177406 EN investigating preservice secondary mathe

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INVESTIGATING PRESERVICE SECONDARY MATHEMATICS TEACHERS’
PEDAGOGICAL CONTENT KNOWLEDGE: A CASE STUDY IN
MICROTEACHING COURSE

Veronika Fitri Rianasari
Dosen Pendidikan Matematika, FKIP, Universitas Sanata Dharma
Alamat korespondensi: Kampus III Paingan, Maguwoharjo, Yogyakarta
E-mail: veronikafitri@usd.ac.id

ABSTRAK
Guru yang efektif memiliki pengetahuan yang mendalam tentang konten materi pelajaran
yang mereka ajarkan. Selain pengetahuan yang mendalam tentang materi yang diajarkan, guru juga
harus memiliki pengetahuan yang mendalam tentang proses dan praktik belajar dan mengajar.
Pengetahuan konten pedagogi adalah perpaduan pengetahuan disiplin ilmu atau materi ajar tertentu
dan pengetahuan pedagogi. Tujuan dari penelitian ini adalah untuk menyelidiki Pedagogical
Content Knowledge (PCK) 6 calon guru matematika di pembelajaran mikro. Data dikumpulkan
dalam bentuk pengamatan, kuesioner dan dokumen tertulis. Selama microteaching, peneliti

mengamati pemahaman preservice guru komponen PCK. Lembar observasi dirancang berdasarkan
kerangka konseptual untuk menganalisis PCK yang dikembangkan oleh Chick, Baker, Pham, dan
Cheng (2006).Temuan menunjukkan bahwa banyak siswa telah mengembangkan PCK
mereka.amun masih banyak juga keterampilan dan pengetahuan yang harus ditingkatkan.
Kata kunci: PCK, pembelajaran mikro, calon guru matematika sekolah menengah.
ABSTRACT
Effective teachers have a deep knowledge about the content of the subject matter they
teach. As well as a deep knowledge of the material being taught, teachers must also have a deep
knowledge about the processes and practices of teaching and learning. Pedagogical content
knowledge is the intersection of discipline specific subject content knowledge and pedagogical
knowledge. The purpose of this study is to examine Pedagogical Content Knowledge (PCK) of 30
preservice secondary mathematics teachers in microteaching course. The participants of this
research are third-year preservice secondary mathematics teachers at Sanata Dharma University
undertaking microteaching course. The data were collected in the form of observation,
quesstionare, and written document. During the microteaching course, researcher observed
preservice teachers‟ comprehension of PCK components. The observation sheet is designed based
on the conceptual framework for analysing PCK developed by Chick, Baker, Pham, and Cheng
(2006). The findings revealed that many students have developed their PCK. However there were
also some skills and knowledge that should be improved.
Keywords: preservice secondary mathematics teachers, PCK, microteaching

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In Indonesia, in order to provide

Introduction

additional experience before the teaching

Background of the research
The major goal of teacher education

practice program,

preservice teachers

programs is to help preservice teachers

should

improve their knowledge of and skills for

Microteaching was invented in the middle

effective teaching through coursework and

of 1960s and has been used to prepare

practice. Mathematics teacher education

teacher candidates to the real classroom

programs heavily provide mathematical

setting. Most of microteaching practices in

content and general pedagogy courses to

Indonesia are carried out in artificial

support the development of preservice

classroom environment known also as

teachers‟ subject-matter and pedagogical

laboratory environment. Microteaching

knowledge. However, teachers not only

practices

need to possess knowledge of subject-

teachers will create an opportunity for

matter and pedagogy but also knowledge

them to use their theoretical content

of

instructional

knowledge and pedagogical knowledge in

tools, and assessment and be able to

classroom environment (Kartal, Ozturk,&

interweave them effectively (Shulman,

Ekici,

1986). Teaching practice program is

teachers should develop and articulate,

conceived as an arena for preservice

what

teachers to develop their ability of

pedagogical content knowledge (PCK).

curriculum,

students,

take

microteaching

carried

2012).

