Mathematics Education

Title:        A child with maths anxiety may become a parent or a teacher with maths anxiety
Speaker: Dr Flávia H. Santos
Time:       November 11, 2022, 2pm

Abstract: Maths is the basis for the most advanced discoveries in science such as satellites and robotic surgeries. Yet, one rarely thinks that these triumphs were grounded during maths classes in primary and secondary schools. These schooling years will prepare individuals for the workforce, and some of them to apply for a university degree. Recent international large-scale assessments found an average high maths score for Irish students compared with other countries. However, when the students’ distribution across the levels of maths performance was analysed, the percentages of Irish students who succeeded in the most complex items, were lower in comparison with other countries with the same average scores (Pitsia et al., 2022). One possible explanation is that Irish students’ achievement was hampered by maths anxiety. Maths anxiety has been observed globally regardless of the country’s wealth; and higher levels have been reported among Irish students (Perkins & Shiel, 2016).
 This article aims to help readers to understand the importance of minimising maths anxiety in home and school environments and to drive the attention of policymakers to the fact that maths anxiety prevalence is shaped by gender and socioeconomic status, among other factors. Because maths anxiety can harm students’ performance, career choices and teachers’ well-being and instruction skills, it must be addressed for the benefit of society and individuals. The article concisely describes maths anxiety and its impact on maths education, good practices in the school environment to mitigate it and showcases a continuous professional development elaborated, under the Arithmós Project, to support teachers to deal with both maths anxiety in students and the anxiety about teaching maths.

Title:        Framing Organizational Change
Speaker: Professor Deborah Moore-Russo, University of Oklahoma
Time:       June 3, 2022 - E1.19 Science East.

Abstract: This talk will begin with an introduction to framing in mathematics education research. Then, it will focus on the theoretical framing being used to study mathematics education-related organizations, such as mathematics tutoring centers. Three different organizational frames will be introduced with time for a participatory discussion comparing the three.

Title:          Computational thinking and mathematical problem solving: the role of animated graphs.
Speakers: Alice Barana & Matteo Sacchet - University of Turin.
Time:         May 13, 2022, 2pm

Abstract: Computational thinking and problem solving are key competences that all individuals need for professional fulfillment, personal development, active citizenship, social inclusion, and employment. In Mathematics, during contextualized problem solving using an Advanced Computing Environment, the differences between these two skills become thinner.
 In this talk, we will discuss a theoretical framework for computational thinking in Mathematics. Then, we will analyze the computational thinking processes behind the creation of animated graphs (animations obtained by generalizing a static graph through the choice of the parameter to be varied and its interval of variation) for the resolution of contextualized problems using an Advanced Computing Environment. To this end, we selected and analyzed some resolutions of problems carried out by 12-grade students. Moreover, we will discuss through some examples how computational thinking in the creation of animated graphs can support the learning of scientific concepts at the school level and in higher education.

Title:        Aiding student success: A multiple methods approach to mathematics support engagement and evaluation
Speaker: Claire Mullen - UCD
Time:       May 6, 2022 at 2pm - Room H1.12 SCH.

Abstract: Mathematics support – an established part of academic support in most English-speaking universities – is shown to increase students’ grades, retention, and confidence yet often students engage too late or not at all, an issue exacerbated by the COVID-19 pandemic. This research aims to increase student engagement in mathematics support in University College Dublin (UCD) and evaluate the impact of that engagement in the context of the changing nature of mathematics support.
 
MathsFit, a suite of online and in-person mathematics supports specifically designed for UCD first-year service mathematics students, seeks to identify and aid those who would most benefit from mathematics support during their transition to university mathematics. A reflective, student-centred cycle of design is used to build a student-specific introduction to university mathematics support. Analysis of the first two iterations of MathsFit is ongoing with the third iteration taking place in September 2022.
 
To evaluate the impact of mathematics support, first thematically analysed interviews of Irish and Australian support students and tutors captured the key issues around online support. Secondly, moderation analysis of longitudinal support data provided evidence of the positive impact of mathematics support in UCD. Finally, the first systematic literature review of mathematics support evaluation literature is in progress to explore the effect of mathematics support internationally. These results, together with MathsFit analytics will show how mathematics support aids student success.

