The aim of this research is to investigate the impact of the COVID-19 closures from the perspective of students studying mathematics at university level in Ireland. A survey was designed and administered to students who were enrolled in at least one mathematics module in an Irish university at the time of the closures. The survey comprised three sections: teaching and learning, assessment and personal experience, with a focus on how the changes in teaching and assessment were viewed by students. A total of 263 students from six universities responded to the survey. The corresponding data are described, as are various trends that were identified through open-response questions. The data offer a window into the student experience during the tertiary level closures and show the effect that the sudden shifts (e.g., in delivery and support) had on learning, assessment and student well-being. The survey responses show that most students dealt with the rapid changes in a resilient and mature manner, particularly when confronted with adversity. Numerous insights can be gleaned from the students’ perspectives that have the potential to improve the teaching and learning of mathematics at tertiary level in Ireland in the future. Many of the findings could also apply to teaching and learning in other subjects and internationally.

Introducing direction fields to students learning ordinary differential equations (ODEs) through guided inquiryThis paper reports on an intervention as part of which direction fields were introduced to students learning ordinary differential equations (ODEs). The intervention was designed and implemented to address issues with students' conceptions of the solutions of ODEs. These were identified by a diagnostic survey and through a review of the literature. The intervention comprised fifteen guided inquiry tutorials, one of which introduced students to direction fields in the context of first order ODEs. A combination of interviews and immediate and delayed post-testing was used to measure the impact of the tutorial. The design of the tutorial and the results of the interviews and post-test data are reported. A large majority of the students who completed the tutorial were able to successfully complete tasks linking direction fields to their study of ODEs. A significant improvement was also observed in relation to students' conceptions of solutions to an ODE.

This paper reports on the first part of a multiphase research project that seeks to identify and address the difficulties encountered by physics students when studying differential equations. Differential equations are used extensively by undergraduate physics students, particularly in the advanced modules of their degree. It is, therefore, necessary that students develop conceptual understanding of differential equations in addition to procedural skills. We have investigated the difficulties encountered by third-year students at Dublin City University in an introductory differential equations module. We developed a survey to identify these difficulties and administered it to students who had recently completed the module. We found that students' mathematical ability in relation to procedural competence is an issue in their study of differential equations, but not as severe an issue as their conceptual understanding.Mathematical competence alone is insufficient if we expect our students to be able to recognize the need for differential equations in a physical context and to be able to set up, solve, and interpret the solutions of such equations. We discuss the implications of these results for the next stages of the research project.

In this study, we conducted a survey of all tertiary level institutions in Ireland to find out how many of them use diagnostic tests, and what kind of mathematical content areas and topics appear on these tests. The information gathered provides an insight into what instructors expect students to know on entry to university and what they expect students to have difficulty with. In total, 12 diagnostic tests from 11 Irish institutions were collected during the study. An item-by-item analysis was carried out on each diagnostic test to determine the content areas and topics that are assessed on the diagnostic tests and to identify any additional knowledge required for successful completion. We compare the tests administered in the university sector and the Institute of Technology (IT) sector of the Irish tertiary level education system. In addition, current diagnostic tests are compared with two tests from the 1980s to see if the level of mathematical preparedness expected of first-year students has changed over time. Our analysis is situated in a discussion of previous research on diagnostic testing both nationally and internationally.

This paper reports on data obtained during semi-structured interviews with students who had recently experienced a guided inquiry approach to learning ordinary differential equations (ODEs) in a service-taught module. Previous research identified the strengths and weaknesses of similar cohorts of students. The results from that research informed the design of an intervention (15 guided inquiry tutorials) which sought to improve the outcomes for students taking a subsequent version of the module. This paper reports on the data gathered during interviews with these students that describe their perceptions of the guided inquiry approach used. The students noticed the change in emphasis toward conceptual understanding that the intervention was trying to instil. They cited the change in questioning style most frequently as being where they saw this change, but also noted the prevalence of group work and change in interaction pattern as keys to its success. Thus, by probing students' opinions in this way, we find validation for a guided inquiry approach to teaching ordinary differential equations in third level that emphasizes active learning and lateral interactions among students. The students' personal goal orientation and the goal structure of the learning environment are also discussed.