STEM Education (Peer-reviewed publications)

Permanent URI for this collectionhttps://dspace.mic.ul.ie/handle/10395/2267

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Teachers' professional identities and development education
(Centre for Global Education, 2019) Jeffers, Gerry; Quirke-Bolt, Nigel
This article explores the relationship between development education (DE) and the notion of teachers’ identity. The Teaching Council’s Code of Professional Conduct for Teachers (2016a) is seen as a significant step forward in clarifying the essential role of teachers. In interrogating the four underpinning ethical values associated with teaching in the Code - respect, care, integrity and trust - we find strong resonances with the traditions and ambitions of DE. We contend that a commitment to the advancement of human rights and to global justice perspectives generally follows organically from embracing the Code of Professional Conduct for Teachers. Furthermore, we believe our conclusions have implications for Irish Aid, The Teaching Council, teachers, student-teachers, initial and ongoing teacher educators as well as DE practitioners.
Preface: statistics in early childhood and primary education
(Springer Nature, 2018) Leavy, Aisling; Meletiou-Mavrotheris, Maria; Paparistodemou, Efi
Indexing distributions of data: preservice teachers’ notions of representativeness (Pre-published version)
(Wiley, 2004) Leavy, Aisling
The purpose of the study was to identify strategies used by preservice elementary teachers to index distributions of data. A secondary purpose of the study was to investigate whether representational form influenced the type of representative values constructed. Two hundred eighty‐three preservice teachers were administered a selection of tasks requiring them to construct representative values for a variety of distributional shapes. Participants were asked to provide justifications for their chosen representative measures. Data were analyzed from two perspectives: nature and adequacy of representative measure. Results indicated that when presented with skewed data sets, over half of the participants constructed poorly representative values. Symmetric data sets were best indexed with 67% of participants constructing highly representative values. Representational form played a significant role in determining representative values. Data presented graphically were more likely to be represented using measures of variability than were those presented nongraphically. Conversely, measures of central tendency were more frequently used to represent nongraphical data. The information arising from this study indicates that many preservice teachers construct poorly representative values to index data sets and utilize identical measures of representativeness regardless of distributional shape. The findings of the study highlight the need for exploratory data activities at the preservice level, call for provision of experiences affording insights into construction of representative values, and thus, have implications for the design of preservice mathematics education curricula.
Practical problems: using literature to teach statistics
(NCTM [National Council of Teachers of Mathematics], 2016) Hourigan, Mairead; Leavy, Aisling
Elementary and middle grade students’ constructions of typicality
(Elsevier, 2011) Leavy, Aisling; Middleton, James A.
This study addresses the measures chosen by students when selecting or constructing indices to properties of distributions of data. A series of individual teaching experiments were conducted to provide insight into the development of five 4th to 8th grade students’ conceptualizations of distribution over the course of 8 weeks of instruction. During the course of the teaching experiment (emergent) statistical tasks and analogous teacher activities were created and refined in an effort to support the development of understanding. In the process of development, attempts were made by students to coordinate center and variability when constructing measures to index properties of distributions. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions, and subsequent coordination of indices of variation and center. In particular, the defining features of student's self-constructed “typical” values and notions of spread were examined, resulting in a model of development constituting eight “categories” ranging from the construction of values that did not reflect properties of the data (Category 1) to measures employing conceptual use of the mean in combination with other indices of center and spread (Category 8).
The design space of student learning: Who is accountable and accountable for what? (Pre-published version)
(Taylor & Francis [Routledge], 2013) Leavy, Aisling; Kelly, Anthony
Mathematical under-preparedness: The influence of the pre-tertiary mathematics experience on students’ ability to make a successful transition to tertiary level mathematics courses in Ireland (Pre-published version)
(Taylor & Francis, 2007) Hourigan, Mairead; O’Donoghue, John
Internationally, the consequences of the ‘Mathematics problem’ are a source of concern for the education sector and governments alike. Growing consensus exists that the inability of students to successfully make the transition to tertiary level mathematics education lies in the substantial mismatch between the nature of entrants’ pre-tertiary mathematical experiences and subsequent tertiary level mathematics-intensive courses. This paper reports on an Irish study that focuses on the pre-tertiary mathematics experience of entering students and examined its influence on students’ ability to make a successful transition to tertiary level mathematics. Brousseau's ‘didactical contract’ is used as an intellectual tool to uncover and describe the contract that exists in two case mathematics classrooms in Irish upper secondary schools (Senior Cycle). Although the authors are professional mathematics educators and well informed about classroom practice in Ireland, they were genuinely surprised by the very restrictive nature of this contract and the damaging consequences for students’ future mathematical education.
