Learning Mathematics in an After-school Mathematics Club

Abstract

Learning mathematics is as much about developing relationships with mathematics as the development of mathematics concepts and skills. Mathematics clubs usually support learners to develop relationships with mathematics through engaging with challenging mathematics problems, exploring mathematical ideas, and communicating and sharing their ideas. This paper reports on research on such a mathematics club. Data sources included learners’ mathematics results, short written responses after club sessions and interviews with club learners. Data were analysed quantitatively and qualitatively. The study shows that club learners’ school results improved relative to non-club learners, that learners’ experiences of mathematics in club and class were very different from each other and that the club supported different relationships with mathematics than learners experienced in class. The study suggests that mathematics clubs can support learners’ positive relationships with mathematics.

Keywords:

• Mathematics clubs
• learner relationships with mathematics
• experiences of mathematics
• mathematics teaching

Introduction

Learning mathematics is as much about developing mathematical identities and relationships, as the development of mathematical concepts and skills (Black, Mendick, & Solomon, 2009; Darragh & Radovic, 2018), particularly for marginalised students (Joseph, Hailu, & Matthews, 2019). A quest for social justice in mathematics must pay attention to both the substance of what is and can be learned, and how learners develop their relationships with and through mathematics, including their relationships with each other and their mathematics teachers.

Mathematics clubs are usually established to support learners’ sense-making and problem solving in mathematics (e.g. Diez-Palomar, Varley, & Simic, 2006; Turner, Gutierrez, & Sutton, 2011). Mathematics clubs support different ways of participating with mathematics and allow for the development of different relationships with mathematics from those promoted in school. Teachers in South African schools are usually constrained by an overfull mathematics curriculum, annual teaching plans and a strong assessment regime, which tend to support predominantly procedural approaches, and do not leave much time and space for exploration and communication. Mathematics clubs therefore provide a complementary space for different kinds of mathematical relationships (Lampen & Brodie, 2020).

This paper reports on research on a mathematics club that aimed to develop learners’ mathematical achievement through supporting positive relationships with mathematics.

The paper is guided by the following research questions:

1. How did a mathematics club influence learners’ achievement in and relationships with mathematics?

2. What were learners’ experiences of the mathematics club and how did these relate to their experiences of school mathematics?

I show that club learners’ school results improved relative to non-club learners, that learners’ experiences of club and class were very different and that the club showed them a different side of mathematics that they did not see in class. The study suggests that there is a role for mathematics clubs in high schools as complementary to school mathematics.

Relationships with Mathematics

Research into relationships with mathematics shows that mathematics can be strongly alienating, even for successful learners (Black et al., 2009; Brown, Brown, & Bibby, 2008; Joseph et al., 2019). Some of this alienation stems from strong emotions that are often associated with success or failure in mathematics (Brown et al., 2008; Frenzel, Lampen, & Brodie, 2019; Hannula, 2002), and from the judgement that seems to be inherent in mathematics classrooms, where answers are right or wrong, leading to attributions of ability in binary ways, such as being good or not good at mathematics.

Drawing on Truitt (2003, cited in Joseph et al., 2019), Joseph and her colleagues argue for two important characteristics of classrooms that support black girls in mathematics: social interaction and power-sharing. These two concepts capture both the intent and design of the mathematics club and the theoretical framing of the research discussed in this paper. Social interactions refer to how learners engage with each other and with their teachers as they learn mathematics. Power sharing supports collaborative inquiry in mathematics, valuing and working with all learners’ mathematical contributions to build better understandings. Joseph et al. (2019) show that black girls appreciate working collectively with others and being appreciated by their teachers. Such practices humanise black girls in what are often otherwise racialised and gendered classroom contexts. I used the two constructs: social interaction and collaborative inquiry to frame the data collection and analysis in this research.

