Now showing 1 - 6 of 6
  • Publication
    Investigating Cognitive demand of Higher-level Leaving Certificate Mathematics Examination Tasks Pre- and Post- Curriculum Reform
    (Institute of Education, Dublin City University, 2019-10-11) ; ;
    In 2010 the phased introduction of the new Project Maths curriculum began in post-primary schools in Ireland. This new curriculum aimed to enable students to develop problem-solving skills by providing relevant, contextual applications of mathematics, while simultaneously increasing the levels of cognitive demand required of students. This research aims to investigate whether the levels of cognitive demand required to complete tasks in the Leaving Certificate Higher-level mathematics examinations changed as a result of the curriculum reform. The methodology of this research includes the systematic analysis of Leaving Certificate examination tasks, from 2007 to 2017, using an adaptation of the Stein and Smith (1998) task analysis framework. Using this framework, tasks were classified as being of high- level or low-level cognitive demand. Analysis of the data collected suggests that a statistically significant increase in the levels of high-cognitive demand tasks did occur following the curriculum reform. Our findings are discussed in relation to two recent studies that used different frameworks to examine the cognitive demand of tasks in post-primary mathematics.
  • Publication
    Investigating the longitudinal impact of participating in school-based lesson study on mathematics teachers' professional community
    (Institute of Education, Dublin City University, 2019-10-11) ; ;
    Teacher professional communities have recently figured among the most influential factors for supporting teachers in their learning and in enacting educational change in schools. While lesson study has been documented as a means to support the development of such communities, previous studies have not addressed the sustainability of the professional communities which emerge. In this study, we follow-up with six mathematics teachers from two post-primary schools in the Republic of Ireland, who engaged in school-based lesson study in 2012/13, in order to investigate the long-term impact on their teacher professional community. Our findings indicate that the mathematics teachers in both schools had developed a predominantly mature professional community during their participation in lesson study in 2012/13. Moreover, we find that six years on, the community has been sustained in one school and further strengthened in the other. These findings suggest that lesson study may be a viable model to develop and sustain mathematics teachers’ professional communities in the long-term.
  • Publication
    Developing pedagogical content knowledge in initial teacher education: Lesson study and peer assisted tutoring
    (Dublin City University, 2018-07-26) ;
    Learning to teach is a long-term and complex enterprise (Morris, Hiebert, & Spitzer, 2009). In their commentary on initial teacher education (ITE), Hiebert, Morris, and Glass (2003) suggest that programmes are more valuable when they support pre-service teachers to acquire the tools they will need to learn to teach, rather than focus on achieving complete and polished competencies of high-quality teaching. Peer-assisted tutoring and lesson study are models which can build pre-service teachers’ awareness of the knowledge and skills required to teach, while also providing them with tools to continue their path as life-long learners (Amador & Carter, 2018). In this paper, we will discuss the incorporation of these two models, conducted in tandem during one semester, in the third year of a concurrent, undergraduate ITE programme in Science and Mathematics. Seven pre-service teachers volunteered to participate in this research and qualitative data, generated through planning documents and weekly reflections, was analysed utilizing the Mathematical Knowledge for Teaching framework (Ball, Thames, & Phelps, 2008). Findings suggest that due to their participation in peer-assisted tutoring and lesson study, these pre-service teachers developed important skills in noticing and reflection as part of their repertoire of learning to learn to teach. Furthermore, findings suggest a development of their knowledge of content and teaching (KCT) and knowledge of content and students (KCS) over the course of the semester. This research may provide useful insight for ITE providers and teacher educators.
  • Publication
    The university mathematics lecture: to record, or not to record, that is the question
    (Springer, 2023-03-07) ;
    While recordings of lectures proved invaluable for students’ learning during the pandemic, as our university transitioned back to in-person teaching there was a call from many lecturers to remove the requirement to provide lecture recordings due to the perceived negative impact on attendance. To examine in detail the relationship between recordings and the corresponding face-to-face lectures, we conducted a study on the formats of lectures across our undergraduate mathematics programmes pre- and post-lockdown in March 2020, and students’ perceptions of how beneficial they felt each was for their learning. In May 2020, 156 mathematics students completed a survey containing both quantitative and qualitative questions. Findings indicate that pre-pandemic almost 70% of the lecture formats classified by students were traditional in nature, with 20% classified as containing some interactions, and the remainder as including group work. While students did not perceive great differences in terms of the benefits to learning between the face-to-face and online lecture formats in the majority of modules, those who experienced interactions or group work in lectures before lockdown, reported a greater drop than those who experienced a traditional lecture. Irrespective of preferences for face-to-face or online learning, students were clear about the value of lecture recordings and interactions with peers and lecturers to their learning. Based on our findings, and those of others, we discuss implications for mathematics lecturers’ practice. Specifically, we argue for the provision of lecture recordings or short pre-recordings, especially when the lecture is traditional in nature.
  • Publication
    Engaging with feedback: How do students' remediate errors on their weekly quiz?
    Maths for Business is a first-year mathematics module for approximately 500 nonmathematics specialists. It has continuous assessment consisting of ten weekly quizzes, worth 40% of the final mark. In 2016/17, students who did not receive the maximum five marks on their weekly quiz were offered the opportunity to resubmit their quiz, with correction(s) and an explanation of their error(s), for one additional mark. We refer to this process as ‘remediation’. In this paper, we examine how students remediate their errors in order to identify features of a ‘good’ remediation. These features are identification, description, and correction of errors. By analysing a subset of students (n=31), we observe that a student’s quiz mark, and the cognitive level of the quiz question may impact the nature of the remediation provided.
  • Publication
    Students' sense of belonging to mathematics in the secondary-tertiary transition
    (International Group for the Psychology of Mathematics Education, 2018-07-08) ; ; ; ; ; ;
    A “sense of belonging to math” (SBM) scale has been shown to predict undergraduate mathematics students’ intent to study mathematics in the future. In this study, we use the scale to examine the impact of the transition from secondary school to university on 33 first year undergraduate students’ SBM. Using a cluster analysis, we identify three clusters: students in both Cluster 1 (n=21) and Cluster 2 (n=9) display a strong SBM at secondary school. Following the transition, those in Cluster 1 exhibit a decrease in SBM, while those in Cluster 2 show only a marginal decrease. Students in Cluster 3 (n=3) show a strong increase in their SBM, but they started with the lowest SBM initially. From an analysis of interviews with seven of the students, factors that might impact students’ SBM during the transition are discussed.