-ISBN-13: 978-80-210-9983-8
- Page Count: 373
- Publication Year: 2021
- Language: English
Introduction
Introduction
(Introduction)
- Author(s):Reinhard Hochmuth, Barbara Jaworski, Inés Gómez-Chacón
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:1-4
- No. of Pages:4
- Keywords:University Mathematics teaching; IBME; PLATINUM;
- Summary/Abstract:Mathematical demands in university courses represent a considerable hurdle for many students and for quite a few this is known to lead to dropping out or changing studies. But even among students who successfully pass mathematics exams, there are many who do not achieve the intended teaching goals. Instead of a reflected understanding of mathematical concepts and their internal and external mathematical use, rote learning often dominates. Concepts such as complex numbers or derivatives of functions are technically mastered, which is certainly important, but meanings that go beyond this, for example, reasoning of properties or relationships, are not acquired. If one does not want to attribute these results one-sidedly to deficits in the students, such as a lack of talent or commitment, then one must question the dominant teaching and also the prevailing examination practices.
Conceptual Foundations of the PLATINUM Project
Conceptual Foundations of the PLATINUM Project
(Conceptual Foundations of the PLATINUM Project)
- Author(s):Reinhard Hochmuth, Barbara Jaworski, Inés Gómez-Chacón
- Language:English
- Subject(s):Higher Education , Pedagogy
- Page Range:7-27
- No. of Pages:21
- Keywords:University Mathematics; PLATINUM; Inquiry-Based Mathematics Education; redefining teaching;
- Summary/Abstract:This chapter addresses the conceptual background underpinning PLATINUM, a project in the EU Erasmus+ programme. PLATINUM focuses on teaching and learning in university mathematics and particularly on IBME, Inquiry-Based Mathematics Education, involving mathematics teaching and learning and their development through the use of inquiry-based processes.
Spidercharts: A Tool for Describing and Reflecting IBME Activities
Spidercharts: A Tool for Describing and Reflecting IBME Activities
(Spidercharts: A Tool for Describing and Reflecting IBME Activities)
- Author(s):Sarah Khellaf, Reinhard Hochmuth, Jana Peters, Johanna Ruge
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:29-48
- No. of Pages:20
- Keywords:Spidercharts; IBME activities; University Mathematics; Community of Inquiry; PLATINUM;
- Summary/Abstract:The main goal of PLATINUM was to strengthen IBME in university mathematics teaching within a collaborating network of European partner universities, which saw itself as a Community of Inquiry (CoI) (see Section 2.5). As the visions of IBME present among project partners as well as local conditions at the partner universities were very diverse, efforts were made to account for local specificities in the development and implementation of ideas and concepts of IBME|in accordance with the notion of CoI. In this process of community building, its diversity became a fruitful resource, which enriched interactions at jointly conducted workshops (cf., Chapter 7). A key factor for successful cooperation within the community was good project communication.
Students With Identified Needs and IBME
Students With Identified Needs and IBME
(Students With Identified Needs and IBME)
- Author(s):Lukáš Másilko, Clare Trott
- Language:English
- Subject(s):Higher Education , Educational Psychology, Individual Psychology, Personality Psychology, Behaviorism, Pedagogy
- Page Range:49-69
- No. of Pages:21
- Keywords:IBME; University Mathematics; students with identified needs; University students; tools in the learning process; learning difficulties;
- Summary/Abstract:In this chapter we will focus on students with identified needs and try to analyse the differences they may display when participating in inquiry-based mathematics education. Students in universities are diverse by their characteristics and it is difficult to comply with all their needs individually and on demand. Therefore, we will follow the social model of disability and its main idea emphasising the responsibility of educational institutions as the key factor in creating an inclusive learning environment (see Section 4.2). According to our own perspective as explained in Section 4.3 it is much easier to be prepared in advance to try to satisfy all the possible students' needs, preferences and requirements. In Section 4.6, we will introduce readers to the principles of Universal Design, a methodology to follow if one wants to create an inclusive learning environment that reaches the needs of as many learners as possible. However, it is necessary to know the specific needs of each student, and therefore the categorisation of the needs should rather help to and appropriate support, methods, forms and tools in the learning process" (Ceresnova, 2018, p. 16). Such typology of students with identified needs will be introduced in Section 4.4 and followed by a detailed study of students' differences when they undertake an inquiry within university mathematics courses (Section 4.5).