International research provides some examples of teachers who create mathematics classrooms where learners talk mathematically to each other, feel seen, heard and respected by their teachers and classmates, and develop robust relationships with mathematics (Boaler & Staples, 2008; Staples, 2007). Boaler argues that it is possible to support different kinds of success and joy in mathematics: success in working together, communicating ideas and making connections, and joy in persevering towards a solution and learning something while doing so, rather than only the joy of an answer judged correct (Boaler, 2016). It is possible to create mathematical environments characterised by care and support—environments that make possible a broader range of mathematical identities and relationships for learners. A key element of strong positive mathematical relationships is a focus on productive disposition (Kilpatrick, Swafford, & Findell, 2001), which refers to whether learners see mathematics as useful and worthwhile, accessible to themselves and others, and how learners see themselves as mathematics learners: whether they enjoy and persevere with challenging problems, and are confident in making progress in learning mathematics even if they make errors or struggle to understand.

However, such environments are rare in mathematics classrooms, even in well-resourced schools. It is likely that positive relationships with mathematics are not possible in the context of the high-stakes assessments that characterise many education systems today. Moreover, many contexts are extremely uncomfortable and oppressive for marginalised learners (Black et al., 2009; Joseph et al., 2019). In South Africa, the vast majority of learners, who are poor and black, study in schools that are not well resourced, with some being quite dilapidated. Classes are large and many learners do not achieve even basic mathematical skills such as addition and subtraction in primary school, and by the time they reach high school, many have missed out on key conceptual understandings of important mathematical concepts. This means that many high school teachers spend time ‘catching up’ key concepts that learners have missed out on previously, or ignoring the gaps and trying to build on ‘shaky foundations’.

Mathematics Clubs

A number of literature searches turned up very few papers on mathematics clubs. These papers illustrate various examples of mathematics clubs, but they do not amount to a robust literature on whether, how and why mathematics clubs work. The mathematics clubs that are reported on have been set up for similar reasons- to support learners to: engage in mathematics as a sense-making activity; become problem-solvers; relate mathematics to real-world situations; and to support increased enjoyment of mathematics (Amit & Naaman, 2014; Diez-Palomar et al., 2006; Graven, 2011, 2015; Karp & Niemi, 2000; Prescott & Pressick-Kilborn, 2015; Schlosser & Balzano, 2014; Sherman & Catapano, 2011; Turner et al., 2011). One club was specifically set up to support middle school girls in mathematics (Karp & Niemi, 2000), with another two aiming for culturally inclusive environments, taking into account social justice concerns (Amit & Naaman, 2014; Diez-Palomar et al., 2006). Two clubs supported learners to think about careers that involved mathematics (Graven, 2011; Karp & Niemi, 2000).

Almost half of the clubs reported on took place in the United States, with others in Sweden, Australia and Israel, and only one in South Africa (Graven, 2011, 2015). Most of the clubs were located in primary or middle schools. Most clubs were inclusive and encouraged attendance, welcoming all learners who were interested in spending time working on challenging mathematics problems. Three clubs worked with pre-service and/or in-service teachers. Prescott and Pressick-Killborn (2015) had pre-service primary teachers work with primary students in a lunchtime mathematics club, while Schlosser and Balzano (2014) engaged teachers in professional development workshops and the teachers tried out what they had learned in mathematics clubs in their schools. One elaborate design included current teachers, community members, pre-service teacher education students and ninth-grade students tutoring primary school learners in the mathematics club (Sherman & Catapano, 2011).

While most of the clubs took place at schools, they were maintained as informal spaces for mathematics learning. Direct instruction was rare, rather problem solving through tasks that allowed for multiple strategies and solution paths was encouraged. Club mentors supported learners to become problem solvers and to persevere with challenges. Only one club reported on formal assessment (Amit & Naaman, 2014). In Sweden, Wallin, Noren, and Valero (2019) report that mathematics clubs that used to be informal spaces for learning mathematics have become ‘schoolified’, with a formal curriculum and a guide for planning the sessions. This has introduced tensions for a number of the teachers who preferred the separation from school and the freedom that this gave to explore mathematics differently.

Research foci differed across the studies. Only one study investigated a shift in club learners’ school achievements. Sherman and Catapano (2011) showed that learners who attended the club regularly made statistically significant gains in tests on mathematics concepts and applications. In the same study, the high school student tutors reported that they also developed mathematically, saw improvements in their own mathematical skills and would consider teaching as a career choice. The classroom teachers saw new ways of teaching in the club and used the club activities and methods in their classrooms.

