STEM Education (Conference proceedings)

Permanent URI for this collectionhttps://dspace.mic.ul.ie/handle/10395/2272

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Abstract: Applying results of statistics education research to teaching statistics in Irish primary schools (Pre-published version)
(ISI [International Statistical Institute], 2011) Leavy, Aisling; Sloane, Finbarr
In this research paper we explore the relationship between pre-service teachers' secondary mathematics scores and their readiness for teaching the new data analysis curriculum in Irish primary schools. Next we explore the leaving certificate items and the procedural responses they evoke. We examine student teacher conceptual understandings and the gaps between these understandings and their procedural knowledge as indexed in their secondary school results. Finally, we explore and test a curricular model to bridge this gap in the practice of instruction.
Staticical preparation of teachers: preservice elementary teachers (PSTs) conceptions of distributions of data – thinking about measure of center and variability
(PME-NA [Psychology of Mathematics Education - North America], 2011) Leavy, Aisling; Thanheiser, Eva; Noll, Jennifer
Prior research investigating PSTs’ statistical thinking is sparse, yet teacher educators need to know how best to prepare future teachers for their work and given the increasing importance of STEM education we need teachers who are capable of preparing students at an early age to think about data. In this paper we share the results from a study investigating pre-service teachers’ (PSTs’) initial thinking about distributions of data in four different contexts. In particular we investigated how PSTs reasoned about different distributions of data - including how they consider measures of center and measures of variability. Data was collected through surveys and interviews conducted prior to their beginning a statistical unit in their elementary teachers mathematics content course.
Next steps in statistics education: identifying teacher professional development needs for teaching the data analysis component of primary level mathematics
(IASE [International Association of Statistics Education], 2009) Leavy, Aisling
This study reveals the pedagogical decision making undertaken when designing instruction for primary level statistics. We report on the activity of five groups of preservice teachers when engaging in Lesson Study and identify the content and pedagogical content knowledge needed for teaching statistics. The research highlights the power of lesson study to reveal aspects of statistical reasoning that are drawn heavily upon in the teaching of statistics and identifies fundamental weaknesses in statistical understanding that may not be uncovered through standard methods of assessment. The paper concludes with suggestions for how we can better prepare teachers for implementing statistics curricula at the primary level.
Lesson study in teacher preparation: driving inquiry and teacher noticing
(WALS [World Association of Lesson Studies], 2018) Leavy, Aisling; Hourigan, Mairead; Ó Ceallaigh, T.J.
Prospective primary teachers understandings of graphicacy (Pre-published version)
(Springer Verlag [Germany], 2016) Leavy, Aisling; Sloane, Finbarr
This paper reports on the statistical knowledge of 456 entry-level, prospective teachers relating to data representation. We report on the responses of participants to three items sourced from the OECD Programme for International Student Assessment (PISA) and the National Assessment of Educational Progress (NAEP). We discuss the implications for the teaching of statistics in classrooms and provide recommendations to improve the statistical experiences of future teachers, and in turn the children they will teach.
An bhearna idir an teanga agus an t-ábhar a dhúnadh sa tumoideachas: Cur chuige bunaithe ar staidéar ceachta
(An Chomhairle um Oideachas Gaeltachta agus Gaelscolaíochta, 2015) Ó Ceallaigh, T.J.; Leavy, Aisling; Hourigan, Mairead
Tá sé léirithe sa taighde go bhfuil éifeacht leis an bhFoghlaim Chomhtháite Ábhar agus Teangacha (FCÁT) i suíomhanna teanga éagsúla. Mar sin féin, níl tuiscint iomlán againn fós ar chomhtháthú teangacha agus ábhar in oideolaíocht an oideachais lán-Ghaeilge. Tugtar tuairisc san alt seo ar conas a thacaigh speisialtóireacht churaclaim i FCÁT, inar díríodh ar theagasc na matamaitice i seomra ranga lán-Ghaeilge, le múinteoirí bunscoile réamhsheirbhíse an bhearna idir an teanga agus an t-ábhar (matamaitice) a dhúnadh sa tumoideachas. Baineadh leas sa staidéar taighde as an Staidéar Ceachta mar chreat struchtúrach chun ceachtanna matamaitice a dhearadh i suíomhanna tumoideachais. Bailíodh sonraí cáilíochtúla ó fhoinsí éagsúla, mar shampla pleananna ceachta na mac léinn, cuir i láthair, machnamh, agus breathnóireachtaí ar an teagasc sa seomra ranga. Soláthraítear leis na torthaí léargais ar leith ar a chasta atá sé ceachtanna ábhair a dhearadh agus a chur i bhfeidhm i suíomhanna tumoideachais. Léirítear freisin leis na torthaí go mbíonn deacrachtaí ag múinteoirí réamhsheirbhíse tuiscint a fháil ar chastacht an teagaisc chothrom teangacha agus ábhar sa tumoideachas. Soláthraítear fianaise leis an taighde seo ina dtaispeántar a éifeachtaí atá próiseas an staidéir ceachta mar atá curtha in iúl le tuiscintí feabhsaithe, saineolas comhroinnte, bailiú eolais, agus dearcthaí úra ar FCÁT arna léiriú ag na rannpháirtithe.
