9962_How student teachers engage with the making of teaching tools for mathematics pedagogy

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How to cite this thesis
Surname, Initial(s). (2012). Title of the thesis or dissertation (Doctoral Thesis / Master’s
Dissertation). Johannesburg: University of Johannesburg. Available from:
http://hdl.handle.net/102000/0002 (Accessed: 22 August 2017).

University of Johannesburg
Faculty of Education
How student teachers engage with the making of teaching tools
for mathematics pedagogy

Refilwe Judy Ntsoane
201147390
Dissertation submitted for the degree
Masters Education
in
Childhood Education
at the
University of Johannesburg
Supervisor: Professor Elizabeth Henning
Co-supervisor: Professor Nadine Petersen
Date: July 2018

i
DECLARATION
I Refilwe Judy Ntsoane (201147390) declare that, except where indicated by
reference in the text, this is my own work. Any view expressed in the dissertation
other than referenced material are mine.

Signature__________________ Date______________ Place______________

ii
SUMMARY
Keywords: Pedagogical content knowledge, cognitive apprenticeship, tool mediation,
teacher career path, teaching tools, makerspace, homo faber.
In my practice as a foundation phase mentor teacher for student teachers, I have
witnessed how hard it is for them to create effective teaching tools in a low-tech,
informal ‘makerspace’ during their practicum. As teacher educator at a teaching
school, I was motivated to investigate this topic in order to improve my mentorship.
Although the design of teaching aids appeared less challenging in their practicum
planning groups, the same activity posed a serious challenge for them when they had
to implement the tools individually in different schools where they continued their
practicum beyond our teaching school on the campus. They often came back to our
school to borrow teaching tools that they had created at the school and where they
worked together as a group. The safe environment of the teaching school on the
campus was a ‘maker’ place where they could design their tools and learn to use them.
I wanted to study the students to find out how they developed this part of their pre-
service education.
I thus initiated this study to explore how student teachers at the university teaching
school behave during their practicum session with a mentor teacher. I utilised the
Thomas and Brown (2009) model of design and creativity, which is viewed from the
three perspectives of human activity namely “knowing” (Homo sapiens), “making”
(Homo faber) and “playing” ( and imagining) (Homo ludens). I coupled this perspective
with Collins, Brown and Holum’s (1991) typology of cognitive apprenticeship.
Data for the study was collected by myself as participatory and practitioner researcher,
with field notes, photos, artefacts, and individual- and focus group interviews. Two
groups of third year BEd foundation phase education student teachers were selected
form to take part in the study. The data were collated and analysed with Atlasti software
and also manually.
The results indicated that despite the student teachers’ ability to design and make
creative artefacts, they found it hard to integrate their tools as mediational ‘signs’ in
practice. Additionally, they used teaching tools that were not always relevant to the
content they were teaching. Through the inductive analysis, seven themes were

iii
identified from the collated data, highlighting that the student teachers found it hard to
bridge design and practice and to teach conceptually with the tools. The findings reflect
a need for an addition to the methodology modules in the teacher education
programme on how to design and create teacher toolkits that will come in handy as
they embark on their teaching career.

iv
ACKNOWLEDGEMENTS
I was not alone when writing this dissertation and therefore would like to acknowledge
the following people.
To the student teachers who took part in my study. Your contributions are highly
appreciated.
I am obliged to my colleagues who supported and motivated me during this period of
intense learning.
I am truly indebted and thankful to, my supervisor Prof Elbie Henning, our journey has
not only been about professional development but also on a personal level.
Professor Nadine, thank you for your valuable guidance.
To my parents: Thank you for being there in my times of need. To my father,
Matsobane Bennett Mphahlele, thank you for constantly reminding me of the
importance of education. To my mother, Raesibe Mary Mphahlele, thank you for moral
support and encouragement. Love you.
I owe a sincere and earnest thankfulness to my boys, Nthato Ntsoane and Karabo
Ntsoane. Thank you for being there whenever I need you. Love you.
My daughter, Monthati Ntsoane Thank you for inspiring me to be a better mom and a
better person. I love you.
Family and friends thank you for your unfailing support.
To God be the glory

