Supporting adults to become numerate citizens: a study of adult numeracy provision in Ireland

This paper revisits and reanalyses data from a study carried out in the further education and training sector in the Republic of Ireland to investigate (1) how adults access and participate in numeracy courses and (2) how adult numeracy provision might support active citizenship. We analysed 45 interviews with adult education providers, adult numeracy tutors, and adult learners to identify themes that connect adult numeracy with a human rights conception of citizenship as access to and participation in economic, social, and community life. This analysis found that the most common barriers to accessing adult numeracy courses arose from dispositional factors relating to fear, anxiety and lack of confidence with mathematics, largely due to negative experiences in formal schooling. To overcome these barriers, adults’ participation in numeracy courses was encouraged by integrating numeracy learning activities into real world contexts in a non-threatening learning environment. The interview analysis also illustrated ways in which adult numeracy education supported active citizenship in the economic, social, and community spheres, by (i) enhancing financial literacy and preparing adults for employment; (ii) fostering individual empowerment, family learning and social inclusion; and (iii) enabling civic engagement. Policies for promoting adult education typically aim to develop active citizenship, but without specifying how this is to be achieved. Our study is valuable because it illuminates potential connections between citizenship and numeracy as a dimension of adult education that is separate from literacy. The findings lead to recommendations for translating national and international policy frameworks into research-informed adult education programs.


Introduction
International research on policy and practice in adult numeracy endorses the critical importance of numeracy for active citizenship, individual life chances, and the social and economic health of nations.Adults who struggle with numeracy earn less income, have more trouble finding employment, and experience poorer physical and mental health than people with higher numeracy skills (Carpentieri et al., 2010;Grotlüschen et al., 2019;Parsons & Bynner, 2005).
different picture emerges of the capabilities of Ireland's adult population.The OECD's Programme for International Assessment of Adult Skills (PIAAC) conducted in 2012 showed that around one-quarter of Irish adults scored at or below Level 1 on the six-level numeracy scale (Central Statistics Office, 2013).At Level 1, adults struggle to carry out basic arithmetic operations and procedures needed to function in everyday life.For this reason, the original aim of our national study was to develop guidelines for adult numeracy provision to improve the numeracy capabilities of Irish adults.However, the interviews conducted as part of this study also yielded insights into the significance of numeracy for citizenship.In this paper, therefore, we apply a citizenship lens to the interview data to further explicate this relationship and advance knowledge of numeracy for citizenship in international contexts.

Background and context
Adult education in Ireland has historically subsumed numeracy within a broad definition of literacy.The government's current adult literacy strategy states that "literacy involves listening and speaking, reading, writing, numeracy and using everyday technology to communicate, access services, and make informed choices" (Government of Ireland, 2021, p. 7).Although this definition does not clearly distinguish between literacy and numeracy, the strategy document argues that more attention needs to be given to building adults' numeracy skills.
In Ireland, adult numeracy education typically targets those who have had limited opportunities or significant difficulties in learning mathematics in a formal school environment.These difficulties usually affect older adults and may have arisen from interruptions to schooling or early school leaving.Other vulnerable groups in need of numeracy support include migrants and refugees, long-term unemployed or low-paid workers, persons with disabilities, and ethnic minority groups such as Irish Travellers (Government of Ireland, 2021).Historically, Travellers have experienced exclusion and disadvantage in housing, health, employment, and education.For example, Boyle et al. (2020) reported that "only 8% of Travellers have completed secondary education compared with 73% of non-Travellers, and only 1% have a college degree" (p.1390).
Responsibility for providing numeracy education to adult learners in Ireland lies with a number of state bodies.SOLAS, the agency that manages Further Education and Training (FET) programs, along with the Education and Training Boards (ETBs), fund all numeracy programs so that adult learners participate free of charge.The ETBs are also responsible for the design and delivery of numeracy courses, which may be either standalone or integrated.
Standalone numeracy courses explicitly address the mathematical demands of particular contexts, such as mathematics for trades and financial mathematics.Numeracy is also integrated into general learning certificate programs in areas such as gardening, horticulture, and internet skills (Byrne, 2017).There is no national curriculum for adult numeracy education in Ireland and no standardised course materials or textbooks for numeracy courses.Instead, each ETB and its numeracy tutors can either draw on existing resources or develop new materials.Most tutors are employed parttime or are volunteers.While professional development is offered to tutors, there is no formally accredited numeracy tutor training and no requirement for tutors to possess recognised teaching qualifications in mathematics or any other subject discipline.
Responsibility for the accreditation of numeracy programs lies with Quality and Qualifications Ireland (QQI).Adult numeracy courses are accredited using the 10-level National Framework of Qualifications (QQI, 2021) and tend to be offered at Levels 1-4 (see Table 1), corresponding to knowledge and skills that are mainly concrete and applied in practical contexts.
In 2021, there were over 50,000 Irish adults participating in literacy programs, mainly provided by the ETBs (National Adult Literacy Agency [NALA], 2021).Because adult numeracy is considered to be a component of adult literacy, there is no data collection to show how many adults access or persist with numeracy-specific provision.However, the most recent QQI data shows that adults received 1708 Level 2 awards and 1733 Level 3 awards for courses with a mathematics component (Byrne, 2017).Lack of data on adult numeracy is a challenge for most countries that needs to be addressed to inform evidence-based national policies for improving adults' numeracy capabilities (UNESCO Institute for Lifelong Learning, 2020).
3 Research and policy in adult numeracy and its relevance to citizenship