Coordinating student learning and teacher activity – The case of Savannah: Motivating an understanding of representativeness through examination of distributions of data
(St. Patrick's College, Dublin, 2007) Leavy, Aisling
This research study investigated the measures chosen by five 4th to 8th grade students when selecting statistical measures to describe distributions of data. Over the course of eight weeks of instruction, individual teaching experiments were conducted to investigate the development of understanding of distribution. The results indicate that consideration of representativeness was a major factor that motivated modification of approaches to constructing indices of distributions. This paper outlines the case of a 4th grade student who participated in the study and narrates her journey as she grappled with increasingly complex statistical ideas relating to representativeness.
A picture is worth a thousand words: Insights into graphicacy skills of primary prospective preservice teachers
(St. Patrick's College, Dublin, 2009) Leavy, Aisling
Graphs are an integral component of primary and secondary level mathematical experiences as a part of the probability and statistics strand. A review of curriculum implementation in primary mathematics revealed that, relative to other areas of mathematics, teachers found the data strand least useful in the planning for and teaching of mathematics. Furthermore, it was ascertained that data received the least classroom attention leading to the recommendation that research is needed to help ‘develop guidance to support teachers in implementing this aspect of the Mathematics Curriculum’ (NCCA, 2005b, p.7). This paper presents an analysis of the content knowledge skills of 456 preservice teachers in the area of graphical representations in an effort to identify their professional development needs. Participant responses on a survey of statistical knowledge are analyzed and discussed in an effort to identify strengths and weaknesses in graphicacy skills. Tasks were derived from the OECD Programme for International Student Assessment (PISA, 2003) and the National Assessment of Educational Progress (NAEP), the largest nationally representative assessment of school mathematics in the United States. Analysis of the data indicates wideranging difficulties with graph construction, graph selection, and understandings of data type.
Using lesson study to help pre-service teachers bridge the theory-practice gap
(St. Patrick's College, Dublin, 2013) Leavy, Aisling; Carroll, Claire
Lesson study in mathematics: Authentic assessment of inquiry learning
(DCU [Dublin City University], 2014) Leavy, Aisling; Hourigan, Mairead; Carroll, Claire
Classrooms are complex and unpredictable learning environments. Preparing future teachers to respond to the fast changing needs of learners in mathematics classrooms is the challenge of teacher educators. In our paper, we describe the structures we have put in place to support pre-service teachers move beyond being passive recipients of educational theories to becoming critical consumers capable of designing creative and innovative pedagogical approaches. Our approach to inquiry learning in mathematics takes the form of Japanese Lesson Study carried out in partnership with primary schools. Our presentation draws on data collected from 7 years of Lesson study research carried out with 140 pre-service teachers in 28 primary classrooms in Limerick city. Insights into inquiry teaching and learning of primary level mathematics will be provided by the display of video of classroom teaching of mathematics. Video of pre-service teachers reflecting on the process of engaging in inquiry learning is pivotal also to our presentation, in part, because the challenge for us as teacher educators continues long after our pre-service teachers teach their lessons. Our challenge is how to assess their developing understandings of mathematics and mathematics pedagogy? How do we attempt to capture the multiple and interconnected facets of good teaching and planning of mathematics? We share our efforts in assessing the learning of our pre-service teachers as they engage in planning for and teaching inquiry based lessons in mathematics. We report on our attempts to capture and assess learning through the focus on our students’ ability to: engage in research, link pedagogical theories to classroom practice, work collaboratively in groups, design mathematics lessons, observe learners as they engage with mathematics, diagnose difficulties, respond flexibility and thoughtfully to classroom events and reflect on their own development of mathematics content knowledge and pedagogical content knowledge.
