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.

Animals can use both allocentric and egocentric strategies to learn a spatial task. Our results suggest that allocentric cues are more dominant than idiothetic cues in guiding navigation. Animals do not necessarily learn an egocentric strategy automatically, instead they probably hold just one solution to any particular task at a time until forced to learn an alternative strategy. Further, with overtraining animals do not always switch from allocentric to an egocentric learning strategy perhaps challenging suggestions of a stored hierarchy of strategies.

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Mathematical thinking is difficult to define precisely but most authors agree that the following are important aspects of it: conjecturing, reasoning and proving, abstraction, generalization and specialization. However, recent studies have shown that many sets of mathematical tasks produced emphasize lower level skills, such as memorization and the routine application of algorithms or procedures. In this paper we survey the literature on the design and use of tasks that aim to encourage higher level aspects of mathematical thinking in learners of mathematics at all levels. The frameworks presented here aim to guide task designers when writing a set of exercises.

Mathematical thinking is difficult to define precisely but most authors agree that the following are important aspects of it: conjecturing, reasoning and proving, abstraction, generalization and specialization. However, recent studies have shown that many sets of mathematical tasks produced emphasize lower level skills, such as memorization and the routine application of algorithms or procedures. In this paper we survey the literature on the design and use of tasks that aim to encourage higher level aspects of mathematical thinking in learners of mathematics at all levels. The frameworks presented here aim to guide task designers when writing a set of exercises.