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Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015

ISBN 9786021570425 Page ii

SCIENTIFIC BOARD

1. Prof. Dr. Abdul Wahab Jufri, University of Mataram

2. Dr. Elyzana Dewi Putrianti, Charite Universitaetmedizin, Berlin, Germany

3. Prof. Helmut Erdmann, University of Applied Sciences Flensburg, Germany

4. Dr. Imam Bachtiar, University of Mataram

5. Prof. James Gannon, University of Montana, USA (present address American

University of Sharjah, United Arab Emirates)

6. Dr. Lalu Rudyat Telly Savalas, University of Mataram

7. Assoc. Prof. Dr. Mian Muhammad Awais, Bahauddin Zakariya University,

Pakistan

8. Prof. Dr. Moh. Faried Ramadhan Hassanien, University of Zagazig, Egypt

9. Dr. Muhammad Roil Bilad, Nanyang Technological University, Singapore

(present address Universiti Teknologi Petronas Malaysia)

10. Dr. Saprizal Hadisaputra, University of Mataram

11. Dr. Syamsul Bahri, University of Mataram

12. Prof. Dr. Unang Supratman, University of Padjajaran

Technical Editors:

1. Baiq Nila Sari Ningsih, S.Pd.

2. Alfian Eka Utama

ISBN 9786021570425

Copyright: Penerbit FKIP Universitas Mataram


ISBN 9786021570425 Page ii

PREFACE

Assalamu’alaikum warahmatullah wabarakatuh

It is my pleasure to be able to bring the International Conference on Mathematics

and Natural Sciences Proceeding to our readers. It took an extra effort, time and patience

to accomplish this proceeding and it involved reviewers from all over regions. I personally

thank to our reviewers and subsequently apologize for the delay in making this

proceeding available for you to read. It is largely due to the inevitably extensive reviewing

process and we persist on our initial idea to keep the proceeding both readable and

academically meet a higher standard.

This proceeding is presented in six sections: 1) Invited Speakers; 2) Physics; 3)

Mathematics; 4) Biology (including pharmacy and agriculture); 5) Chemistry; and 6)

General Education. All sections consist of papers from oral and poster presentation in

respective subject, including science and science education.

I hope that this proceeding may contribute in science and science education.

Wassalamu ‘alaikum warahmatullahi wabarakatuh

Lalu Rudyat Telly Savalas

Chief Editor


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OME-16 Implementation of Democratic Classroom in Teaching

Multiplication

Rahmah Johar*, Cut Khairunnisak, Suhartati

Syiah Kuala University, Banda Aceh, Indonesia

[email protected]

Abstract-Everyone is familiar with the term of democratic, especially in Indonesia is known as a democratic

country. However, how true democratic classroom and how it is applied in teaching mathematics? This study

examines the efforts of one elementary school teacher in Banda Aceh in implementing democratic classroom

on teaching multiplication at third grade. Data were collected through observation and field notes. The results

showed that the efforts of the teachers in implementing democratic classroom on teaching multiplication is to

involve students actively in working groups to solve problem, agree with rules and sanctions, to be a

facilitator, appreciate to students opinions, raise the open-ended problem related to multiplication, and

encourage students make a decision, foster students to respect the opinion and responsibility.

Keywords: democratic, mathematics, teaching, elementary school

1. Introduction

Multiplication is more difficult than addition and subtraction (Anghileri as cited by Barmby,

Harries & Hinggins, 2009) especially for lower grade students at primary schools. In Indonesia,

most text books do not allow students to obtain multiplication results by using their own strategies

(Zulkardi, 2002, Armanto, 2002). Teachers introduce multiplication as a repeated addition for

simple numbers and few activities then immediately ask students to memorize multiplication table.

Multiplication of 2-digit numbers both by 1-digit number and 2-digit numbers is derived by using

multiplication algorithm (Johar and Khairunnisak, 2013; Mujib & Suparingga, 2013). This

condition did not make students feel free in sharing their ideas, causing many students dislike

mathematics.

Some authors have investigated students‘ perception on considering mathematics as food. A

student said that mathematics looks like Nutela, because ―I enjoy doing it for a while because I can

do it. But too much and you get sick on it‖ (Frid, 2001). Even prospective secondary mathematics

teachers viewed mathematics as a broccoli with terrible taste but we should have to consume it

because it is good for our health, thus mathematics is necessary but they do not enjoy learning it

too much (Goos, 2006). Teachers have a key role to make a good perception of their students about

mathematics.

