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This suggests that student teachers should learn about different cultures in order to understand the diversity of the learners that they will work with and the knowledge they may have acquired. In this context, Gerdes suggests that people:. 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. 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.

In the Classroom

Upon reflection, I was able to see that numerical values as well as counting, addition and subtraction skills are developed through childhood games. This exploratory investigation transformed the way that I used to comprehend teaching and learning of mathematical skills in FP teacher education, and I was able to impart this knowledge to my students to capacitate them to do the same as teachers in the classroom one day.

Figure 4 shows two examples of collages compiled by student teachers in the module Mathematics in the Early Years.

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In these examples, the collages depict an ILA. The student teachers indicated that this represented a celebration and that birthday celebrations promote socialisation and link with the Life Skills learning area. They also suggested that the image represented the age of the learners and their dates of birth, which linked with numbers, which are pivotal in the acquisition of mathematical skills.

Figure 5 shows the two concept maps that were created by the student teachers. Different keywords and phrases were grouped together in the concept maps to show the links within the ILA concepts. For example, numerical and other concepts depicted by the images in Figure 4 such as the number of dogs, many people wearing traditional attire, a long queue of ballerinas and a comparison of the cutlery items in the collage are captured in the concept map on the left in Figure 5.

Concepts such as large, many, long and more that emerged were grouped together Group 4 to represent measurement concepts. 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.

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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 Weber argues that although arts-based approaches are used for a wide range of purposes, they are highly useful in self-study education.

I learned that for so many years as a teacher educator I had been using other learner-centred methods such as presentations and group discussions yet I had never ventured into an arts-based approach as I had thought these activities were for artistic people. When I embarked on this journey, I was forced out of my comfort zone — and what an amazing experience it proved to be!

The choice of using artistic endeavours such as creating collages was beneficial to my students as it made the teaching of mathematical concepts fun. One of my journal entries reads as follows:. 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 suggest that students are excited when confronted with such a task and that they will gain confidence once they have achieved what they set out to do. I concur with this view as using a visual media approach was both challenging and rewarding. Moreover, by modelling how to utilise this strategy I was given valuable opportunities to interact with my students and I came to know them better, which improved my relations with them. 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. Lee notes that the classroom environment is part of a sociocultural dimension that is neither culture nor context free.

Therefore, regardless of our differences, I got to know the students better, and going forward was easier as I soon started to understand the problems they experienced regarding understanding and teaching mathematical concepts, because mathematics is labelled as a difficult subject. This process also made me think about how we assess students. In most cases we assess students when we do not really know them.

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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. This was a process that taught me to be patient and not to take things for granted, especially when working with first-year students. For example, at the beginning of the project the students tended to focus on aspects other than mathematics.

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I had to be aware of this and I had to ensure that mathematics remained the focus during the implementation of this approach. 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. I thus received positive feedback, which was beneficial in helping me to obtain new ideas and illuminations about my research and work. To illustrate, a few comments that were offered by critical friends are presented in the following. She said:.

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. Critical Friend 1, National Conference, October 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.

Learning outcomes

Samaras argues that Vygotsky maintained that we learn through others and that mental processes can be understood if we comprehend tools that intercede them. I was thus not just telling the students to use the ILA, but I was studying my own teaching practices and methodology as well. 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:. 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:. Critical Friend 3, National Conference, October The comments and the questions I received in response to my presentations were invaluable. A deeper understanding of ILA became possible through the use of essential feedback from critical friends who offered suggestions on how I could improve my practices as a teacher educator in early childhood mathematics. I realised that it was essential to constantly reflect on my practices and to explore new ways of teaching mathematics. For example, I had to reconsider my lesson plans and embark on techniques specifically geared towards teaching students about mathematics teaching in the FP through the use of an ILA in the hope of enabling and enhancing teaching and learning of this subject not only for the benefit of my students but also in the interest of the pedagogics they will adopt as teachers in the FP.

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.

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I needed to have an open mind when I consulted critical friends for feedback. 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.

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  6. 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 am at the very beginning of this new journey. 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. 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.