Secondary-tertiary Transition Research Articles

Exploratory Study on the Emotions of Undergraduate Mathematics Students during the Secondary-Tertiary Transition

This descriptive, qualitative research explores the evolution of emotions in students of the bachelor’s degree in mathematics and applied mathematics during the secondary-tertiary transition. It uses the Theory of the Cognitive Structure of Emotions (better known as the Ortony, Clore, and Collins's [OCC] theory) as a theoretical framework. The study was carried out at the Faculty of Physical and Mathematical Sciences of the Meritorious Autonomous University of Puebla, Mexico, with the participation of seventeen first-year students, selected by convenience sampling. Three emotions were identified, of which four were positive and nine were negative. The findings indicate that emotional experiences have a considerable effect on the ability of students to acquire advanced mathematical language. The research is based on a descriptive empirical design, focusing on the experiences of the participants. The data collection instruments include an incomplete sentence questionnaire, a questionnaire, and a semi-structured interview. The research highlights the importance of considering emotions in the secondary-tertiary transition, stating that experiences are crucial in the transition and it is essential to address these aspects to improve support for students in their mathematical learning.

Changes in mathematical skills among freshman engineering students

This study investigates the critical transition from secondary to tertiary mathematics education, focusing on students’ challenges and the impact of curriculum reforms in Sweden. Through an analysis of diagnostic test scores and admission data from Umeå University over the period 2006–2021, we examine the evolving mathematical competencies of incoming engineering students and the broader implications of these shifts for educational policy and student preparedness for higher education. Our findings indicate a significant improvement in students’ mathematical readiness in the latter years of the study, correlating with the implementation of curriculum changes and variations in admission statistics. This research documents the positive outcomes of these educational reforms on student preparedness. It places these findings within a global context, highlighting the universal challenges and responses in mathematics education transitions. The study underscores the complex dynamics of the secondary-tertiary transition and provides valuable insights into the specific mathematical areas where students have shown varying degrees of improvement.

The development of mathematics expectancy-value profiles during the secondary–tertiary transition into STEM fields

BackgroundTo master the secondary–tertiary transition into fields of science, technology, engineering, and mathematics (STEM), academic self-beliefs play a pivotal role, especially those related to learning mathematics. The framework of expectancy-value theory has been used widely in primary and secondary education and partly in tertiary education to assess the self-beliefs of students in terms of expectancy of success and perceived value of mathematics. Based on this framework, we measured how the intrinsic value, the attainment value, the utility value, and the cost of learning mathematics as well as the expectancy of success when learning mathematics developed during the secondary–tertiary transition of students into STEM fields. Data were collected in a quantitative repeated-measures questionnaire study with two measurement points (measurement point 1: n = 710, measurement point 2: n = 487, listwise: n = 409). We conducted a latent profile analysis to identify the prevalent patterns of mathematics self-beliefs, called profiles, at each of the two measurement points. We studied the relation of these profiles to prior education, achievement at school, and achievement at university. By performing a latent transition analysis, we determined the probabilities of transitioning from the initial profiles to the posterior profiles.ResultsOur analysis revealed four distinct prevalent profiles at each measurement point, ranging from highly favorable (i.e., high expectancy, high value, low cost) to highly unfavorable with respect to learning mathematics. The profiles with favorable manifestations remained stable over time, while those with undesirable manifestations deteriorated further. We observed a sharp increase in cost across all profiles. Prior achievement correlated strongly with profile membership.ConclusionsThe expenditure of time and energy increased sharply during the secondary–tertiary transition, independently of the students’ initial motivational patterns. The perceived utility of mathematics for potential future careers was shown to be a significant source of motivation. The role of mathematics in future careers should thus be made visible in university teaching. Keeping the detrimental development of initially undesirable motivational profiles in mind, university teachers should create ample opportunities for students to gain a sense of accomplishment.

Understanding the challenges of the secondary-tertiary transition in mathematics for economics in higher education: a literature review

Abstract This review paper examines the issues identified by research regarding students transitioning from school mathematics to service mathematics modules within economics education at the tertiary level. Literature was gathered in four steps, mainly through hand-searching strategies from journals, books, conference proceedings and reports. The results show that existing research addresses the challenges of students to cope with changed roles of students and teachers, as well as with new approaches to teaching and assessment, in the transition phase between education levels. Special issues identified for service mathematics in economics education are (i) issues of heterogeneous mathematics background in the student group, (ii) of mismatch in expectations about mathematics level and demand and (iii) the issue of relevance of mathematics. This review helps practitioners gain deeper insights into these multifaceted issues of transition. Furthermore, several potential directions for further research in the field are recommended.