Some learner and teacher participants reported that their mathematical knowledge increased, that they saw mathematics in new ways and that they enjoyed the challenges that the clubs presented (Amit & Naaman, 2014; Schlosser & Balzano, 2014; Sherman & Catapano, 2011). Some teachers saw improvements in club participants’ mathematical engagement in class (Graven, 2015; Schlosser & Balzano, 2014), and some teachers, both pre-service and in-service, said that they could see ‘less capable’ students as more engaged and more capable in the clubs (Prescott & Pressick-Kilborn, 2015). Increased opportunities for mathematical dialogue and increased identification with mathematics were seen in some clubs (Diez-Palomar et al., 2006; Graven, 2011; Turner et al., 2011).

What emerges from this somewhat disparate literature are common goals for mathematics clubs across grade levels and contexts and some success in developing deeper understandings of and stronger relationships with mathematics. In one case learners achieved better results in mathematics tests and in others there was some transfer of ways of participating in and understanding mathematics from club to classrooms.

A Mathematics Club

In this paper, I present a case of one mathematics club in Johannesburg, which was intended to develop learners’ relationships with and understandings of mathematics, through providing experiences of engaging in mathematical reasoning and supporting collaborative inquiry among learners. The club was located in a reasonably well-resourced, quintile 5 school in central Johannesburg, close to Wits University. All of the learners and many of the teachers in the school are black. The school is a selective school, meaning that learners should achieve better results than South African learners in general. However, the mathematics results were not strong with the end of year average in Grade 10 in 2018 being 31%.

The club started in July 2016, when the learners were in Grade 8, continued through the whole of 2017, when they were in Grade 9, and ended in May 2018, at the end of the first semester in Grade 10. Sessions took place for two hours once a week during school terms except when other school activities intervened. In total there were nine sessions in 2016, 17 in 2017 and eight in 2018.

Attendance at the club was voluntary but learners were encouraged to attend regularly, as they were more likely to enjoy and benefit from the activities. In 2016, 25 learners joined the club, with average attendance of 7.8 sessions. In 2017, a number of new learners joined the club, with a total of 52 learners in the club and an average attendance of 12.2 sessions. In 2018, the numbers dropped to 27, with an average attendance of 4.9 sessions. Of the 25 learners who joined in 2016, 18 were still in the club in 2018, six stayed in the club during 2017 and one left after 2016. Over the two years, seven learners attended 30 or more sessions, 13 attended between 20 and 29, 21 attended between 10 and 19, and 13 attended fewer than 10 sessions.

The club facilitators were pre-service teachers majoring in mathematics at our university (six over the two years) with the lead facilitators a post-graduate student and a staff member (four over the two years). Facilitators were aware of the club principles outlined below and met after each club session with the lead facilitators to discuss how the principles were enacted during their ongoing interactions with learners in the club. Facilitators also contributed to the development of club tasks based on their reflections on how previous tasks had worked with different learners.

The club curriculum and pedagogy were based on the following principles (for more detail see Lampen & Brodie, 2020):

• The club would deal with mathematics concepts in the official high school curriculum, without following the curriculum but would revisit some concepts already covered and would develop some concepts in advance of the school curriculum.

• The club tasks would be low-floor, high-ceiling tasks, allowing all learners to access the tasks, to progress through the tasks using different routes and methods, and to extend the tasks as much as possible.

• There would be consistent messages, both explicit and implicit, that all learners can do mathematics and that all learners would be expected and supported to explore and contribute to the mathematics in the club.

• Talk and discussion were encouraged, explicitly showing learners how talking through ideas deepens understandings.

• Making errors, admitting confusion and asking questions, were explicitly supported as normal parts of learning mathematics, showing learners that these lead to mathematical growth and deeper understandings.

• There would be no formal assessment in the clubs; the only assessment would be informal and formative in support of the learners’ growth.

The principles supported our focus on social interactions and collaborative inquiry, through explicitly supporting learners to talk about their ideas and showing them that all of their ideas were valued as contributions, as even errors, confusions and questions could help everyone to understand the mathematics more deeply.