v
TABLE OF CONTENTS
DECLARATION ……………………………………………………………………………………………..
i
SUMMARY
……………………………………………………………………………………………………
ii
ACKNOWLEDGEMENTS
………………………………………………………………………………
iv
TABLE OF CONTENTS
………………………………………………………………………………….
v
LIST OF TABLES ……………………………………………………………………………………….
viii
LIST OF FIGURES
………………………………………………………………………………………..
ix
CHAPTER 1 OVERVIEW OF THE STUDY
……………………………………………………….
1
1.1
Introduction ……………………………………………………………………………………………… 1
1.2
Research question, aim and objectives………………………………………………………. 4
1.3
Research design: A case study utilizing ethnographic tools ……………………….. 5
1.4
Data collection and analysis ……………………………………………………………………… 6
5. TERMINOLOGY………………………………………………………………………………………………………5
1.5.1 Student teachers
……………………………………………………………………………..
7
1.5.2 Mentor teachers ………………………………………………………………………………
7
1.5.3 Teaching tools
…………………………………………………………………………………
7
1.5.4 Triarchic model of learning and design
……………………………………………
7
1.5.5 Cognitive apprenticeship ……………………………………………………………………
7
1.7
Conclusion ………………………………………………………………………………………………. 8
CHAPTER 2 STUDENT TEACHERS LEARNING IN A PRACTICUM ………………….
9
2.1
Introduction: Making tools as mediational artefacts ……………………………………. 9
2.2
Learning practice in a teaching school with a ‘dual curriculum’ …………………. 10
2.3
Teacher knowledge and PCK of foundation phase teachers ………………………. 14
2.4
Learning in an apprenticeship of ‘thinking’, ‘making’ and ‘playing’
…………….. 17
2.5
Situating tool-making in practice
……………………………………………………………… 19
2.6
Tool-mediation in early number concept learning
……………………………………… 21
2.7
Conclusion: Limitations of a practicum and the promise of a career ………….. 26
CHAPTER 3 THE RESEARCH PLAN ……………………………………………………………
28

vi
3.1
Introduction ……………………………………………………………………………………………. 28
3.2
The unit of sampling ……………………………………………………………………………….. 31
3.3
Ethnographic elements of research design ………………………………………………. 31
3.3.1 Ethnography in the study of student teachers ……………………………………. 32
3.4
Data Collection
……………………………………………………………………………………….. 33
3.4.1 ‘Ethnographic’ observations and the ‘emic’ perspective ……………………… 34
3.4.2 Photographic data ………………………………………………………………………..
35
3.4.3 Artefacts ……………………………………………………………………………………..
36
3.4.4 Interviews ……………………………………………………………………………………
35
3.5
Reliability and validity of the study
…………………………………………………………… 37
3.6
Data Analysis …………………………………………………………………………………………. 38
3.6.1 Computer assisted data analysis ……………………………………………………… 38
3.7
Research ethics
………………………………………………………………………………………. 40
3.8
Conclusion …………………………………………………………………………………………….. 41
CHAPTER 4 DATA OF THE STUDY
……………………………………………………………..
42
4.1
Introduction ……………………………………………………………………………………………. 42
4.2
Data collection………………………………………………………………………………………… 42
4.3
Data analysis: From codes to categories and themes ……………………………….. 43
4.4
Outcome of the analysis
………………………………………………………………………….. 60
4.4.1 Theme 1: Inability to mediate via artefacts ………………………………………… 60
4.4.2 Theme 2: Lack of design thinking tools……………………………………………… 62
4.4.3 Theme 3: Limited use of artefacts in school ………………………………………. 65
4.4.4 Theme 4: Tools as memory aids ………………………………………………………. 67
4.4.5 Theme 5: Connect with life outside school ………………………………………… 64
4.4.6 Theme 6: Limited interaction with theory …………………………………………… 65
4.5
Conclusion: Glimpses of the data process ……………………………………………….. 75
CHAPTER 5 DISCUSSION AND CONCLUSION …………………………………………….
76
5.1
Introduction ……………………………………………………………………………………………. 76
5.2
Themes constructed from the data
…………………………………………………………… 77
5.2.1 Inability to mediate via artefacts ……………………………………………………….. 77

vii
5.2.2 Lack of design thinking tools ……………………………………………………………. 79
5.2.3 Limited use of artefacts in schools ……………………………………………………. 80
5.2.4 Limited practical work ……………………………………………………………………… 81
5.2.5 Teaching tools as memory aids ……………………………………………………….. 82
5.2.6 Connection with life outside school …………………………………………………… 84
5.2.7 Limited interaction with theory
………………………………………………………….. 85
5.3
Readily available resources …………………………………………………………………….. 86
5.4
Limitations
……………………………………………………………………………………………… 88
5.5
Conclusion …………………………………………………………………………………………….. 90
REFERENCES
…………………………………………………………………………………………….
92
ADDENDUM A: PERMISSION TO CARRY OUT RESEARCH IN SCHOOL ………..
95
ADDENDUM B: ETHICS CLEARANCE APPROVAL ……………………………………….
96
ADDENDUM C: PARTICIPANT CONSENT FORM
…………………………………………..
97
ADDENDUM D: OBSERVATION SCHEDULE
……………………………………………….
101
ADDENDUM E: MEMORANDUM OF AGREEMENT BETWEEN UNIVERSITY OF
JOHANNESBURG AND GAUTENG DEPARTMENT OF EDUCATION….
99
ADDENDUM F: EXAMPLE OF STUDENT TEACHER’S LESSON PLAN
………….
117
ADDENDUM G: EXAMPLE OF TRANSCRIBED RAW DATA
………………………….
128
ADDENDUM H: HOW DATA WAS CODED
…………………………………………………..
142

