The transition from secondary school into university mathematics – also referred to as secondary-tertiary transition (STT) – is a sensitive moment for many students, also for those who have achieved high marks at the end of their schooling and are considered excellent in mathematics in the school context. The cognitive aspect has interested researchers since the late seventies, but the interest in other two aspects (social and emotional aspects) is growing. Recently we have investigated the emotional aspect further and we will report here on some of our findings underlying the necessary developments

DI MARTINO, Pietro

Gregorio, Francesca

Paola, Iannone

English

Francesca Gregorio (7286888)

Pietro Di Martino (7282610)

Paola Iannone (2612890)

Loughborough University Institutional Repository

DiscussionEMS Newsletter September 2019 45The Secondary-Tertiary Transition in Mathematics Successful Students in CrisisFrancesca Gregorio (HEP Vaud, Lausanne, Switzerland and LDAR, Université Paris Diderot, France), Pietro Di Martino (Università di Pisa, Italy) and Paola Iannone (Loughborough University, UK)IntroductionThe transition from secondary school into university mathematics – also referred to as secondary-tertiary transition (STT) – is a sensitive moment for many stu-dents, also for those who have achieved high marks at the end of their schooling and are considered excellent in mathematics in the school context. For this reason, the EMS Education Committee iden-tified STT to be one major issue for mathematics depart-ments across Europe and their students, as explained in the last EMS newsletter (Koichu & Pinto, 2019). In order to shed some light onto this process and to sup-port mathematics departments in implementing appro-priate measures to help students overcome the difficul-ties connected to the move into university mathematics, the EMS has recently designed and distributed a survey for mathematicians across Europe. The EMS Education Committee’s interest reveals the concern of the math-ematics community for the experiences of students join-ing degree courses in mathematics and the will to under-stand this phenomenon in order to alleviate some of the problems connected to this transition. Indeed, the STT has been of interest to mathematics educators for a while now, and many empirical studies have been carried out to better understand all aspects of this transition. Gueudet (2008) highlights three aspects of this transition: a cog-nitive aspect, which focuses on the increased cognitive difficulties of university mathematics and its increased formalism and rigour (e.g. Tall, 1991); a social aspect, which focuses on the social changes that students face when moving to university, where they receive less sup-port than in school and where they often experience liv-ing away from their families for the first time (e.g. Pam-paka, Williams and Hutcheson, 2012); and an affective aspect, linked to the feelings and emotions that students experience during the STT. The first aspect – the cogni-tive one – has interested researchers since the late seven-ties, but the interest in the other two aspects is growing, as research reveals just how important social and emo-tional experiences are for students moving into univer-sity. Recently we have investigated the emotional aspect further and we will report here on some of our findings (Di Martino & Gregorio, 2018) underlying the necessary developments. The STT can be seen as a real rite of passage (Clark and Lovric, 2008) characterised by three stages: - separation stage (from secondary school – when stu-dents leave behind the context in which they have been successful mathematics learners),- liminal stage (from secondary school to university – where students join the new context, but they are still relative novices in the practices and norms of this new context) and - incorporation stage (when students become full par-ticipants of the practices of university mathematics). Each stage of this passage is often associated with a peri-od of crisis caused by the need to reorganise well-estab-lished mathematical routines and negotiate new methods of interaction with the subject, the peers and the instruc-tors in the new context. Difficulties in reaching the incor-poration stage of this passage may cause students to drop out from their courses.In line with a general movement in mathematics edu-cation, we have dedicated more attention to a holistic approach to the STT, focusing on the affective factors that shape this crisis and to this extent we developed a research study at the University of Pisa, in Italy (Di Martino & Gregorio, 2018). Students at this university are usually considered excellent in mathematics at the end of their schooling: more than 65% of the students in the first year of the bachelor in mathematics in Pisa achieve a final mark at secondary school between 90/100 and 100/100, but despite the high results these students face many difficulties during their bachelor’s degree, and more than 22% of them drop out at the end of the first year (in line with the average Italian dropout rates for the bachelor in mathematics).Our research was organised into two phases: the first phase consisted of the design and administration of a questionnaire, the second phase involved interviews with volunteering students. We included in the questionnaire and interviews both successful students and those who had dropped out of their course so that we could collect both experiences of success and failure. We chose mainly qualitative methods and open-ended questions in order to stimulate students to compose narratives