Exploring probability concepts using a mini games environment: Ideas for primary and secondary classrooms
(NCE-MSTL [National Centre for Excellence in Mathematics and Science Teaching and Learning], University of Limerick, 2014) Leavy, Aisling; Hourigan, Mairead
Using a simulation to explore the law of large numbers
(NCE-MSTL [National Centre for Excellence in Mathematics and Science Teaching and Learning], University of Limerick, 2014) Leavy, Aisling; Hourigan, Mairead
Review of the Droichead teacher induction pilot programme (Report)
(ESRI [The Economic and Social Research Institute], 2016) Leavy, Aisling; Smyth, Emer; Conway, Paul F.; Darmody, Merike; Banks, Joanne; Watson, Dorothy
Budding architects: Exploring the designs of pyramids and prisms
(AAMT [Australian Association of Mathematics Teachers], 2015) Leavy, Aisling; Hourigan, Mairead
The context of students as architects is used to examine the similarities and differences between prisms and pyramids. Leavy and Hourigan use the Van Hiele Model as a tool to support teachers to develop expectations for differentiating geometry in the classroom using practical examples.
Pre-service primary teachers’ geometric thinking: Is pre-tertiary mathematics education building sufficiently strong foundations? (Pre-published version)
(Routledge [Taylor & Francis], 2017) Hourigan, Mairead; Leavy, Aisling
Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level pre-service teachers’ geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that develop pre-service teachers’ geometric knowledge to support the task of teaching. This study examines the geometric thinking levels of entry-level Irish pre-service primary teachers (n=381). Participants’ geometric thinking levels were determined through a multiple-choice geometry test (van Hiele Geometry Test (VHGT)) prior to commencing a Geometry course within their ITE programme. The findings reveal limited geometric thinking among half of the cohort and question the extent to which pre-tertiary experiences develop appropriate foundations to facilitate a smooth transition into ITE mathematics programmes. The study also examines the nature of misconceptions among those with limited geometric thinking and presents suggestions for appropriate ITE response.
Gifted students’ understanding of statistics: analysis of data arising from a small group teaching experiment
(Routledge, 2003) Leavy, Aisling
The principal objective of the study was to gain insight into cognitive processes related to three gifted students’ understanding of data. Small group teaching experiment methodology was used to uncover students’ understanding of the notion of distribution and consisted of a clinical interview phase, teaching phase and analysis phase. Fifteen teaching episodes followed the initial clinical interview and involved students working together on a variety of mathematical activities. The study examined how students organized data, described and indexed distributions of data, in addition to investigating their conceptualization of the mean. Results suggest that (a) modes and ranges were the most salient features of distributions, (b) typical values were generally located in clusters of data, (c) the mean was not utilized in the constructed measures of typicality, and (d) students had a relatively sophisticated understanding of samples and populations. Implications for curricular treatment of statistics for gifted students are discussed.
Varying your approaches to teaching variables
(INTO [Irish National Teachers Organisation], 2011) Leavy, Aisling; Hourigan, Mairead; McMahon, Aine
Our previous article Getting the balance right: The equals sign presented activities which can be used to introduce children to translating and solving word problems using equations where the unknown is represented with a frame. The PSMC recommends such algebra work for third and fourth class pupils. Children in senior classes are expected to translate word problems into equations where the unknown is represented with a variable. Variables are symbols (e.g. letters) that take the place of numbers or ranges of numbers. At primary school level, the main focus/use of variables is to represent an unknown quantity e.g. 5 + r = 30. Variables are also used to express rules e.g. A = L x W (area = length x width) and D = 2 X R (diameter is twice the radius). This article presents approaches which facilitate the meaningful introduction and consolidation of primary school children’s understanding of variable (i.e. a letter/symbol that represents an unknown). Conceptual understanding of the concept of variable is fundamental to further study of algebra and is “necessary for the meaningful use of all advanced mathematics” (Schoenfeld and Arcavi, 1988: 420).
