This article gives an account of what I learned through the process of a self-study research project. Self-study teacher research allows teacher educators and teachers to improve their learning, plan new pedagogies and impact students’ learning.
The aim of this self-study research was to improve my own practice in early childhood mathematics teacher education through interaction and collaboration with others, such as colleagues and students.
As a South African university-based teacher educator, I piloted an integrated learning approach (ILA) in the teaching and learning of early childhood mathematics in a selected undergraduate programme.
I began by tracking my personal development in mathematics education and in so doing was able to recognise my personal learning of mathematics as a child growing up in an African township context. I then worked with a class of 38 student teachers to create collages and concept maps to explore their understandings and experiences of ILA.
Through this project, I discovered that colleagues in the role of critical friends provided essential feedback on my work in progress. I also learned that student teachers need to be equipped with knowledge and hands-on experience of how integration can take place in teaching and learning early childhood mathematics. I realised that it was essential to constantly reflect on my own personal history and my professional practice to explore new ways of teaching mathematics.
Teacher educators may consider engaging in self-study research that includes art-based self-study methods to reflect on their practices and see how they change for the benefit of their students and ultimately for the benefit of the learners.
As a precursor to my doctoral study on the integrated learning approach (ILA) concept in the teaching and learning of mathematics in the Foundation Phase (FP), I piloted a project with 38 students in the bachelor of education (B.Ed.) programme at the tertiary institution where I am currently based. The discourse commences with an explanation of what is understood by an ILA in the teaching and learning of early mathematics in the FP. I then describe how the sociocultural theoretical perspective was used in cultivating an ILA among student teachers. A description of the research methods and design follows. My personal acquisition of basic mathematical skills during my early childhood is traced and I explain how the games we played as children in a township enhanced mathematical concepts. I then provide an account of my experiences of working with student teachers using art-based methods such as collages and concept maps. I also highlight my interactions with critical friends (i.e. peer-support reviewers) and the importance of constantly reflecting on my practice by recording my observations and reflections in a journal. This facilitated the exploration of new ways of teaching mathematics through collaboration with my colleagues. In conclusion, I consider how and what I learned through my interaction with ‘critical friends’ and how an ILA that had been followed assisted me in developing reflexive self-awareness strategies that enhanced my skills as a teacher educator and will continue to do so in the future.
Currently, I am a lecturer at a higher education institution in KwaZulu-Natal. My decision to undertake a self-study research approach was prompted by both a personal and professional motivation to cultivate a desire among my students to embrace an ILA to teaching mathematics in the FP. This desire was underpinned by reflections on my experiences as a teacher in the FP and as a lecturer at a college of education and a higher education institution. Assisting young learners in the acquiring of early mathematical skills lays a critical foundation for later success in mathematics (DBE
The pilot study that I launched as a precursor to my doctoral study explored strategies that could be used to cultivate ILA awareness among first-year student teachers in the module Mathematics in the Early Years. It was envisaged that the implementation of ILA would enhance student teachers’ understanding of curriculum integration and that this would enable them to integrate their teaching of the Mathematics learning area with the Languages and Life Skills learning areas rather than teaching it in isolation. According to Adamu (
The pilot study aimed to address three research questions:
What can I learn from my personal history that will support the cultivation of an ILA to mathematics in the FP among my student teachers?
What can I learn from working with student teachers using arts-based methods that will support the cultivation of an ILA to mathematics in the FP among my student teachers?
What can I learn from working with critical friends about cultivating an ILA to mathematics in the FP among my student teachers?