related to facts and emotions that they themselves recognised as signifi-cant, using the words they consider more appropriate for their memories. Therefore, our research has been inten-tionally student-centred. As part of this study we collected and analysed 137 questionnaires and 37 interviews.Discussion46 EMS Newsletter September 2019of their year and the only one experiencing difficul-ties, with important consequences to their self-esteem. The same sense of shame often leads students to close within themselves and to avoid sharing their difficulties with peers and university teachers, an attitude which in turn precludes the possibility of improvement and isolates these students. Our data suggests this point is really important and the main difference in behaviour between dropout students and students who success-fully progress in their studies. Successful students man-age to overcome the isolation caused by early failures and difficult experiences, while students who drop out of their studies remain isolated until their situation is so unbearable that dropping out seems to them to be the only solution. Indeed, we see in our data that overcom-ing shame and sharing difficulties reduces the emotion-al charge experienced by the students, enabling them to perceive these difficulties as surmountable and to focus on the new cognitive demands of learning mathemat-ics at university level. Therefore, we believe that the university experience in mathematics requires a deep reconstruction of the students’ perception of mathemat-ics, of the disposition towards the subject, and of their perceived competences. Emotional factors should be taken into account to make the STT easier, for example by promoting reflection on the change in the context, on the acceptance of the difficulties and of a possible new mathematical identity.Our study is ongoing, and the next objective is to investigate the role of the higher educational context (and therefore also the role of cultural factors) in this transition. We have started to collect the data follow-ing the methodology of the Italian study in two other countries with very different higher educational sys-tems: Switzerland and the U.K. We ask in this new part of the study what the institutional features that facili-tate and hinder this transition are, whether the experi-ences of students in very different educational systems can be compared and whether these experiences have common features. BibliographyClark, M. & Lovric, M. (2008). Suggestion for a Theoretical Model for secondary-tertiary transition in mathematics. Mathematics Educa-tion Research Journal, 20(2), 25–37.Di Martino, P. & Gregorio, F. (2018). The mathematical crisis in second-ary-tertiary transition. International Journal of Science and Math-ematics Education, 17(4), pp 825–843.Gueudet, G. (2008). Investigating the secondary–tertiary transition. Ed-ucational Studies in Mathematics, 67(3), 237–254s.Koichu, B. & Pinto, A. (2019). The Secondary-Tertiary Transition in Mathematics. What are our current challenges and what can we do about them?. EMS Newsletter, 6(112), 34–35.Tall, D. (1991). Advanced Mathematical Thinking. Dordrecht: Kluwer.Pampaka, M., Williams, J., & Hutcheson, G. (2012). Measuring stu-dents’ transition into university and its association with learning outcomes. British Educational Research Journal, 38(6), 1041–1071. ResultsFrom the qualitative data collected emerges that stu-dents joining the bachelor in mathematics are generally high achievers and strongly motivated in their academic choice. Nevertheless, they often experience their first failure in mathematics. For the first time, some success-ful students have to come to terms with difficulties in establishing effective studying routines, obtaining poor marks for their work and not being the best in math-ematics amongst their peers. This is a big change for them, and they have to learn to manage this change from a cognitive as well as an emotional point of view.We are interested in describing and understanding this change. From our data, this shift is usually unex-pected, and this surprise makes students’ negative reac-tions even more powerful: their mathematical identity as a successful student is suddenly questioned. In most cases, students start associating negative emotions to their university experience and to mathematics; shame, anxiety, insecurity, sadness and frustration are the emo-tions more often mentioned in our data. Moreover, stu-dents begin to question their own self-image as math-ematicians: switching from feeling highly competent to feeling inadequate for the task can be a hard change. The university experience also elicits an awareness of the difference between secondary school mathematics and university mathematics, questioning the theories of success in mathematics developed during the school experience. Students recognise secondary school math-ematics as a procedural subject – that requires perform-ing calculations following standard steps – compared with university mathematics, a formal and abstract sub-ject that consists of definitions and theorems and deals for the most part with abstract objects. Most students like this new version of their subject, but they find it hard to come to terms with it at the start of their studies, where so many other aspects of their lives are changing. The big differences in teaching methods between secondary school and university do not help students in their STT; relatively small mathematics classes are replaced by large lectures where students may feel lost, and studying strategies which worked at school level suddenly