Impact of a Mathematics Bridging Course on the Motivation and Learning Skills of University Students

AbstractThe transition from secondary to tertiary education is an exciting and yet challenging event in the educational biography of students. During this transition, students often meet with unexpected challenges, which may cause them to drop out from their degree program. Many universities offer bridging courses or longer-term interventions to support their incoming students in this period. To examine the effect of a bridging course designed to reduce gaps in prior mathematical knowledge, promote social-emotional well-being, and foster learning skills, we implement a repeated-measures intervention study. We analyze the outcomes of the intervention, which features tutors with special training, autonomous choice of topic areas, peer learning, and materials for self-directed learning. We measure the development of motivational beliefs reflecting the will to learn (achievement goals, satisfaction of basic psychological needs, implicit theories, self-efficacy) and the skills to learn (reactions to errors, self-regulated learning) at the secondary-tertiary transition. These aspects are captured at multiple measurement points among students (N = 679) who participate in the bridging course (intervention group) and those who do not (control group). The intervention boosts motivational beliefs related to social embeddedness and learning skills in the short term. The observed decrease in autonomy, competence, and self-efficacy might be explained by higher standards that students use for their self-assessment in the new peer group. In the long term, all aspects of the will to learn, except for social relatedness, show stable to strongly negative developments in both groups. Among those students who do not participate in the bridging course, mostly strongly negative developments are observed. The results suggest that the peer tutoring strategy is highly effective and the need for longer-term interventions to uphold the positive short-term effects.

Presenting a New Model to Support the Secondary-Tertiary Transition to College Calculus

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the transition from secondary precalculus or calculus to tertiary calculus. Using the Four Component Instructional Design (4C/ID) model and empirical data from the United States (US) nationally representative FICSMath project, we mapped instructional experiences of students in the transition to theoretical components of the 4C/ID model. From exploratory factor analysis (n=6,140), we found six factors that mapped to the 4C/ID model components and created the new Secondary Precalculus Calculus (SPC) 4C/ID model. In this model, the Learning Task Component represents tasks to engage learners in meaningful problem solving; the Support Component grounds instruction in reasoning and understanding; the Procedure Component integrates group work and graphing calculators to connect concepts to procedures; and the Part-Task Component represents instruction to develop automaticity. The SPC 4C/ID model presents a unique support for precalculus and calculus teachers in the quest of teaching for learning and transfer of learning across the transition.

New insights about the secondary–tertiary transition in mathematics

New insights about the secondary–tertiary transition in mathematics

How narratives about the secondary-tertiary transition shape undergraduate tutors’ sense-making of their teaching

Drawing on the commognitive framework, we construe the secondary-tertiary transition (STT) as a distinctive element in the pedagogical discourses of various communities. Our interest rests with university tutors in light of the emergent recognition of their impact on undergraduates’ mathematics learning in many tertiary contexts worldwide. We aim to understand the roles of STT communication in tutors’ reflections on incidents that took place in their tutorials. Our participants were undergraduate students in the advanced stages of their mathematics degrees in a large New Zealand university and who were enrolled in a mathematics education course. Throughout the semester, the participants led tutorial sessions for first-year students and wrote reflections on classroom incidents that drew their attention. Our data corpus consisted of 58 reflections from 38 tutors collected over four semesters. The analysis revealed that STT communication featured in tutors’ descriptions of classroom incidents, assisted them in making sense of unexpected events, positioned their instructional actions as replications of what was familiar to them from their own STT experience, and contributed toward generating new pedagogical narratives. We situate these findings in the literature concerning undergraduate tutoring and teachers’ perspectives on STT.

Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition

Diverse perspectives and experiences of university mathematics teachers on improving the secondary-tertiary transition

The transition from school to university in mathematics education research: new trends and ideas from a systematic literature review

Investigating the transition between educational levels is one of the main themes for the future of mathematics education. In particular, the transition from secondary school to STEM degrees is problematic for the widespread students’ difficulties and significant for the implications that it has on students’ futures. Knowing and understanding the past is key to imagine the future of a research field. For this reason, this paper reports a systematic review of the literature on the secondary-tertiary transition in Mathematics Education from 2008 to 2021. We constructed two corpuses: one from the proceedings of three international conferences in mathematics education (PME, ICME, and INDRUM) and the other from peer reviewed research papers and book chapters returned by the databases ERIC and Google Scholar. A clear evolution in perspectives since 2008 emerges from the analysis of the two corpuses: the research focus changed from a purely cognitive to a more holistic one, including socio-cultural and — to a lesser extent — affective issues. To this end, a variety of research methods were used, and specific theoretical models were developed in the considered papers. The analysis also highlights a worrisome trend of underrepresentation: very little research comes from large geographical areas such as South America or Africa. We argue that this gap in representation is problematic as research on secondary tertiary transition concerns also consideration of socio-cultural and contextual factors.