Combining disciplines and pedagogical approaches in higher education is not a new phenomenon. Adamu (
Students who intend to become teachers by obtaining a B.Ed. degree can specialise in teaching in any one of the following phases: the FP; the Intermediate Phase; the Senior Phase; or the Further Education and Training band of schooling. According to the Revised Policy on Minimum Requirements for Teacher Education Qualifications, the B.Ed. degree has the key purpose of providing a well-rounded education that prepares graduates with the essential subject content knowledge and methodology that will allow them to demonstrate competence and responsibility as academically and professionally qualified novice teachers (Department of Higher Education and Training
The Department of Basic Education (
According to Ramani and Eason (
According to Lake (
When adopting a sociocultural theoretical perspective, teachers and teacher educators need to be consciously thinking of the means that can be employed to ensure that learners and student teachers get ample opportunities for making sense of everyday experiences. To illustrate this point, Hughes (
The above arguments encouraged me to embrace the concept that FP teacher educators and teachers need to take into account the sociocultural context of learners in order to make the acquisition of mathematical skills a social experience. This may be done through the use of cultural and everyday resources that are familiar to teachers and learners. Berk (
Vygotsky also developed the advanced idea that human cognition is fundamentally based on the social world and on language (Berk
Vygotsky also highlighted the ‘zone of proximal development’ (ZPD) by emphasising the role played in children’s learning by people such as parents, other adults, teachers, coaches and even children and friends (Dimitriadis & Kamberelis
This study was conducted over a 6-month period (a semester) at a South African university in the province of KwaZulu-Natal. The campus at which the study was conducted specialises in undergraduate to postgraduate teacher education. It accommodates student teachers from diverse socio-economic backgrounds, race groups, social demographics, and rural and urban areas. The language of teaching and learning is English. However, student teachers are expected to acquire bilingual language proficiencies and be aware of the importance of a multicultural society and the roles that teachers can play in facilitating awareness and skills in this regard. Because the majority of the students are isiZulu speakers, student teachers are learning in their first additional language, which is English.
I was the primary participant in this self-study project in which I explored the cultivation of an ILA to teaching mathematical skills in the Early Years module. The secondary participants in the study were 38 first-year student teachers enrolled for the B.Ed. FP programme.
According to Samaras (
A self-study research approach was thus appropriate for this pilot project as I sought to improve my practices and inspire my students to adopt an ILA in their classrooms. I undertook self-study research to enable others to understand learning from experience by showing them how they could do it themselves, as suggested by Russell (2002) (as cited in LaBoskey
Numerous self-study methods have been developed by and for self-study teacher educators (Samaras
I began by tracking my personal recollections of developing mathematical skills and was thus able to draw from my experiences of learning mathematical concepts as a child growing up in an African township. According to Samaras (
I delved into personal recollections of my experiences of early childhood acquisition of mathematical concepts and recorded these reflections in a journal. I also took photographs that depict my memories of my experiences of early childhood mathematical concepts. I did this because Weber (
The artistic mode is another major self-study approach (LaBoskey
Self-study researchers interact with their students in a variety of ways. For example, students’ work may be used as ‘a primary data source’ for interpretation and analysis (LaBoskey
To involve the student teachers in creating
Student teachers engaging in the process of making a collage in a and b.
In the following lesson, student teachers transposed the meaning or message of their collages by creating
This project was particularly successful because knowledgeable colleagues in the role of critical friends provided essential feedback on my work while it was in progress. Samaras (
trusted colleagues who seek support and validate the research of another colleague so that the latter person gains new perspectives and understanding and may reframe their interpretations of a topic under investigation. (p. 281)
LaBoskey (
I perused the data that I had generated and re-read the transcripts of the presentations, discussions and reflections a number of times in order to reflect on what I was learning. The data were analysed inductively with reference to the learning zones and the zones of possibility. In this process I paid attention to ‘any repeated statements, behaviours and actions across the data set’ (Samaras
Nieuwenhuis (
Pinnegar and Hamilton (2009) (cited in Samaras
Ethical clearance to conduct this study was obtained through the appropriate channels (ethical clearance number: HSS/0178/016). I also explained to the students what my study would involve and they agreed voluntarily to sign consent forms and to commit to the study. The students could withdraw at any time and their confidentiality was attained through the use of pseudonyms. The participants were aware that the information they provided would be used for research purposes only. The activities that the student teachers engaged in formed part of their classwork for the Mathematics in the Early Years module. All student teachers were required to participate in the class activities irrespective of whether they agreed to participate in the study. All the students in this group participated and consented.