A path analysis of the relationship among critical motivational variables and achievement in reform-oriented mathematics curriculum
(Routledge, 2013) Leavy, Aisling; Middleton, James A.; Leader, Lars
This study investigated the relationship among critical motivational variables and mathematics achievement as middle grades students engaged in a reform-oriented curriculum, Mathematics in Context. We tested 327 students in fifth, sixth, and seventh grade before and after two years of implementation. We performed a path analysis with subscales representing latent motivational variables and with achievement on the Iowa Test of Basic Skills as the outcome variable. The variables stimulation and control interacted to produce task interest, which, in turn, contributed to achievement gains. Effort was a byproduct of the stimulation afforded by the mathematical tasks. Attributions of success and failure were outcomes of interest. Utility mediated the effort on tasks and the attributions the tasks engendered. Results show that, with curriculum designed to emphasize utility and interest, students forged a high degree of motivation. Also, their achievement increased dramatically, in part, as a function of this increase in motivation.
'If you're doubting yourself then, what's the fun in that?' an exploration of why prospective secondary mathematics teachers perceive statistics as difficult
(Taylor & Francis, 2013) Leavy, Aisling; Hannigan, Ailish; Fitzmaurice, Olivia
Most research into prospective secondary mathematics teachers’ attitudes towards statistics indicates generally positive attitudes but a perception that statistics is difficult to learn. These perceptions of statistics as a difficult subject to learn may impact the approaches of prospective teachers to teaching statistics and in turn their students’ perceptions of statistics. This study is the qualitative component of a larger quantitative study. The quantitative study (Hannigan, Gill and Leavy 2013) investigated the conceptual knowledge of and attitudes towards statistics of a larger group of prospective secondary mathematics teachers (n=134). For the purposes of the present study, nine prospective secondary teachers, eight of whom were part of the larger study, were interviewed regarding their perceptions of learning and teaching statistics. This study extends our understandings garnered from the quantitative study by exploring the factors that contribute to the perception of statistics as being difficult to learn. The analysis makes explicit the tensions in learning statistics by highlighting the nature of thinking and reasoning unique to statistics and the somewhat ambiguous influence of language and context on perceptions of difficulty. It also provides insights into prospective teachers’ experiences and perceptions of teaching statistics and reveals that prospective teachers who perceive statistics as difficult to learn avoided teaching statistics as part of their teaching practice field placement.
Mathematics subject matter knowledge (SMK) for teaching at primary level: How much is enough?
(NCE-MSTL [National Centre for Excellence in Mathematics and Science Teaching and Learning], University of Limerick, 2010) Hourigan, Mairead
Facilitating inquiry based learning in mathematics teacher education
(SMEC [Science and Mathematics Education Conference], 2010) Leavy, Aisling; Hourigan, Mairead; McMahon, Aine
A driving question in teacher education centers on how to help prospective teachers become expert teachers. The absence of a shared professional curriculum to prepare teachers to teach mathematics combined with the difficulty translating traditional research knowledge into forms that teachers can use in their practice have motivated this study. This paper reports on the combined efforts of teacher educators, teachers, and preservice teachers to engage in inquiry-based teaching of primary mathematics. What is innovative is the use of the classroom lesson as the unit of analysis combined with engagement in cycles of inquiry to produce exemplar mathematics lessons. Lesson Study was the primary method used to support a focus on examining teaching through the design and implementation of ‘study lessons’. Insights into preservice teachers’ reflections on inquiry-based teaching are presented in addition to a discussion of the benefits of efforts such as this which translate traditional research knowledge into forms preservice and practising teachers can use to improve their practice.
Teaching algebra in the primary classroom: Functions, the function machine
(NCE-MSTL [National Centre for Excellence in Mathematics and Science Teaching and Learning], University of Limerick, 2012) Hourigan, Mairead; Leavy, Aisling; McMahon, Aine
Providing challenge in pattern work in the infant classes
(NCE-MSTL [National Centre for Excellence in Mathematics and Science Teaching and Learning], University of Limerick, 2012) Hourigan, Mairead; Leavy, Aisling; McMahon, Aine

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