We were very clear that the club was not ‘extra lessons’, i.e. repeating what teachers were doing in class. Repeating the curriculum was not practically possible, since we only had two hours per week for the club and it also suggested that we could do teachers’ work better than them. We wanted to be clear that we respected what teachers did in the classroom and were explicitly using the club space to engage learners differently. We wanted to help learners who had missed out on important concepts earlier in their schooling to able to develop these and allow learners to return to prior concepts in the light of more complex knowledge, thus rethinking and integrating their ideas.

Data Collection

A number of different kinds of data were collected:

• learners’ school results from June 2016, i.e. before the club started and from December 2018, i.e. after the club ended, from the entire grade that the club learners were in;

• short written responses after club sessions on selected days in 2017 and 2018, from all the learners who were in the club on those days;

• interviews with selected club learners in May of each year, in 2016 before the club started, in 2017, and in 2018 towards the end of the club.

The learners’ results came from the school’s yearmark and examinations. The Grade 8 mean in June 2016 was 31.65% and the Grade 10 mean in December 2018 was 30.72%, suggesting consistency in the testing across the two measures.

Two quick response questions were given to learners at the end of seven sessions in 2017 and three sessions in 2018. These were completed by each learner in the club on those days amounting to a total of 588 responses—474 on 14 questions in 2017 and 114 on six questions in 2018. These provide a large sample of learners’ ideas about the club and were triangulated with the interviews. The quick response questions probed learners’ relationships with mathematics and whether they experienced differences between the club and class curriculum and pedagogy.

Examples of questions were:

1. Playing with tangrams is not proper mathematics. Do you agree? Please explain.

2. I enjoy challenging problems in mathematics. Do you agree? Please explain.

3. How is the maths club similar to/different from your maths class this year?

The quick responses were read each week, informing decisions about subsequent questions.

Sixteen learners were interviewed in May 2016, before the club started and of these four left the school and/or the club in 2017. The 12 remaining learners and an additional nine learners in the club were interviewed in May 2017. In May 2018, 17 learners were interviewed, all of whom had been interviewed in 2017 and seven of whom did not attend the club in 2018 but had attended previously. In total, interviews with 11 learners over three years and seven over two years were analysed. The average attendance of the learners who were interviewed was seven sessions in 2016, 12.7 sessions in 2017 and 5.3 in 2018, similar to the average attendance of all the club learners.

The interview questions were framed in terms of how learners experienced their mathematics learning in class and in the club, what they enjoyed in mathematics and how they engaged with mathematics and interacted with others in relation to mathematics. Questions and probes aimed to provide data in relation to the two key concepts: social interactions and collaborative inquiry, as indicative of relationships with mathematics. Interviews of the previous year were read and coded before subsequent interview questions were developed.

All ethics protocols were followed through the relevant university, government department and the school. The ethics protocol number is 2016ECE001S.

Data Analysis

One-way ANOVAs were conducted on the examination results data. Two groups were set up for comparison: those who had attended 10 or more sessions over the three years (regular participants) and those who attended fewer than 10 sessions, including those who did not attend at all (non(regular)-participants). We chose 10 as the cut-off point because attending 10 or more sessions meant that learners had attended for more than one year. Learners were included in the sample if they had been at the school in both 2016 and 2018, so we had both sets of marks for them. Taking this group of learners, we then divided them into the two groups: regular, consisting of 30 learners and non-regular, consisting of 68 learners. The 30 regulars consisted of 23 learners who joined the club in 2016 and another 7 who joined in 2017, all of whom attended more than 10 sessions.

The quick responses were coded with a process of open coding. They were read through carefully and coded with an initial set of codes based on the questions and coming out of the data. The codes were refined a number of times, through reading and re-reading the data until a set of codes was able to describe the data comprehensively. The codes were: 1, maths is easy; 2, maths is hard; 3, positive about self/others/maths; 4, negative about self/others/maths; 5, maths involves different methods; 6, maths involves proving, convincing and is systematic; 7, maths involves following steps to get the right answer; 8, maths is challenging, requires thinking, learning from mistakes; 9, maths requires perseverance; and 10, in maths I get help and work with others.

