The an illustration of my knowledge to the

purpose of the concept map was meant to assist me in identifying those aspects
of learning that required development so that I can take action in improving
them. Kinchin, et al., (2000) argue that concept maps are useful in
revealing thought processes that generally remain private to the mapper. Therefore
the concept map indicates my understanding of electromagnetism and serves as an
illustration of my knowledge to the reader of this study in documented form.     

also corresponds with the three Big Ideas
represented in the CoRe, as well as the seven video-recorded lessons presented.Kinchin,
Hay and Adams (2000) recommend three ways in which concept maps could be
structured. These are spoke, chain and net structures. Kinchin et al. define
a spoke concept map as a circular structure in which all the related aspects of
the topic are linked directly to the core concept, but these aspects are not necessarily
directly linked to each other. Kinchin et al. describe a chain concept
map as consisting of a linear arrangement of concepts where each concept is
only linked to those immediately above and below it. A net concept map can be
described as a highly and hierarchical network that demonstrates a deep
understanding of a specific topic.

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concept map constructed for this study consisted of words or phrases enclosed
in boxes (Appendix  C). These words or
phrases represent concepts or ideas about the core concept of electromagnetism.
The boxes are connected by lines with directional arrows which represent links
or relationships between different concepts. Each link is accompanied by
linking words or phrases which together with the concepts or ideas about these
concepts forms a complete thought called a proposition. The concept map was
initially constructed in such a way that concepts closely related to the core
concept were closely linked directly to the core concept. Concepts not so
closely related to the core concept were connected further away resulting in a
hierarchical network.

concept map in this study takes the form of a net structure as it can easily accommodate
the addition of other concepts at various levels of the concept map without
disrupting the knowledge structure. Kinchin, et al., (2000), suggest
that a hierarchical network structure offers a number of routes to access a
particular concept and that this makes knowledge more flexible.

construction of the proposed concept map was meant to illustrate my knowledge and
how it is arranged in my mind. Changes were made to the initial concept map in
red pen at a different time of my learning about the concept of
electromagnetism. This was meant to monitor my progress of learning the topic
of electromagnetism. While teaching the process of EMI more changes were made
in green pen and this led to the construction of the final concept map. The
final concept map includes all concepts presented in the first two concept
maps. Therefore, only the final concept map will be discussed and analysed.


            12.3.3   Structural and contextual analysis

structure of the concept map indicates that the initial concept map grew in the
number of concepts I acquired during the study as the study progressed. This
was confirmed by the way in which the number of concepts increased each time
the concept map was constructed (initially in black, then red, then green). The
increase in the complexity of each phase of construction revealed that the
concepts I had acquired were developing from simple thoughts into more complex
coherent ideas about the topic. This gradual growth in the complexity of the
concept map’s structure confirmed that my breadth and depth of knowledge of the
topic was developing. The increases in the levels of connectedness from the
initial concept map to the other confirmed my ability to group, order and
connect ideas therefore indicating a deeper understanding of the topic.

search for meaning across the various
concepts revealed that:

(1)        Electromagnetism is a process involving
the generation of electricity using the effects of magnetism.

(2)        The topic electromagnetism consists of
six main concepts, namely magnetic field             strength,
magnetic flux, changing magnetic flux, induced emf, induced magnetic field and       induced current.

(3)        There are rules and laws that govern the
process of electromagnetism, including The        RHR,
RHSR, Faraday’s law, Lenz’s law, and Ohm’s law. (The latter two not         necessarily prescribed to know according
to CAPS, but good to know for the teacher how            it
is linked)

(4)        Each concept of electromagnetism is
structured in such a way that it consists of   definition(s),
equation(s), units of measurement, factors influencing its magnitude and            direction (vector nature), and how
each concept is applied in everyday situations.

The search for meaning within the different concepts revealed


(1)        A
changing magnetic field produces a current, just like an electric field in
electric circuits (category 1).

(2)        The
effects of a changing magnetic field (magnetic flux that increases or decreases
and its         magnetic
field strength) induces an emf, current and its magnetic field (category 2).

