A23 armoni

Looking at Secondary Teacher Preparation Through the Lens
of Computer Science
MICHAL ARMONI, Weizmann Institute of Science
Teaching computer science (CS) in high schools, rather than just programming or even computer literacy, is
important as a means of introducing students to the true nature of CS, and enhancing their problem-solving
skills. Since teachers are the key to the success of any high school educational initiative, any discussion of
high school programs must consider the teachers, and specifically the teacher preparation needed to make
the implementation of such programs possible. However, there is scant research on CS teacher education,
probably because CS is a relatively young discipline. Very few of the publications in the area of CS teacher
preparation are research-based. Most are descriptive papers, including recommendations for specific pro-
grams or courses. The purpose of this survey is to import from what is already known in other disciplines in
this context. We therefore examine the body of research on teacher education in other disciplines, especially
in mathematics and science, to shed light on important challenges for CS teacher education and draw some
initial conclusions regarding CS teacher preparation programs.
Categories and Subject Descriptors: K.3.2 [Computers and Education]: Computer and Information Sci-
ence Education—Computer science education
General Terms: Human Factors
Additional Key Words and Phrases: Computer science teachers, secondary teacher preparation, pre-service
teachers
ACM Reference Format:
Armoni, M. 2011. Looking at secondary teacher preparation through the lens of computer science. ACM
Trans. Comput. Educ. 11, 4, Article 23 (November 2011), 38 pages.
DOI = 10.1145/2048931.2048934 http://doi.acm.org/10.1145/2048931.2048934
1. INTRODUCTION
Teaching computer science (CS) in high school has been discussed in the computer
science education community since the 1970s. Many in this community believe that
exposing high school students to the scientific discipline of computer science, develop-
ing their problem-solving skills and introducing them to the real nature of this science
is important, and thus teaching computer science (rather than just programming
or even computer literacy) in high schools is important as well. Since the ”dot-com”
explosion, these views have been reinforced: The enrollment in CS studies does
not keep up with the demands of the job market [Panko 2008; Wilson et al. 2010],
and research indicates that among the factors negatively affecting enrollment in CS
This research was supported by the Computer Science Teachers Association (CSTA).
Parts of an earlier and partial version of this survey were included in chapter 2 of the CSTA report on CS
teacher certification [Ericson et al. 2008].
Author’s addresses: M. Armoni, Department of Science Teaching, Weizmann Institute of Science, Rehovot,
Israel; email: Michal.armoni@weizmann.ac.il.
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c 2011 ACM 1946-6226/2011/11-ART23 $10.00
DOI 10.1145/2048931.2048934 http://doi.acm.org/10.1145/2048931.2048934
ACM Transactions on Computing Education, Vol. 11, No. 4, Article 23, Publication date: November 2011.

23:2 M. Armoni
studies are students’ misperceptions of CS, and their resulting negative attitudes
towards it [Yardi and Bruckman 2007].
Over the years ACM has initiated three task forces to examine computer science ed-
ucation in high schools, and has issued detailed recommendations (in 1985, 1994, and
2003, respectively). An extensive survey on research dealing with teaching computer
science in high schools is included in a report issued by the Computer Science Teacher
Association (CSTA), “The New Educational Imperative: Improving High School Com-
puter Science Education” [Stephenson et al. 2005], which discusses computer science
within the K-12 curriculum.
Obviously, any discussion of high school programs must consider the teachers as
well, since, as is frequently pointed out [e.g., Gal-Ezer 1995; Gal-Ezer et al. 1995;
Soloway 1996], teachers are the key to the success of any high school educational ini-
tiative. Shulman [1986] argued that teacher preparation programs should be research-
based. However, computer science is a relatively young discipline, and therefore it is
not surprising that there is still scant literature on computer science teacher educa-
tion. Very few of the publications in the area of computer science teacher preparation
are research-based. Most are descriptive articles that present recommendations for
specific programs or courses.
By contrast, there is a rich body of research on teacher education and preparation
in other disciplines that can contribute to computer science teacher education. Work
in this area deals with many complex issues, such as the knowledge teachers should
have, the way to prepare pre-service teachers for future self-development, and the way
theory and practice should be interwoven in an effective teacher preparation program.
The purpose of this survey is to draw from this extensive body of knowledge, taking
from it whatever might be relevant for computer science teacher preparation. Some
of the lessons learned may lead directly to specific recommendations for CS teacher
preparation programs, whereas others can shed light on important issues that need to
be addressed when designing such a program.
The research on teacher education is indeed a deep and wide ocean, so a few guide-
lines were set: This survey looks at some fundamental work in the area of teacher ed-
ucation in general, and then at two disciplines that share common characteristics with
computer science; mathematics and science. As noted below, CS also has much in com-
mon with the discipline of engineering. However, the body of research on engineering
teacher education is certainly not as mature or developed as in mathematics and sci-
ence teacher education, thus motivating the decision to focus on these two disciplines.
The survey focuses on pre-service secondary teachers, with very few exceptions.
Thus in general it does not deal with research on elementary or junior-high prospec-
tive teachers, or on teacher educators. Some articles dealing with elementary pre-
service teachers are cited, but only when relevant to secondary teacher preparation
as well. Extensive work has been done on in-service teachers in the areas of mathe-
matics and science. However, only a small portion of it, relevant to pre-service teacher
education, is represented in this survey through articles that project from the domain
of in-service teacher studies to the domain of pre-service teachers. Further, only ar-
ticles which have some applicability to teacher education in general and to computer
science teacher preparation in particular are cited. In other words, articles that deal
with issues that are discipline-specific, for example, student teachers’ perceptions of
geometry, are excluded.
The context of this survey is reform-based teaching and learning (e.g., National
Council of Teachers of Mathematics [1989, 1991]), which has guided work on teacher
education over the last 20 years or so. Reform-based instruction is rooted in the con-
structivist view [von Glasersfeld 1995] (see Ben-Ari [2001] for an introduction to con-
structivism that relates it to computer science education). According to constructivism,

Secondary Teacher Preparation Through the Lens of Computer Science 23:3
students do not learn simply by absorbing knowledge but rather through the integra-
tion of new experiences into existing knowledge structures. Thus a teacher should no
longer be seen as a knowledge transmitter, but rather as a mediator, assisting stu-
dents in constructing their knowledge. Teaching is therefore student-centered rather
than teacher-centered, and the teacher should consider students’ previous knowledge
and students’ possible ways of perceiving concepts. In addition, reform-based teach-
ing aims at introducing the true nature of the discipline. For example, in the case of
mathematics, this implies helping students experience mathematics as a living disci-
pline in continuous development, and not as a set of truths, rules, and procedures that
they must acquire. In practice, these principles are expressed in inquiry-based learn-
ing and discussions of students’ solutions, rather than introducing just one solution
by the teacher, emphasizing multiple representations, making connections between
various mathematical topics, emphasizing and discussing general mathematical con-
cepts and habits of mind (such as proofs of various kinds or different problem-solving
strategies) in addition to topic-specific discussions. In the words of Cooney (cited in
Lin [2000]) reform-based mathematics teacher education programs “encourage reflec-
tion, highlight attention to context, and characterize mathematics and its teaching as
problematic” (p. 183).
This survey is organized as follows: Section 2 discusses the nature of CS and the con-
nection of CS to the disciplines of mathematics and science, justifying the rationale of
this survey. Sections 3 to 7 discuss various aspects of teacher education. It is important
to note that these sections are not independent. On the contrary, there are multiple
dependencies, inducing a very dense graph. For example, reflection (Section 4.1) plays
a certain role in enhancing various types of knowledge (Section 3). Similarly, there
are multiple connections between the methods course (Section 6) and field experience
(Section 5). Such connections are explicitly stated throughout the survey. Section 8
deals with the controversial issue of the effect of teacher preparation programs.
Section 9 includes an extensive survey of publications on computer science teacher
education in the light of other sections. Section 10 examines the implications of the
whole survey in the context of CS teacher education.
2. THE DISCIPLINE OF CS AND ITS CONNECTIONS TO SCIENCE AND MATHEMATICS
Even though, and perhaps because CS is a relatively young discipline, the issue of
what CS is, its essence, and its nature are widely debated. A clear, clean, up-to-date,
and widely agreed-upon definition of CS is not easy to come up with. A deep and broad
discussion of this issue is beyond of the scope of this survey. The modest objective of
this section is to convince the readers that the essence of CS has many important char-
acteristics in common with the disciplines of mathematics and science, and that many
of the challenges faced by a CS teacher overlap or resemble those dealt with by math-
ematics and science teachers. Thus, in this sense this section justifies the rationale
behind this survey; namely that examining the body of research on teacher education
in mathematics and science has direct implications for CS teacher education.
2.1 What is CS?
In 1989, the ACM-IEEE task force on the core of computer science [Denning et al. 1989]
published its report. This task force was appointed to address fundamental and urging
questions such as: Is CS a science or an engineering discipline? What is the intellec-
tual substance of CS? The task force characterized CS as formed by three paradigms:
theory, which is rooted in mathematics and whose practice involves definitions, the-
orems, and proofs; abstraction (modeling) which is rooted in experimental science,
and whose practice includes forming hypotheses, modeling, and experimenting; and

