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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. [ABSTRACT FROM AUTHOR]

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. ]. This paper aims to examine the performance of 1st year undergraduate students' procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students' skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the 'why' of the results presented here. [ABSTRACT FROM AUTHOR]

Every student who enrols in a degree programme involving service mathematics in the University of Limerick in Ireland is given a mathematics diagnostic test. The diagnostic test was developed due to mathematics lecturers’ anxiety regarding students’ mathematical competency levels. Students receive the 40 question paper-based test in their first service mathematics lecture without prior notification. Initial analysis of students’ work revealed that many students were having difficulties with basic algebra and arithmetic in particular [Gill, O. 2006. “What Counts as Service Mathematics? An Investigation into the ‘Mathematics Problem’ in Ireland.” PhD diss., University of Limerick]. Further research highlighted the significant decline in diagnostic test performance and the changing profile of service mathematics students between 1998 and 2008 [Faulkner, Fiona, Ailish Hannigan, and Olivia Gill. 2010. “Trends in the Mathematical Competency of University Entrants in Ireland by Leaving Certificate Mathematics Grade.”Teaching Mathematics and Its Applications29 (2): 76–93]. One of the most notable changes to the student profile over time was the increase in mature students (non-standard students) entering service mathematics programmes. Although non-standard students had a lower mean performance in the diagnostic test, they were found to have a higher mean performance in some cases in service mathematics compared to standard students. This paper explores some of the possible reasons for such findings. [ABSTRACT FROM PUBLISHER]

This paper reports on a research project which aims to improve prospective mathematics teachers’ relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme. [ABSTRACT FROM PUBLISHER]

Universities invest significant resources in the provision of mathematics tuition to first year students, through both traditional and non-traditional means. Research has shown that a significant minority of students do not engage with these resources appropriately. This paper presents findings from a study of two groups of students at Maynooth University. Both groups had similar mathematical backgrounds on entry to university. The first group consisted of seven students who had failed first year mathematics and had very low levels of engagement with available supports. The second group consisted of nine students who had passed first year mathematics and had engaged with the supports to a significant extent. It emerged that while both groups initially displayed similar tactics and encountered similar difficulties, their levels of reaction to a number of critical events in their mathematical education were key to their engagement levels and their subsequent progression. Further analysis revealed aspects of the students' behaviour which caused them to approach or avoid difficulties. The reasons behind the different student behaviours were investigated, and the main categories of influence on student behaviour which emerged from the interview data were fear, social factors, and motivation. [ABSTRACT FROM PUBLISHER]

Deficiencies in beginning undergraduate students’ basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously. [ABSTRACT FROM PUBLISHER]