(3)        The
laws and rules of EMI relate the vector nature (magnitude and direction) of
these       concepts (category 3).

(4)        The
main concepts of EMI are somehow defined in terms of the changing magnetic
field             concept (category 4).

(5)        The
induced emf equation (Faraday’s law equation) is a symbolic representation of
all the            concepts of EMI
(category 5).

(6)        The
relationships amongst the main concepts of EMI can be expressed in terms of:

= 1Wb.s-1 = 1T.m2.s-1 (category 6).

(7)        All
the main concepts of EMI are vector quantities of which the factors that
influence their            magnitudes and
directions should be known (categories 7 & 8).

(8)        The
EMI process is applied in equipment such as transformers, generators,
microphones,             seismographs and
induction stoves (category 9).The
search for meaning within the instructional delivery of electromagnetism (use
Table 3) revealed that:

(1)        Verbs such as solve, demonstrate and
explain represented some of the actions that          needed
to be taken by either the teacher or learners during instructions (category 1).

(2)        Lesson indicators which were attached in
some of the leading concepts in the third            concept
map (Green) indicated how I intended to structure the sequence of the lessons when teaching this topic (category 2).

(3)        Textual and visual representations would
have to be used during instruction to promote     conceptual
understanding (category 3).

(4)        The phrase “not for grade 11? and
phrases like “solving strategy?, “unit conversions? and   “area formulae? show that the teacher should be aware of actions to
take and/or not to        take during
instructions (category 4).

(5)        Learners need to be exposed to devices
that use the process of EMI (category 5).

(6)        Apparatus such as magnets, coils and
galvanometers need to be used to develop             conceptual
understanding of the topic (category 6).

            12.3.4  Analysis of results

themes emerged in the analysis of the concept map. These themes are discussed
below using the Mavhunga and Rollnick’s 
(2013) model of PCK as illustrated within the theoretical framework
(Fig.1.1) of the study. The model uses four components of teacher knowledge that
are used to capture aspects of learning and teaching. These components include:

            i.          Knowledge of context

            ii.          Knowledge of students

            iii.         Subject matter knowledge

            iv.        Pedagogical knowledge


These four domains can
be used to describe a teacher’s Topic Specific Pedagogical Content Knowledge

The manifestations of a
teacher’s TSPCK include:

            i.          Student’s prior knowledge

            ii.          Curricular saliency

            iii.         Subject matter representations and

            iv.        Conceptual teaching strategies.



Data analysis in terms of the three domains:

(i)         Knowledge of context

The concept map also
indicates teacher awareness of the resources to be used during instruction. The
phrases ‘magnets’, ‘coils’, and ‘galvanometers’ represent the resources that the mapper intended
using during instruction. The phrases ‘microphones’,
‘seismographs’; ‘card swiping machines’ and ‘transformers,
generators and induction stoves’ represent some of the resources that the
mapper might use in the form of pictures to link what learners have learned in
the classroom with the devices that learners usually encounter in their
everyday life.

(ii)        Subject matter knowledge

The analysis of the
concept map reveals that electromagnetism is a process that involves the
generation of electricity using the effects of magnetism. During this process,
a changing magnetic field induces an emf in the conductor which in turn induces
an electric field. This electric field induces a current in the conductor which
produces its own magnetic field. The two opposing magnetic fields interact to
produce a magnetic force. The relative motion of the magnetic field and the
conductor results in kinetic energy being transformed into electrical energy.

This is indicative that
EMI consists primarily of six main concepts, namely:

1.         magnetic
field strength,

2.         magnetic

3.         changing
magnetic field/flux,

4.         induced

5.         induced
current, and

6.         induced
magnetic field (as already reported).


Each main concept is structured in such a
way that it consists of definition (s), equation(s), units of measurement,
factors influencing its magnitude and direction, and how each concept is
applied in everyday situations. Each of these concepts (excluding changing
magnetic field) is defined in terms of a changing magnetic field. For example,
induced current and induced emf are defined respectively as: Current produced by a changing magnetic
field and; Voltage produced by a
changing magnetic field.