viii
LIST OF TABLES
Table 3.1: Charecteristics of the case study (adopted from Cresswel,
2011: 223 ) …………………………………………………………………………………
32
Table 3.2: Definitions of ethnography and elements invoked in the study
……………
35
Table 3.3: Ethicalconsiderations …………………………………………………………………..
43
Table 4.1: Interview and observation schedule ……………………………………………….
45
Table 4.2: schoolteachers’ demographics
………………………………………………………
46
Table 4.3: Categories derived from collapsed codes ……………………………………….
55
Table 4.4: Final categories and themes …………………………………………………………
57

ix
LIST OF FIGURES
Figure 1.1:
Mentoring of student teachers in making teaching artefacts …………….
4
Figure 2.1:
The progression of the chapter ………………………………………………….
10
Figure 2.2:
Learning in an apprenticeship at a teaching school ………………………
11
Figure 2.3:
Teacher knowledge: Career pathway as levels of development
(adapted from Snow et al. 2005:)
……………………………………………….
16
Figure 3.1:
Integrated data collection ………………………………………………………….
37
Figure 3.2:
Steps of analysis ……………………………………………………………………..
42
Figure 4.1:
Some of the examples of coding
………………………………………………..
41
Figure 4.2:
Second level of coding ……………………………………………………………..
46
Figure 4.3:
Conceptual pattern of the main findings
………………………………………
59
Figure 4.4:
Backward tracing from the pattern to 1st levels of codings …………….
60
Figure 4.5:
Mathematics resource designed by student teachers ……………………
61
Figure 4.6:
Some of the resources used to show the difference between 2D
and 3D shapes
………………………………………………………………………..
65
Figure 4.7:
Dice as mediational artefact
………………………………………………………
68
Figure 4.8:
Mediational artefact created by student teachers
………………………….
71
Figure 4.9:
Student teachers as knowing beings
…………………………………………..
67
Figure 4.10:
Student teachers as maker of tools (Homo faber)
…………………………
68
Figure 4.11:
Student teachers as players (Homo ludens ) ……………………………….
69

Chapter 1

1
CHAPTER 1
OVERVIEW OF THE STUDY
1.1
Background, problem and motivation for the study
This study is about the use and making of tools for pedagogical purposes: Teachers
of young children regularly use material teaching aids as mediational artefacts in their
classrooms. How they use them and with what effect is not always clear. When
education students learn to make and use such artefacts, they often mimic existing
ones and fail to reflect on the mediational value of the artefacts. It is here that the
problem of this study is situated. I set out to capture how university students in a
foundation phase teacher education programme learn to design, make, and use these
tools, arguing that it requires specialized skills to conceptualize and to produce such
tools, and that it warrants a close-up inquiry. I, furthermore, argue that the use of these
tools requires careful planning, taking cognisance of child learning and conceptual
development (Henning & Ragpot, 2015) and of pedagogical craftsmanship to foresee
the usability of the tools. I thus started the study with the idea that I wanted to see how
the students go about planning and making artefacts and what they observed during
their teaching practice at schools. One of these schools is the teaching school where I
am a head of the foundation phase department. A part of my work is to mentor
(Hamilton & Riley, 1999; Gratch, 1998) student teachers. It is, thus, in this capacity that
I undertook the study as a practitioner in the field.

Mentor teachers in a teaching school that is affiliated to a university teacher education
programme are expected to train student teachers to design and make teaching tools
as part of their student mentorship programme at the school (Hobson, Ashby, Malderez
&Tomlinson, 2001:2). Such teachers are briefed to attend to specific aspects of student
apprenticeship in pedagogical content knowledge (PCK) (Sothayapetch, Lavonen &
Juuti, 2013:85). In the case of making concrete/material teaching tools, mentor
teachers at the research site of this study work with groups of students who make
pedagogical artefacts that they can add to their teacher toolkit. The work we do can
be likened to what is currently referred to as makerspaces; the spaces for pre-service
teachers in the context of this study are decidedly low-tech, using recycled materials
Chapter 1