become ineffective at university level. Stu-dents then become stuck in this first impression of fail-ure and they do not know how to change the situation. In addition, despite the increasing efforts made by the institution to help students during tertiary transition, some struggling students   believe  that they have to smoothly adapt to the new context and  materials. This attitude exacerbates the difference with the secondary school experience of mathematics. To sum up, students feel a sense of impotence, in the conviction that they cannot gain control of the situation of failure which then becomes unavoidable and unchangeable for them.Facing failure for the first time and the change of their perceived competence in mathematics makes stu-dents feel ashamed. Students become afraid of disap-pointing people close to them and are afraid of being compared to their peers. This attitude supports the mis-conception that students often have of being the worst DiscussionEMS Newsletter September 2019 47Francesca Gregorio [francesca.gregorio@hepl.ch] is a PhD student and teaching as-sistant at the HEP Vaud (Switzerland) and the lab LDAR of the Paris Diderot Univer-sity (France). Her research focuses are on STT transition and on mathematical learn-ing disorders. She is a teacher trainer for primary and secondary pre-service teachers.Pietro Di Martino [pietro.dimartino@unipi.it] is an associate professor in mathematics education at the University of Pisa (Italy). He is the president of the Italian Commit-tee for Mathematics Teaching (CIIM). His main research interests concern the role of the affective factors in the processes of mathematics teaching and learning, the difficulties in the STT transition and the main aspects involved in problem solving at the primary school level.Paola Iannone [p.iannone@lboro.ac.uk] is senior lecturer in mathematics education at Loughborough University (UK). Her main research interests concern mathemati-cal reasoning and students’ proof produc-tion, students’ note-taking habits at univer-sity level and the summative assessment of mathematics at university. EPFL is an equal opportunity employer and family friendly university. It is committed to increasing the diversity of its faculty.  It strongly encourages women to apply.The School of Basic Sciences (Physics, Chemistry and Mathematics) at EPFL seeks to appoint a Tenure-Track Assistant Professor of Math-ematics.  We seek outstanding candidates with research interests in analysis and/or geometry, broadly construed. Areas of interest include differential geometry, dynamical systems, geometric analysis, geo-metric flows, kinetic theory, multiscale analysis and homogenization, (stochastic) PDE.We expect candidates to establish leadership and strengthen the EPFL’s profile in the field. Priority will be given to the overall originality and promise of the candidate’s work over any particular specialization area.Candidates should hold a PhD and have an excellent record of scientif-ic accomplishments in the field. In addition, commitment to teaching at the undergraduate, master and doctoral levels is expected.  Profi-ciency in French teaching is not required, but willingness to learn the language expected. EPFL, with its main campus located in Lausanne, Switzerland, on the shores of lake Geneva, is a dynamically growing and well-funded in-stitution fostering excellence and diversity. It has a highly international campus with first-class infrastructure, including high performance computing.As a technical university covering essentially the entire palette of en-gineering and science, EPFL offers a fertile environment for research cooperation between different disciplines. The EPFL environment is multi-lingual and multi-cultural, with English often serving as a com-mon interface. Applications should include a cover letter, a CV with a list of publica-tions, a concise statement of research (maximum 3 pages) and teach-ing interests (one page), and the names and addresses (including e-mail) of at least three references. Applications should be uploaded (as PDFs) by November 1st, 2019 to: https://facultyrecruiting.epfl.ch/position/18186242 Enquiries may be addressed to: Prof. Victor Panaretos Chair of the Search Committee E-mail: mathematics2019@epfl.chFor additional information, please consult www.epfl.ch, sb.epfl.ch, math.epfl.chat the Ecole polytechnique fédérale  de Lausanne (EPFL)Faculty Position  in MathematicsNew book published by theEighteen Essays in Non-Euclidean Geometry (IRMA Lectures in Mathematics and Theo-retical Physics Vol. 29)Vincent Alberge (Fordham University, Bronx, USA) and Athanase Papadopoulos (Université de Strasbourg, France), EditorsISBN 978-3-03719-196-5. 2019.  475 p. Hardcover. 17 x 24 cm. 78.00 EuroThis book consists of a series of self-con-tained essays in non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyper-bolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski, Hermitian geometries, and some axiomatically defined geometries. Some of these essays deal with very classical questions and others address problems that are at the heart of present day research, but all of them are concerned with fundamental topics.All the essays are self-contained and most of them can be understood by the general educated mathematician. They should be useful to researchers and to students of non-Euclidean geometry, and they are intended to be references for the various topics they present.European Mathematical Society Publishing HouseTU Berlin, Mathematikgebäude, Room MA266Straße des 17. Juni 136, 10623 Berlin, Germanysubscriptions@ems-ph.org / www.ems-ph.org