Shulman

out

by

Therefore

(1986)

course.

preservice

preservice

called,

their

interweaving all types of knowledge for
effective

teaching.

In

such

courses,

Theoretical Framework

preservice teachers discuss whether a

Pedagogical Content Knowledge (PCK)

particular topic is difficult or easy for

Shulman (1986, 1987) classified

students, what learning goals are defined

teachers‟

for that topic in the curriculum, what

knowledge, pedagogical knowledge, and

teaching strategies and instructional tools

pedagogical content knowledge. Shulman

facilitate

and

(1986) explained that PCK conceptualize

the

„the ways of representing and formulating

instruction to address the needs‟ of the

the subject that makes it comprehensible

students and how to assess students‟

to others‟ (p. 9). Later, in 1987, Shulman

understanding (Killic, 2010).

rephrased the defintion of PCK as a

students‟

understanding,

how

learning
to

tailor

knowledge

into

content

„special amalgam of content and pedagogy

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75

that is uniquely the province of teachers,

classroom management and KOC means

their own special form of prefessional

that teachers know how to address the

understanding‟ (p. 8). PCK is an essential

learning needs of students according to

area of teacher development in higher

their cognitive differences, social, cultural,

level teaching (Shulman, 1987).

and language background.

Cochran (1991) defined PCK as follows

Microteaching

Pedagogical content knowledge is

Microteaching course is a course in

an integrated understanding that is

which the prospective teachers for the first

synthesized from teacher knowledge

time learn to manage learning in a

of pedagogy, subject matter content,

structured

student

the

preparation for practice teaching program

environmental context of learning.

in schools. Based on Microteaching

In other words, PCK is using the

Handbook of Sanata Dharma University

understandings of subject matter

(2013), student teachers are expected to

concepts, learning processes, and

master some basic teaching by applying

strategies for teaching the specific

the

content of a discipline in a way that

through microteaching courses. Some

enables students to construct their

basic skills that must be mastered by

own knowledge effectively in an

students are opening and closing skills

given context (p.11).

lessons, asking questions and giving

characteristics,

and

Chick, Baker, Pham, and Cheng (2006)
proposed a framework for investigating
PCK, and applied it to the content domain
of decimal numbers. On the other hand
See (2013) had conducted a research to
examine teachers‟ PCK in three domains
of

PCK

which

are

subject

matter

knowledge (SMK), general pedagogical
knowledge (GPK) and knowledge of
context (KOC). SMK is similar to subject
content knowledge, GPK refers to the
broad

principles

and

strategies

AdMathEdu | Vol.7 No.1 | Juni 2017

of

way.

specific

reinforcement,

This

course

approach/learning

explaining

and

is

a

model

giving

varying stimulus. Microteaching is a "real
teaching" but it is not a "real classroom
teaching", therefore, prospective teachers
are expected to do a lot of teaching
practice and they are required to be able to
put the experience into practice in a
comprehensive manner in a real classroom
teaching.
Allen and Ryan in Benton-Kupper
(2001) stated that microteaching is “a
training concept that can be applied at
various pre-service and in-service stages
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of

the consideration of teachers' academic

teachers.” During microteaching, teachers

ability. Two teachers have high academic

have opportunities to practice in an

ability,

instructional setting in which the normal

academic ability, and two teachers have

complexities of the classroom are limited

low academic ability. At the end of the

and in which they can receive feedback on

course, researcher assessed all preservice

their performances. Magnusson, Krajacik,

teachers‟ PCK in three domains of PCK.

& Borko (1999) pointed out that having

The instruments used in this research are

teaching experience is an important factor

questionnaire and observation sheet. The

for the development of pedagogical

observation sheet is designed based on the

content knowledge. Pedagogical content

conceptual framework for analysing PCK

knowledge develops along with teaching

developed by Chick, Baker, Pham, and

experience.