Title:        How can we solve the problem of problem-solving? A focus on classroom-based assessments in Junior Cycle mathematics classrooms.
Speaker: Róisín Neururer
Time:       April 22, 2022, at 2pm - Room E1.19 SCE Science East

Abstract: Problem-solving has been highlighted in recent curriculum reforms internationally and nationally. In Ireland, Project Maths aimed to encourage teachers to incorporate a problem-solving approach into their classroom practice. Problem-solving is further emphasised in the new Junior Cycle mathematics specification, where one of two Classroom-based Assessments (CBAs) focuses on problem-solving. Despite the curricular emphasis, there is little evidence that classroom practice has significantly changed (Jeffes et al., 2013) and teachers are reporting high levels of concern and discomfort regarding these reforms (Byrne & Prendergast, 2020; Berry et al., 2021). While there is a role for professional development to play in alleviating these concerns, we must first gain a deeper understanding of these concerns and the factors that contribute to them.

In this talk, following a brief overview of the relevant literature, I will outline the research I have carried out to date as part of my PhD which investigates the nature of secondary mathematics teachers ‘concerns in relation to problem-solving and the recent reforms. Qualitative data was generated through interviews with 16 post-primary mathematics teachers. I will discuss some of the initial findings before outlining the next steps in this project.

Title:        Performance Assessment for Mathematics Tutor Centers
Speaker: Dr Carolyn Johns - Ohio State University
Time:       Apr 8, 2022, 2pm

Abstract: Evaluation has become a common, and even an expected, practice across undergraduate mathematics tutoring centres in the U.S., U.K., and other countries.  However, these evaluation efforts could benefit greatly from leveraging organisational theory research.  In this study, we situate mathematics tutoring centres as non-profit organisations to consider how an organisation performance assessment framework can be adapted to study mathematics tutoring centre data and characteristics.  We use qualitative and quantitative data, collected from six mathematics tutoring centres, and adapt Lee and Nowell’s (2015) nonprofit organisation performance framework to situate our study.  Using thematic analysis, the research team underwent iterative cycles of data collection and analysis to code for alignment with Lee and Nowell’s framework. 

 By adapting Lee and Nowell’s framework to mathematics centres, each of the six centres was given a more relevant lens to consider its performance.  Regardless of the university setting, previous evaluations for centres have focused primarily on outputs (e.g., number of visits), behavioral change outcomes (e.g., correlating visits to grades), and client satisfaction outcomes (e.g., student surveys) that ignore the particular context of a centre.  However, Lee and Nowell’s framework takes into account additional performance indicators that provide a more nuanced understanding of a centre’s performance by bringing to light the interplay among its various dimensions.  Lee and Nowell’s framework allows centres to look beyond outputs and outcomes to understand why these outputs and outcomes come to be.  The use of this adapted performance framework, for the six mathematics centres in this study, allows an interpretation on a variety of dimensions using relevant data while indicating possible areas for change for each centre. 

Title:        Inclusive learning using intelligent technology
Speaker: Cathal O'Connor Microsoft Ireland and UCD
Time:       March 25, 2022, 2pm

Abstract: Text to speech (TTS) and read aloud tools are widely used in higher education to provide support for students with reading difficulties such as dyslexia. The development of neural TTS systems based on deep learning and artificial intelligence (AI) has significantly improved the quality of synthesised speech in the last 3 years, however, challenges remain. This talk will examine the latest research in speech, language, and AI, and discuss how future research can help reduce barriers to inclusive learning for students with dyslexia.

Title:        Irish post-primary students’ knowledge of algebra.
Speaker: Aoife O'Brien - Galway-Mayo Institute of Technology
Time:       Feb 18, 2022, 2pm

Abstract: This research aims to investigate the algebraic under performance of second year post-primary students in Ireland (approximate age 14 years). To this end a diagnostic test for algebra has been developed to profile and identify students who are struggling with algebra. This paper examines the development of the test, which involved the identification of key mathematical content areas that are critical for success in algebra. Both prerequisite, and algebra content areas are key to a studentsâ success in algebra and how each of these areas contribute to a studentsâ progress with algebra is discussed in this theoretical paper. Test items have been selected and adapted from the literature which are aligned with both the key content areas and the Irish mathematics syllabus at junior cycle, the initial three years of post-primary education in Ireland.