Crossing boundaries into secondary mathematics concepts: The case of functions
(St. Patricks College, Dublin, 2013) Hourigan, Mairead; Leavy, Aisling
This paper reports on the use of a particular function machine which was based on the context of the ‘faulty oven’ to develop conceptual understanding of the concept of function among 4th class children. While the concept of functions is traditionally associated with secondary level mathematics, this research shows that the identification of appropriate models and contexts supports primary level children in accessing complex mathematical ideas. This approach was researched, developed, and tested in classrooms as part of a Lesson Study project with pre-service elementary teachers and mathematics teacher educators.
Scholarly electronic journals: economic and technical issues
(Arizona State University, College of Education, 2000) Leavy, Aisling; Ganesh, Tirupalavanam G.; Glass, Gene V.; Andrews, Sandra; Middleton, James A.; Jennings, Tara A.
In this paper we discuss scholarly communication and the emergence of electronic journals. Scholarly electronic journals are expanding their influence. Currently, about 70 peer-reviewed scholarly journals in education are freely available through theWorld Wide Web (http://aera-cr.ed.asu.edu/links.html/). Wider access to scholarship, new possibilities inherent in the electronicmedium, and a shortened publishing lag are some of the issues relating to this expansion. Also, the collision of the financialaspects of traditional print publishing with the ground rules of academic scholarship is contributing to the progress of electronicdissemination of scholarship. Concerns about the quality of scholarly electronic communication are misplaced, since the peerreview can be even more rigorous with on-line journals than with traditional print publications (G. V Glass, 1994). In addition to economic issues, there are a number of medium-specific technical features of electronic publication that offer a huge potential to revolutionize scholarly communication.
Insights into informal inferential reasoning in the primary classroom
(IPMS [International Programme in the Mathematical Sciences], 2009) Leavy, Aisling
Mathematics teaching matters: making complex mathematical ideas accessible to primary level children
(St. Patrick’s College, Dublin, 2011) Leavy, Aisling; McMahon, Aine; Hourigan, Mairead
Reform of mathematics curricula has led to the expansion of topics such as algebra, data and probability being taught to primary level children. This new subject matter can be challenging for primary teachers to teach as some teachers have not previously engaged with these topics as students themselves and also some of these areas have traditionally been considered secondary school topics. Furthermore, while there is a wealth of concrete manipulatives available to teach topics such as number and shape and space there is less so for these ‘newer’ areas of mathematics curricula. This paper reports on the combined efforts of teacher educators, teachers, and pre-service teachers to conceptually engage primary children with algebraic concepts, function and variable, through the use of appropriate models. Lesson Study was the primary method used to support a focus on examining teaching and the effectiveness of models through the design and implementation of ‘study lessons’. Insights into children’s learning of algebraic concepts are presented in addition to an examination of how good teaching using manipulatives can lead to powerful mathematical reasoning by young children. Video evidence of the findings will be presented and discussed.
Teaching statistics at the primary level: identifying obstacles and challenges in teacher preparation from looking at teaching
(IASE [International Association for Statistical Education], 2010) Leavy, Aisling
Preparing preservice primary teachers to teach statistics is a complex endeavor. The challenge is to enrich content knowledge, advance pedagogical understandings, and develop the types of thinking and dispositions necessary to support instruction. This paper reports on two studies of 51 final year preservice primary teachers engaged in ‘lesson study’. Working with preservice teachers provided unique insights into the types of understandings they draw on and the difficulties they encounter when teaching and reflecting on design lessons. The study revealed that for participants the teaching of statistics is perceived as straightforward, content knowledge understandings tend to be weak and limited to procedures, and experiences of investigation is limited. Experiences planning lessons and teaching in classrooms, however, present opportunities for the development of content understandings and for developing sophisticated perspectives on data.