23:4 M. Armoni
design, which is rooted in engineering, and whose practice includes stating require-
ments and specifications, design and implementation, and testing.
The work of this task force inspired the curricular committees and task forces that
were appointed in the years that followed. As can be seen in the report Computer
Science Curriculum 2008 by the latest task force, the main theme is still relevant: ”All
computer science students must learn to integrate theory and practice, to recognize
the importance of abstraction, and to appreciate the value of good engineering design”
[Cassel et al. 2008, p. 13].
According to Wing [2006], ”Computer science inherently draws on mathematical
thinking” (p. 35). Many today, including Wing, view CS as a discipline of problem solv-
ing, a characteristic that is undoubtedly shared with science and with mathematics:
In both disciplines, a major thread of educational research deals with teaching and
learning problem solving.
From another perspective, Schwill’s list of fundamental ideas of CS [1994] puts for-
ward ideas which are obviously mathematical in nature and essence, such as recursion,
nondeterminism, consistency, completeness, diagonalization, and many more. Simi-
larly, the Great Principles of Computing project [Denning and Martell 2007] aims at
developing a framework for discussing the fundamental principles of computing. It de-
fines seven top-level categories of principles. One of these is evaluation, and the first
principle listed under this category is “the principal tools of evaluation are modeling,
simulation, experiment, and statistical analysis of data,” undoubtedly a principle that
is characteristic of the discipline of science.
2.2 Teaching CS in High Schools
Not only does the discipline of CS share important characteristics with the disciplines
of mathematics and science, an introduction to this discipline at the high school level
involves these common characteristics. Hence a CS high school teacher faces profes-
sional challenges that resemble those faced by mathematics and science teachers.
A CS high school teacher should convey CS to the students as a scientific discipline
[Gal-Ezer et al. 1995]. CS is not about computer literacy or computer applications. It is
not even just about programming. It is about solving problems and sometimes imple-
menting the solutions in a programming language. It is about analysis of solutions in
terms of correctness and efficiency. It is about reasoning on the domain of algorithmic
problems, asking questions such as what can be computed, and what can be efficiently
computed. It is about abstraction. It is a teaching process that always integrates theory
and practice, introducing concepts and ideas and implementing them.
The depth and breadth of the introduction of CS in high school and its character-
istics can best be illustrated by looking at two examples of CS high school curricula.
The Israeli CS high school curriculum (detailed in Gal-Ezer and Harel [1999]) cov-
ers knowledge units such as algorithm efficiency, algorithm correctness, and computa-
tional models, which involve a high level of mathematical thinking. The courses in the
ACM K-12 CS Model Curriculum [Tucker et al. 2003] include (at all levels) mathemat-
ically flavored knowledge items, such as binary representation of numbers, graphs,
logic, etc.; in both curricula CS is more than programming.
Consider for example a high school teacher who sets out to teach his or her students
problem solving by means of recursion. The idea of recursion itself is very abstract and
mathematical in nature (usually exemplified through mathematical terms, such as
the factorial function or the Fibonacci series). Conveying principles of problem solving
to the students requires the teacher to discuss various strategies and heuristics
(divide-and-conquer, backtracking), to discuss the correctness of the solution, etc. This
kind of challenge is by no means unfamiliar to high school mathematics teachers.

3. PRE-SERVICE TEACHERS’ KNOWLEDGE BASE
3.1 What Knowledge Should Teachers Have?
When discussing teacher preparation programs, a major issue is the knowledge
prospective teachers are expected to have. Shulman discussed teachers’ knowledge in
a series of frequently-cited articles [Shulman 1987; Wilson et al. 1987] and identified
several types of teacher knowledge: content knowledge, knowledge of other content
(that is, not in the main discipline), knowledge of learners, knowledge of educational
aims, and general pedagogical knowledge (PK). Traditional programs emphasized
pedagogical knowledge (defined in Zeidler [2002] as: “teacher’s knowledge of generic
instructional variables, such as classroom management, pacing, questioning strate-
gies, handling of routines and transitions, and the like” (p. 28)). In contrast, Shulman
[1986] called for emphasis (in research and in teacher preparation) on teachers’
content knowledge. But for Shulman, content knowledge is much more than a set of
rules, truths, and procedures. Content knowledge consists of three domains: subject
matter knowledge, pedagogical content knowledge, and curricular knowledge.
Subject matter knowledge (SMK) consists of both the substantive structures—the
relations between the facts of the discipline, and the syntactic structures—the rules
that determine truth or falsehood within the discipline. In Zeidler’s words SMK is
“teachers’ quantity, quality, and organization of information, conceptualizations, and
underlying constructs in their major area of study” (p. 28). We can see that both
Shulman and Zeidler emphasize underlying connections between concepts, ideas, and
sub-areas as an important component of SMK.
Pedagogical content knowledge (PCK) refers to what one has to know in order to
teach a certain subject matter: how to make it understandable, cognizance of the diffi-
culties, preconceptions of students, misconceptions, strategies for coping with miscon-
ceptions, etc. Zeidler characterizes this as the “teachers’ ability to convey the under-
lying details and constructs in their field of specialization in a manner that makes it
accessible to their students” (p. 28).
Curricular knowledge is about the tools which can be used for teaching—available
textbooks, software, etc.—their goals, attributes, correspondence with the educational
goals, etc.
In each of these domains one can look at propositional knowledge (facts: principles
that derive from empirical research; maxims: learned by experience; norms: values),
case knowledge: examples through which one can teach general rules, prototypes to
exemplify theoretical principles, precedents that convey maxims, and parables that
convey norms; and strategic knowledge: judging and analyzing.
Ever since Shulman presented his model of knowledge, most studies in the area of
teacher education have related to this model as a basis for discussing teacher prepa-
ration. Some relate to it directly, using terms such as PK, SMK, and PCK coined by
Shulman. Others relate to it indirectly or implicitly, while yet others define variations
of this model. For example, Bromme [1994] suggested five types of knowledge that
mathematics teachers should possess. These resemble Shulman’s types in a sense,
but place greater emphasis on the underlying discipline and specifically on an un-
derstanding of school mathematics. These types are school mathematics knowledge,
philosophy of school mathematics, pedagogical knowledge, subject-matter-specific ped-
agogical knowledge, and cognitive integration of knowledge from different disciplines.
3.2 The Role of Knowledge in Teachers’ Practice
What is the role of each of these different kinds of knowledge and specifically that of
SMK, PCK and PK, in teachers’ actual practice? Kahan et al. [2003] describe a study
that examined correlations between Mathematics pre-service teachers’ SMK (referred

23:6 M. Armoni
to as MCK—Mathematical Content Knowledge in their terminology) and their les-
son plans and observed lessons. The findings showed that lower MCK can emerge in
teaching practice by failing to make connections across mathematics during lessons;
namely by not taking advantage of “events” happening in class, most of which are
unanticipated, that can serve as bridges to other concepts.
The somewhat similar phenomenon of beginning teachers not fully comprehending
underlying connections in their disciplines was discussed by Zeidler [2002] and by
Sperandeo-Mineo et al. [2006]. According to Sperandeo-Mineo et al., this is simply
because the SMK of beginning teachers is inadequate, because it is mainly procedural,
and lacks overarching views and connections between concepts and sub-areas. Zeidler
however argued that this phenomenon indicates that SMK by itself, even if it is
rich and multiple-structured, is not enough to induce effective teaching. According
to Zeidler, further exposure to SMK results in little improvement, whereas teaching
practice does, suggesting that the act of teaching influences SMK more than the other
way around.
Cooney and Wiegel [2003] went even further to point out that pre-service teach-
ers should explicitly study and reflect on school mathematics. The authors argue,
based on presented evidence, that pre-service teachers might have difficulties with,
and even lack an understanding of school mathematics, in spite of having an extensive
background in collegiate mathematics. Therefore, they called for providing pre-service
teachers with opportunities to engage in school mathematics in an explicit and reflec-
tive way. This should be done differently from the way they were taught mathematics
in school. It should be far more sophisticated, and also involve PCK (i.e., the develop-
ment of an understanding of how students think about school mathematics).
As for PK, Zohar [2004] examined teachers’ pedagogical knowledge in the context of
instruction of higher order thinking. The findings indicate that deficiencies in pedagog-
ical knowledge, specifically regarding teaching as knowledge transmission rather than
from a constructivist point of view, affects their teaching and decreases the probabil-
ity of their students learning higher order thinking. Tsamir [2005] also recommended
exposing pre-service teachers to general learning theories, such as Stavy and Tirosh’s
[2000] intuitive rules, Fischbein’s theory of intuitive knowledge [1987] and Tall and
Vinner’s model of concept image [1981]. Tsamir’s findings indicate that exposure to
the theory of intuitive rules promoted students’ PCK and SMK.
Many studies that have focused on teachers’ PCK (e.g., Van Dijk [2009], Van Dijk
and Kattmann [2007]), present findings indicating insufficient PCK and argue that the
teaching quality and in turn students’ learning are directly influenced and harmed.
The Education Commission of the States [2003] issued the report ”Eight Questions
on Teacher Preparation: What does the Research Say?”, which is actually a meta-study
that examines the body of research on teacher preparation. The report refers to the
influence of various factors, including SMK, PK, and PCK, on teachers’ effectiveness.
This meta-study examined teacher preparation at all levels and in all subjects, which
may make the conclusions too general for the purposes of this survey. Nevertheless, it
is worth mentioning that its findings indicate moderate support for the importance of
solid subject matter knowledge but are inconclusive regarding the need for a subject
major. This report cites studies that argue that there is a saturation point of subject
matter knowledge, beyond which additional subject matter courses do not have addi-
tional effect. There is limited support for the importance of PK and PCK preparation.
3.3 Integrating Knowledge into Teachers’ Preparation
Based on evidence such as presented above, and by combining the recommendations,
it would appear that all these types of knowledge are equally important and should