Cheng

METHODOLOGY

questionnaire is addressed to guide the

in

the

profesional

development

two

teachers

(2006).

have

medium

Meanwhile,

the

This study employed the qualitative

students to reflect on their microteaching

case study methodology. Qualitative case

experiences towards three domains of

study methodology was chosen because it

PCK designed based on the framework

provides tools for researcher to study

developed by See (2013).

complex phenomena within its contexts

RESEARCH

using variety of data sources (Baxter &

DISCUSSION

Jack, 2008).

Below is the description of six preservice

This study investigated secondary
preservice

mathematics

Pedagogical

Content

teachers‟

Knowledge

in

FINDINGS

AND

teachers‟ performance analysed based on
the framework developed by Chick,
Baker, Pham, and Cheng (2006).

microteaching course. The participants of

Teaching Strategies

this research are third-year preservice

In practicing learning process, all teachers

secondary mathematics teachers at Sanata

used some teaching strategies such as

Dharma

making

University

undertaking

mathematical

microteaching course.
During the microteaching course,

relationship
concepts

between
to

real

life,

organising games, and engaging students

preservice

to participate in learning process by

of

PCK

posing problems. Only two teachers

components. This selection was based on

showed some specific strategies related to

researcher
teachers‟

observed

six

comprehension

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77

a certain mathematics concepts, including

can identify aspects of the task that affect

making connections between two related

its complexity.

concepts (sine and cosine rule) and

Representations of Concepts

approximating

Teachers did not provide many ways to

the area of

curvilinear

regions to introduce integral concept.

illustrate a mathematics concept. Teachers

Students Thinking

tended to directly use formal symbols and
real

most of the teacher only used picture or

classroom teaching, therefore there is not

two dimensional figure to illustrate a

enough evidence that show teachers‟

concept. For example, there was a teacher

effort to discuss or respond to possible

who used rectangles to determine the area

student ways of thinking about a concept,

under a curve to illustrate the concept o

or

definite integral.

Since

microteaching

recognize

is

typical

not

a

levels

of

understanding. Most of the teachers

Knowledge of Resources

assumed that all students can think in a

The types of learning resources used by

formal way particularly in understanding

teachers in the learning process are very

formulas or theorems. In doing discussion,

limited. All teachers only used one book

the

accommodate

source that is high school mathematics

students'

textbook. Two teachers engaged students

understanding. Moreover, teachers did not

to explore various sources as references to

stressed or addressed typical student

solve problems. Two other teachers use

misconceptions about a concept. Teachers

mathematics software, that is GeoGebra,

focused on what they have planned, which

to explore the properties of vector and

are learning goals written in their lesson

definite integral.

plan.

Curriculum Knowledge

Cognitive Demand of Task

None of the teachers explained how a

Four teachers only gave routine problems

certain mathematics concept fit into the

to their students. Therefore, it was not

curriculum. In the beginning of a lesson,

clearly shown their ability to identify

teachers only mentioned the learning goals

aspects of the task that affect

and they did not explain the link between

teachers

different

did
variety

not
of

its

complexity. However, there are two

a mathematics concepts and curriculum.

teachers who gave some problems with

Profound

varying levels of difficulty so that they

Fundamental Mathematics

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Understanding

of

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Only two teachers showed deep and

teachers pointed among concepts or

thorough conceptual understanding of

between

identified aspects of mathematics. The

example,

other teachers failed to demonstrate a deep

relationship between the rules of law of

understanding of a concept. It can be seen

sines and cosines with the area of a

from their explanation which is very

triangle.

superficial, limited to the application of a

Procedural Knowledge and Methods of

formula (how to solve a problem), less in

Solution

the explanation of why a certain method

All teachers have good skill in solving

works in solving a problem.

mathematical problems. However, three

Deconstructing

Content

to

key

concepts
the

and

teacher

topics.

For

explain

the

teachers only provide routine problems.