Origins and Implementation of the Project
Origins and Implementation of the Project
(Origins and Implementation of the Project)
- Author(s):Josef Rebenda, Yuriy Rogovchenko
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:73-92
- No. of Pages:20
- Keywords:PLATINUM project; IBME; Mathematics; mathematicians; educational projects; teaching and learning mathematics;
- Summary/Abstract:The main theme of the book about the PLATINUM project is inquiry-based mathematics education and, in general, inquiry as a form of exploration and discovery in the classroom. In this chapter, we inquire into the following important issue: How did it happen that the project became the reality? How did the project evolve and what was its impact on the individuals who worked together on the project? It is not very common to see mathematicians and mathematics educators collaborate productively in a large-scale joint educational project (see Mohn, 2018). Therefore, we would like to provide the reader with an honest insiders' account of what might bring mathematicians and mathematics educators to the collaboration in a joint project about teaching and learning mathematics. Our narrative might surprise those who believe that a project should always start with a concrete idea|for us it did not begin with an idea, our starting point was a heterogeneous group of university teachers and researchers interested in the collaboration in a project on university mathematics teaching. At the outset, let us briefly review the key characteristics of the PLATINUM project.
Creating Teaching Units for Student Inquiry
Creating Teaching Units for Student Inquiry
(Creating Teaching Units for Student Inquiry)
- Author(s):André Heck, Lukáš Másilko
- Language:English
- Subject(s):Higher Education , Educational Psychology, Cognitive Psychology, Pedagogy
- Page Range:93-126
- No. of Pages:34
- Keywords:Student inquiry; developing mathematical thinking; memorisation; reasonong; cognitive demands;
- Summary/Abstract:Tasks determine to a large extent how students develop mathematical thinking abilities and become fluent in applying mathematical methods and techniques. As Stein et al. (1996, p. 459) put it: \The mathematical tasks with which students become engaged determine not only what substance they learn but also how they come to think about, develop, use, and make sense of mathematics." They distinguish (p. 466) in mathematical tasks four increasing cognitive demands: (1) memorisation; (2) use of formulas, algorithms, or procedures without attention to concepts, understanding, or meaning; (3) use of formulas, algorithms, or procedures with connection to concepts, contexts, understanding, or meaning; and (4) \doing mathematics," including complex mathematical thinking and reasoning activities such as making and testing conjectures, framing problems, looking for patterns, and so on. Tasks at the highest level of cognitive demand are complex, possibly ill-structured, and require students to make strategic decisions, make connections between concepts and contexts, reason in a mathematical way, and explain their thinking. In other words, student are invited to work as a mathematician or as a professional using mathematics in her/his field.
Methods and Materials for Professional Development of Lecturers
Methods and Materials for Professional Development of Lecturers
(Methods and Materials for Professional Development of Lecturers)
- Author(s):Inés Gómez-Chacón, Reinhard Hochmuth, Svitlana Rogovchenko, Nataša Brouwer
- Language:English
- Subject(s):Higher Education , Educational Psychology, Methodology and research technology, Pedagogy
- Page Range:127-146
- No. of Pages:20
- Keywords:lecturers; professional development; IBME; PLATINUM; methods;
- Summary/Abstract:Traditional lecturing in universities is still a common teaching practice, although research has shown that lecturing on its own is often not sufficient and leads under the existing examination conditions to surface learning (Biggs, 2003; Freeman et al., 2014). In many science and engineering programs, mathematics is still learned mainly procedurally instead of having a purposeful balance between procedural and conceptual learning (Mason et al., 2010). Occasionally there is the belief that being able to teach mathematics is automatically acquired along with years of teaching (Chalmers & Gardiner, 2015) and the unsuccessful learning results are more or less the necessary consequence of untalented students. In the professional development programmes that are organised together for university lecturers from different disciplines, there is usually no specific focus on mathematics education at university level.
Mathematical Modelling and Inquiry-Based Mathematics Education
Mathematical Modelling and Inquiry-Based Mathematics Education
(Mathematical Modelling and Inquiry-Based Mathematics Education)
- Author(s):Mariia Astafieva, Yuriy Rogovchenko, Oksana Lytvyn, Paul Hernandez-Martinez, Zuzana Pátíková, Nataliia Morze, Josef Rebenda, Svitlana Rogovchenko
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:147-170
- No. of Pages:24
- Keywords:Mathematics education; University level education; Mathematical modeling; PLATINUM; IBME;
- Summary/Abstract:Mathematical modelling (MM) is a powerful tool used by scientists and engineers to solve important problems for humankind. MM opens many possibilities for inquiry and has been included in the PLATINUM project as one of the Intellectual Outputs, IO5 (see Chapter 5 for the complete list). We consider MM an important part of the teaching and learning process. We believe that helping to develop students' modelling competencies we equip them with a valuable understanding of practical and theoretical concepts, prepare them for a life-long learning, and form them as critical citizens.