Problem posing and primary pre-service teachers: An initial study
(St. Patrick’s College, Dublin, 2011) Leavy, Aisling; O'Shea, John
Problem solving is an important component of primary mathematics. Central to the activity of problem solving is the task of problem posing. This study examines the skills and predispositions of pre-service teachers when posing problems for use in primary classrooms. The preliminary study was carried out with 36 pre-service teachers at the end of their first semester of a teacher education programme. Participants were asked to construct a problem for use in a primary classroom. Analysis of the problems revealed that problems were very similar across participants and tended to be single step problems with one possible solution. Problems were predominantly computational and focused on procedures and operations relating to quantities. The mathematical content of problems was situated within the number and measurement strands of the primary curriculum. We identify experiences, models and structures that have been shown to be effective in bringing improvements in problem posing in international contexts. Recommendations are made for practice in teacher education contexts to support pre-service teachers in developing the pedagogical skills required to teach problem solving.
Understanding the knowledge demands of teaching statistics: insights gained from examining practice
(CERME [Conference of the European Society for Research in Mathematics Education], 2015) Leavy, Aisling
This research examines the knowledge demands placed on 73 pre-service teachers who are observed as they plan, teach and re-teach data lessons in classrooms. Problems of practice are identified and categorized using the Ball, Thames and Phelps (2008) subdomains of common content knowledge (CCK), specialised content knowledge (SCK), knowledge of content and students (KCS) and knowledge of content and teaching (KCT). The results provide insights into the specific knowledge demands placed on early career teachers when teaching data and statistics and identifies the ways in which these knowledge demands are revealed as pre-service teachers engage in Japanese Lesson Study. The results illustrate that development of understandings in one knowledge subdomain can motivate and impact learning in another subdomain. These interrelationships were found to exist both within and between the domains of content and pedagogical content knowledge.
Insights into the approaches of young children when making informal inferences about data
(CERME [Conference of the European Society for Research in Mathematics Education], 2017) Leavy, Aisling; Sloane, Finbarr
There is growing awareness of the statistical reasoning abilities of young children. In this study the informal inferential reasoning skills of a class of 5-6 year old children are examined as they reason about data in the context of a week-long data investigation unit. The strategies young children use to make predictions about data are identified. A discussion ensues around what these strategies communicate about early understandings of statistical inference. The findings suggest that making inferences from data can be challenging for younger students primarily due to the powerful influence of their developing understandings of number. However, there is evidence that children possess some of the building blocks of informal inference most notably in the approaches that point to a pre-aggregate view of data. Situating data investigations within interesting and relevant contexts, alongside good teacher questioning and opportunities to listen to the reasoning of their peers, contributes to the creation of statistical environments that support and develop early understandings of inference.
Introduction to the papers of TWG05: probability and statistics education
(CERME [Conference of the European Society for Research in Mathematics Education], 2015) Leavy, Aisling; Hahn, Corinne; Eichler, Andreas; Kazak, Sibel; Primi, Caterina
TWG gathered 37 participants from 16 countries. 22 papers and 11 posters were accepted. We started with two ice-breaker activities. The first one allowed participants to introduce themselves. During the second activity, we collected answers to two questions and organized a debate from their answers. The papers were organized into five groups, each of which was managed and chaired by one of the co-leaders.
Moving closer to solving the 'mathematics problem' where it arises: The influence of the 'typical' Irish pre-tertiary mathematics experience on under-preparedness among numerate entrants
(St. Patricks College, Dublin, 2006) Hourigan, Mairead; O'Donoghue, John
The contribution of mathematics proficiency to the numerate (e.g. science, engineering) disciplines is well-documented. Internationally concern exists that graduates of these disciplines are persistently demonstrating mathematical deficiencies i.e. the ‘Mathematics problem’. A connection has been made between this problem and the worldwide reportage of numerate entrants to numerate courses demonstrating insufficient and incomplete mathematical knowledge. While the characteristics of ’at risk’ students are more or less equivalent internationally, the same consensus does not exist in relation to the causes of this phenomenon. There is growing consensus however that ‘under-preparedness’ is caused by the apparent mismatch between the nature of the pre-tertiary and subsequent Tertiary level mathematics experience. This study focuses the ‘Mathematics problem’ from an Irish perspective, exploring the nature of the ‘typical’ pre-tertiary mathematics experience, which in turn provides insight into the nature of the transition required of Irish students entering the numerate disciplines. Brousseau’s ‘didactical contract’ is used as an intellectual tool to uncover the features of the mathematics experience in two case classrooms in Irish upper secondary schools (Senior Cycle). While the authors are both professional mathematics educators and therefore acutely aware of prevalent classroom practice, the restrictive nature of contract and its implications for students’ future mathematics education left all concerned astounded.

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