therefore be integrated into a preparation program. Many call for enhancing the part
of SMK in teachers’ preparation programs (e.g., Nehm and Schonfeld [2007], Kahan
et al. [2003]). Many studies stress including PCK in teacher preparation programs
(e.g., Ball [2000], Van Dijk [2009], Van Dijk and Kattmann [2007]), either as a bridge
between SMK to PK or as an important component of its own. Many argue not to
neglect the component of PK (e.g., Zohar [2004], Tollefson [2000]).
How can this be implemented in practice? Zeidler [2002] pointed to the problematic
interface between subject matter specialists who are usually in science faculties, and
teacher educators in schools of education. It is not at all clear how the responsibilities
for SMK, PK and PCK are divided between them.
3.3.1 Enhanced Content Courses and Integrated Courses. Many of the empirically-based
suggestions for integrating various kinds of knowledge into teachers’ preparation call
for changes in the way content courses are taught in teacher preparation programs.
Such strategies can be implemented in programs that include content courses as an
integral part, taught by content and educational experts, and not programs whose
starting point is an undergraduate degree in the discipline. For example, based on
their findings, Kahan et al. [2003] argued that content courses in teacher preparation
programs should emphasize the component of underlying connections in SMK by look-
ing backward to connect advanced content to previously learned content. Bolte [1999]
described a strategy to be implemented in mathematics content courses that requires
student teachers to construct concept maps and write interpretive essays (correspond-
ing to students with various learning styles). The author claims that as student teach-
ers work on these tasks that involve linking related concepts and reflecting on their
thinking, they are provided with an opportunity to mature mathematically and to ex-
perience an alternative approach to instruction and assessment. The author describes
an integration of this strategy in courses for elementary teachers, in which the maps
and essays served as assessment tools. However, the study examined student teachers’
attitudes toward the maps and essays, and did not examine whether student teachers’
perceptions of mathematics or other conceptions and beliefs changed as a result of
this strategy. Evidence regarding the actual effect of the strategy on student teachers’
different kinds of knowledge was not presented either.
Blanton [2002] suggested another kind of integration in a similar setting. Following
an undergraduate mathematics course in which classroom discourse was explicitly
discussed, prospective teachers made a transition toward seeing discourse as an active
process in which students build mathematical understanding. Again, in this case,
mathematics content setting was utilized to enhance PCK.
The problematic interface between the mediators of different kinds of knowledge
was addressed by Collins et al. [1999] who described collaboration in a specific course
for elementary science pre-service teachers. This course, integrating the contents
of courses in science, science teaching methods and technology, dealt with all types
of knowledge and the instructors were subject matter specialists as well as teacher
educators.
3.3.2 Meta-Cognition as a Means for Knowledge Development. Meta-cognition is often sug-
gested as a tool that in combination with other strategies (such as integrated courses)
may lead to an integrated development of different kinds of knowledge. Sperandeo-
Mineo et al. [2006] examined the effect of a physics education course, most of which
consisted of workshops, each dedicated to different physics content. The workshop
aimed at enhancing SMK and developing PCK using meta-cognitive instruction (em-
phasizing learning activities and processes rather than learning outcomes, reflecting
on learning strategies and self-regulation skills). They implemented a constructivist

23:8 M. Armoni
view that built on student teachers’ initial models of physics to construct the desired
models. The findings indicated that student teachers’ initial SMK was not sufficient
to enable PCK development and that the implemented teaching/learning environment
was effective in guiding the student teachers toward PCK construction, in that many
student teachers achieved good levels of PCK.
Dhindsa and Anderson [2004] showed how a conceptual-change approach can be
used to help pre-service science teachers identify their knowledge structures. The
study indicates the effectiveness of metacognitive intervention in helping chemistry
pre-service teachers reorganize their cognitive structures. This approach was also
constructivist in that it drew on previous knowledge while aiming to change its struc-
ture and interconnections, etc. Unlike the strategy in Sperandeo-Mineo et al. [2006],
Dhindsa and Anderson’s [2004] approach was not implemented as part of a con-
tent course, but after the pre-service teachers had learned about interconnectedness,
knowledge construction, etc.
3.3.3 Learning by Doing as a Means for Knowledge Development. Another aspect of con-
structivism emphasized by several studies in the context of knowledge development
is learning by doing. For example, Peterson and Treagust [2001] studied a problem-
based approach for the teaching of science education. They aimed at developing stu-
dents’ subject matter knowledge, curricular knowledge, and knowledge of learners
while working in small groups without tutor assistance. The student teachers were
guided by a predetermined structure and questions, inspired by Shulman’s framework
for pedagogical reasoning [Wilson et al. 1987]. The student teachers’ views were pos-
itive, stating that the approach had indeed enabled them to develop the three types
of knowledge. In fact, most of them considered the learners’ prior knowledge in their
planning of science activities.
Da Ponte et al. [2002] also focused on developing information and communication
technology (ICT) skills by doing, thus also promoting the identity of a skilled teacher.
The course they describe also helped pre-service teachers to enhance their content
knowledge by better understanding the connections among mathematics topics, learn-
ing about historical development and application, and their pedagogical content knowl-
edge relating to classroom learning processes. The guiding principle was integration
through learning by doing, affecting beliefs and identity rather than just knowledge,
and working in such domains that a contribution was made to enhancing CK, PCK,
and PK.
The population of a study described in Bleicher and Lindgren [2005] was elementary
science teachers, and the findings are consistent with some of the above-mentioned
work. The study indicates that teaching more science content may not be sufficient to
overcome a reluctance to teach science, unless some learning takes place in a construc-
tivist environment.
Another example in the context of learning by doing is Zevenbergen’s work.
Zevenbergen [2001] describes a strategy according to which during the preparation
program students were required to peer-assess students’ posters. The assessment was
fairly reliable, but its importance did not necessarily derive from being an alterna-
tive to teacher-based assessment, but as a learning tool. This project helped students
to learn about poster construction, assessment and also about mathematics (subject
matter content knowledge), knowledge acquired when reading and analyzing other
students’ posters.
3.3.4 Concreteness as a Means for Developing Effective Knowledge. Another important fac-
tor is the need to give prospective teachers specific tools rather than just general PCK
related knowledge. Several researchers (e.g., Sperandeo-Mineo et al. [2006], Niess

and Scholz [1999]) argue that to become effective, PCK development should focus on
specific topics rather than just general elements, and therefore subject matter-specific
teaching strategies should be incorporated into secondary science teacher preparation.
In line with this rationale, Pringle [2006] described a course dealing with specific PCK,
focusing on alternative science conceptions and implications for teaching. This course
was intended to give teachers tools for coping with alternative conceptions, accord-
ing to constructivist view. Pringle reported that teachers participating in this study
“learned that the teacher’s role involves identifying the children’s alternative concep-
tions and using this information to facilitate further learning by organizing children’s
knowledge into meaningful and valid schema” (p. 305).
In many preparation programs, a special course is devoted to establishing concrete
links between various kinds of knowledge, such as SMK, PCK, PK, and curricular
knowledge. It is usually called the methods course, and is discussed in Section 6.
3.4 Summary
There is a general consensus that teacher preparation programs should cover all dif-
ferent kinds of knowledge, especially content knowledge, pedagogical knowledge, and
pedagogical content knowledge. Many believe that the best and most effective way to
promote the acquisition of knowledge in its various forms is to integrate these kinds
of knowledge, either through subject matter courses or through education-related
courses, such as methods courses. Prospective teachers should be exposed to various
educational theories on one hand and to specific pedagogical content knowledge issues
on the other. Preparation programs should provide opportunities for meta-cognition
in general and reflection in particular and opportunities for learning by doing, such as
peer-assessment, and team problem-solving, to name but a few. Such experience has
been shown to have a positive effect on knowledge acquisition.
4. PREPARING PRE-SERVICE TEACHERS FOR FUTURE PROFESSIONAL DEVELOPMENT
In the words of Adler [2000] teacher learning is “usefully understood as a process of
increasing participation in the practice of teaching, and through this participation, a
process of becoming knowledgeable in and about teaching” (p. 37). Obviously, as men-
tioned by many (see for example, Hiebert et al. [2003] and references cited therein)
this goal, with the huge body of knowledge accompanying it, is too vast for pre-service
teachers to acquire in a relatively short period of training. Pre-service teachers are un-
likely to become expert teachers as a result of a relatively short preparation program,
and much of their professional development is expected to take place when they are al-
ready teachers. Thus, teacher preparation programs should aim at giving pre-service
teachers the tools that can enable them to continue their professional development as
in-service teachers.
Hiebert et al. [2003] addressed this issue explicitly and presented a model aimed
at teaching pre-service teachers how to learn to teach mathematics when they become
teachers. Their model is based on two goals, the first of which is to become mathe-
matically proficient in five interwoven strands: conceptual understanding, procedural
fluency, strategic competence, adaptive reasoning, and productive disposition. The
second goal is to prepare to learn to teach for mathematical proficiency, which actually
consists of two sub-goals: prepare to learn to teach and prepare to learn to teach for
mathematical proficiency. In a way, this model exploits the advantages of each set-
ting, since as the authors state, schools supply an excellent environment for learning
to teach, but they do not supply the support needed for doing so. On the other hand,
preparation programs are better suited to providing tools to be used for future, on-site
learning.