2
and natural objects, much like the teacher who was interviewed on a ‘makerspace’
blog recently:
Laser cutters, robots, 3D printers: when people talk about educational
makerspaces, images of expensive, high-tech gadgetry comes to mind. In
Colleen Graves’ library, they make use of a much cheaper resource. “It’s trash,”
she said. “But don’t call it that.” (https://hechingerreport.org/teachers-share-tips-
on-making-makerspaces-accessible-to-all/)
Hannah Arendt (Arendt, 1958) articulated the concept of Homo faber as the tool that
humans use to control the environment. ‘To know’ is to use the tool (of knowledge as
well) to control the environment. I refer to her view because I would argue that children
need to be partners in making the artefacts that are used to teach them, so that their
thinking and their attraction to design and to playfully create is given some space in
classrooms, instead of letting teachers make these or use ready-made tools. My view
is that every classroom could be a ‘makerspace’ of some kind and children should have
the opportunity to ‘control’ some of their learning by being free to express themselves
by design and by being learner-makers. In other words, I would say that children need
to create these learning artefacts themselves sometimes – asking them to make
something that would help others understand the topic that is in the theme of a lesson.
In Chapter 5, I will come back to this issue of learners needing to be co-developers of
instructional tools. Young children are makers of idea tools and material, concrete tools
to teach themselves and each other (Vygotsky, 1933). I argue that it is not just the
domain of teachers and traders who sell ‘educational material’ and ‘toys’. 1 I also argue
that student teachers need to learn and apply this type of principle.
To this end I utilised an epistemological model of design and creation, as formulated
by Thomas and Brown (2009) to situate tool making conceptually (Thomas & Brown,
2009:1-2). The construct of student teachers’ learning in a specific mentorship
programme is further framed by the cognitive apprenticeship model as described by
Collins, Brown and Holum (1991), and Brown, Collins and Duguid (1989). In these two
models pre-service teacher education is seen as an apprenticeship in tool-making for
learning and teaching purposes.

1 See Lev Vygotsky’s treatise for play and ‘making’ ( Vygotsky, 1933)
Chapter 1

3
As researcher, I was motivated to investigate the design, production and usability of
innovative materials for the teaching of mathematics in the foundation phase. During
the early grades, children learn many mathematical concepts through concrete
manipulatives and demonstration materials. In practice, as a foundation phase teacher
in a teaching school, I have witnessed much repetition (and copying) in the making of
such teaching tools by student teachers. I seldom come across tools that truly
exemplify the pedagogical content knowledge of teachers, as formulated by Shulman
(1987:5), which would include students’ knowledge of children’s early conceptual
development in mathematics as, described for example, by Fritz, Ehlert and Balzer
(2013:40). In a country with a limited public budget, it is necessary for teachers to be
self-sufficient and to be able to improvise teaching tools. Pre-service teachers can
experiment with different kinds of materials, including recycled material, especially in
a teaching school set-up, where pedagogical artefact production is a requirement. In
this school, teachers are also encouraged to use natural objects from the school
grounds as teaching aids.

My interest, and with that also the framing of this research, comes from a blend of
theoretical areas. I use an integrated lens in my approach of this investigation: 1) I see
the study as an inquiry of ’cognitive apprenticeship’ (Brown, Collins and Duguid,
1989:33; Collins et al., 1991) in learning to use and to make teaching tools as
apprentices of the teaching profession and 2) I also utilise Thomas and Brown’s (2009)
model of design and creation/production of such tools (See Figure 1). In this model,
knowledge-making as a design and creation phenomenon is viewed from three
perspectives of human activity, namely ’knowing’ (Homo sapiens) ’making’ (Homo
faber), and ’playing’ (Homo ludens) (Thomas & Brown, 2009:5). Incorporated in this
blend is also 3) the model of a teacher’s career path (Snow, Griffin & Burns, and
2005:201), to reflect on what can be realistically expected of pre-service teachers in
their practicum.

Therefore, from the outset, I accepted that pre-service teachers would not be where
they could be after a few years in practice, but that they would be able to form the
foundations of designing and using tools for teaching. In combining these three
theories I argue that, as apprentices in teaching, the students can learn in the daily
practice of school how to integrate 1) knowledge – what they know about child learning,
Chapter 1

4
the content of mathematics (specifically) and those artefacts which exemplify their
knowing, and 2) tool-making and design with 3) playfulness and innovative design
(Thomas & Brown, 2011:121).2

Figure 1.1:
Mentoring of student teachers in making teaching artefacts
This amalgamated theoretical lens incorporates, heuristically, ideas to think about how
students can design teaching materials for their lessons. This is an important part of
the teaching practicum at the university’s teaching school – both in mentoring practice
and in activities around making tools for pedagogical use. In this practice, there could
be typical patterns, routines and pedagogical rituals of action, which is regarded as
salient indicators of students’ apprenticeship in the mentoring situation. I noticed from
my first encounters with students that they had fixed ideas and routines about ‘teaching
aids’. My sense was that they had been enculturated into certain practices of tool-use
in their own school lives, in what Lortie (1975) refers to as an ‘apprenticeship of
observation.’