Understanding adult numeracy
Numeracy involves more than simple arithmetic skills and it cannot be defined solely by reference to the content of mathematics learned at school (Hoogland & Díez-Palomar, 2022).Instead, numeracy is inseparable from its context and is driven by issues that people encounter in their everyday lives and work.Contemporary scholarship views numeracy as a multi-dimensional concept involving the use of mathematical knowledge, tools, dispositions, and critical thinking in a variety of real-life contexts (Geiger et al., 2015).
Although the importance of numeracy in the modern world is widely acknowledged, the numeracy knowledge and practices that people use can often be invisible to them (Diez-Palomar, 2020;Keogh et al., 2019).This is particularly the case with adult numeracy.Adult numeracy relates to the ways people manage the mathematical, quantitative, and statistical demands of adult life (Gal et al., 2020).There has been increased attention to adult numeracy in recent years because society is undergoing rapid technological, digital and environmental transformation (Hoogland et al., 2019).The United Nations Sustainable Development Goals (SDGs) Target 4.6 calls on countries to "ensure that all youth and a substantial proportion of adults, both men and women, achieve literacy and numeracy" by 2030 (United Nations, 2015, p. 21).Such increased attention to adult numeracy and its evolving role is also evident through its inclusion in large-scale international assessment programs.
The OECD's PIAAC defines adult numeracy as "the ability to access, use, interpret and communicate mathematical information and ideas in order to engage in and manage the mathematical demands of a range of situations in adult life" (PIAAC Expert Numeracy Group, 2009, p. 21).A recent review of the PIAAC assessment framework recommended incorporating additional competencies, such as dispositions to use mathematics, the ability to "see" mathematics in a numeracy situation, critical reflection on methods used and results obtained, consideration of the degree of accuracy required in real-life calculations, and use of digital technologies (Tout et al., 2017).These proposed developments to the PIAAC framework show that the concept of adult numeracy continues to evolve with the changing mathematical demands of 21st -century life and work.
From an Irish perspective there has been much research since the turn of the century in understanding adult numeracy.For example, the work of O'Donoghue (2002) and Maguire and O'Donoghue (2003) has been central to the evolving conception of numeracy, shifting from a narrow view founded on basic arithmetic to include more complex cognitive skills such as problem solving and communication.These skills are particularly important in the workplace, as Keogh, Maguire, and O'Donoghue (2019) demonstrate in their analysis of the mathematics and numeracy skills embedded in different types of work in Ireland.