23:10 M. Armoni
This section discusses two sets of instruments that can contribute to teachers’ future
professional development.
4.1 Reflection in Particular and Higher-Order Thinking in General
An important tool for continuous professional development is the instrument of reflec-
tion, mentioned above as one of the components to be taught in a reform-based teacher
education program, according to Cooney (cited in Lin [2000]), and as a means to pro-
mote knowledge enhancement (as discussed in Section 3).
Reflection [Schön 1983, 1987] is a necessary skill for a teacher, a necessary tool for
teachers’ professional growth in the long run and for teachers’ immediate improvement
of practice, in the short run. The ability to reflect on one’s own actions and thoughts is
considered a meta-cognitive ability [Paris and Winograd 1990] and a characteristic of
higher-order thinking. Schön distinguishes between two types of reflection: Reflection-
in-action is ongoing and occurs simultaneously with the teaching event. Reflection-on-
action is based on recall of the teaching event. However, teaching pre-service teachers
to reflect, thus turning them into reflective practitioners in Schön’s terms, is not an
easy task. “[Students] cannot at first understand what [they need] to learn, can only
learn it by educating [themselves], and can educate [themselves] only by beginning to
do what [they do] not yet understand” [Schön 1987, p. 93].
Artzt [1999] cites research indicating that reflection is indeed an important factor
in teachers’ development, and that there is a connection between teachers’ cognition
and their teaching practice. The author presents a structured framework for reflec-
tion and examines this framework in terms of pre-service teachers’ stage of teaching.
She argues that such a structure for reflection enables pre-service teachers to advance
to a higher stage of teaching. An initial stage of teaching might lean on traditional,
knowledge-transmission-based instruction, whereas higher stages focus increasingly
more on the student and on a constructivist point of view. The reflection took place
in preplanned points during a teaching semester (the second semester of the prepara-
tion program, preceded by a semester in which the students took a methods course).
According to guiding questions, that directed pre-service teachers to think of their
students, their teaching goals in terms of students’ behavior, and their students’ prior
knowledge, use pre-learned pedagogical theories and PCK elements, and monitor their
pre-declared goals. The reflection relates to three dimensions: pre-service teachers’
knowledge, beliefs, and goals.
Nichols et al. [1997] describe a set of tools to be used during pre-service preparation
that are aimed at developing critical reflection, (i.e., reflection that takes into account
social and cultural facets of the school, classroom, and the tradition of science teacher
education.) Among these tools are portfolios, journals, cases for class, learning maps,
and metaphors. A specific tool for reflection is also described by Bryan and Tippins
[2005]. According to Wallace and Oliver [2003] keeping a journal is a way to teach
reflection in a field-experience which is integrated in a methods course taking place
in school. The journal writing was guided by a matrix developed by the authors. The
reflection level of the students became deeper after the course.
Reflection is considered a characteristic of higher-order thinking, and many aim
at developing pre-service higher-order thinking in general, rather than just reflec-
tion. For example, Weinberger and Zohar [2000] showed how higher-order thinking
of junior high prospective teachers can be developed using a special course on the
subject. This course had three main components: theory, conveyed by mini-lectures
and class discussions; active practice, in which the pre-service teachers worked with
and experienced learning materials that were designed to develop high school stu-
dents’ higher order thinking skills; and reflective practice, in which the pre-service

teachers reflected upon the thinking skills they applied while performing active
practice.
4.2 Teachers as Researchers
A sub-goal in the model described above [Hiebert et al. 2003] is to prepare to learn
to teach for mathematical proficiency. The authors suggest achieving this sub-goal by
teaching pre-service teachers to treat the lessons they teach as classroom teaching ex-
periments. In order to do so they need to learn to plan the experiments, “in a way that
affords learning and then reflecting on the outcomes in order to maximize the benefits
that can be gained from the experience” (p. 206 and they refer to Artzt [1999] in this
context). The lessons should be planned with “clear goals in mind” (p. 206), their im-
plementation should be monitored, feedback should be collected and interpreted, and
future practice should be rectified according to the results of the experiment. Thus, just
like any experiment, better knowledge or improved performance is not guaranteed, but
the results can be used to contribute to future success. Pre-service teachers should be
taught to define learning goals for their lessons, and design the lessons according to
these goals, while making predictions on the outcomes of specific instructional activi-
ties. That is, there should be an emphasis on selecting appropriate problems, predict-
ing the way students will cope with these problems and solve them, and predicting the
contribution of these problems to the lesson process. Pre-service teachers should also
be taught to collect data, interpret them, and draw conclusions.
Keating et al. [1998] called for preparing pre-service teachers to conduct action re-
search in their classes to develop their reflection skills, thus growing to be reflective
practitioners, that is, teachers who are reflective and critical thinkers, integrating re-
flective processes into teacher preparation. Action research is defined as “an inquiry
that applies scientific thinking to real life problems,” or in other words a “small-scale
intervention in the functioning of the real world and a close examination of the effects
of such an intervention.” They state that “the goal is for pre-service teachers to be-
come active learners with a disposition to continuously research, assess, apply, and
refine knowledge throughout their careers.” In their preparation programs students
observed lessons at assigned school sites from the beginning of the first semester, kept
reflective journals, and at a later phase submitted an action plan proposal, collected
appropriate data, analyzed them, and presented their findings in a written report and
in an oral presentation. The authors argued that developing reflection and action re-
search skills increased the likelihood that teachers take more informed actions (i.e.,
actions that can be explained and justified to themselves and to others.)
4.3 Summary
To enable teachers to develop while in-service, pre-service preparation should enhance
prospective teachers’ higher order thinking skills and specifically their reflection skills.
This is not a trivial task, but studies indicate that explicit exposure to reflection and
the use of different strategies that incorporate reflection into the preparation program
have a positive effect on prospective teachers’ reflection skills. In addition, a teacher
preparation program should convey some research skills to prospective teachers, not
necessarily for the purpose of assisting them in future graduate studies, but to help
them develop while in service through small-scale research that they will conduct in
their own classes.
5. INTEGRATING PRACTICE AND THEORY IN TEACHER PREPARATION
Even if a certain body of knowledge and certain tools for future professional develop-
ment are agreed upon as necessary components in teacher preparation programs, a

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key question is how these components should be integrated into a complete, effective
program.
Shulman [1986, 1990] described how teacher preparation has evolved from
technical-professional training following an apprentice model and taking place in
schools, to university-based academic programs. An academic environment is war-
ranted since current programs do not focus on training pre-service teachers how to
teach specific topics in class, but rather integrate educational theories rooted in psy-
chology, sociology, and other fields to give student teachers a wider context for their
practice. Thus, current programs are a combination of theory and practice, following
Dewey’s model of a laboratory [Dewey 1896, 1904], connected to the real world, but
where intellectual methods are learned and not just practical skills.
How can such an effective combination be achieved? This question has many facets:
When should educational theories or even more basic, underlying theories in sociology
and psychology be taught (in which courses and in which phase of the program)? How
should field experience be interwoven into preparation programs and what should its
characteristics be? How should responsibility for these various facets be distributed
between teaching practitioners and theoreticians?
5.1 Teaching the Theoretical Foundations
Many teacher preparation programs include foundation courses that cover topics in
psychology, sociology, and other disciplines relevant to education. Other courses, usu-
ally taught at a later phase, are more practice-oriented (usually called “methods”
courses), and discuss the way various topics in the school curriculum should be taught.
Shulman [1990] argued that teacher preparation program foundation courses should
not include philosophy, psychology, sociology, or similar courses. Rather, “the true foun-
dation disciplines are the arts and sciences themselves” (p. 307). Psychology, sociology,
and similar disciplines should be taught “in a way that is bound up with the content
of instruction” (p. 309). They should be taught throughout the program, as scaffolding
that supports a building all the way up and not just at the bottom. These fields should
be taught as a bridge between pedagogy and content, through specific cases, that are
always connected to real teaching practice, “as an integral part of the connective tissue
that gives shape and meaning to the education of teachers—as the framework for con-
necting and integrating the knowledge acquired in the liberal arts and sciences with
the practice of pedagogy” (p. 304).
Pietig [1997] rejected Shulman’s position and argued that social and psychological
foundations should be taught as theoretical foundations, not as a part of the methods
course, since pre-service teachers should be familiar with these fields in a wider con-
text than their own classrooms and their own discipline. “Education students take
courses in foundations not to make them better content area teachers but to help
them become more caring and reflective teachers. Thinking of foundations this way
avoids the trap of assuming that foundations courses must be integrally related to
the subject matter that teachers teach.” According to Pietig, teaching these founda-
tions thoroughly is part of what makes teacher preparation programs belong in uni-
versities and be more than technical training programs. However, they should not
be necessarily taught as separate disconnected courses, but can be “thematically con-
nected with one another and artfully tied to other components of the teacher education
curriculum”.
When designing the structure of teacher preparation programs this should be care-
fully considered. Foundation courses should probably be part of the program as Pietig
argues, but should relate to practice. On the other hand, in practice-oriented courses,
such as methods courses, relevant theory should be referred to, as Shulman suggests.