Addressing issues of ethics was crucial in this self-study research project, particularly because I was both a researcher and a teacher educator with a pedagogic responsibility towards my students who assisted me in working towards improving my practice. Samaras (
In this section I discuss how my childhood experiences of acquiring mathematical skills addressed the first research question: ‘What can I learn from my personal history in order to cultivate an ILA to Early Childhood Mathematics Education?’ I simulated two of the games we played as children and took photographs to illustrate what I remembered about these games.
I grew up in a township and I remember how we enjoyed playing different games in the street and in the backyard of our home. Without being aware of it, these games taught us basic mathematical skills as we were growing up.
Heaped stones in a circle.
Two to six players could play the game. We would sit in a circle with a big pile of stones (or pebbles) in front of us. We would draw a circle around the stones called
Another game that we played involved three ordinary canned food tins, as depicted in
Three tins.
This popular game was called ‘three tins’ and was played in the street. We would stack three tins, one on top of the other. We would then draw a circle around them and draw a line a few metres away from the circle. Two teams would be involved – the attacking and defending teams. The attacking team would throw a tennis ball and try to hit the tins so that they would come tumbling down. The thrower would then run towards the circle and reset the tins within the circle. Each player had three attempts to hit the tins. While this was happening, the defending team would run to retrieve the ball and then throw the ball, aiming to hit the attacker. A hit would mean that the attacker was out, just like hitting the wickets of a cricket player. If the attacker was able to reset the tins without getting hit, a point was scored. All the members of a team were given a chance to attack, while the defenders were placed strategically around the area of the tins (almost like a game of cricket). The idea was to aim and throw the ball as hard as possible at the tins, thus allowing the ball to bounce far away and giving the attacker a chance to reset the tins. Mathematical concepts were strengthened when hits were scored and counted.
Looking back through a sociocultural theoretical lens, I can see how, by playing these games, we acquired counting and number skills using everyday objects such as pebbles and discarded tins. Nkopodi and Mosimege (
may be doing mathematics, may be engaged in thinking that involves mathematical thought processes without themselves calling their activity ‘mathematical’; they may even say that they do not know mathematics, or that they are not able to do mathematics. (p. 48)
As children, we learned about turn taking and sequencing in our games without being aware of it. By playing games, children learn to count, add and subtract without consciously thinking about these skills as being the basis of mathematics. Although they may differ in nature and application, games are universal among children of all sociocultural contexts where mathematical concepts are first acquired, which challenge the subjective notion that subjects such as mathematics and sciences ‘are associated with western culture and are never linked with African culture’ (Nkopodi & Mosimege
The above arguments clearly imply that teacher educators at tertiary level who lecture in the field of mathematics need to take into account the sociocultural contexts of their students. By being conscious of this reality, lecturers will inspire their students with the insight that the acquisition of mathematical concepts is a social experience in which learners should participate actively. Moreover, resources that are familiar to student teachers should be used. By engaging students in practical activities, they may be able to assist learners in ‘crossing the border between their own culture’ and the culture of mathematics or science (Lee
Upon reflection, I was able to see that numerical values as well as counting, addition and subtraction skills are developed through childhood games. Therefore, to create a meaningful learning environment in which student teachers can develop their own understanding of the pedagogy that will be required to teach their learners, it is important that teacher educators take into account what their students already know and build on this knowledge (Nkopodi & Mosimege
This section is a response to the second research question: ‘What can I learn from student teachers about cultivating an ILA to teaching mathematics in the FP using arts-based methods?’
Collages a and b depicting an integrated learning approach.
Concept maps created by student teachers in a and b.
During the process of concept mapping, I was able to help the students integrate ideas of an ILA that were sometimes difficult to put into words (Butler-Kisber & Poldma
In the 15 years that I had worked as a teacher educator, I had never before embarked on arts-based methods, so I was somewhat apprehensive to use this approach. However, when I taught this module I learned more about my students through my interaction with them. For example, I learned that many would embrace the celebration of family connectedness such as birthdays and family get-togethers and that they could effectively utilise this knowledge to teach their learners numerical values, dates and counting skills. In turn, the students learned that family connectedness is an important element of prior knowledge that they can utilise to teach their learners.