There are laws, rules and principles that
govern the process of EMI. These are Faraday’s law, Lenz’s law, Right-hand rule,
Right-hand solenoid rule and the general Principles of EMI. The rules and laws
used in EMI relate to the vector nature (magnitude and direction) of the six
main concepts to one another. For example, Faraday’s law relates to the
magnitude of the induced emf to the rate of change of magnetic flux whereas the
right-hand rule relates the direction of induced current to its magnetic field.
The first Principle of EMI shows how a changing magnetic field induces other
quantities so that current is produced in the conductor.

These results show how the structure of
the EMI content is organised, how each of the main concepts are structured, as
well as the laws, rules and principles governing the process of EMI. These
results confirm Shulman’s view of subject matter knowledge.


Shulman (1986) refers to subject matter
knowledge as the amount and organisation of knowledge as viewed by the domain
experts in a particular discipline. According to him, this knowledge includes
knowledge of facts or concepts, laws, principles, theories as well as the
structures governing the discipline.


(iii)       General pedagogical knowledge

The concept map also
indicates some examples of general pedagogical knowledge in that teaching
strategies should be employed during instruction. These strategies include
problem-solving strategies; demonstrations; explanations as well as lessons
sequencing intended to assist learners understand the topic.

General pedagogical
knowledge refers to knowledge of basic skills required for teaching. According
to Rollnick, et al., (2008) general pedagogical knowledge includes
knowledge of what counts as good teaching, the best teaching approaches,
different learning theories, classroom organisation and management, physical
and psychological behaviour of learners, and specific educational purposes.


Data analysis in terms of the four


(i)         (Prior) Knowledge of learners

The inclusion of Ohm’s
law indicates that I was aware of what learners had learned prior to the
teaching of EMI. The phrases ‘solving
strategy’, ‘unit conversion’ and
‘area formulae’ connected to the
equations in the concept map suggest that I was aware of my learners’ learning
difficulties and prior knowledge. I was aware of the mathematical problems
encountered by the learners with regards to steps followed in solving problems,
their ability and inability to convert from one unit to the other and their
difficulty to work with area formulae. Furthermore, writing the change in
magnetic flux as:

                        ?? = ?BA = (Bf – Bi)A = ?f – ?i    instead of just: ?? = ?BA

suggests that I was
aware of the difficulty the learners had with working with ‘changing quantities’.

I was also aware of
other learners’ language difficulties judging by the way I used words such as ‘pictures’ and ‘artefacts’ in the concept map. The inclusion of these words in the
concept map suggests that I saw the need of using visual representations in the
lessons in order to assist my learners in overcoming language barriers
associated with the understanding of the topic.


(ii)        Curricular saliency

Some instances of
teacher knowledge indicate curricular saliency. The phrase ‘not for grade 11’  is linked to Lenz’s Law and Ohm’s Law in the
concept map and implies teacher awareness of what to include or exclude in
instruction. These concepts were included to make me aware of how
electromagnetism relates to electricity. It has also been mentioned to the
learners as to teach them that electromagnetism is not excluded from
electricity and other related topics.

The lesson indicators (L1.1;
L1.2; etc) used in the concept map indicates the order of the lessons, relating
to curricular saliency in that they indicate how the structure of the content
is organised.

The equation of Ohm’s
Law equation was included in green as to show a link between the topics of electric
circuits and EMI. Learners had learned about this law and its application in
solving problems involving electric circuits previously in grade 10. Thus the
inclusion of this law in this topic served two purposes: (1) to promote
conceptual progression and (2) to show a relationship between the two topics.
This equation would assist learners to solve problems involving induced current
as the EMI equations used in grade 11 do not have an equation that has current
as one of the quantities. Thus, the equation ? = IR served the purpose of
linking the two topics as the induced emf equation is ? = -N??/?t and to
promote conceptual progression.