5.2 Field Experience
Obviously, teacher preparation should also include a component of practical experi-
ence. However, the integration of this component into a preparation program is not
trivial. In the ECS report mentioned above [The Education Commission of the States
2003] there were inconclusive findings as to the characteristics of high-effective field
experience. Yet again, the difficulties in reaching conclusive findings may be rooted in
the generality of this report, and looking at specific work in the areas of mathematics
and science teacher education might be more fruitful.
Jaworski and Gellert [2003] dealt with the integration of theory and practice in
mathematics teacher preparation programs. The authors surveyed four possible mod-
els for initial teacher education, in the context of the relation between theory and
practice: (1) No specific teacher preparation, (2) Teacher preparation in which theory
and practice are treated separately. Usually, preparation starts with a theory phase
in a university, followed by a practice phase, in a school. Such a model is referred to
by Meyer [1975] as “end on” training. (3) Teacher preparation in which theory and
practice start to be integrated (Meyer calls this “concurrent” training”). (4) Teacher
preparation in which theory and practice are fully integrated.
The authors discuss “the controversial debate over the extent to which practicing
teachers of mathematics should be involved in the preparation of future teachers of
mathematics” (p. 833). Some argue that too much influence of practicing teachers
might result in mathematics being taught in the same manner over generations of
teachers, whereas the converse argument is that theoretical preparation, disconnected
from the schools, results in novice teachers who are unprepared to cope with real situ-
ations. In the same spirit, in an earlier publication, Jaworski [1999] called for greater
involvement of teachers in preparation programs, since most leaders of teacher edu-
cation programs are university researchers and only few also teach mathematics to
students in schools.
Jaworski and Gellert [2003] emphasized that integrating more practice into a prepa-
ration process need not necessarily cause a decrease in exposure to theory; rather, the
two components can be interwoven: “[T]heory can be used as a lens to reflect on prac-
tice, and practice can develop from theoretical reflections” (p. 833).
The authors claim that both Models 1 and 2 can lead to stagnation of mathematics
teaching. Model 1 teachers tend to teach the way they were taught at schools, and
Model 2 teachers tend to follow the practice in the school where they do the second
phase of preparation. Model 3 encapsulates a variety of possible preparation pro-
grams, differing in terms of the level of integration of theory and practice, whereas
Model 4 is in a sense an ideal, an extreme of Model 3. What characterizes Model 4
is high collaboration among student teachers, teacher educators in the universities,
mentor teachers in the schools, and other stakeholders (tutors, heads of departments
in schools, colleagues, etc.), all acting as learners and reflective practitioners.
The authors illustrate Model 4 with an existing program. In this program students
were interns in schools, guided by mentors that were from the schools but had ongoing
connections with the university, as did other members of their departments in school.
The students started their internship with a strong background in mathematics, and
the program focused on PK and mainly PCK (what the authors call Mathematical
Knowledge for Teaching – MKT), and offered opportunities for reflection (for all those
who were involved in the programs, interns as well as mentors, tutors and teacher
educators), developing a relational or connected view of mathematical concepts rather
than an instrumental view (in the terms of Skemp [1978]), and exposure to teamwork
on the one hand and autonomous work on the other. The program involved collab-
orative work between school and university: interns planned their lessons based on
theories studied at the university, discussing them with peer interns in the university

23:14 M. Armoni
and with peer interns and mentors in the school, instructing planned lessons and then
getting feedback from these same circles. The mentors themselves discussed their
work with peer mentors, and the tutor did the same with tutors from other schools
and with teacher educators in the university.
Like Jaworski and Gellert [2003], Schoon and Sandoval [1997] point to the prob-
lematic nature of field experience that follows Model 2, where pre-service teachers
take university courses in foundations, subject matter, and method courses, and only
then do their practice teaching in schools which are disconnected from the university.
Schoon and Sandoval focus on several difficulties: The supervising teachers in the
school are not always familiar with the strategies or theories taught in the methods
course, whereas the university teacher educators are not very involved in school prac-
tice. Success at student teaching is determined by the school supervising teachers and
the criteria for success do not always correspond to the theories taught in university
courses. To overcome these difficulties, the authors recommend a seamless field expe-
rience model (implemented successfully in their institution), where student teaching is
done in schools that are in constant contact with university departments, and are akin
to school laboratories, in the spirit of Dewey [1896] or with teaching hospitals [Darling-
Hammond 1994]. The students visit these schools during their methods course, and
when they start student teaching they do so in the same class that they observed. The
field experience is mentored by an instructional team combining school and university
staff.
Blanton et al. [2001] looked at a field experience guided by a university supervisor.
They present a case study of one mathematics pre-service middle school teacher. The
guide used open-ended questions, emphasized PCK and was sensitive to the teacher’s
zone of proximal development (the gap between a learner’s current or actual devel-
opment level determined by independent problem-solving and the learner’s emerging
or potential level of development [Vygotsky 1978]). The authors report that “The na-
ture of the teaching episodes seemed to open the student teacher’s zone of proximal
development” (p. 177).
Geddis and Roberts [1998] also discussed the relation between coursework and a
science teaching practicum. On their program, a 16-week practicum is followed by 16
weeks devoted to an in-campus course. The relation was in two directions: through
coursework students can see the limited but yet insightful perspectives that theories
provide on practical situations, and coursework enables reflection on practical experi-
ence. The authors claim that if coursework is disconnected from practical experience
it may become irrelevant. However, they emphasize that coursework should not fo-
cus only on students’ teaching experience, since then it may be too narrow, whereas a
broader view of the theories can enrich students’ PK and PCK.
It is important to note that field experience also includes observing actual teach-
ing and not just actual teaching. In this context it is worth mentioning Cooney and
Wiegel’s work [2003] that argues that pre-service teachers should experience mathe-
matics in ways that support the development of process-oriented teaching styles. The
authors relate to findings of other studies, indicating that even teachers who have been
taught mathematics in a pluralistic perspective, and have had extensive experience
with school mathematics, do not teach mathematics in a process-oriented manner, even
if they valued process oriented teaching methods. The authors recommend that prepa-
ration programs should “provide contexts in which perspective teachers can envision
such teaching even though they do not engage in such teaching themselves” (p. 812).
5.3 Non-Traditional Field Experience
Some feel that pre-service teachers should be given even more opportunities to expe-
rience the practice of teaching, and that interesting ways should be found to cope with

the limited resources of tutoring schools. For example, Eick et al. [2004] described a
science methods course that included a component of co-teaching (in addition to a later
practicum phase). A team of two students co-taught (but did not plan the lessons) al-
ternating with an experienced teacher (when one student taught the other observed).
This model enables an enhanced, yet gradual, field-teaching experience. The authors
reported some advantages but noted that there were also disadvantages that influence
the over-all effect of the project: co-teaching a lesson planned by another is problem-
atic; co-teaching in turns causes discontinuity since one teacher has to continue a
teaching process from a point reached by another.
Vithal [2003] described a project in which pre-service mathematics teachers visit
shelters for street children on a regular basis, where they tutor the children. The
author argues that this project demonstrates “how working at the margin can raise
important issues of theory and practice in mathematics teaching and learning that are
equally valid and present, if not more so, at the centre where they may be difficult to
render visible” (p. 181). The results of the project indicate that pre-service teachers
participating in this project learned about learners, about relationships, and about
teaching.
Weld and French [2001] described an undergraduate science laboratory field expe-
rience for pre-service science teachers. The student teachers acted as assistants in
university labs. This gave them an opportunity to experience the teaching of inquiry
to k-12 graduates. The authors report that the project enhanced pre-service teachers’
SMK and PCK.
5.4 On the Effectiveness of Field Experience
How effective can field experience be? Section 8 discusses the overall effect of teacher
preparation programs, but in the narrower context of this section it is worth examining
two other studies. Hancock and Gallard [2004] studied the influence of field experience
on pre-service science teachers’ beliefs about teaching and learning. Their findings
indicate that field experiences both reinforce and challenge the beliefs of pre-service
science teachers. Some students tended more toward student-centered instruction and
the belief that teachers should design their instruction around students’ needs and
interests. Others developed a belief that students “lack the skills, motivation, or both
necessary to implement the teacher’s ideal vision of science education” (p. 290).
Peterson [2005] was motivated by studies [Stigler and Hiebert 1999] that indicate
that mathematics is taught differently in Japan, compared to the USA. Concepts are
developed rather than stated, and the depth of mathematics content presented in class
is higher. Peterson’s study examines whether preparation is also different. Peterson
came to the conclusion that in Japan during the practicum there was much more focus
on the process of teaching a lesson: preparing, teaching, reflecting, and also when
observing lessons. All these components related to student thinking, lesson content,
and idea sequencing during the lesson. This is in line with Shulman’s recommendation
[1986] that teacher preparation programs should emphasize processes rather than just
content.
5.5 Summary
Teacher preparation programs should give prospective teachers a solid theoretical ba-
sis, but this basis should not be detached from practice. It is important to expose
prospective teachers to the field, emphasizing processes, an exposure that can start
through observations and then extend to student teaching. Non-traditional forms of
field experience can be exploited to give the students even more opportunities to prac-
tice their teaching skills. On top of the theoretical basis, theoretical aspects can and