Adult numeracy and citizenship
Adult education policy and practice aims to develop active citizenship (European Association for the Education of Adults [EAEA], 2019; UNESCO Institute for Lifelong Learning, 2019).However, the meaning of citizenship is dynamic, contested, and multidimensional.Schugurensky (2006) proposes that citizenship can be understood through at least four dimensions: status, identity, civic virtues, and agency.The status dimension is usually associated with nationality, through one's membership of a nation-state.Identity refers to feelings of belonging to a particular community.Civic virtues denote the dispositions expected of a "good citizen", while citizenship as agency sees citizens as social actors who navigate the possibilities and constraints inherent in society's structures and power relations.
In Ireland, the notion of citizenship implied by the national adult literacy strategy relates citizenship to "well-being and active participation in modern society" (Government of Ireland, 2021, p.53), with the strategy document also citing access to everyday human rights related to employment, housing, health, education, welfare and social inclusion.The Adult Literacy for Life (ALL) document highlights that unmet numeracy needs "impacts areas of active citizenship, such as the likelihood to volunteer or to vote, and influences the overall trust in institutions" (p. 7).Such impacts were also highlighted by Tout (2020), who noted the importance of numeracy for enabling citizens as critical consumers to discern between trustworthy and dishonest sources.These skills are recognised as important not only within Ireland, but also from a European and a global perspective.The UNESCO (2019) Fourth Global Report on Adult Learning and Education (GRALE) illustrates how adult learning and education can promote active citizenship.Similarly, the European Association for the Education of Adults (EAEA) community, and civic life and thus reduce their capacity for active citizenship.
Given the policy context of our study of adult numeracy provision in Ireland, we take a human rights conception of citizenship in terms of access to and participation in economic, social, and community  Two interview schedules were used, one for ETB staff (AEOs, ALOs) and tutors and one for adult learners.Because the aim of the larger study was to map the provision of numeracy support in adult further education and training to develop good practice guidelines, the interview questions were designed to elicit participants' views on adult numeracy policy and practice and recommendations for future development.For these reasons, interviews with ETB staff and tutors asked about their perception of the ethos that informs adult numeracy provision; how numeracy programs and activities are developed; how participants gain access to and are recruited to programs; the content, activities and strategies used in delivering numeracy sessions; how local community partners are involved; the qualities needed by adult numeracy tutors; and the benefits experienced by those who participate in numeracy activities or programs.Adult learners who were interviewed were asked to describe when they left school; how they experienced learning mathematics at school and what difficulties they faced; what job they worked at after leaving school and whether they had ever felt unable to fulfil their plans for the future.They were then asked to describe their experiences in accessing and participating in adult numeracy classes, notes that the aim of adult education is to promote learning as a "necessary prerequisite to access participation in democratic processes" (EAEA, 2019, p. 9).However, despite active citizenship being identified by the European Commission (2016) as one of eight key competences for lifelong learning, its New Skills Agenda for Europe report highlights that more must be done to ensure that competencies such as citizenship have an established place in education systems.Thus, while international and national policies claim there are links between numeracy, adult education, and citizenship, the nature of these connections remains unclear and little guidance is available on how to design adult numeracy programs that promote active citizenship.
Poor numeracy denies adults their human rights as active citizens and has significant impacts on individuals, their families and communities.At the individual level, adult numeracy learners have often had poor experiences of formal education leading to fear, anxiety and lack of confidence with mathematics.Bibby (2002) suggests that many adults have experienced shame as a lasting affective response to traditional mathematics teaching that emphasises memorisation of rules and procedures and punishes students whose answers are not "correct".Because the affective domain is so significant as a cause of negative attitudes and beliefs towards mathematics, adult numeracy programs aim to create an informal and non-judgmental learning environment that is noticeably different from the normal school experience (Carpentieri et al., 2010).Adult numeracy tutors are encouraged to link mathematics to learners' lives and work (Ackland, 2014), which contributes to a sense of social belonging consistent with the identity dimension of citizenship (Schugurensky, 2006).
Individuals' numeracy capabilities are also related to employment prospects and earnings (Carpentieri et al., 2010;Parsons & Bynner, 2005;Shomos & Forbes, 2014), with low numeracy skills associated with unemployment, under-employment, low incomes, and unskilled jobs.Low levels of numeracy among adults have other far-reaching consequences for family members when they do not have real learning opportunities (NALA, 2019).In the UK, Carpentieri et al. (2013) found that parental numeracy skills were a stronger predictor of the numeracy skills of their children than parental qualifications or profession, which draws attention to the damaging potential of intergenerational cycles of inequality and disadvantage.In addition, community and social participation, indicated by involvement in clubs or community activities, volunteering, and voting, is lowest amongst adults with the poorest grasp of numeracy or literacy (Bynner & Parsons, 2006).Taken together, the damaging consequences of low numeracy skills can act as barriers to adults' access to and participation in social, this process we became aware of patterns of meaning that indicated the potential for adult numeracy support to promote active citizenship -a new focus we had not anticipated when beginning the data analysis.This awareness guided a search for latent themes (stage 4) that would allow us to view the data through the dual theoretical lenses of adult numeracy and citizenship.An iterative process of reviewing (stage 5), defining and naming themes (stage 6), in tandem with deeper reading of theoretical and policy literature on citizenship in the adult numeracy context, led us to formulate the two new research questions that are addressed in this paper (stage 7).Table 2 shows the primary data codes and the associated participant sources, as well as the themes that connect adult numeracy and citizenship.(Note that not all the identified codes are assigned to the citizenship-related themes discussed in this paper.)

Results for research question 1: how adults access and participate in numeracy courses
To address the first research question, we draw on the perceptions of ETB staff, tutors, and adult learners about access and barriers to participation and the numeracy learning activities offered to adults.