Evaluation of Inquiry-Based Mathematics Education
Evaluation of Inquiry-Based Mathematics Education
(Evaluation of Inquiry-Based Mathematics Education)
- Author(s):Inés Gómez-Chacón, Nataša Brouwer, Paola Iannone, Maria Králová
- Language:English
- Subject(s):Higher Education , Evaluation research, Pedagogy
- Page Range:171-183
- No. of Pages:13
- Keywords:PLATINUM project; IBME; Inquiry-Based Mathematics Education; evaluation;
- Summary/Abstract:The PLATINUM project is a joint effort to develop an approach for teaching and learning mathematics at university level that will improve the balance between procedural and conceptual learning of mathematics and build a community of inquiry that will disseminate this approach across European universities. It promotes inquiry-based practices while encouraging collaboration across regional, European and international institutions. This chapter focuses on one of the main intellectual outputs on the project: \Guidelines and recommendations for quality assessment in Inquiry Based Learning environment" (IO6). One of the main goals of the project is not only to provide lecturers with the tools to implement inquiry-based practice, but to offer practical guidelines that enable them to independently monitor their progress in mastering Inquiry-Based Mathematics Education (IBME) methods and students' engagement with more efficient learning approaches (see Guideline Document available on the PLATINUM website).
Introduction to the Case Studies in PLATINUM
Introduction to the Case Studies in PLATINUM
(Introduction to the Case Studies in PLATINUM)
- Author(s):Barbara Jaworski
- Language:English
- Subject(s):Higher Education , Methodology and research technology, ICT Information and Communications Technologies, Pedagogy
- Page Range:187-196
- No. of Pages:10
- Keywords:PLATINUM project; teaching and learning matheatics; Univesity education; IBME; Use of Information and Communications Technology; Inquiry-Based Developmental Activity in University Mathematics;
- Summary/Abstract:PLATINUM is a project in which the main focus is the development of teaching and learning mathematics through an inquiry-based approach in which our students, through their own inquiry in mathematics, engage more deeply and develop more conceptual mathematical understandings. The project spans seven countries with partners in eight universities. In each of these universities the partner team has engaged with ideas about inquiry-based learning and teaching in mathematics and, in so doing, members have developed their own practices. In our submission to the EU Erasmus+ programme, we promised a book in which each partner would write a case study, from their inquiry community, in which they would discuss their learning and development through engagement with the six Intellectual Outputs of the project (see Chapters 2 and 5 and below). This chapter provides an introduction to these case studies and a brief perspective on the main elements of each case study.
Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience
Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience
(Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience)
- Author(s):Svitlana Rogovchenko, Yuriy Rogovchenko
- Language:English
- Subject(s):Higher Education , Educational Psychology, Cognitive Psychology, Pedagogy
- Page Range:197-214
- No. of Pages:18
- Keywords:thinking mathematically; inquiry; University of Agder; PLATINUM;
- Summary/Abstract:The University of Agder (UiA) is a public university located in the southern part of Norway on two campuses, one in a larger city of Kristiansand where the university administration and most faculties are situated and another in a smaller town of Grimstad, about 45 kilometres distant from the main campus. UiA is one of the youngest universities in Norway, yet its history dates back to 1839 when the Teacher Training School was established at Holt rectory. Being one of the major driving forces for the regional development, UiA is also internationally oriented; it contributes to many international projects in education and research as a leading organisation (as in PLATINUM) or as a partner. The university is the home to about 13,000 students and 890 academic staff. It is organised in six faculties: Faculty of Engineering and Science, Faculty of Fine Arts, Faculty of Health and Sport Sciences, Faculty of Humanities and Education, Faculty of Social Sciences, School of Business and Law and has a Teacher Education Unit.