I also realised that there could be specific discursive practices of mentoring around
mathematics learning tools as contained in discussions and logbooks of students
(Collins et al., 1991:1). These authors postulate that patterns of lesson preparations

2 This view of ‘play’ is not to be equated with games, or gaming and ‘gamefication’, which has a different epistemology, with an
added element of structured rules and terms of engagement, often with a competitive element.
Cognitive
apprenticeship
Homo sapiens
Homo faber
Homo ludens
Teacher career
path
Chapter 1

5
and selection of tools may yield usable data for a study that adopts ethnographic
research tools -. albeit not a full educational ethnography in the traditional sense such
as the one of Henning (1992).
1.2
Research question, aim and objectives
To investigate the object of study, the research question that guided the study
addresses a two-sided issue about the making of educational tools for the classroom:
How do student teachers engage with the making of teaching tools?
Sub-questions:
 How is the Thomas and Brown (2009) epistemological model exemplified in
tools student’s teachers design and make?
 How do students act as apprentices of tool design and creation with the mentor
teacher?
The overall aim of the study was to produce a description of a sample of third-year
B.Ed students’ journey in making teacher tools with their mentor teacher.
The objectives were:
 To describe and analyse how the students exemplify the Thomas and Brown
(2009) epistemological model in the tools they design and make.
 To depict how students engage, with the mentor teacher’s assistance, in tool
design and creation in the practicum apprenticeship.
1.3
Research design: A case study with ethnographic tools
In this study, as practitioner researcher (and also participatory researcher), I utilised
ethnographic tools to provide a description of student’s “way of life” (Wolcott, 1994) in
an aspect of their work during the apprenticeship programme at the school. The study
is thus more of a case inquiry (Yin, 1993; Stake, 2013) with the construct as a ‘bounded
system’ (Stake, 2013) rather than a full, anthropological type of ethnography. The
study does have ethnographic qualities, however, because the inquiry describes the
way people do things in everyday practice in a specific setting and as a defined group
(Wolcott, 1994; Henning, Van Rensburg & Smit, 2004; Henning, 1992, 1995). With this
approach, a researcher observes and records human activity as it happens. In the
instance of this inquiry the student teachers were observed by an insider, thus by a
practitioner researcher, or participatory observer, collecting data through everyday
Chapter 1

6
interaction, with participants in their natural setting (MacMillan & Schumacher,
2006:315).
To provide an in-depth understanding of the phenomenon that is studied, a descriptive
analysis is required. In this analysis, from different data sources, I aimed to show how
the epistemological model (Thomas & Brown, 2009) – featured in the student’s work,
especially how patterns that relate to the phenomenon (of tool-making) could be
identified. Furthermore, in my role as the participatory observer and the mentor, I had
the double task of ’making visible’, how he elements of cognitive apprenticeship
(Collins et al., 1991)featured.
1.4
Data collection and analysis
Data was collected from scheduled logbook entries of the mentor teacher and the
students as well as video recordings of lessons and audio recordings of focus group
discussions/interviews about lessons. In addition, teaching tools of the selected sample
of participants were analysed according to criteria of the epistemological model
(Thomas & Brown, 2009). I also observed mentor teachers and had informal interviews
with them.

The various data was analysed in different modes. Data from the logbook and the focus-
group discussions and interviews were coded and categorised broadly in a grounded
theory mode (Strauss & Corbin, 1998; Henning, Van Rensburg & Smith, 2004) without
aiming to theorise directly from it, but just using the inductive ‘open’ and ‘axial’ coding
mechanism of this analytical method. The content of lessons and the artefacts and their
use, were coded according to requirements/criteria for pedagogical content knowledge
and tool-use in foundation phase mathematics teaching. In both these analyses I was,
invariably, influenced by the idea of Thomas and Brown (2009), much as I was trying to
do ‘open coding’. Integration of thinking, making and playing, as described in the
Thomas and Brown (2009) model of design and creation, was thus considered
throughout the analysis. The video recorded lessons were analysed per episodic unit
for the use of the learning tools.
1.5
Terminology
Terms were used in specific relation to the context of the study and its setting.
Chapter 1