The secondary-tertiary transition in mathematics: Successful students in crisis

Francesca Gregorio

Pietro Di Martino

Iannone, Paola

Archivio della Ricerca - Università di Pisa

DiscussionEMS Newsletter September 2019 45The Secondary-Tertiary Transition in Mathematics Successful Students in CrisisFrancesca Gregorio (HEP Vaud, Lausanne, Switzerland and LDAR, Université Paris Diderot, France), Pietro Di Martino (Università di Pisa, Italy) and Paola Iannone (Loughborough University, UK)IntroductionThe transition from secondary school into university mathematics – also referred to as secondary-tertiary transition (STT) – is a sensitive moment for many stu-dents, also for those who have achieved high marks at the end of their schooling and are considered excellent in mathematics in the school context. For this reason, the EMS Education Committee iden-tified STT to be one major issue for mathematics depart-ments across Europe and their students, as explained in the last EMS newsletter (Koichu & Pinto, 2019). In order to shed some light onto this process and to sup-port mathematics departments in implementing appro-priate measures to help students overcome the difficul-ties connected to the move into university mathematics, the EMS has recently designed and distributed a survey for mathematicians across Europe. The EMS Education Committee’s interest reveals the concern of the math-ematics community for the experiences of students join-ing degree courses in mathematics and the will to under-stand this phenomenon in order to alleviate some of the problems connected to this transition. Indeed, the STT has been of interest to mathematics educators for a while now, and many empirical studies have been carried out to better understand all aspects of this transition. Gueudet (2008) highlights three aspects of this transition: a cog-nitive aspect, which focuses on the increased cognitive difficulties of university mathematics and its increased formalism and rigour (e.g. Tall, 1991); a social aspect, which focuses on the social changes that students face when moving to university, where they receive less sup-port than in school and where they often experience liv-ing away from their families for the first time (e.g. Pam-paka, Williams and Hutcheson, 2012); and an affective aspect, linked to the feelings and emotions that students experience during the STT. The first aspect – the cogni-tive one – has interested researchers since the late seven-ties, but the interest in the other two aspects is growing, as research reveals just how important social and emo-tional experiences are for students moving into univer-sity. Recently we have investigated the emotional aspect further and we will report here on some of our findings (Di Martino & Gregorio, 2018) underlying the necessary developments. The STT can be seen as a real rite of passage (Clark and Lovric, 2008) characterised by three stages: - separation stage (from secondary school – when stu-dents leave behind the context in which they have been successful mathematics learners),- liminal stage (from secondary school to university – where students join the new context, but they are still relative novices in the practices and norms of this new context) and - incorporation stage (when students become full par-ticipants of the practices of university mathematics). Each stage of this passage is often associated with a peri-od of crisis caused by the need to reorganise well-estab-lished mathematical routines and negotiate new methods of interaction with the subject, the peers and the instruc-tors in the new context. Difficulties in reaching the incor-poration stage of this passage may cause students to drop out from their courses.In line with a general movement in mathematics edu-cation, we have dedicated more attention to a holistic approach to the STT, focusing on the affective factors that shape this crisis and to this extent we developed a research study at the University of Pisa, in Italy (Di Martino & Gregorio, 2018). Students at this university are usually considered excellent in mathematics at the end of their schooling: more than 65% of the students in the first year of the bachelor in mathematics in Pisa achieve a final mark at secondary school between 90/100 and 100/100, but despite the high results these students face many difficulties during their bachelor’s degree, and more than 22% of them drop out at the end of the first year (in line with the average Italian dropout rates for the bachelor in mathematics).Our research was organised into two phases: the first phase consisted of the design and administration of a questionnaire, the second phase involved interviews with volunteering students. We included in the questionnaire and interviews both successful students and those who had dropped out of their course so that we could collect both experiences of success and failure. We chose mainly qualitative methods and open-ended questions in order to stimulate students to compose narratives related to facts and emotions that they themselves recognised as signifi-cant, using the words they consider