Tiltes:        1. Teachers’ Perceptions of The Impact of The Grinds Culture: A Focus on Post-Primary
 Mathematics, and 2. The Uptake of Higher Level  Mathematics: A student analysis.
Speakers: Mark Prendergast (UCC) and Niamh O'Meara (UL)
Time:         Jan 14, 2022, 2pm

Abstract: 1. Grinds can be defined as education outside the formal schooling system where a tutor teaches a particular subject(s) in exchange for a financial gain. Their provision has become a widespread phenomenon internationally in recent years, no more so than for the subject of mathematics. In this talk we seek to investigate mathematics teachers' perceptions of the impact of the grinds culture in the subject at post-primary level in Ireland. The data was gathered using an online survey designed by the authors and circulated to post-primary mathematics teachers in November 2020. The findings from responding teachers (n = 305) revealed mixed opinions, with both positive and negative impacts identified. Many teachers acknowledged the benefits of one-to-one support that grinds can provide and the resulting increase in students' confidence in the subject. However, teachers also noted that for some students' grinds can be a substitute for a lack of motivation and work ethic and their provision can often lead to disengagement in class.

2. There is a large body of research which highlights the importance of students studying mathematics at an advanced level and many Governments and policy makers worldwide are constantly looking at ways to increase the uptake of advanced mathematics. In Ireland, the Bonus Points Initiative was introduced in 2011 in an attempt to increase the number of Senior Cycle students opting to study higher level mathematics and to improve Irish students’ mathematical capabilities. Despite a rise in the number of students studying higher level mathematics at this time very little research has been conducted to determine if it was the initiative, the new curriculum or other factors that led to the surge in uptake. This study investigates Irish students’ reasons for participating in higher level mathematics and seeks to determine if the reasons for studying higher level mathematics differs across gender. The findings suggest that the points system currently in place in Ireland is the main driving factor behind students’ participation in higher level mathematics while parents are very influential actors in the decision-making process also. Differences in the reasons offered by males and females were also unearthed with higher levels of mathematical self-efficacy among male respondents influencing their decision to study higher level mathematics.

Title:        Developing an Algebra Concept Inventory to inform the design of teaching materials for students.
Speaker: Dr Diarmaid Hyland - Maynooth University
Time:       Dec 3, 2021

Abstract: In this talk, I will describe my current work on the teaching and learning of algebra at third level in Ireland. The overall aim of the project is to design targeted teaching materials (e.g., tutorials, workshops, etc.,) based on students' understanding of school algebra as they enter third level education. In order to measure their understanding, we designed an Algebra Concept Inventory (ACI). Concept Inventories are MCQs where items assess conceptual understanding only - that is, there are no questions that require calculations, or recall of facts. Based on the results of the ACI, we can identify areas where improvements to student understanding can be made. I discuss one such area, as well as how the project has progressed and what we learned.

Title:        SPIRIT Maths: From student perceptions to targeted digital resources
Speaker: Dr Violeta Morari - Munster Technological University
Time:       October 22, 2021 at 2pm

Abstract: SPIRIT Maths is a project that was established in Munster Technological University (MTU) in 2020 to investigate students' attitudes towards mathematics and to explore a more student-centred development of mathematics resources. This talk presents an overview of the SPIRIT Maths project. First, we will discuss some of the findings of a survey of first-year students in MTU that focused on students' expectations and the realities of experiencing mathematics in college, their views on remote delivery and approaches to learning. Informed by the findings of this survey, three interlinked digital resources were developed: 

(1) a series of H5P interactive self-assessment questions, 

(2) corresponding videos showing worked solutions and 

(3) an associated bank of practice questions developed through Numbas. 

Next, we will explain how the resources that were created are being promoted to students. We also report on the feedback received from a number of students who tested the resources and discuss how to measure student engagement with the resources over the coming academic year. Finally, we consider how to measure the impact that the resources might have on students' success in their mathematics modules. The talk will be of interest to mathematics lecturers who wish to explore the use of targeted digital resources to support learners.

Title:        The Knowing How of Topology
Speaker: Dr Ashley Berger - University of Oklahoma
Time:       June 4, 2021

Abstract: Research on students' thought processes shows that many undergraduate students and even beginning graduate students find a first course in Topology challenging. My dissertation work aims to study the nature of students’ difficulties with grasping Topology using the lens of a schema. Skemp (1979) defines a schema as a structure of connected concepts that determine the effectiveness of our director systems, which are what directs our thoughts and actions, including problem-solving, proof-writing, and other ways of thinking about mathematics. Based on Skemp’s theories, I have created a conceptual framework to analyze Topology students’ thought processes while solving specific tasks. In this talk, I will present this framework, coupled with some data from my dissertation work.