Access and barriers to participation
All ETB centres reported a variety of strategies for recruiting participants to numeracy courses, including print/radio/ television advertising, referrals from social welfare agencies, home-school liaison officers, and outreach to other community groups.Table 3 shows the categories that were developed in response to interview questions about barriers to participation and the numbers of ETB sites in which these responses were recorded for the three participant groups -AEO/ALOs, tutors, and adult learners.
their reasons for enrolling in the course, their relationship with the adult numeracy tutor, and how they had benefited from participating in numeracy activities.
We used qualitative, interpretive methods of data analysis to understand the meanings that people give to their experiences.Braun and Clarke's (2006) approach to thematic analysis of qualitative data allowed us to move back and forth between theoretically derived themes and those that occurred naturalistically within the data.The seven stages of their thematic analysis framework are: 1. transcription.2. familiarisation with the data.3. generating initial codes.4. searching for themes.5. reviewing themes.6. defining and naming themes, and 7. writing the report.
Following transcription of the recorded interviews (stage 1), the first author selected 20 transcripts from six ETB sites to share between research team members for repeated reading and annotation (stage 2).A summary table was created to copy and paste excerpts from each transcript into cells defined by the interview questions.The inductive process of generating initial codes (stage 3) involved identifying aspects of the data that related to our starting goal of documenting participants' views on numeracy policy and practice.After the team compared and verified interpretations of transcript excerpts, a second round of familiarisation and generating initial codes was undertaken, involving scrutiny of nine transcripts from a further four ETB sites.The team met again to compare interpretations of this second group of transcripts.At this point it appeared that the generation of codes was approaching saturation, since few new insights were emerging.Thus, the third round involved only a scan of transcripts from the remaining six ETB sites to check for any further examples or contradictory evidence.During For adult learners (7 ETB sites), school experience was likely the cause of their sense of fear and failure: The study by Boyle et al. (2020) of Irish Traveller parents' experiences of their own schooling unearthed stories of alienating school environments that left them feeling ignored, unchallenged, stereotyped, and marginalised.In these circumstances, it is not surprising that many Travellers learned very little at school and left early with no qualifications and poor literacy and numeracy.
Survey research investigating reasons for participation and non-participation generally in adult basic education has identified a range of motivational factors, low perception of need, high perceived effort, dislike for school, and situational barriers such as family and work responsibilities to explain why adults are deterred from participating or choose not to participate (e.g., Beder, 1990;Beder & Valentine, 1990).In Ireland, there is some evidence that dispositional factors are the most common barriers to participation specifically in adult literacy programs (NALA, 2010): these factors arise from adults' prior negative experiences of formal education and the stigma attached to literacy difficulties, manifested as low self-esteem and lack of confidence in learning.However, because adult numeracy is subsumed into adult literacy provision, little attention has been given to numeracy-specific barriers.Our interview data sheds some light on this phenomenon.
Table 3 shows that AEOs and ALOs interviewed at two ETB sites cited situational barriers, including family and work commitments, lack of transport, and individual circumstances (e.g., mental health issues, homelessness) as barriers to accessing adult numeracy courses.These factors were also mentioned by adult learners at another two ETB sites.Overwhelmingly, however, all participant groups identified dispositional factors as the main hurdle.
Table 3 indicates that negative affective reaction such as fear, anxiety, stigma, and lack of confidence was the most common dispositional barrier identified by AEO/ALOs (7 ETB sites) and tutors (11 ETB sites) as discouraging participation in numeracy courses: Tutor: Fear, yeah they're terrified, they hear the word maths and they just blank out.(Site 6) ALO: The formality, the idea of having to go in and meet somebody and sit down and explain your difficulty.Especially to somebody local.So the fear a lot of people would have is that "I'll meet my neighbour.Or it'll be someone I know will be working in there.And I'll have to explain to them why I'm after walking in the door."(Site 6) Similarly, adult learners (7 ETB sites) spoke of the embarrassment attached to approaching an ETB centre: The third dimension of numeracy learning activities stressed by tutors involved creating an informal, non-threatening learning environment (12 ETB sites) so that "They feel like there's no stupid question, you can say whatever you want" (Tutor, Site 7).
Adult learners described a wide range of practical activities they experienced in numeracy courses, such as working out discounts when shopping, reading a measuring tape when measuring windows for making curtains, or learning to add and subtract by playing darts and keeping the score.However, as can be seen in Table 4, the most salient aspect of their numeracy learning experience (identified at 10 ETB sites) was the non-threatening numeracy learning environment that contrasted with their prior experience of learning mathematics in school: Adult learner: It's a very safe environment and we all feel comfortable.And usually when I was going to school you'd never ask a question in class because you'd be made to feel so stupid whereas here in ETB you can ask any question you like.(Site 5)