7
1.5.1
Student teachers
This term refers to a university student who is studying to be a teacher and who, as
part of the training, observes classroom instruction or does closely supervised teaching
in a primary or secondary school. Student teachers in the school where the study takes
place are monitored by mentor teachers over a period of four years.
1.5.2
Mentor teachers
Mentoring is defined as the one-to-one support of a novice or less experienced
practitioner (mentee) by a more experienced practitioner (mentor), primarily to assist
the development of the mentee’s expertise and to facilitate their induction into the
culture of the profession (in this case teaching) and into the specific local context
(Hobson, Ashby, Malderez & Tomlinson, 2009:207)
1.5.3
Teaching tools
This tern refers what is generally known as learning and teaching support material
(LTSM) in the South African discourse; in this study it includes a variety of pedagogical
materials used in the classroom. These materials range from resources made by
teachers (and rarely by learners) to commercially produced classroom resources such
as wall charts, workbooks, textbooks, e-books, readers, stationary, science kits,
dictionaries, encyclopaedias and so forth. Teacher-created resources refers to material
created by teachers for use in their classrooms. For this study the LTSM will be referred
to as ‘teaching tools’ (Department of Basic Education, 2014:7)
1.5.4
Triarchic model of learning and design
This term refers, in various guises in the study, to the Thomas and Brown (2009:5)
model of design and creation/production of tools. In this model, knowledge-making as
a design and creation phenomenon is viewed from three perspectives of human
activity, namely ’knowing’ (Homo sapiens) ’making’ (Homo faber), and ’playing’ (Homo
ludens).
1.5.5
Cognitive apprenticeship
This term refers to a theory of how people learn from one another through observation,
imitation and modelling (Collins, Brown & Newman, 1989; Collins, Brown & Holum,
1990) and under the guidance of an expert.

Chapter 1

8
1.6
Components of the dissertation
In the first chapter I gave the background and motivation of the study, as well as the
blended theoretical framework underpinning the study, with the overall aim and
objectives embedded and clearly stated.
The second chapter gives a discussion of some of the literature that I engaged with to
investigate the unit of analysis (Linden, Trochim & Adams, 2006) of the research,
namely, student teachers’ design and creation of teaching tools in a practicum
apprenticeship with a mentor teacher.

The third chapter provides a description of the methods that I used during the data
collection and the analysis. This chapter also describes the ethical considerations
pertaining to the research.

The fourth chapter focuses on the data collection and analyses, with some examples
of the process
.
The last chapter presents the discussion. Woven into this chapter are the limitations
and recommendations of the study.

1.7
Conclusion
The chapter has given an overview of the study and the contents of the dissertation.
The problem statement accentuated the unit of analysis (Linden, Trochim & Adams,
2006), namely of how student teachers learn to design and implement artefacts in the
teaching of early grades mathematics and how they use it. The research problem of
the study has an underlying claim, namely that although students are trained to make
and use teaching tools, they may be unable to use them functionally if they do not aim
to teach a concept with the tools as mediation and unless children use the tools in a
goal-directed way.

Chapter 2

9
CHAPTER 2
STUDENT TEACHERS LEARNING IN A
PRACTICUM
2.1
Introduction: Making tools as mediational artefacts
This chapter contains a brief discussion of the scoped literature with which I engaged
during the study and which will clarify the theoretical framework as set out in the first
chapter. I will be dealing specifically with the socialisation of student teachers as future
professionals with regard to the specific knowledge and skills they may need to start
off as new teachers, especially with regard to the production and use of tools in their
practicum. The argument of this chapter is that student teachers need to understand
that, in addition to their knowledge development, they need to learn specific methods
and skills while being exposed to teacher educators’ demonstrations of practice.
(Joyce & Showers, 2002:2). One of these skills is to design, make and use personally
made artefacts and to aim to let children also participate in the making of such learning
tools – thus shifting the emphasis to children’s grasp of the notion of ‘making’ to learn
and doing so playfully, or though play.

The chapter includes a discussion of apprenticeship as a form of learning in a
practicum in a specific type of school. In this school, the students learn to teach while
the teachers at the school educate the learners in tandem (Petker, 2018). Petker has
argued that this combination shows that the teachers at the school have a dual
portfolio; they teach children and they teach student teachers. One of the briefs of
these teachers is to assist students to design and use handmade, or technologically
constructed, materials. While doing this, the mentor teachers aim to make the students
aware of how they can build their pedagogical content knowledge (PCK), by showing
their understanding of how children learn, combined with knowledge of the subject
content and with classroom methods. Shulman (1987) suggested that PCK includes
skills of teaching with knowledge of content and knowledge of the learner.