more appropriate for their memories. Therefore, our research has been inten-tionally student-centred. As part of this study we collected and analysed 137 questionnaires and 37 interviews.Discussion46 EMS Newsletter September 2019of their year and the only one experiencing difficul-ties, with important consequences to their self-esteem. The same sense of shame often leads students to close within themselves and to avoid sharing their difficulties with peers and university teachers, an attitude which in turn precludes the possibility of improvement and isolates these students. Our data suggests this point is really important and the main difference in behaviour between dropout students and students who success-fully progress in their studies. Successful students man-age to overcome the isolation caused by early failures and difficult experiences, while students who drop out of their studies remain isolated until their situation is so unbearable that dropping out seems to them to be the only solution. Indeed, we see in our data that overcom-ing shame and sharing difficulties reduces the emotion-al charge experienced by the students, enabling them to perceive these difficulties as surmountable and to focus on the new cognitive demands of learning mathemat-ics at university level. Therefore, we believe that the university experience in mathematics requires a deep reconstruction of the students’ perception of mathemat-ics, of the disposition towards the subject, and of their perceived competences. Emotional factors should be taken into account to make the STT easier, for example by promoting reflection on the change in the context, on the acceptance of the difficulties and of a possible new mathematical identity.Our study is ongoing, and the next objective is to investigate the role of the higher educational context (and therefore also the role of cultural factors) in this transition. We have started to collect the data follow-ing the methodology of the Italian study in two other countries with very different higher educational sys-tems: Switzerland and the U.K. We ask in this new part of the study what the institutional features that facili-tate and hinder this transition are, whether the experi-ences of students in very different educational systems can be compared and whether these experiences have common features. BibliographyClark, M. & Lovric, M. (2008). Suggestion for a Theoretical Model for secondary-tertiary transition in mathematics. Mathematics Educa-tion Research Journal, 20(2), 25–37.Di Martino, P. & Gregorio, F. (2018). The mathematical crisis in second-ary-tertiary transition. International Journal of Science and Math-ematics Education, 17(4), pp 825–843.Gueudet, G. (2008). Investigating the secondary–tertiary transition. Ed-ucational Studies in Mathematics, 67(3), 237–254s.Koichu, B. & Pinto, A. (2019). The Secondary-Tertiary Transition in Mathematics. What are our current challenges and what can we do about them?. EMS Newsletter, 6(112), 34–35.Tall, D. (1991). Advanced Mathematical Thinking. Dordrecht: Kluwer.Pampaka, M., Williams, J., & Hutcheson, G. (2012). Measuring stu-dents’ transition into university and its association with learning outcomes. British Educational Research Journal, 38(6), 1041–1071. ResultsFrom the qualitative data collected emerges that stu-dents joining the bachelor in mathematics are generally high achievers and strongly motivated in their academic choice. Nevertheless, they often experience their first failure in mathematics. For the first time, some success-ful students have to come to terms with difficulties in establishing effective studying routines, obtaining poor marks for their work and not being the best in math-ematics amongst their peers. This is a big change for them, and they have to learn to manage this change from a cognitive as well as an emotional point of view.We are interested in describing and understanding this change. From our data, this shift is usually unex-pected, and this surprise makes students’ negative reac-tions even more powerful: their mathematical identity as a successful student is suddenly questioned. In most cases, students start associating negative emotions to their university experience and to mathematics; shame, anxiety, insecurity, sadness and frustration are the emo-tions more often mentioned in our data. Moreover, stu-dents begin to question their own self-image as math-ematicians: switching from feeling highly competent to feeling inadequate for the task can be a hard change. The university experience also elicits an awareness of the difference between secondary school mathematics and university mathematics, questioning the theories of success in mathematics developed during the school experience. Students recognise secondary school math-ematics as a procedural subject – that requires perform-ing calculations following standard steps – compared with university mathematics, a formal and abstract sub-ject that consists of definitions and theorems and deals for the most part with abstract objects. Most students like this new version of their subject, but