The results discussed
above indicates teacher awareness of what to include and/or exclude when
teaching the topic, how the lessons should be sequenced to promote learner
understanding of the topic and how this topic should be linked to other topics.
These results confirm Rollnick, et al.’s (2008) and Geddis, et al.’s
(1993) arguments for curricular saliency. Rollnick, et al., (2008) refer
to curricular saliency as the conscious decisions that the teacher make with
regards to what comes before and after the topic, what to include or omit in
the topic as well as how a particular topic links with other topics within and
outside the subject. Geddis, et al., (1993) maintain that such decisions
are determined by teacher’s knowledge of the structure of the content, the
learners being taught and the purpose for teaching the topic


(iii)       Subject
matter representations


A variety of representations were used to
represent subject matter. Words such as “words”, “pictures” and “artefacts”
within the concept map suggests that both textual and visual representations
would be used during instruction to promote conceptual understanding of the
topic. The inclusion of apparatus such as magnets, coils and galvanometers in
the concept maps suggests that scientific tools would be used as forms of
representations to transform subject matter knowledge into knowledge suitable
for conceptual understanding.


The equations listed in the concept map
represent ways of representing subject matter. Equations are symbolic
representations of subject matter which when interpreted correctly can result
in conceptual understanding. For example, the equation ? = BA can be used to
define magnetic flux as: product of
magnetic field strength and the area enclosed by a conductor.


This equation can also be used to
identify the factors influencing the magnitude of magnetic flux, namely the
magnetic field strength and the area enclosed by the conductor.


Shulman (1986) refers to subject matter
representations and analogies as forms of representations used by the teacher
to make the subject comprehensible and understandable to learners. The variety
of subject matter representations discussed above indicated my intention to use
representations to transform subject matter into knowledge suitable for
teaching. Geddis, et al (1993),
however warn that the choice of subject matter representations should be
carefully made as failing to do so may result in the meaning of phenomena being


 (iv)      Conceptual Teaching strategies


Action verbs such as ‘solve’, ‘demonstrate’, and ‘explain’
were used in the concept maps. These verbs indicate actions that either the
teacher or learners could take to develop their understanding of the topic.
These verbs in turn represent some of the teaching strategies that could be followed
to facilitate the course of instruction. Based on these action verbs, it means
that teaching strategies such as problem-solving, demonstrations, group work
and explanations could be used to facilitate learning.


The lesson indicators
(L1.1, L1.2, L1.3, L1.4, L2.1 and L2.2) attached in the main concepts of the
topic also represent a teaching strategy. These indicators represent how I
intended to present the lessons in a particular logical sequence to promote
conceptual understanding and coherence. For example, the lesson indicator L1
attached to the EMI concept in green indicated my intention to introduce the
concept of EMI first before teaching the other main concepts in the sequence
indicated in the concept map.

Rollnick, et al., (2008),
refer to teaching strategies as the approaches employed by the teacher to
facilitate the course of instruction. According to Rollnick, et al., (2008)
these strategies include methods that the teacher employ to sequence the
lessons, questions asked to assess progress as well as learner activities
provided to direct the course of the lesson.


            12.3.5  Conclusion

The use of a concept
map in this study was an attempt to assess my knowledge development that took
place when I was learning to understand the topic and process of EMI. Concept
mapping was a reflective attempt on my side to monitor my metacognitive ability
in terms of how my conceptual understanding evolved over the period of
learning. This entailed constant revisiting of the learning process with a
purpose of establishing gaps in my knowledge, identifying relationships and
tracing connections between my prior knowledge and the new knowledge I was
acquiring from time to time.

The structural and
contextual analysis indicate that learning took place with regards to the
development of my content knowledge. During the construction of the concept map
my knowledge of the concepts, laws, rules and principles as well as knowledge
of the organisation of the structure of EMI developed. The analysis also
indicate that during concept mapping, other aspects of teaching also developed.
These aspects of teaching include my ability to identify subject matter
representations, teaching strategies and possible assessment strategies that I
would employ when teaching this topic; knowledge of what to teach and not to
teach, how to link this topic with other topics as well as how to sequence the
lessons so that my learners could better understand the topic (curricular
saliency); understanding learners’ prior knowledge and their learning
difficulties (knowledge of learners); awareness of learners’ cognitive abilities and how
classrooms should be organised so that learners could learn at their optimal
level (general pedagogical knowledge); and the ability to select relevant
resources that would assist learners to develop understanding of the topic
(knowledge of context).