The chapter argues for a specific approach to the type of mentoring and coaching of
student teachers – one that will elicit originality in the tools they make and use for their
teaching, while converting the tool-use to learning activity. The chapter also argues
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that student teachers learn optimally in apprenticeship mode (Brown, Collins & Duguid
1989; Collins, Brown & Holum, 1991, Rogoff, 1990), while taking cognisance of a three-
component model of human thinking and design (Thomas & Brown, 2009). The chapter
is rounded off by a discussion of reflective practice and the use of tools, drawing the
conclusion that students are not likely to engage with a full range of opportunities in
their undergraduate years. They are likely to learn ‘just enough’ to cope, but will need
a longer experience in their career to design and make usable tools with good effect
as mediators of learning. In Figure 2.1 the development of the chapter is set out.

Figure 2.1:
The progression of the chapter
2.2
Learning practice in a teaching school with a ‘dual curriculum’
The diagram below shows how student teachers encounter learning at the university
teaching school (Figure 2.2). It shows students learn in what Ramsaroop (2016) and
Gravett and Ramsaroop (2017) refer to as a “pedagogical laboratory”. This means that
the practicum at the teaching school is a place where students can freely experiment
with ideas and methods and also with the use of tools to mediate children’s learning.
That is the ‘real life’ setting, which is a live laboratory. In this study I go a bit further and
look at this live laboratory from the view of three models: 1) I see the students as
apprentices with a mentor, at the beginning of their career as a teacher (pre-service)
and as 2) thinkers, makers and designers in their ‘human activity’. I thus see them as
Homo sapiens, Homo faber and Homo ludens in their thinking design and use of
1. Introduction and
claim: Making tools
as mediational
artefacts
2. Learning practice
in a teaching school
with a dual
curriculum
3. Teacher
knowledge as PCK
of foundation
phase teachers
6. Tool-mediation in
early number
concept learning
5. Mentoring
student teachers in
situated practice
4. Learning in
apprenticeship of
‘thinking’, ‘making’
and ‘playing’
7. Conclusion:
Limitations of a
practicum and the
promise of a career
in which to develop
skill
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materials. 3) I also view them as beginners, who only learn the foundations of the
profession, and who will become adaptive experts of teaching only during their years
of classroom experience (Snow, Griffin & Burns, 2005)

Figure 2.2:
Learning in an apprenticeship at a teaching school
“Though the theory of a need to actively participate in reactive change is appealing, it
has to be coupled with both teacher educators and student teachers embracing the
theory of becoming: (Thomas & Brown, 2009:1). Before the constant change in
learning that we are witnessing now in the 21st century, knowledge used to be static.
Lately, learning is different and this requires mentor teachers to look at the student
teachers as participants in a productive inquiry, or, as Hickman argued: “The function
of (productive) inquiry is the production of new artefacts, including new habits”
(Hickman, 2007:9).
I agree with Marais and Meier (2004) who say that practical pre-service teacher training
in South Africa needs to improve, because teacher educators do not show the
commitment which is needed to positively influence the way student teachers link
theory (and design) to practice. These lecturers at a university in South Africa allude
to the fact that the quality of teacher educators plays an important role in initiating
student teachers into the culture of good practice (Marais and Meier, 2004:221).
• B.Ed. FP in a
teaching school
• Dual curriculum
(university and
school)
• Knowledge for
teaching
• Knowledge of
child learning
1. Student teachers in
a teaching school
• Mentoring
• Reflective practice
2. Cognitive
apprentinceship
Teacher career
development
• The three
perspectives on
human activity
• Student teachers
as developers of
their own
mediational
artefacts
3. Situated practice
for preparing
toolkiits for
teaching
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In my experience teacher educators at universities generally do not have sufficient
school teaching experience at a suitable grade- or phase level themselves. Elliot
(2001) suggested that initial teacher training should entail a close collaboration
between the schools where the student teachers do their practical teaching with the
institution where they are trained. This is also what Darling-Hammond (2010)
advocates. Mindful of the effect on student teachers’ competence of practicum
sessions and how they are conducted, Gravett and Ramsaroop (2017:8) allude to the
fact that student teachers need to spend time in a ‘model’ teaching environment as a
remedy to unpreparedness when leaving the university with qualifications but being
unable to teach and to adapt to changing conditions (see also Snow et al., 2005). They
further add, referring to pre-service years, that, “(i)t is during this time that student
teachers are afforded the opportunity of strengthening skills and abilities that will help
them to function effectively in schools with limited resources (and to learn) how to
improvise, how to make the best of the situation” (Gravett & Ramsaroop 2017:8).
Focusing on student teachers’ custom designed teaching tools as an essential part of
the lessons they teach at the teaching school, this “strengthening of skills and abilities”
(Joyce & Showers, 2002:2) happens through their entire practicum at the school over
four years – particularly during the time when they teach micro-lessons (Gravett,
Petersen & Petker, 2014; Petker, 2018), when they observe mentor teachers in action
as well. It is also during this time that they observe the individual child allocated to each
one of them for observation over four years, to record their development. One of the
pedagogical principles that is stated by (Shulman,87:6) is the ‘principle of observation’,
which relies on lived experiences.
However, when students go to different schools, away from their home base ‘model’
school, most of the common teaching aids (mediational artefacts) that they encounter
during their teaching practicums have already been designed with specific learning
objectives in mind. Students just use them almost in an ad hoc way. These are seldom
analysed for their effect and purpose and are often purchased from traders in
educational materials who visit schools to sell their wares. In the school where this
study was conducted the teachers’ artefactual toolkits were no different; yet, the
student teachers were expected to learn to be innovative in their design and making of
teaching aids. What they encountered were ready-made commercial objects. If one
uses an object to clarify thinking, I would argue that a personally made object has much
more currency than one made in a factory. The question I pose is: How else can the
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design be original? I acknowledge that there are powerful artefacts, such as Lego-
blocks and that they can be used creatively, but that is not the point I am trying to make
in this study. I am arguing for custom-crafted tools that show how a future teacher’s
mind works in relation to teaching a specific topic. I am, thus, thinking about ‘design
thinking’ in a teacher education context (Schon,1987).

