**Investigating Mathematical Thinking and Reflection in First Year Engineering Students**

Lauren Matthews & Paul Robinson & Fiona Faulkner & Ciaran O’Sullivan

*Technological University Dublin, Dublin, Ireland*

A new second level pre-university entrance mathematics curriculum was introduced into schools across Ireland between 2008 and 2015. One aim of the curriculum is to improve students interpretation, formulation and presentation of mathematical ideas. After taking this 2 year program students then take a Higher or Ordinary Level Paper.

As part of a wider PhD study of the challenges students may be having when engaging with both procedural and problem solving skills in mathematics, we have attempted a pilot study to investigate mathematical thinking in a group of first year engineering students doing basic procedural problems. Typically, these students enter with Ordinary Level mathematics and find even basic mathematics challenging.

Over a semester students take a series of similar tests. Between tests students complete a Relection Sheet describing in words a problem they could not do, where they found material to help them do it, any appropriate formulas they think they need and a fully worked out example solution. Volunteers are also invited to do a 40 minute ‘think aloud’ interview where they articulate their thoughts as they work through problems. Many questions arise: how clear is their thinking, does it matter much when solving procedural problems, does it improve over time through reflection, are there persistent inaccuracies?

In this paper we will present insights from the student reflection process and examine the effect this process has on student engagement and performance.

**Investigating the Level of Mathematical Preparedness of Students who Transfer from the Further Education Sector to Higher Education STEM Courses **

John McHugh, Dr Michael Carr, Dr Fiona Faulkner

*Technological University Dublin, Ireland
*

A student’s level of mathematics as they begin degree courses at Higher Education (HE) in the Science, Technology, Engineering, and Mathematics (STEM) disciplines has been recognised as a key indicator of their success in those courses. Much research has taken place into the teaching of mathematics at second level, and much work has gone into a reshaped Leaving Certificate syllabus designed to better equip students to succeed at third level, with greater emphasis on applicable rather than procedural knowledge. A comparatively under-researched area has been that of Further Education (FE), a sector which supplies a smaller proportion of HE’s student intake, typically in the form of one- or two-year Post-Leaving Certificate (PLC) courses.

Such considerations have led the author to investigate the mathematical preparedness of students at FE level, with a particular emphasis on those students hoping to progress to a STEM degree course. The project is being conducted using a mixed-methods approach, incorporating analysis of both quantitative and qualitative data.

The quantitative analysis component will involve analysis of diagnostic testing and examination results from both FE and HE in mathematics, and an application will be made to SOLAS/ETBI to access administrative data linked to education and employment outcomes for students who have progressed from the FE to HE sectors.

The qualitative analysis component will consist of surveys, focus groups and interviews, aiming to explore students’ experiences of progressing from FE to HE, difficulties they may have with mathematics, and whether they are at risk of dropping out or failure because of mathematical issues. The principal participants in this component at this point of the research are those studying Engineering-focussed PLC courses for the purposes of progression to courses at HE level, with an intention to broaden this out to other STEM disciplines at a later point.

**Improving mathematical skills towards undergraduate studies**

Päivi Porras & Jarkko Hurme & Henry Lähteenmäki

*Lab University of Applied Sciences, Finland, Oulu University of Applied Sciences, Finland, South-Eastern Finland University of Applied Sciences, Finland*

In the OECD’s PISA study, the decline in the level of competence has been visible among youth in Finland specifically in literacy, mathematics, and science. The skills of immigrants are also of concern, as the difference in learning outcomes between pupils with an immigrant background and those belonging to the native population is one of the largest in the reference countries. (Ministry of Education and Culture 2019, 122-125.) Based on Pietiläinen’s report (2021), ninth graders’ proficiency in mathematics study has decreased and differentiated compared to previous studies. Furthermore, Niemi et. al. (2021) reported that the level of competence declines if a student does not enter the upper secondary school. The Union of Professional Engineers in Finland stated that competence in mathematics, environmental studies, science, and technology must be increased to secure the future of the field of technology (Ranta 2022).

The KoKo – Towards Education project, started in February 2023, aims to solve these challenges. LAB UAS, XAMK UAS and OUAS are developing an operating model that promotes the mathematical and scientific competence of the most vulnerable and, thus, enhancing their access to postgraduate studies. The project produces supporting material to all who are planning undergraduate studies, for example in the field of technology. The material enables self-development and finding one’s own study path towards work career. The aim is also to develop individual learning, self-regulation, and motivation, in science-mathematical subjects. Feeling confident in their own abilities and being motivated, students are most successful in mathematics (Niemi et al. 2021).

**Lowering time stress in STEM exams**

Alexandra C. Niculescu^{a}, Cécile Hardebolle^{a}, Himanshu Verma^{b}, Roland Tormey^{a}, Simone Deparis^{a}

*a. Ecole Polytechnique Fédérale de Lausanne, EPFL-AVPE-LEARN, EPFL-AVPE-CEDE, EPFL-AVPE-CAPE, EPFL-AVPE-CePro, b. Knowledge and Intelligence Design Group, Faculty of Industrial Design Engineering, TU Delft, Netherlands*

Success and study progress are issues of great interest in STEM and especially in higher education.. At EPFL, a large proportion of students who enrol in a study program leave the institution without completing the first year (Times Higher Education, 2022). In particular, students with a weaker mathematics background and women seem to be most at risk as introductory courses can play a role in pressuring and discouraging them in continuing their studies.

To cope with this unwanted situation, the school has responded with a series of course and exam redesign practices in the introductory courses, such as implementing flipped classrooms (Hardebolle et al., 2022) and exams with fewer questions. From June 2022, a new measure was adopted in the form of allowing an extra thirty minutes duration for the exams of the first year courses. This could prove to be a remedial measure for students with less fluency in mathematics who have to put more effort during high stakes situations such as exams, when compared to students with a stronger mathematical background. Consequently, they may require and benefit from additional time in which they can demonstrate what they learned during a course.

We present an analysis of the exam scores in two first year STEM courses at EPFL, before and after the introduction of the additional 30 minutes time. We expect the students with a weaker mathematics background to benefit from the prolonged exam duration. Based on data from the study on a Linear Algebra class by Hardebolle et al 2022, we want to assess the impact of adding 30 minutes of extra time in the exam on the performance of students depending on their background and gender.