Moreover, the arts-based lessons offered hands-on creative tools from a cultural context that helped the students to better grasp the concepts I was trying to teach (Samaras
Through this experience, I learned that student teachers need to be equipped with knowledge and hands-on experience of how integration should occur in mathematics teaching and learning in the FP, as well as how important placing emphasis on social and cultural practices is (Dimitriadis & Kamberelis
Admittedly, I was worried when I first introduced the concept of creating collages as the students appeared unresponsive. However, as I mingled with the groups and explained what they needed to do and why, they began to understand the concept and gained confidence to tackle the task. It was rewarding for me to see their excitement and sense of achievement when the collages were completed. (Kortjass
Butler-Kisber and Poldma (
However, undertaking this project with the students also made me vulnerable, but in my vulnerability I learned about myself. For example, I learned that I could actually be creative regardless of the fact that I am not an artist. I also learned more about the classroom environment and how to teach my students to make it even more attractive, challenging and learner-centred. I understood my students through meaningful interactions with them. For example, I learned that most students were learning concepts, such as ‘conservation’ and ‘subitising’, for the first time. Lee (
This process also made me think about how we assess students. In most cases we assess students when we do not really know them. I was afforded the opportunity to know them better and to interact with them in order to understand their struggles and misconceptions in relation to mathematics. Collaging was helpful in conceptualising ILA by presenting it differently in order to get a better understanding of it (Butler-Kisber & Poldma
This section addresses my response to my third question: ‘What can I learn from working with critical friends about cultivating an ILA for the teaching of mathematics in the FP?’ I discussed my experiences with critical friends and also presented the self-study approach at a workshop to a group of colleagues and at a national education conference.
From a sociocultural theoretical perspective, it is evident that collaboration with critical friends allowed me to gain support that assisted me in understanding my research. It also assisted me in evaluating my own teaching methodology in more depth. Samaras (
To illustrate, a few comments that were offered by critical friends are presented in the following.
A positive comment from a critical friend related to the fact that it was a ‘self-study’ project, which allowed me to engage in in-depth reflection. She said:
… you seem to be doing a lot of reflection. And I think [this] as well some of [the] things you [will be] picking up in your next class, you enable you to do things differently. This is not just a class where you say to students ‘Integrate …’ or whatever, but you are also doing a study of your own practice which makes it different from the way integration has [been] taught [before], where it has just been a teacher teaching. (Critical Friend 1, National Conference, October 2016)
This comment illuminated how the pilot study assisted me to better understand my role as a teacher educator who needed to encourage my students to implement an ILA. I learned increasingly from my experiences and I started doing things differently as the semester progressed. Samaras (
Another critical friend raised the question whether the ILA was an established approach or an experimental approach in South Africa. My close perusal of the relevant policy documents helped me to articulate that an ILA is emphasised in the new prescribed curriculum for the FP, especially in the early grades, and that it was an important approach to ensure that learners gain an understanding of the connections among the different learning areas. This was further validated by a critical friend, who said:
‘It [ILA] is one of the values underpinning the CAPS curriculum’. (Critical Friend 2, Self-Reflexive Workshop, June 2016)
I also had to think about the principles of integration to ensure that mathematics teaching and learning did not get lost in the process of the ILA. This was prompted by another critical friend, who said:
‘Just on the idea of what we do so that mathematics does not get lost − I just want to find out if you have thought about engaging the student teachers about the principles of that’. (Critical Friend 3, National Conference, October 2016)
The comments and the questions I received in response to my presentations were invaluable. These contributions validated what Samaras (
Even though it was difficult for me to put myself at the centre of my research, I found that self-study helped me to focus on myself, my growth and my development. However, at the beginning I felt I was being attacked and needed to defend myself. I needed to have an open mind when I consulted critical friends for feedback. Often we get feedback and we just shut out constructive comments because we feel we ‘got it right’ the first time. What I learned is that it does not matter how much we know or we think we know, there is always feedback that can help us to learn something else. In actual fact, we should look forward to such feedback as an exciting opportunity for learning, rather than seeing it as something negative that is a threat to our sense of being. However, I acknowledge that it is sometimes difficult to find and appreciate that space, especially if we see ourselves as experienced and influential educators. I thus humbly acknowledge that, as an FP mathematics teacher educator, I had thought that I was on the right track, but I realised that I needed to move further. The principles of ILA taught me that, as a teacher educator, I needed to read widely to extend my horizons. This assisted me in my teaching and in better understanding the concept of ILA. Delving into the principles of ILA through my reading made me think differently, because previously I had felt confident with this concept, yet I had not incorporated it adequately in practice. I acknowledge that it is a humbling experience to put oneself out there as a learner rather than as a ‘knower’; however, the benefits are that I shall be constantly learning and extending my knowledge and expertise in the field of mathematics teaching in the FP.