I argue that not only should student teachers have a good grasp of making their own
teaching tools that suit their teaching preference and communication style, but they
should also be able to effectively expose the learners to a variety of these mediational
artefacts, suitable for the content of a lesson. I would even go as far as saying that the
learners should assist in developing tools. In doing so student teachers will be showing
the learners to learn from the knowledge they already have, to make new knowledge
and to show it though an artefact that makes their thinking ‘visible’ (Collins et at, 1989)
based on what they know and think, but also designing and making tools to help them
think further, as is often exemplified in ealry grades teaching:
In case of representational pictures, one type of artefact that has
received considerable attention is pictures. What is our notion of the
artefacts picture of a dog that distinguishes it from related kinds such
as a picture of a cat? Just as with chairs, clocks and paws, there is no
physical property that all and only pictures of dogs possess. Some are
tiny black-and-white sketches; others are huge abstract drawings.
Some look like dogs (in the sense that one might even mistake them
for actual dogs in the dim light) others are diffuse smears of colour that
do not readily call dogs to mind (Bloom, 1996:6).
Learning to make meaningful artefacts to add to their toolkit, student teachers should
pay attention to the school curriculum and the university teacher education programme
at the same time. My sense is that this is likely to be hard for them.

It is an issue to consider in that the teaching school hosts these two curriculums,
running concurrently. The core function of the teachers at the teaching school is to
ensure the effective delivery of both curriculums (Department of Basic Education,
2011). Teachers teach children and, at the same time, they have to teach students
how to teach (Petker, 2018). This partnership incorporates, among other programmes,
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14
service learning which, according to Petersen and Petker (2014:130) “allows the
teacher education curriculum planners to make optimal use of central organising
pedagogical stance of the teacher education programme, which in these institutions is
knowledge of how children learn and develop”. A part of this is to learn to make usable
materials to augment their teaching, especially in the teaching of abstract concepts,
such as numbers and patterns in mathematics during their practicum sessions. So, in
the end a mentor teacher engages in much additional work and must try to ignite
students’ creativity in making of tools, while they are in practicum.

Practicum sessions play an important role as a bridge between the university
curriculum (theory) and the school curriculum practice (Gravett & Ramsaroop, 2017).
According to Kaasila and Lauriala, (2010:854), who are authors who write about this
topic in a Finnish context, student teachers operate as adult professionals during
practicum sessions and this puts them in a dual-purpose position, where their task is
to study and learn simultaneously about the school learners and the content that they
have to teach. One of the things they learn for this purpose is how to make material
tools that can mediate their teaching. Students should be alert to what the learners
have to know and at the same time also what they have to do in their university
curriculum. Their work is also dual.

For student teachers to be experienced in both curricula they need to observe a master
(mentor teacher) in action, while also learning form a lecturer at the university about
design thinking and design principles for cognitive development. The mentor teacher,
however, is the one who serves as example. Cain (2009) suggests that mentoring
means that a class teacher (in the school curriculum) entrusts her learners to the
student teachers as she takes the role of scaffolding the student teacher teaching. In
this dual role a mentor teacher trains student and builds relationships with them,
making the student teachers feel welcomed, accepted and supported (Cain, 2009:54)
during the four years of B.Ed. studies.

My claim is that mentor teachers are able to guide students. They are assumed to be
ideal human resources that need to model good teaching practice (Korthagen, 2004;
Petker, 2018). Yet, they are not trained as teacher educators, especially in the
important area of teaching tools, and that their own practice needs to reflect ‘thinking’,