Design and Implementation of an Inquiry-Based Mathematics Module for First-Year Students in Biomedical Sciences
Design and Implementation of an Inquiry-Based Mathematics Module for First-Year Students in Biomedical Sciences
(Design and Implementation of an Inquiry-Based Mathematics Module for First-Year Students in Biomedical Sciences)
- Author(s):André Heck, Marthe Schut, Nataša Brouwer
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:215-234
- No. of Pages:20
- Keywords:Biomedical Sciences; University education; inquiry-based mathematics module; IBME; Students' Mathematics Background;
- Summary/Abstract:How might you design and implement an inquiry-based basic mathematics module for first-year students in biomedical sciences? What mathematical content would you choose? What decisions would you have to make? What issues would you have to address? How would you gain insight into students' learning? In this chapter, these questions are addressed relating to a first semester module in the first year of the bachelor programme Biomedical Sciences at the University of Amsterdam, which started in the study year 2018-2019.
The First Experience With IBME at Masaryk University, Brno
The First Experience With IBME at Masaryk University, Brno
(The First Experience With IBME at Masaryk University, Brno)
- Author(s):Markéta Matulová, Maria Králová, Lukáš Másilko
- Language:English
- Subject(s):Higher Education , Pedagogy
- Page Range:235-252
- No. of Pages:18
- Keywords:Masaryk University; Brno; IBME; The Community of Inquiry at Masaryk University;
- Summary/Abstract:This study provides an insight into the emerging community of inquiry at Masaryk University in Brno, Czech Republic. First, we present the historical and institutional background that determines the conditions in which our teaching team operates. We briefly summarise the possible ways of professional development intended for academics at our university (except for pedagogy students preparing for the future career of primary or secondary school teachers). We believe that the relatively low institutional support of academics in this field dramatically influences the limited professional knowledge of didactics and pedagogy among our team members. Furthermore, we describe our community, which is characterised by considerable fragmentation|both in terms of courses taught and belonging to individual faculties and university workplaces. The physical distance between the buildings where our teachers work is also one of the limiting factors for the functioning of our community. Due to this fragmentation, it is also difficult to characterise the functioning of the community as a whole. Individual sub-teams differ in their approach to designing and implementing IBME tasks in teaching, monitoring, and evaluation. Therefore, we present three different examples of approaches to IBME education, which in our opinion, demonstrate this diversity. Their analysis is presented in three separate sections.
In Critical Alignment With IBME
In Critical Alignment With IBME
(In Critical Alignment With IBME)
- Author(s):Johanna Ruge, Reinhard Hochmuth, Sarah Khellaf, Jana Peters
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:253-272
- No. of Pages:20
- Keywords:IBME; Leibniz- University-Hannover-group; Community of inquiry; PLATINUM;
- Summary/Abstract:The aim of this contribution is to describe the professional growth of the Leibniz- University-Hannover-group (LUH-group). The four authors of this chapter are the core members of the LUH-group and belong to a working group in the mathematics education department of Leibniz University Hannover. In the beginning, a number of people from other departments were interested in joining the LUH-group, but either transferred to other universities (in Germany staff changes between universities are quite common), or didn't and the time to attend meetings on a regular basis. The LUH-group conducts research in the field of university mathematics education and, with regard to teaching, offers courses in mathematics education for prospective mathematics teachers at secondary school level. This means all LUH-group-members are mathematics education researchers as well as mathematics teacher educators. The reported professional growth is connected to our involvement in and reflection of a developmental research project called Leibniz-Prinzip (see Section 14.2).
Two Decades of Inquiry-Based Developmental Activity in University Mathematics
Two Decades of Inquiry-Based Developmental Activity in University Mathematics
(Two Decades of Inquiry-Based Developmental Activity in University Mathematics)
- Author(s):Barbara Jaworski, Stephanie Thomas, Paola Iannone
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:273-287
- No. of Pages:15
- Keywords:Inquiry-Based Developmental Activity in University Mathematics; PLATINUM project;
- Summary/Abstract:The authors of this chapter work at a Mathematics Education Centre (MEC) at Loughborough University (LU) in the UK. We teach mathematics and mathematics education and we do research in mathematics education. This case study discusses research and development activities in which the MEC has been engaged for over 15 years including inquiry-based activity which is now related to the PLATINUM project. Our learning from these has been important for our individual development in both research and teaching.