Nature of numeracy learning activities
As indicated in Sect.2, numeracy courses in Ireland are offered in either standalone or integrated modes.Yet ETB staff reported that standalone numeracy courses rarely attract adult learners because of their desire to hide their difficulties with mathematics.As one ALO commented: "Nobody ever comes in and says, 'You know what, I'd like to do numeracy.'Or even mathematics" (Site 11).Instead, adult learners who approach an ETB enrol in other courses, through which they may gain confidence in tackling courses in which numeracy is embedded.ETBs are skilled at integrating numeracy into courses that do not carry this label (e.g., courses on food and nutrition, personal effectiveness, or information technology).In these integrated courses, adult learners can develop their numeracy abilities in a meaningful context without the stigma of revealing they need help with mathematics.However, ALOs (Site 2) and tutors (Site 7) noted that the prescribed approach to formal evaluations of ETB course effectiveness makes it difficult to capture these "hidden" numeracy moments and to measure how adult learners use their numeracy skills in real world contexts outside the classroom.
Table 4 shows the categories that were developed in response to interview questions about the nature of numeracy learning activities and the numbers of ETB sites in which these responses were recorded for the three participant groups -AEO/ALOs, tutors, and adult learners.
Table 4 reveals that the pattern of interview responses varied across groups.AEO/ALOs responsible for overall program management consistently emphasised the integrated, real world, practical nature of numeracy activities that responded to adult learners' interests and needs rather than being bound by a prescribed curriculum (15 ETB sites): ALO: We want to bring numeracy to life.Like orienteering or practical things, giving someone a skill, an experience, a confidence in doing something they didn't think they'd be able to do.(Site 6) Tutors echoed this emphasis (16 ETB sites) and explained how they looked for authentic materials to support numeracy learning: These examples suggest that growing numeracy skills also developed self-advocacy, supporting a version of citizenship as agency that enables adult learners to question authority.Access to participation in economic life is also closely tied to employment.Many research studies have found a strong connection between numeracy skills, employment status, job type and income, and prospects for career advancement (e.g., Parsons & Bynner, 2005).Table 5 indicates that AEO/ALOs (10 ETB sites), more so than other respondent groups, referred to employment prospects as providing motivation for developing the necessary numeracy skills to find a job and thus participate in the economic life of their community: ALO: They're mostly unemployed, out of the labour force or maybe even on a disability dependent spouse [benefit].So they're looking for work but not necessarily wanting to yet because they want to get their skills where they feel that they should be.(Site 8) This analysis of numeracy learning activities shows how programs use familiar, everyday contexts to re-engage adult participants with functional mathematics following mostly unsuccessful experiences of encountering mathematics at school.While ETB management staff (AEO/ALOs) prioritised the integrated, learner-centred ethos of adult education, tutors who interacted directly with adult learners were more concerned with finding relevant contexts for numeracy.For adult learners, however, an inclusive and non-judgmental numeracy learning environment was central to their engagement with numeracy.