The interview responses were summarized on a spreadsheet in relation to five categories: teacher pedagogy; teacher social relationships; one word for teacher; class experiences; and club experiences. The first three categories taken together supported an analysis of the learners’ relationships with their teachers in class and the club facilitators. The last two codes taken together supported an analysis of learners’ collaborative inquiry in class and in the club, and more specifically their relationships with mathematics.

Findings

The main findings of the study are that the learners who attended the club regularly did significantly better after two years than those who did not attend regularly; that learners spoke about their relationships with mathematics and their teachers very differently in the class and in the club; and that the club supported stronger relationships with mathematics and the club facilitators. We present the results in three sections: learners’ achievements before and after attending the club; learners’ relationships with mathematics; and learners’ relationships with teachers.

Achievement

The ANOVA showed that there was no significant difference between the means of the two groups in their June 2016 marks, before the club started (F = 2.281, p = 0.134). This means that the group who came regularly to the club were not significantly different in achievement from those who did not, when the club began. In December 2018 there was a significant difference in the results of the two groups (F = 12.207, p = 0.001), with those who attended the club regularly doing significantly better than the others. Those who attended fewer than 10 sessions had a mean score of 30.19 in June 2016 and 27.68 in December 2018, while those who attended 10 or more sessions had a mean score of 34.97 in June 2016 and 37.86 in December 2018. All the marks are low, but importantly, while the marks of the non(regular)- participants decreased from Grade 8 to Grade 10, the marks of those who attended the club regularly increased. While the increases are small, the results suggest that the club attendance may have supported the learners to suspend a decrease in their achievement at the end of Grade 10, a phenomenon that occurs often in South African schools.

Relationships with mathematics

An overview of the short responses shows mainly positive responses in relation to mathematics. The highest number of responses (50%) came from learners commenting on mathematics in the club as being challenging, requiring thinking and learning from mistakes. The second highest (12%) was seeing mathematics in the club as a positive learning experience, while 7.5% of learners experienced mathematics in the club as difficult in a negative way, mainly when they found that the challenges were too difficult. This was particularly the case when we asked about algebra, accounting for almost 40% of the responses in this category. These findings suggest that the club was achieving its aim of supporting stronger relationships with mathematics. The interviews give more depth to these findings.

The most striking finding in the interviews in all three years was that when learners were asked about their experiences of mathematics in school, their first response was always whether it was easy or difficult, which was often related to the teacher and how well s/he explained concepts and interacted with learners. When learners were asked about the club, they focused on the mathematics they were learning, with very little said about the club facilitators unless prompted.

In May 2016, the learners were asked what would improve their mathematics learning and what they would like in a mathematics club. Nine of the 12 learners asked for teachers to take more account of learners. The following responses are typical of the broader sample:

listen to every reason of the children [and] view each point of the learners. (Learner 3, 2016)

They could bond more with the learners. And they create maths to be fun, and not only doing strictly maths and building a wall between learners. (Learner 10, 2016)

If you’re kind, they will be able to be, to ask you questions … you need to explain and love people so they can be able to tell you and ask you things. (Learner 12, 2016)

These responses show that learners’ relationships with mathematics are closely related to their relationships with their teachers, that they want to be listened to and heard, and they find it easier to be heard if teachers create a ‘bond’ and show that they care. They want teachers who both explain mathematics and who care about them. The responses suggest that some learners do not currently experience such relationships. One learner saw mathematics as potentially creating a distance between people (‘building a wall between learners’) but thought that teachers could bridge this distance. These responses resonate with the black girls in Joseph et al.’s study (2019), who also asked to be related to in caring and thoughtful ways and to be humanised. The learners’ quotes also suggest that most learners have a relatively individualistic view of mathematics learning in class, they want to be helped by teachers with their individual problems and cared for by teachers as individuals. So while they are not asking for collaborative inquiry, they are asking to be heard.

In the 2017 and 2018 interviews we asked learners about their experiences in the club and they spoke about both positive and negative experiences. The positive views included being able to talk about mathematics to different people including those you may disagree with, talking through ideas in groups and finding different ways to solve problems. These are captured in the quotes below, which are typical of the broader sample:

I like it when there were challenges, challenging each other, finding different ways of solving the problem. (Learner 6, 2017)

I liked the way that we worked in groups so that way, there will be more than just one person thinking and you could compare answers to each other. (Learner 7, 2017)

We got to interact with people whom we don’t see eye to eye … we’re being taught how to talk about your maths problems. (Learner 9, 2017)

These responses suggest that in the club, the learners' relationships with mathematics were interactive and collaborative.