23:16 M. Armoni
should be interwoven into the practicum, and cooperation between university or col-
lege teacher educators and school mentors is essential.
6. THE METHODS COURSE
Most teacher preparation programs include at least one course that is usually refer-
enced as the “methods course”. This is actually an abbreviation, standing for ”meth-
ods of teaching”, as in ”methods of teaching secondary mathematics” or ”methods of
teaching science in elementary school” (names arbitrarily taken from lists of courses
in teacher preparation programs). Due to the key role that such a course usually plays
in teacher preparation programs, it is discussed in this separate section.
6.1 The Goals of the Methods Course
As the title of the course indicates, it discusses actual teaching in class and provides
prospective teachers with the tools to be used in their practice. This is done in the spe-
cific context of the prospective teaching practice—discipline (e.g., “methods of teaching
science”) and level (e.g., “methods of teaching secondary mathematics”). Therefore,
many see the methods course as the place for integrating the three important types
of knowledge—SMK, PK and PCK—including even a practice-based component (thus
aiming at “concurrent training” rather than “end on” training). The integration of
different types of knowledge in the methods course is emphasized in Kinach [2002].
Kinach argued that the mathematics methods course should not focus only on ped-
agogy, but should integrate content and pedagogy, under the theme of teaching for
understanding (the relational level rather than the instrumental level, in the terms of
Skemp [1978]).
Anderson [1997] discussed the important role of the methods course in prospective
science teachers’ preparation. He made the following recommendations.
— “The science methods course should be conceptualized as a foundation for a career-
long process of teacher learning” (p. 272). That is, students should be taught how to
learn to be teachers.
— “The science methods course should operate on the principle that students take
responsibility for directing their own learning” (p. 273).
— “The science methods course should cause students to reflect upon and reassess the
values and beliefs they hold with respect to science learning and teaching” (p. 273).
— “The science methods course should have a considerable amount of student work
that is done in the context of school science classes” (p. 274).
— “The science methods course should have a large amount of student work that is
done in collaboration with other students” (p. 274).
— “The science methods course should give the students a major role in organizing and
directing their own work” (p. 274).
— “The science methods course should give students work to do that [. . . ] challenges
their values and beliefs” (p. 275).
6.2 Integrating Practice into the Methods Course
Although Anderson did not necessarily call for a field-experience component within
the methods course, Ebby [2000] was more explicit on that point. In the spirit of Ja-
worski and Gellert [2003], cited above, Ebby claimed that the “goals of the methods
course should include developing and nurturing particular habits of mind that help
pre-service teachers learn from their own teaching” (p. 69). Instead of developing new
knowledge and beliefs in the mathematics methods course it should emphasize learn-
ing from teaching, through reflection, and making sense of children’s understandings.

Thus the methods course connects theory and practice explicitly and follows Dewey’s
model [1896, 1904] of a laboratory.
One way for the methods course to relate to practice without including a field ex-
perience component is to utilize case studies. Masingila and Doerr [2002] suggested
that a mathematics methods course can use multimedia case studies of experienced
teachers, which the pre-service teachers can analyze and use as a basis for discussion.
This adds to teaching practicum in class, by providing more opportunities for higher-
order thinking. Their findings from teaching such courses indicate that this method
can serve MCK, PK, and PCK.
Barnett [1998] also presented a way of integrating case studies into the mathemat-
ics methods course, and Colburn and Tillotson [1998] proposed a similar approach for a
science methods course, which they illustrated through a specific case study. Herman
[1998] also called for including case studies as a way to promote pedagogical reason-
ing. Herman described a tool (Pedagogical Heuristics Device – P.H.D.), intended to
guide students on using case studies. The study indicated that such tools “encourage
prospective teachers to critically apply what they learn in courses to decision mak-
ing in the classroom,” but the data did not include the pre-service teachers’ classroom
performance as beginning in-service teachers.
6.3 What Else Should Be Included in the Methods Course
As discussed in Section 3, Sperandeo-Mineo et al. [2006], Niess and Scholz [1999] and
Pringle [2006], called for including specific PCK in teacher preparation programs. Sim-
ilar remarks have been made as regards the specific context of the methods course. For
example, Bodzin and Cates [2003] suggested that a science methods course should also
relate to Web-based scientific inquiry. They describe an instrument developed to assist
in the integration of Web-based inquiry. They used this instrument in a science meth-
ods course for several semesters. Another example in this context is that of Moyer
and Milewicz [2002] who claim that a mathematics methods course should also cover
various ways of asking questions. Their recommendation is based on a study they con-
ducted that examined the questioning strategies of pre-service mathematics teachers
and presented ways for improving their strategies.
Manouchehri [1997] refers to another aspect. While arguing, like others, that a
preparation program should touch on all kinds of knowledge, Manouchehri made the
case that a methods course should also deal with prospective teachers’ beliefs, since
their beliefs, acquired mostly in their school years, affect their practice [Swafford
1995].
An approach that combines characteristics of some of the strategies described above
is rooted in Problem-Based Learning. This approach enables students to relate to
specific PCK-issues through active learning. Taplin and Chan [2001] illustrated this
approach in the context of a mathematics methods course. They presented a project
aimed at developing problem solving skills of pre-service mathematics teachers, which
was designed as well to help them understand themselves as “pedagogical problem-
solvers”. Their study examined the effect of problem based learning on teachers’ self
esteem as competent problem-solvers. Similar to other papers, this project also at-
tempted to deal with the issue that beginning teachers teach the way they were taught
in school in spite of a teacher preparation process that instructs them to do otherwise
(this issue is addressed in Section 8). Problem-based learning is known to develop
higher-order thinking skills (analysis, synthesis) that are generalizable to new situ-
ations. In the experiment the methods course was taught with a PBL strategy, with
problems that related to content pedagogical knowledge. The findings indicate that in
spite of difficulties at the beginning of the course, the pre-service teachers’ confidence

23:18 M. Armoni
in their ability to solve problems increased. This article did not examine effects on
actual problem-solving skills in class.
6.4 Summary
The methods course is generally considered as an important and essential component
of a teacher preparation program. In order to make it effective, it should aim at inte-
grating all kinds of knowledge, as well as beliefs, and should incorporate concreteness,
whether by involving a field-experience component or by using other tools such as case
studies and problem-based learning. The course should provide opportunities for col-
laboration and reflection should be extensively employed throughout the course.
7. TEACHING THE NATURE OF THE DISCIPLINE
7.1 The Problem
In reform-based teaching, teachers should convey to their students the true nature
of the discipline they teach, whether it is mathematics or science. They should give
their students the feeling of what it is to do science or mathematics, rather then just
learn a set of rules and procedures developed or invented by others. However, in many
cases, pre-service teachers themselves studied mathematics and science in school in a
traditional, teacher-centered manner, and it is very important to make sure that when
they start teaching they have a true image of the nature of their discipline.
This issue is reflected and exemplified in the work of Roth et al. [1998] who set out to
take a snapshot and study the preparedness of pre-service teachers to teach scientific
inquiry. As they argue, teaching scientific inquiry in reform-based science programs
means, among other things, teaching scientific working habits. The study described
in this article focuses on one such working habit, which is also relevant to CS. Their
findings indicate that “pre-service [secondary] teachers may not automatically engage
in the most basic and most general of all scientific practices – the mathematization
of experience” (p. 28, my emphasis). In fact, “Grade 8 students used more abstract
inscriptions with a higher frequency than the pre-service teachers” (p. 32). This is not
because these grade 8 students were more capable of abstract thinking, but because
they were (just like scientists) “part of a community in which the construction of in-
scriptions constitute ways of observing patterns and building support for one’s claim”
(p. 44). The pre-service teachers were not part of such a community, and according
to the authors, this needs to change, so that they can teach and implement “authentic
science” (p. 44) in their classrooms.
7.2 Suggested Solutions
Lewthwaite [2007] describes a study that evaluated the effectiveness of the instructor’s
pedagogical approach (in a science methods course) in promoting pre-service teachers’
understanding of the nature of science. The evaluation was based on the pre-service
teachers’ critiques of science lessons. The results indicated that the most detailed and
accurate critiques were formulated when nature of science was developed explicitly
throughout the course, through the use of exemplars of historical science develop-
ment and a setting that encouraged collaborative consideration of the nature of sci-
ence. Thus, this study calls for concrete treatment of the nature of the discipline in a
teacher preparation program.
A repeating theme in researchers’ work is to lean on actual hands-on science as a
means to develop a reliable view of the nature of the discipline. There is evidence
that research experience contributes to in-service mathematics and science teachers
[Bazler 1991]. In the same spirit, researchers have called for creating opportunities,
during pre-service teacher preparation, to practice authentic science.