Teaching Inquiry-Oriented Mathematics: Establishing Support for Novice Lecturers
Teaching Inquiry-Oriented Mathematics: Establishing Support for Novice Lecturers
(Teaching Inquiry-Oriented Mathematics: Establishing Support for Novice Lecturers)
- Author(s):Inés Gómez-Chacón, Antonio Diaz-Cano, Juan-Antonio Infante, Adrian Riesco
- Language:English
- Subject(s):Higher Education , Pedagogy
- Page Range:289-306
- No. of Pages:18
- Keywords:PLATINUM project; Universidad Complutense de Madrid; Mathematics education; IBME; CoI at UCM; The Matrix Factorisation Inquiry Project;
- Summary/Abstract:The professional development of novice lecturers is considered to be of crucial importance in the PLATINUM project. In this chapter, we present what a group of lecturers at Universidad Complutense de Madrid (UCM) (mathematicians and mathematics education researchers), constituted as a Community of Inquiry (CoI), considers valuable for the development of the professional knowledge of mathematics lecturers. With this aim, the group has designed learning tasks and developed seminars within the framework of the PLATINUM Project. Referring to the three-layer model outlined in Chapter 2, this chapter describes the interaction between the second layer, inquiry into teaching mathematics (lecturers using inquiry to explore the design and implementation of tasks, problems, and activities in classrooms), and the third layer, inquiry into research for a professional development programme for mathematics lecturers, which takes the results in developing the teaching of mathematics in order to systematise advanced areas and professional development programs at the institutional level.
Development of a Community of Inquiry Based on Reflective Teaching
Development of a Community of Inquiry Based on Reflective Teaching
(Development of a Community of Inquiry Based on Reflective Teaching)
- Author(s):Josef Rebenda, Zuzana Pátíková, Gabriela Rebendova, Eva Sedláková, Hanna Demchenko
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:307-326
- No. of Pages:20
- Keywords:Community of Inquiry; Reflective teaching; Brno University of Technology; PLATINUM;
- Summary/Abstract:In this case study we give an overview of the development of a local Community of Inquiry (CoI) at Brno University of Technology (BUT) in Brno, the Czech Republic, during the implementation period of the PLATINUM project. The key word of this chapter is `development' and it concerns history, goals, achievements, challenges and lessons learned of the local CoI. Other important key phrases are `classroom observations' and `discussion' that contributed to the professional development of the local CoI members and their teaching practice significantly.
Experience in Implementing IBME at the Borys Grinchenko Kyiv University
Experience in Implementing IBME at the Borys Grinchenko Kyiv University
(Experience in Implementing IBME at the Borys Grinchenko Kyiv University)
- Author(s):Mariia Astafieva, Mariia Boiko, Oksana Hlushak, Oksana Lytvyn, Nataliia Morze
- Language:English
- Subject(s):Higher Education , Educational Psychology, Pedagogy
- Page Range:327-348
- No. of Pages:22
- Keywords:IBME; Borys Grinchenko Kyiv University; Mathematics; innovative pedagogy;
- Summary/Abstract:In recent years, Borys Grinchenko Kyiv University has faced the problem of low motivation of future students in choosing mathematics programmes, and in teaching| with the problem of involving students in active learning through the use of new methods of teaching mathematics. One of the ways to tackle these problems is the use of innovative pedagogy and educational technology by mathematics teachers, which stimulate students' motivation to study mathematics and their involvement in the learning process. This includes inquiry-based mathematics education (IBME). With this in mind, an educational community of mathematics teachers was created at the university to acquaint teachers with IBME and the peculiarities of its use. The purpose of creating such a community was: to acquaint teachers with the concept, types, and cyclic structure of inquiry; examples of use; discussion of the use of inquiry in the teaching and learning of mathematics at the university. Initially, theoretical problems were analysed, the experience of creating educational communities was studied as well as forms of their activities to attract university teachers to participate in the community.
Epilogue
Epilogue
(Epilogue)
- Author(s):Inés Gómez-Chacón, Barbara Jaworski, Reinhard Hochmuth
- Language:English
- Subject(s):Higher Education , Methodology and research technology, Pedagogy
- Page Range:351-354
- No. of Pages:4
- Keywords:PLATINUM project; IBME; Inquiry at University Level; Mathematics teaching and learning;
- Summary/Abstract:The production of this book is the last stage in a journey which 31 authors, belonging to the 8 university institutions, partners of the PLATINUM Project, have shared focusing on Inquiry-Based Mathematics Education (IBME). The journey has been a recurring metaphor in an attempt to illustrate the meaning of life. We find the term in the displacement from one territory to another, the walk that separates a departure from an arrival, as a space to give meaning to what has been lived. The metaphor of the journey thus becomes a commonplace worth analysing and so we wish to use it to synthesise the lessons learned from the production of this book. In the following paragraphs we will take a brief tour, like someone moving her finger to find herself on a map, to analyse this commonplace that we recognise as valuable for the university community in mathematics.