Sparking curiosity and opening doors: using active learning in Mathematics as a tool for promoting access to college
Ciaran O’Sullivan† & Paul Robinson†† & Chris Keogh†† & Aisling McGlinchey†
†School of Mathematics and Statistics, Technological University Dublin, Dublin, Ireland, ††School of Mechanical Engineering, Technological University Dublin, Dublin, Ireland
Under-performance in, and fear of, mathematics can be perceived as a barrier to progression to higher education by secondary school students. This is particularly true for students who come from areas of social disadvantage. In this paper we describe a programme which seeks to help address this perceived barrier by providing active learning opportunities in mathematics at Technological University Dublin, for secondary students who come from schools in socially disadvantaged areas of Dublin. There are two aims of the programme. The first aim is to spark the students’ curiosity with well-chosen active learning workshops, which show them that engaging with mathematics is needed in real world situations. The second aim is to contribute to the broader access to college agenda, by engaging the students in a positive way with the university and nudge open the door of possibility that attending higher education may provide for them. In the paper we will describe the key aspects of the programme and feedback on the programme from participants. We will also identify the features central to it being repeatable in other educational settings.
Discovery and communication in the mathematics classroom
Faculty of Engineering and Design, Atlantic Technological University Sligo, Ireland
A number of sources have commented on the benefits of encouraging students to become more active in their learning, and to communicate their mathematical thinking. For instance, in her findings from a survey of over 365 engineers in Ireland reflecting on their maths education, Eileen Goold  suggests that an active social learning environment would benefit engineering mathematics education. Students would be required to present and defend their mathematical solutions to both their peers and their lecturers. This type of learning environment would develop students’ mathematics communications skills and enhance their mathematics thinking and confidence, providing a better match to the mathematics required in engineering practice.
In his book “A Mathematician’s Lament”, Paul Lockhart  suggests a way to teach students by choosing engaging and natural problems suitable to their tastes, personalities and levels of experience, by giving them time to make discoveries and formulate conjectures, by helping them refine their arguments and creating an atmosphere of healthy and vibrant mathematical criticism.
In this paper we look at recent changes to the teaching of mathematics to a group of engineering students at Atlantic Technological University (ATU) Sligo. In particular how adopting a tutorial style has proved to be a successful model for engaging students and allowing time for exploring different approaches. We look at the use of a large bank of questions and solutions  to create randomised assessments. The question bank makes writing exams much easier and faster. Exams are also less predictable, rewarding students for understanding concepts rather than memorising procedures.
Learning through discussion
Slovak University of Technology, Faculty of Mechanical Engineering
The paper will discuss the role of dialogue in teaching and learning process. It will deal with forms of communication in pedagogic use, and especially it will focus on not so traditional handling of discussion in examination, the gains it makes for students as well as limits, which have to be taken into consideration within implementation. The changes, extorted by covid restrictions transferring education into on line space, influenced the communication sphere maybe in the most visible way and its consequences can be seen till these days. The long lasting lack of face to face conversation allowed students to absolutely misunderstand what presentable learning outcome should be. The irreplaceable on-site position of a teacher is undisputed in this context as well as it is very important for students’ common comprehension along with their motivation and overall activation. We will present good practice forms of communication resulting in improvement of mathematical competencies and which are worth to use also in the post covid time for recovery process.