The main negative view in the interviews was that the club content did not relate closely to what was being taught in class. Learners also told us this during club sessions, and a few wrote this in their short responses. At times the facilitators felt pressured to teach what was being taught in class but we found a way to maintain the stance that we were not giving extra lessons, while also linking explicitly the concepts developed in the club with the school curriculum, both what had been done in the past and what was still to come.

In 2017 some learners found the club overcrowded and noisy compared with 2016 and found it difficult to share ideas comfortably (the facilitators experienced this as well), and a number of learners had difficulties staying after school because of transport challenges. In 2018, the learners who had left the club were a lot less positive than in 2017. Most of them left because they could not fit the club in with their additional homework and extra lessons in mathematics and other subjects. Those who stayed experienced similar difficulties with increased work pressure in Grade 10, but still enjoyed the challenges, the different perspectives on mathematics ideas and working with others in groups.

In comparing the learners’ talk about the experiences of mathematics in class and the club, two key differences were apparent. First, when talking about school, the learners spoke about mathematics being easy or difficult, and they preferred it to be easy. In contrast, in the club, they spoke about mathematics being challenging and fun (i.e. the challenges were fun), they spoke about solving problems and thinking about mathematics in different ways. Second, the learners had a greater sense of mathematics as an interactive and collaborative activity in the club. They liked to share, to interact and to hear different opinions. A third key difference relates to the different experiences of teaching in class and club, to which I now turn.

Relationships with Teachers

When speaking about school mathematics in the interviews, the teacher was central to learners’ experiences, and the main reason why they found mathematics easy or difficult. A good teacher could explain and make the work easy. When speaking about the club experiences learners focused more centrally on the mathematics with little or no talk about the club facilitators in 2017 and only when prompted in 2018. In the short responses only one question garnered more than one or two responses about the maths club facilitators: ‘If someone wanted to come to the maths club, what would they like about it?’ Seven out of 21 responses said they would like the helpful and kind teachers.

In all three years the interviewed learners were asked about their own mathematics teachers and in 2016 and 2018 learners were asked what makes a good mathematics teacher. Responses about their own teachers varied across teachers but were generally consistent for each teacher. These were also consistent with the remarks about what makes a good teacher: someone who cares about learners; does not get angry; explains well; responds to questions; does not go too fast; makes sure that everyone understands; and sees them as both mathematics learners and whole people. While some teachers do some or all of the above, it is clear that some do not, and in these cases, the learners struggled to enjoy their classes and learn mathematics. The following responses were typical:

A good teacher:

[Is] somebody who is willing to give you their time, like when you are struggling with something, they are willing to sit down with you and explain to you. (Learner 2, 2018)

Makes sure the kids understand the work, she doesn’t shout at the kids or make them feel intimidated, … she makes sure the kids are comfortable with her, she gives a challenge to the kids so they understand the topic further and she allows questions. (Learner 8, 2018)

Patience, understanding, got listening skills and knowing maths because if you listen to kids because there’s no way you can want people to listen to you and then you don’t listen back. (Learner 16, 2018)

Similar to the previous quotes, these quotes suggest that learners want to be heard and treated with respect, although they do not necessarily ask for power-sharing as in mathematical inquiry and co-construction of knowledge. One learner does note that listening is mutual: if teachers want learners to listen to them, then they should listen to learners. The interviews showed that some learners do experience care and respect from teachers, while others do not:

My teacher is very kind and he is helpful. He wants us to get good marks. (Learner 13, 2016)

When I asked her she would shout, so I never asked her again because I knew she would shout. (Learner 11, 2016)

When asked about the club facilitators, the learners’ discourse was different—they spoke about the mathematical activities—suggesting that the club facilitators were able to focus them onto the mathematics and interacting with the mathematics. The following responses were typical:

Sometimes I become lazy to think but you guys make me think and think and think, but it makes me feel good every time you do that. (Learner 6, 2018)

