A Design of Professional Teacher Training with PMRI and LSLC

System

Rini Herlina R.

, Zulkardi

and Ratu Ilma

High School Supervisor of National Education Services in South Sumatera Province, Indonesia

Mathematics Education Department, Doctoral Program , Univeristas Sriwijaya, Palembang, Indonesia

Keywords: Professional Teachers, Teacher Training Design, PMRI, LSLC.

Abstract: This paper aims to provide an example of mathematics teachers training design as a solution to improve the

competence of high school mathematics teachers to be more professional in carrying out the classroom

instruction. This training is designed using In-On-In patterns, consisting of In1 activities where the high school

mathematics teachers are trained on how to design PMRI-based instruction with 3 principles and 5

characteristics, the instruction using the LSLC (Lesson Study for Learning Community) system, consisting

of four stages namely design, do (implementation), see (reflection), and re-design. After training the teacher

is asked to implement their knowledge from the training in a class as an On activity which is documented and

analyzed. The weaknesses of the instruction during On activities are retrained during In2 activities by

individual or group assistance according to their weaknesses. The results of the design of this training design

can be an alternative in improving the competence of professional mathematics teachers.

1 INTRODUCTION

The low competence of teachers in conducting

mathematics instruction is very influential on the poor

quality of students’ learning outcomes. Based on this

reality, it is necessary to change the system in the

instructions. The instruction developed by the teacher

should be able to encourage an increase in students’

thinking ability to improve their creativities and build

their independence in solving the problems given.

Related to the issue of teacher development at the

international level, according to the results of the

United Nations Educational, Scientific, and Cultural

Organization (UNESCO) survey, on the quality of

teachers in developing countries in Asia Pacific,

Indonesia is ranked 10th out of 14 countries. As for

the teachers, the quality is at level 14 of 14 developing

countries. One factor that contributes to the low

quality of teachers in Indonesia is their lacking of

exploring the students' potential. Teachers often

impose their will without paying attention to the

needs, interests and talents of their students. Teachers

should pay attention to the needs of children instead

of imposing something that makes children less

comfortable in studying. In general, (Marpaung,

2006) mentions that one of the problems in

mathematics education is to know how students learn

and master complex concepts, rules, procedures, or

processes in mathematics. Thus, the teachers need to

understand not only mathematical material, but also

how their students understand the materials, including

their reasoning skills. In other words, a good teacher

provides opportunities for children to be creative.

A professional teacher is required to master a

number of competencies. The law no. 14 (2005)

describes these competencies as a set of knowledge,

skills, and behaviors that must be owned,

internalized, and mastered by the teacher in carrying

out his professional duties. One effort that can be

done in addressing this is by improving the

mathematics instruction in terms of the process and

the quality.

One approach to mathematics instruction that is in

accordance with the revised 2013 curriculum is the

learning approach of PMRI (Pendidikan Matematika

Realistik Indonesia-Indonesian Realistic

Mathematics Education). The students’ real-life

situation is not only limited to what is visible, but also

all things that are accessible by their imagination

(Putri, 2015). In order to improve students'

mathematical reasoning skills, firstly the teachers

need to understand students' reasoning abilities. This

204

Herlina R., R., Zulkardi, . and Ilma, R.

A Design of Professional Teacher Training with PMRI and LSLC System.

DOI: 10.5220/0009995600002499

In Proceedings of the 3rd Sriwijaya University International Conference on Learning and Education (SULE-IC 2018), pages 204-208

ISBN: 978-989-758-575-3

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

is in accordance with the 3 principles and 5

characteristics of PMRI.

The implementation of teacher professionalism

development programs in Japan has proved that

Lesson Study can improve teacher (Masaki, 2012).

There has been a lot of research on lesson study which

shows its success when applied to Indonesian

teachers. This program, now under the name Lesson

Study for Learning Community (LSLC), is a system

of teacher professional development through the

study of collaborative learning and based on the

principles of collegiality and mutual learning to build

learning communities and improve the quality of

learning which ultimately creates dynamic

interactions between teachers so that creativity and

motivation are built continuously. This practice will

be optimal if the teachers understand the concepts and

application methods of the LSLC system and PMRI-

based learning. Thus, this paper will discuss the

design of PMRI and LSLC system-based professional

teacher training.

2 BACKGROUND THEORY

2.1 Professional Mathematics Teachers

According to Law No. 14 of 2005, professions are

jobs or activities carried out by a person which

become a source of income for life that requires

expertise, proficiency, or skills that meet certain

quality standards or norms and require professional

education. In the meantime, teachers are professional

educators whose main jobs are educating, teaching,

guiding, directing, training, evaluating, and

evaluating students in early childhood education in

formal education, primary education, and secondary

education. In this paper, teachers refer to

Mathematics teachers.