Title:          An Analysis of Tutors’ Responses to Linear Algebra Students’ Queries in a Mathematics Support Center
Speakers: Dr. Anthony Cronin, University College Dublin and Prof Sepideh Stewart, University of Oklahoma
Time:         May 7th, 2021, 2pm

Abstract: In this study, we utilized Mason’s (2002) pedagogical tactics and built a conceptual framework to analyze mathematics tutors' responses to Linear Algebra 2 students’ queries in a mathematics support center (MSC). The overarching dimensions were questions, examples, being mathematical, problem solving, and creating an atmosphere of mathematical thinking. The aim of this research was twofold: firstly, to investigate the nature of difficulties students experienced with various concepts in a second course in linear algebra emphasizing theories and proof, from the perspective of MSC tutors; secondly, to examine the tactics employed by these tutors to resolve student difficulties. We analyzed 227 feedback comments from 44 tutors based on their interactions with 82 students at the MSC over a six year period. Our findings indicated that the most common areas of difficulty for these students were basis, vector space, subspace, span, and proof.  In this talk, we will present more results based on the framework as well as some implications for linear algebra tutor training.

Title:        Integrating Programming in Mathematics Education: A Case of Undergraduate Students’ Combinatorial Thinking in a Computational Setting
Speaker: Professor Elise Lockwood - Department of Mathematics, Oregon State University
Time:       Thursday 29th April 2021, 4pm

Abstract: Computational activity, and programming in particular, comprise an increasingly essential aspect of mathematical activity, and engaging in computing is as accessible as it ever has been. Given the growing influence of computers within mathematics, we, as mathematics educators, should strive to integrate computational activity into our students’ mathematical experiences, providing opportunities for students to engage with computational tools as they reason about and learn mathematical concepts. In this talk, I present findings from a study in which undergraduate novice programmers engaged with Python programming as they solved combinatorial problems. I highlight noteworthy aspects of students’ experiences with computing in this mathematical context, including benefits and drawbacks of a computational environment. I suggest that even for students with little programming experience, the computational environment supported their combinatorial reasoning in valuable ways. I conclude by addressing practical issues related to implementation and discussing pedagogical implications.

Title:        Changes in curriculum and assessment for school mathematics: Ireland in international context
Speaker: Elizabeth Oldham, Trinity College Dublin
Time:       9 April, 2021, at 2pm

Abstract: This will be interactive with Elizabeth to send on materials closer to the time.

Title:        Commognition Theory & Transition to university mathematical discourses: A commognitive analysis of first year examination tasks, lecturers’ perspectives on assessment and students’ examination scripts
Speaker: Dr Athina Thoma - University of East Anglia, UK
Time:       Friday 26th March 2021, 2pm

Abstract: Commognition (Sfard, 2008) is a widely used theoretical approach within the mathematics education research community. In this talk, I first discuss the main tenets of Sfard’s commognitive theory (discourse, object and meta-level learning, and commognitive conflict). Then, I present data (examination tasks, lecturers’ interviews and students’ scripts) from my doctoral study (Thoma, 2018), focusing on the transition from secondary school to university mathematics at the setting of closed book examinations. The analysis illustrates that students are given directions aimed at their enculturation; lecturers design the tasks being aware of students’ difficulties and aiming to assist in a smooth transition between the mathematical discourses. However, students’ scripts showcase evidence of commognitive conflicts between school and university discourses; and, different mathematical discourses. Finally, I share some highlights of the recent publications in the Journal of Mathematical Behaviour Special Issue on Advances in Commognitive Research (Editors Cooper & Kontorovich).

Title:        Educational Leadership for STEM: The Gender Dimension
Speaker: Dr. Mary Cuneen - UCD
Time:       November 27th, 2020 at 2pm

Abstract: In Ireland there are significant gender imbalances in STEM (science, technology, engineering, and mathematics) subject choices made by male and female students at the post-primary level. Data on STEM subject enrolments indicate that the take up of the physical sciences and technology subjects is lower amongst girls, and the availability of these subjects is also more limited in all-female schools. It is critical to encourage greater participation of girls in these subject areas in order to address national skills needs and respond to the actions required in the STEM Education Policy Statement 2017-2026 (Department of Education and Skills, 2017).