Results for research question 2: how adult numeracy provision might support active citizenship
We consider the second research question in terms of our previously articulated human rights conception of citizenship as access to and participation in economic, social, and community life.Table 5 shows the categories that were developed in response to interview questions about the benefits experienced by adult learners from participation in numeracy programs and the numbers of ETB sites in which these responses were recorded for the three participant groups -AEO/ALOs, tutors, and adult learners.
The analysis summarised in Table 5 indicates that numeracy contributes to citizenship by supporting economic, social, and community participation.Numeracy enhances economic participation in two ways: (i) by developing adult learners' financial literacy and (ii) by preparing them for employment.All respondent groups acknowledged the powerful benefits of developing financial literacy (AEO/ ALOs at 10 ETB sites; tutors at 11 sites; adult learners at 8 sites).For example, ETB staff noted that newfound confidence served to dispel the fear adults had experienced when handling money: bonded as a group, all the women did, and then they went out afterwards and had their walking group after their maths … You know, in a community where there were new people moving in, so they wouldn't have known someone.New housing estates and so on.So it was really -that was really positive.(Site 11) Tutors (5 ETB sites) sometimes described the essential purpose of adult numeracy programs as promoting community and civic engagement: Tutor: Personally, I think it's to give people the confidence to question and to be more active in their communities.To be more vocal and to not sit back, but to have the confidence to read numbers and take part in numbers.Not to opt out.(Site 6) Adult learners (3 ETB sites), while tending to focus on the more intimate contexts of family and their immediate social circle, occasionally explained how increasing confidence in their numeracy abilities led them to participate in community projects such as homework clubs for school children or the local Men's Shed.A Men's Shed is a community-based organisation that provides a friendly environment where men are able to work on meaningful projects together, for example by making furniture, repairing machinery, or tending gardens.One adult learner even compared the ETB numeracy classes with the Men's Shed movement: The second category of numeracy benefits shown in Table 5 derives from social participation, through (i) individual empowerment, (ii) family learning and (iii) social inclusion.All groups, but particularly AEO/ALOs (11 ETB sites) and tutors (16 ETB sites), referred to the empowering effects on individual adult learners gaining more independence and control over their lives: ALO: If it's about their budgets, that totally empowers them because that means for their household budgets they're more in control and maybe their lives are more in control.(Site 11) Tutor: What you're trying to do is to build a person's independence and their ability to manage their everyday life.(Site 5) In the interview data all groups referred to family learning where parents were motivated to improve their numeracy skills so that they could help their children with mathematics homework and feel more confident and competent in their parental role: ALO: If they've been belittled in school by teachers, that takes time to get over, that thing of self-belief and self-doubt.But if it's to do with their children, they want to feel like they're like the parent, that I do know something in front of the child.(Site 11) Adult learner: Children, help them to do sums.And you'd be embarrassed when it comes to your own kids that you can't actually help them.(Site 6) Intergenerational effects of adults' unmet numeracy needs have been identified as reproducing cycles of social and economic inequality in families (NALA, 2019).On the other hand, efforts to improve adults' numeracy skills could help to break these cycles of disadvantage.Although less frequently mentioned as a benefit for adult learners, tutors recognised broader implications for families, referring to the intergenerational effects of poor numeracy on earning capacity (4 ETB sites): Tutor: I think it's just going to have a knock-on effect back to their own families … when you think of, especially where we are, there's a lot of generational unemployment and that's because kids saw their parents not working.(Site 4) The summary data in Table 5 indicates that all respondent groups gave examples of how participation in adult numeracy programs fosters social inclusion (AEO/ALOs at 9 ETB sites, tutors at 9 sites, adult learners at 7 sites), a benefit previously identified in the adult numeracy literature (Carpentieri consistent with contemporary interpretations of numeracy as the ability to confidently apply mathematical knowledge and practices in a range of real-life contexts (Geiger et al., 2015), especially contexts relevant to adult life (Hoogland & Díez-Palomar, 2022;PIAAC Expert Numeracy Group, 2009).On the other hand, the "invisibility" of numeracy in integrated courses (referred to by one ALO in our study as "maths by stealth") can be a systemic disadvantage as it under-represents the breadth and scale of adult numeracy provision.Providers of adult numeracy education in our study also found it more difficult to collect reliable data on learners' numeracy progress in integrated courses.Resolving these tensions between visible and invisible numeracy is important for further education systems, not only for capturing the scope and impact of adult numeracy programs, but also for tracking progress towards achieving national and international targets for numeracy education (e.g., Government of Ireland, 2021;United Nations, 2015).
Third, the study contributes tentative insights into connections between adult numeracy education and active citizenship (Sect.6), which is identified by the European Commission as one of eight key competences for lifelong learning.Citizenship has long been acknowledged as potentially providing a context or purpose for numeracy (Gal, 1997;Hoogland & Díez-Palomar, 2022; UNESCO Institute for Lifelong Learning, 2020).Further, in Ireland and other countries, policies and strategies for promoting adult education typically refer to active citizenship in their rationale for program delivery (e.g., EAEA, 2019; Government of Ireland, 2021; NALA, 2020).Yet policy documents addressing citizenship development in adult education do not distinguish between the literacy and numeracy components of these programs; nor do they provide examples of how adult numeracy programs could promote active citizenship (e.g., UNESCO Institute for Lifelong Learning, 2019).Our study begins to explore this relatively unknown territory.Our analytical approach, while limited to one of many possible conceptions of citizenship, points to ways in which adult education systems might be able to evidence claims that numeracy promotes active citizenship.
Finally, in looking for connections between numeracy and active citizenship in our data we also uncovered some missing links.Here, we use Schugurensky's (2006) citizenship dimensions of identity, civic virtues and agency to take a more critical stance in interpreting our findings.According to Schugurensky, identity relates to feelings of belonging; civic virtues emphasise a set of dispositions and values; and agency is concerned with developing an active, engaged, and committed citizenry.Our analysis of the interview data found that feelings of belonging were fostered by providing adult learners with an environment where they need not fear being shamed by their numeracy needs.In relation Adult learner: See, there's a lot of people living on their own, so it's great to have a chat with a group of people.You could call this the academic side of the Men's Sheds.(Site 6) The evidence summarised in this section suggests that adult numeracy provision in Ireland's ETBs worked to address past barriers to educational participation and thus supported adults to develop fundamental numeracy capabilities needed for active citizenship.

Discussion
This study provides an initial exploration into how adults access and participate in numeracy programs in Ireland and how these programs might support active citizenship.While the study was grounded in a specific national context, it contributes more broadly to advancing understanding of adult numeracy education and especially its connection with citizenship education in the following ways.

Contributions to knowledge
First, the findings regarding barriers to participation in adult numeracy programs (Sect.5.1) underline the need to give greater emphasis to both promoting and researching numeracy as a separate dimension of adult education.Much is already known about factors that motivate participation in adult education in general, as well as reasons for nonparticipation (e.g., Beder, 1990;Beder & Valentine, 1990).However, adult education studies such as these cannot adequately capture the numeracy-specific motivations and experiences of adult learners.Our study identified dispositional factors as the most common barrier to participation in adult numeracy programs and highlighted the impact of fear and anxiety arising from negative experiences of formal schooling.This finding aligns with research on the prevalence and consequences of mathematics anxiety amongst adults (Bibby, 2002;Carpentieri et al., 2010;Coben et al., 2003) and provides evidence to inform recruitment of adult learners and the preparation of adult numeracy tutors.
Second, analysis of the nature of numeracy learning activities from the perspectives of ETB managers (AEO/ ALOs), adult numeracy tutors, and adult learners highlighted inherent tensions in designing numeracy programs within adult basic education (Sect.5.2).On the one hand, integrated courses that embed numeracy in contexts relevant to adult learners' interests and needs seem more successful in overcoming dispositional barriers to re-engagement with learning mathematics than standalone courses that teach conventional mathematical content.Integrated courses are also empathy rather than identifying any need for qualifications in mathematics or mathematics teaching (SOLAS, 2021).Thus, no conclusions can be drawn about the capacity of these tutors to develop adult learners' mathematical abilities, much less their potential to use numeracy learning as a means of promoting active citizenship.We cannot determine whether the tutors in our interview study exemplified the highly variable and often minimal formal preparation of adult numeracy tutors that has been discussed in the international literature (e.g., Gal et al., 2020).Nor do we know how the backgrounds and qualifications of these tutors compares with that revealed in an earlier national survey (NALA, 2013), which found that 90% of the 207 participating adult numeracy tutors had tertiary qualifications but only 8% were qualified in mathematics.Gathering reliable data on tutors' existing qualifications and developing appropriate formal training for adult numeracy educators is a systemic challenge that invites further research.