Roth et al. [1998] for instance suggested participating in research laboratories (in-
dustrial or university-based) as part of the pre-service preparation. Langford and
Huntley [1999] described a preparation program with a unique component (a program
for middle school pre-service teachers that may be relevant to secondary pre-service
teachers as well) where in addition to school-based practical experience, the program
included an 8–10 week summer internship, mentored by mathematicians, scientists,
museum personnel, environmental educators, or curriculum developers in business,
industrial or scientific institutions, or informal education settings (such as zoos, mu-
seums, etc.) The study indicated a change in the interns’ conceptions and beliefs in
various contexts, as a result of the internship. Specifically, following the internship the
interns thought about the effect of their internship on their future practice as teach-
ers, projecting their experience during the internship on teaching practice: “[T]hey
envisioned themselves as risk-taking teachers who intended to question and pursue
understanding alongside their students . . . envisioned themselves as encouraging cu-
riosity in their students . . . hoped to encourage their future students to take an active
role in their own learning” (p. 294) and intended “to bring a holistic, conceptually ori-
ented view of mathematics and science to their classrooms” (p. 296). Obviously, what
they intend to do is not necessarily the same as what they will eventually do in class,
but the findings are encouraging.
Raphael et al. [1999] specifically claimed that a missing component in teacher
preparation programs is opportunities for real research in mathematics and science.
The authors describe a program in which prospective mathematics and science teach-
ers have the opportunity to do full summer paid research in departments across the
campus. The study examined the effects of this program on the pre-service teachers
and showed that they “perceived it [the program] as extremely valuable to their ped-
agogical approach and the content of their future or current teaching assignments”
(p. 156). A byproduct of the program was that “participating research scientists be-
came more aware of education issues” (p. 157).
In the same spirit, Melear et al. [2000] described a course aimed at teaching pre-
service science teachers “how to do science”. The course was based on lab research
activities. The authors report that student teachers “learned to: work cooperatively
and independently, design extended open-ended self-initiated experiments, interpret
experimental data, formulate results, and present a portion of their work in a scientific
format” (p. 89). The student teachers developed reflection skills as well.
Although more studies have dealt with the nature of science, the nature of
mathematics is not an easier issue to cope with. To address the beliefs of pre-service
mathematics teachers regarding the nature of mathematics, Cooney and Wiegel [2003]
suggested that pre-service teachers should experience mathematics as a pluralistic
subject. This has two implications: first, teachers need to acknowledge multiple ways
of solving a given problem, multiple representations of mathematical concepts and
the connections among them. The next step is presenting mathematics as a subject
in which multiple modes of thinking or analysis may be of use and complement each
other. This involves intuitive thinking in which students use pattern recognition to
discover mathematical concepts and generalizations, empirical analysis in which
students’ investigations motivate mathematical concepts and generalizations, and
formalistic thinking used to prove mathematical claims.
7.3 Summary
To prepare prospective teachers for the important responsibility of conveying the real
nature of their discipline to their students, teacher preparation programs should in-
clude an explicit discussion of the nature of the discipline as an integral part, and

23:20 M. Armoni
engage the prospective teachers in activities that enable them to practice ”doing” sci-
ence or mathematics.
8. THE EFFECT OF TEACHER PREPARATION
Ball [1988, 1990] argued that mathematics teachers usually teach the way they were
taught in high school and that the effect of a standard methods course is not strong
enough. Similarly, Zeichner and Tabachnick [1981] claimed that the effects of teacher
education are washed out once teachers enter the more conservative setting of school.
A central factor in this context is apparently teachers’ beliefs regarding their discipline
and its teaching. These beliefs, as pointed out by Swafford [1995] affect teachers’ prac-
tice. However according to a survey included in Cooney and Wiegel’s work [2003], the
beliefs of pre-service mathematics teachers are persistent, and mostly affected by the
way they were taught mathematics as high school students. Even though preparation
programs may sometime cause some changes in these beliefs, the change might not
be deep enough as to affect the manner in which these pre-service teachers eventually
teach.
Obviously, this indicates that the issue of effectiveness is a central aspect in any
examination of teacher preparation programs, and can serve as a tool for improving
the preparation.
8.1 The Problematic of Measuring Effectiveness of Teacher Preparation
The issue of the effectiveness of teacher preparation programs has been addressed by
many, but a deep examination calls for longitudinal studies. The need for a critical
look at studies that examine effectiveness of teacher preparation programs is exempli-
fied in Baxter et al. [2004]. They describe an evaluation of a reform-based secondary
science methods course. On the whole, their findings seem positive. They indicate a
change from perceiving science only as a product to also perceiving it as a process, no
change in the students’ understanding of science teaching as “being solely defined as
pedagogical techniques” (p. 220), a shift in lesson planning considerations, develop-
ment of “sophisticated understanding of the definition of science literacy and its role
in teaching” (p. 220), and an increased understanding of assessment as a way to deter-
mine the efficacy of teaching. However, their findings do not necessarily indicate that
all these changes will affect the actual teaching practice in class when they start to
teach as in-service teachers.
Boujaoude’s study [2000] suffers from the same shortcoming. The study examined
the effect of changes in pre-service teachers’ conceptions and beliefs regarding their
roles in the classroom on their classroom behaviors. However, the (positive) change
in classroom behaviors was measured during the preparation program and not during
actual teaching in class as in-service teachers.
In fact, in previous sections, several studies that examined effectiveness were cited,
but these were always studied within the scope of pre-service teacher preparation and
not after it. Lesson plans and even lessons given by pre-service teachers do not neces-
sarily resemble real teaching practice, which may be compromised by school pressures
or other interfering factors. The focus of this section is on studies that try to examine
effectiveness on actual in-service practice.
8.2 Focused Longitudinal Studies that Support Appropriate Preparation
A few longitudinal studies have been conducted, and these either report a positive
effect of teachers’ preparation, or indicate that a positive effect could be achieved pro-
vided that teachers’ preparation programs are modified and improved according to
specific guidelines.

An example of the first kind of studies can be found in Ensor [2001], who conducted
a longitudinal study that followed seven mathematics pre-service teachers from the
methods course to the end of their first year as teachers. The results showed that be-
ginning teachers drew in two ways from the methods course: they reproduced a small
number of discrete tasks that had been introduced to them, and they also deployed a
professional argot—a way of talking about teaching and learning mathematics. Ensor
argues that the teachers participating in the study “recontextualized in ways that
suggest that the effects of teacher education were not “washed out” (as Zeichner and
Tabachnick [1981] suggest) but transformed”. Ensor claims that the mathematics
methods course enabled this, and though there were variations in recontextualizing
on the basis of school setting and educational biography, the preparation was effective.
Steele [2001] looked for explanations why changes in pre-service teachers’ beliefs
and knowledge (as a result of their preparation) do not always induce a real effect in
their classrooms when they start practicing as teachers. Steele’s longitudinal study
examined the effect of a reform-oriented pre-service mathematics teacher prepara-
tion on actual teaching in class as novice elementary teachers. The findings indicate
that besides known significant factors, such as school culture, or school administrative
cooperation, other factors that can be addressed by proper preparation also affected
teacher actual practice in a reform-based curriculum. For example, teacher’s weak
content knowledge may cause teacher-centered instruction (due to lack of confidence),
that fails to link mathematical concepts or different part of the curriculum. Also, a
lack of reflection-emphasized preparation might have a similar effect. The author ar-
gues that reflection integrated within a preparation program should relate to PCK as
well; namely how to teach specific content. This may help increase novice teachers’
confidence.
8.3 Measuring Effectiveness through the Perspective of Teacher Certification
Work on the effectiveness of teacher preparation is often reviewed through the perspec-
tive of teacher certification. The issue of teacher certification (i.e., what requirements
should be fulfilled by candidates before they are permitted to teach in (public) schools)
is both problematic and can have political overtones. As such, it has been in the focal
point of several heated debates among researchers.
Loosely speaking, there are three kinds of publications dealing with teacher
certification.
(1) Some publications focus on the issue of traditional certification vs. alternative
certification. Traditional certification is granted by college or university under-
graduate teacher preparation programs that combine subject matter courses
and educational courses. Alternative certification routes are usually shorter, are
based on a previously earned degree in the subject matter discipline, and add a
component focusing on education. Most of these publications discuss and compare
the effectiveness of the preparation in each of these tracks.
(2) Other publications focus on the issue of certification vs. what they sometimes
call “no certification” (which usually means no educational preparation, relying
on a degree in the subject matter discipline such as an undergraduate degree in
mathematics).
(3) A few studies have looked at specific certification tests and examine their effects
and characteristics.
Publications in the first and second groups are within the scope of this survey and this
section. However, it should be noted that most of the work on certification is general,