Title:        Mathematics Education Research at University: Collaboration with Mathematicians
Speaker: Associate Professor Sepideh Stewart (University of Oklahoma, USA)
Time:       Wednesday 22nd May 2019, 12.00-13.00
Location: Room N1.25 North Science (O'Brien Centre), UCD

Abstract: In this talk I will discuss some studies from my research program on collaboration with mathematicians over the past decade. During these studies, the mathematicians took daily journals and reflected on their teaching on a variety of mathematical topics (Abstract Algebra, Calculus, Linear algebra, Algebraic Topology). The duration of these studies ranged from 1-2 years. The unique and extremely valuable aspect of these studies was the fact that the participants were active members of the research team and were not treated as subjects. The participants were involved in every aspect of the research as well as writing the manuscripts and sometimes presenting at mathematics education conferences. Two mathematics education frameworks, namely, Tall’s (2013) three-world model of mathematical thinking and Schoenfeld’s (2011) framework of Resources, Orientations and Goals, were employed to further explain our understanding of the complexity of these studies and the data that was generated.
I will also briefly discuss some of our recent case studies of students’ difficulties with school algebra in calculus.

Title:        Linking theory with practice: How mathematics education can inform teaching at 3rd level
Speaker: Diarmaid Hyland (DCU)
Time:       Friday 3rd May 2019, 1.30pm
Location: UCD Maths Support Centre, Library Building

Abstract: An emerging concern in mathematics education in recent years is a widening of the gap between theory and practice. Major conferences have devoted plenaries to this discussion, acknowledging that advances in education research are influencing practice less and less in recent years. Though many factors combine to cause this, what is certain is that student learning is not optimized without meaningful communication and collaboration between researchers and practitioners.
In this talk, task design as a way to bridge the gap between theory and practice is discussed. Empirical research will form the basis for the talk. In addition, examples from research conducted in DCU will punctuate the discussion. The examples used are in the context of basic algebra and calculus, and ordinary differential equations. The talk will be accessible to anyone with an interest in mathematics education at third level.

Title:        Time allocated to mathematics in post-primary schools in Ireland: are we in double trouble?
Speaker: Niamh O’Meara (UL)
Date:       Friday 14th December 2018, 1pm
Location: UCD Maths Support Centre, Library Building

Abstract: Dr Niamh O’Meara is a lecturer in mathematics education based in EPISTEM, the National Centre for STEM Education in the University of Limerick. Her research interests include investigating issues surrounding mathematics teacher education; teacher knowledge; curricular issues; the transition from primary to post-primary mathematics education and the use of mathematics in a variety of careers.
On December 14th Niamh will speak about three projects that she has been involved with in recent times. She will firstly discuss an Irish Research Council funded project entitled Time in Mathematics Education (TiME). This was the first study in Ireland that quantified the time allocated to mathematics and Niamh will discuss some of the findings that emerged from this national study including the variation in time allocated to mathematics across different schools and across different year groups; as well as how time is allocated to mathematics; teachers’ levels of satisfaction with the current allocations and its impact on curriculum implementation; and the prevalence of out – of – school teaching time in the subject of mathematics. Niamh will also discuss a project that she is working on in relation to the provision of Bonus Points for higher level mathematics. The Bonus Points initiative, introduced in 2010, appears to have led to an increase in the uptake of higher-level mathematics but at what cost? Niamh will report on teachers’ opinions of this initiative and discuss how they feel it has impacted on class profiles and on teaching strategies. The impact of this initiative on both teachers and students will be discussed. Finally, an ongoing project that Niamh will report on is concerned with determining pre-service teachers’ levels of knowledge and understanding. She will discuss a potential model that has been used to investigate teachers’ level of knowledge and understanding and will outline some findings in relation to teachers’ knowledge of linear equations and the impact that such levels of knowledge can have for their own teaching.

Title:                   Teaching Undergraduate Mathematics with Clickers and Classroom Voting
Speaker:            Professor Kelly Cline (Carroll College, Helena, Montana, USA)
Time:                  Monday 13th November 2017, 3p.m.
Location:            Room 2.38 Science HUB (O'Brien Centre for Science), UCD
Coffee Meeting: Common Room at 14.15 p.m.
All members of the school, all postdocs and PhD-students are cordially invited!

Abstract: Classroom voting with clickers is a powerful way to create a highly interactive lesson and to engage students in discussions about mathematics. This talk will report on what we’ve learned while conducting several studies of classroom voting in mathematics. How do we organize voting to maximize student engagement and learning? How do we teach all the necessary topics, given the amount of time that classroom voting requires? Research indicates that creating student discussions is a key to how classroom voting impacts student learning. What types of questions produce memorable discussions? What are the best ways to guide student discussions after a vote? What insights can we gain by studying how students vote on different questions? Finally, we’ll introduce our free web-based library containing over 2,000 clicker questions designed for classroom voting in mathematics.