Recommendations for research and policy development
The methodological and systemic limitations discussed above have implications for interpreting the findings, but also lead to recommendations for further research and policy development.We offer four recommendations targeting adult numeracy learners, programs, teachers, and policymakers.These recommendations complement the research directions for numeracy education of vulnerable adults made by Gal et al. (2020).
(1) Learners Barriers to participation in adult numeracy programs contribute only part of the bigger picture showing how and why adults engage with these programs (or not).Unlike in school education, where participation is generally compulsory, the decision to participate in adult education is largely personal.As noted by Comings (2008), adults must make an active decision to participate in each class and this emphasises the importance of student persistence.An Irish report by Forster et al. (2022) revealed the importance of a range of demographic, psychosocial, environmental, educational, and institutional factors in helping mature students to "stay the course" in higher education.It is important that similar research is conducted in the adult education sector.To support learners to develop fundamental numeracy capabilities for active citizenship, we also need to understand the characteristics of those who "persist" and of those who "non-persist" in adult numeracy education (Greenberg et al., 2013).
(2) Programs The extent and nature of numeracy activity in adult education programs is difficult to capture because to civic virtues, ETB staff and tutors uniformly espoused democratic, learner-centred values.However, we did not see strong evidence of the kind of critical citizenship promoted by socio-political interpretations of numeracy (e.g., Frankenstein, 2001;Skovsmose, 2008), despite recognising glimpses of emergent agency amongst adult learners who challenged financial transactions.This missing citizenship element could be a consequence of the demographic characteristics of our interview sample and the type of adult numeracy programs that were represented.Nevertheless, how adult numeracy programs contribute to critical citizenship deserves further investigation.

Limitations
The conclusions that can be drawn from our study are constrained by many methodological and systemic limitations.First, the analysis presented in this paper was prompted by unanticipated insights into the significance of numeracy for citizenship that we observed in interviews with Irish adult numeracy providers and adult learners.However, because the interviews were conducted as part of a larger study, commissioned by the National Adult Literacy Agency, SOLAS, and the ETBs (SOLAS, 2021), they were not designed to investigate numeracy-citizenship links and so any claims concerning such links are necessarily tentative.
In this larger study we collected additional survey data on the range and depth of adult numeracy activity across the Further Education and Training sector in Ireland, including program demand, type and duration; access and recruitment; budgets, staff, and training; participant characteristics, progression, and outcomes (SOLAS, 2021).However, the focus of the survey was not on citizenship and so we cannot draw conclusions from these data on the extent to which the FET system is designed to promote active citizenship through numeracy education.
Also, while both the interview data discussed in this paper and the additional survey data referred to above yielded examples of numeracy learning activities, these were usually integrated into general adult learning programs and so we cannot be sure that the numeracy components make any unique contribution to citizenship education.As well as being a methodological limitation, this is a systemic limitation arising from the way integrated numeracy programs are used to maximise recruitment of adult learners who fear engagement with mathematics.
Another significant limitation of the study was the lack of data on the backgrounds and qualifications of the adult numeracy tutors.While the interviews sought participants' perceptions of the qualities, knowledge and skills needed by adult numeracy tutors (see Table 2), their responses focused mainly on dispositional qualities such as patience and workforce could investigate the implementation and impact of this professional development framework within the Irish context and conduct cross-cultural studies comparing adult numeracy tutors' professional development needs in different countries.
(4) Policy-makers Adult education policy tends to foreground the functional role of numeracy in enabling individuals to contribute to national economic development (Oughton, 2018).Similarly, the view of citizenship implied by policy documents emphasises individuals' rights to access to health services, education, and employment.While these rights are indeed vital for active citizenship, there exist alternative conceptions of citizenship that encourage critical understanding and action addressing social problems and injustices (Schugurensky, 2006).A question deserving of future research is how stakeholders, including education policy-makers, adult numeracy program managers and curriculum developers, perceive the numeracy capabilities needed by adults to exercise their rights as responsible and critical citizens.Such a study might a promote system-level policy shift towards recognising both the functional and critical roles of numeracy in adult education programs (Gal et al., 2020).
The Irish FET sector provided a fruitful site for the research reported in this paper because of the low levels of adult numeracy revealed by the 2012 PIAAC assessment of adult skills.The findings, although situated in the Irish context, might stimulate more thoughtful discussion of the relationship between numeracy and citizenship that helps translate national and international policy frameworks into research-informed adult education programs.
Acknowledgements An earlier version of the research reported in this paper was published by SOLAS (2021) as Good practice in integrated and standalone numeracy provision.