they find it hard to come to terms with it at the start of their studies, where so many other aspects of their lives are changing. The big differences in teaching methods between secondary school and university do not help students in their STT; relatively small mathematics classes are replaced by large lectures where students may feel lost, and studying strategies which worked at school level suddenly become ineffective at university level. Stu-dents then become stuck in this first impression of fail-ure and they do not know how to change the situation. In addition, despite the increasing efforts made by the institution to help students during tertiary transition, some struggling students   believe  that they have to smoothly adapt to the new context and  materials. This attitude exacerbates the difference with the secondary school experience of mathematics. To sum up, students feel a sense of impotence, in the conviction that they cannot gain control of the situation of failure which then becomes unavoidable and unchangeable for them.Facing failure for the first time and the change of their perceived competence in mathematics makes stu-dents feel ashamed. Students become afraid of disap-pointing people close to them and are afraid of being compared to their peers. This attitude supports the mis-conception that students often have of being the worst DiscussionEMS Newsletter September 2019 47Francesca Gregorio [francesca.gregorio@hepl.ch] is a PhD student and teaching as-sistant at the HEP Vaud (Switzerland) and the lab LDAR of the Paris Diderot Univer-sity (France). Her research focuses are on STT transition and on mathematical learn-ing disorders. She is a teacher trainer for primary and secondary pre-service teachers.Pietro Di Martino [pietro.dimartino@unipi.it] is an associate professor in mathematics education at the University of Pisa (Italy). He is the president of the Italian Commit-tee for Mathematics Teaching (CIIM). His main research interests concern the role of the affective factors in the processes of mathematics teaching and learning, the difficulties in the STT transition and the main aspects involved in problem solving at the primary school level.Paola Iannone [p.iannone@lboro.ac.uk] is senior lecturer in mathematics education at Loughborough University (UK). Her main research interests concern mathemati-cal reasoning and students’ proof produc-tion, students’ note-taking habits at univer-sity level and the summative assessment of mathematics at university. EPFL is an equal opportunity employer and family friendly university. It is committed to increasing the diversity of its faculty.  It strongly encourages women to apply.The School of Basic Sciences (Physics, Chemistry and Mathematics) at EPFL seeks to appoint a Tenure-Track Assistant Professor of Math-ematics.  We seek outstanding candidates with research interests in analysis and/or geometry, broadly construed. Areas of interest include differential geometry, dynamical systems, geometric analysis, geo-metric flows, kinetic theory, multiscale analysis and homogenization, (stochastic) PDE.We expect candidates to establish leadership and strengthen the EPFL’s profile in the field. Priority will be given to the overall originality and promise of the candidate’s work over any particular specialization area.Candidates should hold a PhD and have an excellent record of scientif-ic accomplishments in the field. In addition, commitment to teaching at the undergraduate, master and doctoral levels is expected.  Profi-ciency in French teaching is not required, but willingness to learn the language expected. EPFL, with its main campus located in Lausanne, Switzerland, on the shores of lake Geneva, is a dynamically growing and well-funded in-stitution fostering excellence and diversity. It has a highly international campus with first-class infrastructure, including high performance computing.As a technical university covering essentially the entire palette of en-gineering and science, EPFL offers a fertile environment for research cooperation between different disciplines. The EPFL environment is multi-lingual and multi-cultural, with English often serving as a com-mon interface. Applications should include a cover letter, a CV with a list of publica-tions, a concise statement of research (maximum 3 pages) and teach-ing interests (one page), and the names and addresses (including e-mail) of at least three references. Applications should be uploaded (as PDFs) by November 1st, 2019 to: https://facultyrecruiting.epfl.ch/position/18186242 Enquiries may be addressed to: Prof. Victor Panaretos Chair of the Search Committee E-mail: mathematics2019@epfl.chFor additional information, please consult www.epfl.ch, sb.epfl.ch, math.epfl.chat the Ecole polytechnique fédérale  de Lausanne (EPFL)Faculty Position  in Mathematics

The Secondary-Tertiary Transition in Mathematics. Successful Students in Crisis

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The Secondary-Tertiary Transition in Mathematics. Successful Students in Crisis

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