Seeing the continuity behind “double discontinuity”: investigating Hong Kong prospective mathematics teachers’ secondary–tertiary transition

Seeing the continuity behind “double discontinuity”: investigating Hong Kong prospective mathematics teachers’ secondary–tertiary transition

The three worlds and two sides of mathematics and a visual construction for a continuous nowhere differentiable function

A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall’s framework of the three worlds of mathematics. Tall’s framework describes the aspects and the development of mathematical thinking from early childhood to university-level mathematics. In this theoretical article, we further elaborate Tall’s framework. First, we present a division between the subjective-social and objective sides of mathematics. Then, we combine Tall’s distinction to ours and present a framework of six dimensions of mathematics. We demonstrate this framework by discussion on the definition of continuity and by presenting a visual construction of a nowhere differentiable function and analyzing the way in which this construction is communicated visually. In this connection, we discuss the importance to distinguish the subjective-social from the objective side of mathematics. We argue that the framework presented in this paper can be useful in developing mathematics teaching at all levels and can be applied in educational research to analyze mathematical communication in authentic situations.

Predictive tools for university performance: an explorative study

The role of mathematics in secondary-tertiary transition is subject to increasing analysis in several education contexts. We explore the longitudinal relationships among a standardized test used for assessing secondary school mathematics, high school final grades and the academic progress of a sample of Italian undergraduates. Results from regression analyses showed that the standardized test and high school final grades together are predictive both of the student's academic success in terms of Grade Point Average and of academic credits earned, whereas a more specific relationship emerged between the standardized test and the mathematics exam. This study provides findings on the importance of secondary school mathematics as a predictor of university performance, even in courses where mathematics is a service subject.

Comment l’articulation entre théorie de l’activité et théorie anthropologique éclaire la transition secondaire-supérieur : le cas des probabilités conditionnelles

The study of the secondary-tertiary transition requires taking into account institutional evolution but also the point of view of the actors. For this reason we have chosen to network the activity theory adapted to the didactics of mathematics with the anthropological theory of the didactic. In this article we present this networking and illustrate its use through the example of conditional probabilities. We propose to operationalize the complementarity of these two theories by making use of the concept of type of tasks’ variations that we define and illustrate through the example presented. The new theoretical framework constructed allows us to describe praxeologies taught while taking into account the cognitive and mediative dimensions of the subject’s activity.

Compartmentalisation of Mathematical Sectors: The Case of Continuous Probability Distributions and Integrals

This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense those two sectors may be described as compartmentalised in current textbooks. We then study, by means of a questionnaire, the educational effects of the compartmentalisation: do students’ difficulties in completing “bridging tasks” (tasks that require to relate the two sectors) reflect the partial disconnections revealed by the praxeological analyses? The key notion of ostensive, combined with the role played by the technology in the sense of ATD, is used to interpret the data. Altogether, this study sheds light on the deficit of cognitive flexibility required to change mathematical sectors, which is understood as a result of deficient praxeologies developed within the institutions.

The Secondary-Tertiary Transition in Mathematics: What High School Teachers Do to Prepare Students for Future Success in College-Level Calculus

Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers’ abilities to teach for conceptual understanding is a significant and positive predictor of student performance in single- variable college calculus. To explore these findings further, we gathered and analyzed interview data gained from a representative sample of high school precalculus teachers from across the U.S., identified by their students as requiring high levels of conceptual understanding (n = 13). Seventeen themes were identified and then combined into five overarching phenomenological themes. These overarching themes suggest that teachers who teach for high conceptual understanding (a) support relational understanding during problem solving, (b) require students to learn how to study to build on prior knowledge and learn from mistakes, (c) use mathematical language and ask critical questions to support learning, (d) focus on content knowledge necessary to make connections, and (e) use technology to support learning concepts but limit calculator use. Comparison of these results to quantitative findings further illuminate that intentional development of disciplinary knowledge, cognition, and language are noteworthy points of intersection for teachers and researchers alike.

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

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

A Pathway to a Student-Worded Definition of Limits at the Secondary-Tertiary Transition

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students, which led to the formulation by the students of a correct formal definition of the infinite limit for sequences, with minimal background logical prerequisites and in the course of a 2-h session. On a more theoretical level, the teaching project was developed in the framework of didactic engineering, and provides opportunities to contribute to the ongoing work on its adaptation to the specific context of tertiary education. In the a priori analysis, we highlight the didactical potential of tasks of differentiation between neighboring concepts as a pathway to advanced mathematical concepts. In the a posteriori analysis, we focus on the nature and extent of teacher intervention in the shaping of a mathematical milieu that is conducive to the definition of an advanced mathematical concept.

The Secondary-Tertiary Transition in Mathematics. What are our current challenges and what can we do about them?

The Secondary-Tertiary Transition in Mathematics. What are our current challenges and what can we do about them?

The Mathematical Crisis in Secondary–Tertiary Transition

Tertiary transition in mathematics appears to be an insurmountable struggle for many students, including for high achievers in secondary school. The high dropout rates in many Western Countries represent a big issue from an individual and social point of view. It appears particularly significant to analyse this phenomenon in the context of the degree course in Mathematics, studying students’ cognitive and affective reactions to the (often unexpected and severe) difficulties encountered in the tertiary transition. With this aim, we developed a narrative study in a specific context in Italy—that involves excellent students from secondary school—to investigate how successful and dropout students describe their experience in transition. Implications for the educational practice are discussed.