They bring liveliness to maths, we use different methods, like we draw … we’re able to add imagination. (Learner 10, 2018)

They gave us challenges then we worked as a group and we were successful … they let you face those challenges, like conquer what defeats you … they wouldn’t just leave us not knowing what we’re working with, … like when you’re doing the challenges and you ask her, she would give you the most challenging questions. (Learner 13, 2018)

The learners’ experiences of their teachers in both club and class confirms that they want teachers who attend to both the cognitive and affective aspects of learning. They want patient teachers, who connect with them as people, who challenge them and help them to make sense of mathematics. It is clear that a number of learners had experienced teachers who got angry, shouted at them and did not show interest in the mathematics or them. Learners’ experiences in the club were of teachers who challenged and pushed them but still helped them to feel comfortable, were open to questions and errors, and allowed creativity and imagination.

Conclusion

I have shown that the mathematics club reported on in this paper influenced learners’ achievement in and relationships with mathematics. Learners who attended the club regularly achieved significantly higher results than those who did not, with their results increasing from Grade 8 to Grade 10, whereas the non(regular)-participants’ marks decreased. The mathematics club learners’ relationships with mathematics in the club were very different from their relationships with mathematics in class. In class, mathematics was an individual activity and they wanted it to be easy and well explained by the teachers, whereas in the club, mathematics was challenging and interesting, a social activity to be shared. Learners developed more productive dispositions in the club, and were more willing to persevere and learn from their mistakes and thus enjoy mathematics. They enjoyed the social interaction and the mathematical collaboration around challenging problems.

In relation to social interactions, the learners enjoyed engaging with their peers in the club, hearing different points of view and learning to interact with people they might not agree with. Their relationships with the club facilitators was very different from those with their teachers in class. In class they preferred their teachers to make the mathematics easy, and some suggested that they did not experience their teachers a caring or compassionate. There were strong voices on wanting to be valued, as learners and as people, which was experienced in the club.

The learners experienced collaborative inquiry in the club, speaking about the club mathematics being fun, interesting and challenging, and the club facilitators as challenging, helpful and caring, with these three qualities going together. Learners spoke about themselves more agentically in the club—how they felt challenged by the tasks, remained focused on and enjoyed the mathematics they were learning and how they were positioned differently by the club facilitators, as thinkers who could do and enjoy mathematics.

The findings of this study are consistent with the findings in the literature, that mathematics clubs provide positive experiences for learners that enable them to see mathematics as a multi-dimensional, sense-making, dialogic activity, that they enjoy seeing mathematics in this way, and that mathematics clubs can help to improve mathematics achievement (Diez-Palomar et al., 2006; Sherman & Catapano, 2011; Turner et al., 2011). The findings also resonate with Joseph et al.’s (2019) study with black girls, who want to learn mathematics collectively and be related to with dignity and as human beings.

A key question that this study raises is whether mathematics classrooms can or should become more like mathematics clubs. A key feature of the clubs was that there was no assessment. While a discussion of the negative effects of assessment is beyond the scope of this paper, we know that many teachers focus strongly on procedures and getting right answers because of the pressure on learners do well in examinations. Many learners also experience anxiety, judgement and failure in relation to tests and assessments. While I showed that learners in the club achieved better results, it is important to note that they experienced a supplementary curriculum in the club with additional time for mathematics and with few concerns around assessment, which may have influenced their results. It is therefore not obvious how club experiences can be translated into similar classroom experiences.

One possibility is that clubs become places for experimentation by teachers, both pre- and in-service. Teachers can try out new ideas from professional development programmes in clubs (Schlosser & Balzano, 2014) and by participating in clubs, can learn to see mathematics, teaching and learning in new ways (Amit & Naaman, 2014; Sherman & Catapano, 2011). Clubs can also be places where teachers see learners in new ways, engaged differently than in class (Prescott & Pressick-Kilborn, 2015), and can promote more caring relationships between teachers and learners. This small study has shown that there is much potential in mathematics clubs for developing both enjoyment of and achievement in mathematics among high school learners.

Disclosure Statement

No potential conflict of interest was reported by the author.