23:22 M. Armoni
not discipline-specific and does not distinguish among levels (elementary, junior high,
high school).
8.3.1 An Example: The Abell Foundation vs. Darling-Hammond. To demonstrate the del-
icate nature of the issue of certification and the caution required when examining
literature dealing with this issue, let us start by describing such a debate. In 2001,
the Abell Foundation [Walsh 2001] issued a report, “Teacher Certification Reconsid-
ered”. This was actually a meta-study of the literature. The motivation behind this
report was the reexamination of teacher certification in the state of Maryland, where
“individuals must complete a prescribed body of coursework before teaching in a pub-
lic school” (p. iii). The Abell Foundation’s report claimed that uncertified teachers are
as effective as certified teachers and that teacher education makes no difference to
teacher effectiveness. This conclusion was based on an extensive literature survey
of works dealing with the effectiveness of teacher preparation. It severely criticized
many of the works advocating teacher certification, as based in many cases on old, non
peer-reviewed, selective references and as being based in many cases on non-sound
analysis. The recommendation of the Abell Foundation report was to eliminate course-
work requirements for teacher certification and require only a bachelor’s degree and
a passing score on an exam which primarily assessed verbal ability, and only then
“basic knowledge and skills needed by an elementary teacher, including knowledge of
research-based reading instruction, and the specialized content knowledge needed by
secondary teachers” (p. viii). In a detailed response to this report Darling-Hammond
[2002] argued that teacher preparation is effective. Darling-Hammond pointed to sig-
nificant inaccuracies and deficiencies in the Abell Foundation’s report (among others,
basing their views on old, non peer-reviewed or selective references) and cited studies
that demonstrate the importance of other types of knowledge, besides SMK, which is
usually the only type of knowledge possessed by uncertified teachers.
8.3.2 Is Traditional Certification More Effective? A study that belongs under both the first
and the second groups of publications was conducted by Goldhaber and Brewer [2000].
The authors compared the achievements of 12th-grade students whose teachers had
standard certification (that is, based on university or college teacher preparation
programs) in their subject area with the achievements of students whose teachers
had probationary certification, emergency certification, private school certification, or
no certification in their subject area (which can be either certification in another area
or no certification at all, although the later was less probable). The authors found
that “In mathematics . . . students of teachers who are either not certified in their
subject . . . or hold a private school certification do less well than students whose
teachers hold a standard, probationary, or emergency certification in math” (p. 139).
The results in science showed a similar albeit weaker effect in magnitude and statis-
tical significance. The authors emphasize the surprising finding regarding teachers
with emergency certification and give one (speculative, in their words) explanation;
namely that teachers with emergency credentials were more carefully screened.
The authors also found that “math students who have teachers with Bachelors or
Masters degrees in mathematics . . . have higher test scores relative to those whose
teachers have out-of-subject degrees” (p. 138), but “in science there is no impact of
teachers having subject-specific degrees” (p. 138). Another finding was that “having a
degree in education has no impact on student science test scores and, in mathematics,
having a BA in education actually has a statistically significant negative impact on
mathematics scores of students” (p. 138–139, emphasis in the original). The authors
suggest that this finding can be explained by “major in education” serving as a proxy

for teacher ability, since “most college students selecting education majors tend to be
drawn from the lower part of the ability distribution” (p. 139).
The Goldhaber and Brewer [2000] study can also serve to demonstrate the problem-
atic nature of the discussion on certification. The authors were very cautious in their
discussion, stating no definitive recommendations, yet their work was cited, for exam-
ple, by Good et al. [2006] as indicating that type of certification had little impact on
student test scores. Even Darling-Hammond et al. [2001] argued that “Goldhaber and
Brewer’s article . . . claimed . . . that teacher certification has little bearing on student
achievements” and that they stated “that states should eliminate certification require-
ments.” This view did not remain unanswered, and the debate continued in Goldhaber
and Brewer’s rejoinder [2001].
Similar to the Abell Foundation, other research teams have been asked to review
the literature dealing with teacher preparation and certification. One such example
is another report issued by the Education Commission of the States [2005], this time
looking at eight questions concerning teacher licensure and certification, again dealing
with all disciplines and all levels at once. Focusing here only on issues relevant to the
effectiveness of teacher preparation, this report concluded that the research on the
relation between pedagogical knowledge and practice (components included to some
extent in any preparation program, whether traditional or alternative) and teachers’
effectiveness was inconclusive; moderate support was found for the hypothesis that
academic performance (such as education coursework) predicted teacher effectiveness;
There was strong evidence that students taught by fully certified teachers did better
than those taught by out-of-field certified teachers or teachers with emergency
certification.
Al-Weher and Abu-Jaber [2007] studied the effectiveness of teacher preparation pro-
grams in Jordan, examining several routes to certification. Their study was general
and did not specify subjects or level. Their findings were based on analyzing question-
naires filled out by school principles, the teachers themselves, and their pupils. The
authors argue that “programs where educational and academic courses are taught si-
multaneously excelled over the programs that include academic courses alone followed
by educational programs” (p. 262).
In contrast, Miller et al. [1998] compared traditional certification (TC) program
graduates (that is, graduates of an undergraduate teacher education program, which
usually takes four years) with “individuals completing a carefully constructed AC
[alternative certification] program.” This carefully constructed post-baccalaureate
program, intended for middle-grade teachers, included condensed coursework and a
mentoring program. The results of their three-phase study indicated no major differ-
ences between AC and TC teachers, after three years of experience and mentoring.
Good et al. [2006] compared teachers graduating from an undergraduate program in
education (general or specific, such as mathematics education) with graduates of a
master’s degree in education or a post-baccalaureate program leading to certification.
The latter was considered as nontraditional. Teaching practice (assessment, classroom
management, and implementation of instruction) of the participating teachers was
compared. Their data “indicated that beginning teachers from both types of prepara-
tion programs could teach at desired normative levels” (p. 422). Other findings indi-
cate, though not definitively, that “traditional preparation better served teachers at the
elementary and middle-school levels than did nontraditional preparation” (p. 421) and
“nontraditional preparation appeared a better fit with high school teaching” (p. 421).
Alternative certification programs are quite diverse, varying from programs with
minimal requirements to programs with very high demands. This is probably the
reason why the Education Commission of the States [2005] categorized the research
on the differences in performance between teachers prepared via traditional and

23:24 M. Armoni
alternative routes as inconclusive, and the review by Zeichner and Schulte [2001]
also interpreted research results on this point as inconclusive. However, a report on
teacher preparation issued by the Center for the Study of Teaching and Policy (CTP)
[Wilson et al. 2001, 2002] concluded that subject matter alone (that is, with no edu-
cational preparation) may not be sufficient for new teachers while alternative routes
that have high entry requirements and include pedagogical training, mentoring, and
substantial evaluation tend to be successful in their production of qualified teachers.
The debated issue of teacher certification had also led to other surveys and opinion
essays, such as Darling-Hammond [2000] and Goldhaber and Anthony [2003].
8.4 Summary
Though research on the effectiveness of teacher preparation, in its various forms, is
not always conclusive, it seems to support the findings described in previous sections:
high school teachers should have solid subject matter knowledge, but should also learn
educational aspects. Their preparation must include sufficient exposure to PK and es-
pecially to PCK. In order to make the effectiveness of teacher preparation robust to the
negative effects of school setting and daily challenges of in-service practice, designers
of teacher preparation programs should explicitly expose prospective teachers to these
effects, confront their initial beliefs on teaching practice with the principles guiding
preparation, and keep the connection between real school practice to the preparation
as solid as possible. In other words, following recommendations induced by previous
sections is likely to enhance the effectiveness of the preparation.
9. COMPUTER SCIENCE TEACHER PREPARATION
This section reviews the literature on computer science teacher preparation. As noted
above, very few of the publications in the area of computer science teacher preparation
are research-based. Most of them are descriptive articles, including recommendations
for specific programs or courses, which are in many cases based on the experience and
expertise of leading CS educators.
9.1 Computer Science Teacher Preparation: Early Work
During the mid 1970s up to mid 1980s the issue of CS teachers was addressed by many
CS educators. Computers became a component of school culture, and professionals
were needed to effectively integrate computers into the schools. However, even by this
short introduction one can realize that it was not clear whether computer profession-
als or computer science professionals were required. In fact, at that time the nascent
discipline of computer science was somewhat vague, and was too often confused with
computer applications or computer literacy. Computer science teachers were also ex-
pected to act as computer resource personnel, computer lab directors, etc. Only in
1989, the ACM committee, chaired by Denning [Denning et al. 1989], published its
final report on computing as a discipline, defining the new discipline as having roots
in mathematics, science, and engineering.
The vague borders of the young discipline are clearly shown in the publications
of the 1970s and 1980s. Computer use in education was an important component of
the programs described in these articles, and the CS content knowledge component
focused mainly on programming. For example, Frederick [1975] discussed computer
science education for students training to be secondary teachers. Since there was no
certification process for computer science teachers, their department offered a CS mi-
nor to be taken with an appropriate teaching major. The program described in the
article included content CS knowledge and computer use in education, but not any el-
ements of PCK. Of course, the term of PCK was introduced by Shulman more than a

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