2.2 Teachers’ Professionalism

Development

There are many ways that can be done by teachers in

the context of developing their professionalism. Udin

(2009) mentions several alternatives in teachers’

professional development programs. One of them is

by means of competency-based integrated teacher

training program, followed by ongoing assistance.

2.3 PMRI (Pendidikan Matematika

Realistik Indonesia – Indonesian

Realistic Mathematics Education)

PMRI is a learning approach that adapts Freudenthal's

thinking known as Realistic Mathematics Education

(RME), which has been developed in Indonesia since

2001 (Zulkardi, Pengembangan Materi Pembelajaran

Bilangan Berdasarkan Pendidikan Matematika

Realistik untuk Siswa Kelas V Sekolah Dasar, 2009).

Etymologically, realistic word comes from the Dutch

language "zich realiser" which means "to imagine" or

"to imagine" (Heuvel-Panhuizen, 1998). In the

framework of RME, (Freudenthal, 1991) states that

"mathematics must be connected to reality and

mathematics is a human activity". First, mathematics

must be close to students and relatable to everyday

life situations. Second, he stressed that mathematics

is a form of human activity. This statement means that

mathematics is not a finished product, but rather a

form of activity or process in constructing

mathematical concepts. This process is carried out by

students actively finding a mathematical concept with

teacher guidance or in the term "guided reinvention".

Therefore, many opportunities are given by the

teacher to students to build their own understanding.

The use of the word "realistic" is often

misinterpreted as "real-world." Based on this

misunderstanding, many parties consider that a

realistic mathematical approach is an approach that

must use everyday problems. (Heuvel-Panhuizen,

1998) argues that the use of the word "realistic" does

not merely indicate the connection with the real world

but rather refers to the teacher's focus on realistic

mathematics in placing emphasis on the use of

imaginable situations by students. So, realistic here

does not mean concrete in plain view, but also

includes what can be imagined by students.

There are three principles in PMRI (Zulkardi &

Putri, 2010) namely:

1. Guided Reinvention and Didactical

Phenomenology

Based on the principle of guided reinvention,

students should be given plenty opportunities to

experience the same process when mathematical

concepts are found. This principle can be inspired by

using informal procedures.

2. Progressive Mathematization/Didactical

The concepts that exist in mathematics are made to

regulate existing phenomena, both those originated

from everyday life and those originated from

mathematics itself.

A Design of Professional Teacher Training with PMRI and LSLC System

205

3. Self-developed Models

The role of self-developed models is to bridge

students from real or concrete situations to abstract

situations, or from the informal stage to the formal

stage of mathematics. In the early stages, students

develop a model that they recognize. Then, through

generalization and formalization, the model

eventually becomes a form of mathematical formula

that is in accordance with mathematical concepts. The

four levels or levels of the mathematical model are

illustrated as follows.

` 

Figure 1: Level of model development.

a. Situational level is the most basic level of modeling

where specific areas of specific domains,

situational knowledge and strategies used are still

in the context of the problem situation used.

b. Referential level is the level where the model and

strategy developed are not in the context of the

situation, but have referred to the context. At this

level, students make a model to describe the

context situation so that the results of modeling at

this level are called the model of the situation.

c. General level refers to the model developed by

students that has led to finding solutions. This

model is referred as model for problem solving.

d. Formal level refers to the stage where students

have worked using symbols and mathematical

representations. The formal stage is the stage of

formulation and affirmation of the mathematical

concepts built by students.

In addition to these three principles, PMRI has five

characteristics (Zulkardi & Putri, 2010). They are:

1. Phenomenological exploration or the use of

contexts.

In the first learning activity, concrete or real

context is used as the basis for mathematical

activities.

2. Using models and symbols for progressive

mathematization

The second characteristic of PMRI serves as a

bridge from the concrete stage to a more formal

stage using models and symbols.

3. Using students' own construction and production

4. Interactivity

PMRI learning activities carried out by students

can be seen as individual process as well as social

processes. At this writing, students not only carry

out individual processes in learning mathematics

but also socially involved.

5. Intertwinement

Intertwinement integrates various mathematical

topics in one activity.

2.4 LSLC (Lesson Study for Learning

Community)

According to (Baba, 2007), lesson study refers to a

process in which teachers progressively try to

improve their teaching methods by collaborating with

other teachers. In the meantime, (Sukirman, 2006)

views lesson study as a model of teacher professional

development through the study of collaborative and

sustainable learning based on the principles of

collegiality and mutual learning to build learning

communities. (Masaki, 2012) said that learning club

is needed to improve the quality of teachers in order

to cultivate a habit of doing activities to learn from

fellow teachers. Thus, the name Lesson Study for

Learning Community (LSLC) becomes a system of

teacher professional development through the study

of collaborative and sustainable learning in Indonesia.