Funding Open Access funding enabled and organized by CAUL and its Member Institutions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/. of the great diversity of contexts in which adults' formal, non-formal, and informal learning takes place and the low visibility of numeracy when embedded in the context of daily life.Carefully designed surveys can sample the extent of mathematics-related instruction across an entire adult education system (e.g., Gal & Schuh, 1994), but without necessarily taking account of the evolving meanings and purposes of numeracy (separate from mathematics) in a rapidly changing world.Research is therefore needed to create a methodology for auditing the numeracy demands of both integrated and standalone courses to enable national profiles of the numeracy content of adult education programs to be developed -including those labelled as adult literacy rather than numeracy.This approach should be informed by a contemporary understanding of adult numeracy (e.g., the elaborated PIAAC definition proposed by Tout et al., 2017) that accounts for numeracy's mathematical, affective, contextual, and critical dimensions.
A second strand of research should aim to connect adult education program content with system-level outcomes explicitly related to citizenship.For example, Tout (2020) showed how analysis of PIAAC data could be linked to national data sets documenting positive social and economic outcomes such as being employed, participating in volunteer activities, and having high levels of political efficacy -all of which are aligned with common definitions of citizenship.Such a system-level analysis might also motivate policy-makers to give more detailed consideration to what they mean by "citizenship" when this concept is invoked in national and international adult education policy documents.
(3) Teachers Gal et al. (2020) have documented the diversity of expectations regarding teacher qualifications for adult numeracy: in most countries, no formal qualifications are required and participation in professional development is inconsistent and poorly funded.Teaching mathematics to school children is not the same as supporting the numeracy capabilities of adults with highly diverse needs and interests, but little research has investigated the professional knowledge, practices and attributes needed by adult numeracy teachers.The Irish framework for meeting the professional development needs of adult numeracy tutors proposed by Maguire (NALA, 2015) might provide a useful starting point for this research.The framework's components include an underpinning definition of numeracy, understanding of elementary mathematics, development of "mathematical eyes" to see numeracy in multiple contexts, knowledge of adult learning principles, and willingness to challenge one's own beliefs and attitudes.A future research program to support professionalisation of the adult numeracy teaching Adult learner: I got lost in … I can't remember even what it was.Subtraction, I think.And then I just got left behind.I just never understood it.(Site 16) Adult learner: I left school when I was 13 like some of the girls I was left at the back of the class, thought I was stupid.(Site 1) Early school leaving was compounded by social disadvantage as a member of the Traveller community: Adult learner: When I was going to school I got very little school.And I was being a Traveller in amongst a load of settled people, I got it very, very rough from the beginning when I was young.(Site 5)

Table 1
Levels of Adult Numeracy Courses in Ireland

Table 2
Interview Data Codes, Themes, and Participant Sources You know, it took me another ten years to get the courage to walk in the door.(Site16)Inspection of Table3indicates that poor previous experience of formal schooling, especially in learning mathematics, was the next most common dispositional barrier identified by AEO/ALOs (4 ETB sites) and tutors (7 ETB sites): ALO: They cower at home because "somebody told me in school you're no good at maths because you can't do that algebra".(Site 8) Tutor: An awful lot of the students have had bad experiences at school with numeracy.(Site 1)

Table 3
Barriers to participation: Numbers of ETB sites in which interview response categories were recorded for AEO/ALOs, tutors, and adult Tutor: I've got my bag of recycling -it's food packaging.Because you've got decimals, you've got fractions, you've got percentages.You've got data tables, you've got dates, you've got codes.And you will get a good two-hour class out of people just identifying the numbers that are in that.(Site12)Tutor: I'm currently doing something on invoices with a group, and how the invoice is worked out.How to do a trade discount of it, how to put the VAT on.So I was asking them to get the invoices and even to find out the different types of tax.So it might be an exercise to go off, look up Revenue, look up Citizens Information.

Table 4
Nature of numeracy learning activities: Numbers of ETB sites in which interview response categories were recorded for AEO/ALOs,

Table 5
Benefits for adult learners: Numbers of ETB sites in which interview response categories were recorded for AEO/ALOs, tutors, and adult AEO: We had a group that was helping parents in Project Maths [the new Irish secondary school mathematics curriculum].But they got together, they all