Components

The other teachers not only provide

From teachers‟ lesson plan, it can be

routine problems, but also non routine

shown that most of the teachers showed

problems. However, only two teachers

their ability to indentify keys components

used various methods of solutions that

that are fundamental for understanding

reflect her deep understanding of the

and applying a concept in the subject they

topic.

teach. However, this identification was not

Goals for Learning

clearly shown in learning process. Since

All of the teachers explicitly mentioned

teachers tended to focus on procedural

the learning goals related to specific

knowledge, they did not stressed on the

mathematics content in the beginning of

key components. Only one teacher clearly

learning. Only two teachers mentioned the

deconstructed content (integral content) to

learning goals that are not directly related

key components.

to content, for example: teachers related

Mathematical

Structure

and

ability. However, it was an interesting

Connections
Two

teachers

mathematics content to critical thinking

did

not

the

phenomenon about explaning learning

relationship among concepts or between

goals explicitly in the beginning of

concepts and topics. For example, the

learning process. By mentioning the

teacher did not explain the relationship

learning goals, students know what they

between the concept of vectors with the

are

operations on vectors, why there are

explanation of learning goals might inhibit

operations on vector. While, the other

students to reach their fullest potential.

Investigating … (Veronika)

explain

going

to

learn.

However,

the

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79

Instead of telling the learning goals

real life that show the application of the

explicitly, teachers can pose essential

concepts in real life. Three teachers used

questions or activities that can support

games to attrack students‟ attention, and

students to construct their own meaning

two teachers used mathematics software to

through a variety of activities.

illustrate mathematics concepts.

Getting and Maintaining Student Focus

Based on the questionnaire, the table

There are some strategies used by the

below shows reflection of 26 students on

teachers to get and mantain students focus.

three domains of PCK in the end of

All of the teachers posed questions to the

microteaching

course.

students and showing pictures/videos in
Table 2. Data of students‟ reflection on three domains of PCK
Domains of
PCK
Subject
Matter
Knowlegde
General
Pedagogical
Knowledge
Konwledge
of Context

Percentage of students based on the
criteria *)
VG
G
F
P
VP
47.6%% 47.6%
4.8%
-

General
Criteria
VG

71.4%

28.6%

-

-

-

VG

52.4

47.6%

-

-

-

VG

*)Desription: VG: Very ; G: Good ; M: Fair ; P: Poor ; VP: Very Poor
The table above show that all preservice

This result indicates two things. First, the

teachers have very good criteria in three

preservice teachers had already had good

domains of PCK, including subject matter

quality in subject matter knowledge,

knowledge,

general

general

pedagogical

pedagogical

knowledge,

and

knowledge, and knowledge of context.

knowledge of context, but they did not

However, the result and analysis of six

able to blend it in conducting teaching and

preservice

in

learning process. Second, the preservice

practicing learning process showed that

teachers do not realize that their ability or

there are many skills and knowledge that

knowledge was not optimal and it should

should be improved in order to be able to

be improved to carry out effective

conduct an effective learning process.

learning. They might think that their

teachers‟

performance

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ability

or

knowledge

in

teaching

design

and

implementation

for

mathematics was good enough.

novice researchers. The qualitative

4. CONCLUSION

report, 13(4), 544-559.

Based on the analysis, it can be concluded
that prospective teachers‟ PCK in three
categories, those are „clearly PCK‟,
„content knowledge in a pedagogical
contenxt‟, and „pedagogical knowledge in
a content context‟, should need to be
improved. Magnusson et al. (1999) argued
that a teacher education program can
never

completely

address

all

the

components of PCK that a teacher need.
On the other hand, since PCK is a specific

Benton-Kupper,

J.

(2001).

The

microteaching experience: Student
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Carter, M. & Francis, R. 2001. Mentoring

refers to the transformation of subject-

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Teacher Education, 29(3), 249-261

preservice

teachers

should

master

components of PCK and must have a lot
of experience to teach mathematics both
in microteaching or in real teaching in
school since the major source of a
teachers‟ PCK is teaching experience

Cochran, K. F., King, R. A., & De Ruiter, J.

A.

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