LSLC consists of four stages namely plan/design, do

(implementation), see (reflection), and re-design.

1. Stage of Planning (Plan)

This planning stage, the teacher collaborates with

other teachers in the team to prepare the lesson plans

with student-centered activities, analyze the needs

and problems faced in learning, and then find a

solution to solve all problems found. The results of

the needs and problems analysis must be considered,

so that the lesson plan becomes a plan that is truly

relevant with expectations and applicable regulations,

which include all stages of the implementation of

learning; the initial, core, and final stage of learning.

2. Implementation Steps (Do)

The instruction is carried out by one of the

teachers who are mutually agreed to practice the

lesson plan that has been prepared together. In the

meantime, other teachers make observations (These

observations could be done by members or the lesson

study community which are teachers, principals, or

school supervisors, or other invitees acting as

observer / observer).

3. Stages of Reflection (See)

This stage is very important as part of the efforts

to improve the instruction. This activity is carried out

in the form of discussions attended by all lesson study

participants who were guided by one of the

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designated team members. The discussion begins

with the delivery of impressions of the performing

teacher regarding the instruction that they did, such as

the difficulties and problems in implementing the

lesson plan that has been prepared.

4. Stages of Follow-up (Re-design)

From the conclusions from reflection stage, a

number of new knowledge to improve the learning

process can be obtained. Various valuable findings

and input delivered during the discussion certainly

become the basis for the teachers, both those who

acted as instructors and observers to develop better

instruction. Then all results of the input become a

concern for the preparation of the next lesson plan.

3 DISCUSSION

3.1 Training Design

The government has implemented many ways to

improve teachers’ competencies through IN-ON-IN

training patterns (on the job training and in service

training) because the results are more effective. The

design of teacher training with the IN-ON-IN pattern

in this paper is as follows:



Figure 3.1 Workshop design of mathematics teacher.

3.1.1 Stage IN1

The training participants, i.e. math teachers, are

trained by PMRI experts and LSLC on how to design

lesson plans with 3 principles and 5 characteristics

from PMRI starting from the initial, core and final

activities; the assessment, i.e. task sharing and

jumping tasks which are the characteristics of LSLC,

referring to HOTs questions; the collaborative

teaching simulation, consisting of how the LSLC

system stages start from plan/design (planning), then

do (implementation), see (reflection), and re-design.

At this stage there are also examples of instruments

for PMRI-based lesson plan review, observation

instruments and training participants' satisfaction

instruments to measure the participants’

understanding on the materials.

3.1.2 Stage ON

After the training, at this stage the teacher is asked to

implement all the training materials in their respective

schools, by forming an LSLC team. The activities

consist of: a) setting teaching schedule, b) arranging

classroom in the U-shaped seating plan, c) selecting

students in groups of 4, 2 boys and 2 girls crossed, the

model teacher, the appointed observer team, d)

bringing video recordings, photo documentation, and

notes during classroom learning activities, e) filling

all previously designed instruments, and finally f)

carrying out all stages of LSLC starting from the Plan

(PMRI-based lesson plan that has been designed

during training), do (implementation of the

instruction), see (discussion of the observation report)

and re-design (the result of discussion is revised to fix

the mistakes).

3.1.3 Stage IN2

At this stage, all the weaknesses experienced by the

teacher when ON activities are identified and

analyzed according to the category of weaknesses.

After that, the resource person or designated teacher

(the teacher who is able to carry out all stages

properly) is invited back to provide assistance to

overcome all weaknesses that occurred during ON

activities. This activity is carried out routinely and

continuously until potential effects are seen. After the

teacher is better prepared, the teacher is asked to carry

out "open class" activities which are attended by

school supervisors, principals, LSLC teams, other

mathematics teachers, etc.

4 CONCLUSION

The design of PMRI and LSLC system-based

mathematics teacher training with the IN-ON-IN

pattern is expected to be an alternative in realizing

professional teachers, because it can help

mathematics teachers develop their professional and

A Design of Professional Teacher Training with PMRI and LSLC System

207

pedagogical abilities in conducting classroom

instructions. In addition, teachers’ collaboration

provides many opportunities for them to get new

ideas also and have direct consultation with experts

during training or IN activities. In conclusion, this

design can improve the quality of teachers to become

professional teachers, and the quality of instruction

which in turn can improve the quality of graduates.

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