I am at the very beginning of this new journey. I am still struggling with the idea of ‘I’ and putting myself in a pivotal position. Throughout my interaction with my supervisor and my critical friends, I kept referring to ‘the students’ rather than to ‘me’. However, the experience that I gained through this study brought me to the point where I can now acknowledge that this study was about me. I initially made the mistake of downplaying how I felt and thinking that my position was not important or pivotal. However, by embracing the sociocultural perspective, I have moved from thinking about students’ learning to understanding my own learning. For me, this has been a profound learning experience that has allowed me to be transformed to the extent that I now understand that teaching students to teach mathematics in the FP should occur at a whole new level.
Working with critical friends also equipped me with knowledge and insight that contributed to my research and enhanced my insight. My own experiences prompted me to explore the mathematical strategies and concepts that student teachers struggle with and to discover what skills and knowledge I would need to better assist them. For example, I remember that when we played games during my childhood years, one of my friends could not catch. I now understand that she probably had an eye–hand coordination problem. By continuing with my reflections I shall therefore be better equipped to identify ways in which I can help my students to improve their teaching practice of mathematics in the FP.
Conducting this pilot study from within a sociocultural theoretical perspective guided me to reflect deeply on new approaches to teacher education, particularly with regard to the teaching and learning of mathematics in the FP. The importance of taking into consideration the cultural background and mathematical experiences of student teachers was invaluable. As a mathematics teacher educator in early childhood education (i.e. the FP), I came to realise how I could better understand my student teachers’ thinking about mathematics concepts and how I could support them in teaching mathematical skills and mathematical reasoning in their classes one day. I had to abandon my comfort zone and learn from a position of vulnerability, which was new and frightening. However, I learned about myself and about the pedagogy of what I was required to teach. I also learned that my student teachers and I were creative, even if we were not artists. I was able to embrace constructive critiques from friends, which challenged and channelled my thinking. All things considered, I learned through various interactions with others, namely colleagues and students. Based on my experiences, I strongly recommend that teacher educators consider engaging in self-study research, which may include art-based self-study methods. Teacher educators should reflect critically on their practices and embrace change for the benefit of their students and, ultimately, for the benefit of the learners.
I gratefully acknowledge my first-year students, who contributed to the generation of the data produced in this project. I appreciatively acknowledge my supervisor and my colleagues in their roles of critical friends, who provided valuable feedback in making this project successful. I gratefully acknowledge funding from the University of KwaZulu-Natal (UKZN) Teaching and Learning Office (UTLO) Teaching and Learning Innovation and Quality Enhancement Grant (TLIQEG). I thankfully acknowledge the peer reviewers for their helpful feedback.
This publication has been developed through the Teaching and Learning Development Capacity Improvement Programme which is being implemented through a partnership between the Department of Higher Education and Training and the European Union.
The author declares that she has no financial or personal relationships which may have inappropriately influenced her in writing this article.