Teaching mathematics always need to be investigated and improved. Teachers are expected to

strive for creating activities and managing their class so that their students feel convenient in

learning mathematics in the class. Nowadays, classroom management is the most challenging

problem for teachers (Chamundeswari, 2013) and the most important part of professional teachers‘

competence (König & Kramer, 2015). This study offers one alternative for teachers to manage their

mathematics class, namely to implement democratic classroom in teaching mathematics.

Democratic behavior can be developed in education (Dewey, 1916). Education expects schools

to develop students‘ democratic skill so that they will be democratic citizens (Power, 1999). In

school environment, a class is an important place to do it (Korkmaz and Gümüseli, 2013). Teachers

have a key role to design subject matter and decide how it will be taught regarding democratic

classroom (Topkaya & Yafuz, 2011).

Teachers‘ democratic behaviors in classroom according to Aydo & Kukul (as cited in Topkaya

&Yafuz, 2011) are 1) guidance in free thinking and 2) fostering critical thinking regarding

opposing ideas. Kubow and Kinney (2000) proposed eight democratic classroom characteristics,

that is (a) active participation, (b) avoidance of text book oriented instruction, (c) reflective

mailto:[email protected]


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thinking, (d) student decision-making and problem solving, (e) controversial issues, (f) individual

responsibilities, (g) recognition of human dignity, and (i) relevance. These characteristics are the

constituent elements of open, active and engaging classroom learning. This study attempts to

identify the characteristics of democratic classroom, and how they are implemented in teaching

multiplication.

2. Method

The participant of this study is a teacher of the third grade at an elementary school in Banda

Aceh, Indonesia. Before the teacher taught multiplication, she attended a one-day workshop of

Realistic Mathematics Education (RME). The first author has designed lesson plans of teaching

multiplication for 8 lessons (Johar and Khairunnisak, 2013). During the workshop, the first author

asked 15 teachers to discuss the lesson plans. This study only focused on the sixth lesson which is

more democratic than the others. The first author as a trainer reminded participants about five

characteristics of RME as Treffers (as cited in de Lange 1987) explained. First, use a real life

problem for starting a lesson. Second, use models or symbols to represent the problem and bridge

from a concrete level to more formal one. Third, use students‘ own contribution to solve the real

life problem. Forth, interact among students during learning process facilitated by teacher to

communicate, to share, to construct the solution of a real live problem. Finally, intertwine

mathematics topic to strengthen connection of various topic in one real life problem. All of the

characteristics of RME gave possibility for teachers to implement the democratic classroom.

Data were obtained by observing the teaching multiplication process performed by the teacher

for 70 minutes. There are two observers in the study, the first author observed teachers‘ activity and

the third author observed students‘ activity. The second author took a video of a whole learning

process and pre-service teachers recorded the students‘ group discussion. Observers made a field

note of the evidence related to characteristics of democratic classroom as said by Kubow and

Kinney (2000), Korkmaz (2013), Aydo and Kukul as cited in Topkaya &Yafuz (2011), and

Bergem and Pepim (2013). We differentiate them in terms of teacher and student activities in

learning mathematics, namely

1. Active participation: Teachers interact with students to facilitate, pose questions, moderate

discussion, foster students‘ participation, and give feedback. Students should feel free to share

ideas and any opinions regarding their attitude and personal interest.

2. Avoidance of textbook oriented instruction. Teachers provide various resources, without only

focusing on a textbook. Teachers design a lesson creatively to foster students‘ abilities to make

decision and solve problems. Students investigate their own solution for solving problems,

they do not follow a textbook

3. Reflective thinking. Teachers give students an opportunity to understand a problem critically

and explain their reason in solving the problem. At the end of the lesson, teachers give

students the opportunity to undertake a review of the activities which they have carried out,

explaining why the activity is important for them, what difficulties they face during the

learning process, etc.

4. Decision-making. Teachers and students participate in making all decisions, such as the

solution of problem, class rules and their sanctions, objectives, contents, methods, and

evaluation. All of them are implemented consistently during teaching and learning process

5. Open ended problem. Teachers pose an open problem familiar to students. Through the

problem, students discuss and examine them in multiple perspective/ways. Teachers give

students opportunities to decide their own strategies to solve the problem.

6. Individual responsibility. Teachers develop a warm and trusting atmosphere, provide

constructive feedback when individual comments are offered, and provide sharing

opportunities. Students are responsible individually to share their idea to peer, small group,

and large group. They give reasons for their idea

7. Recognition of human dignity. Teachers appreciate students‘ response even though it is

incorrect or incomplete. Teachers divide group member heterogeneously. Students appreciate

their friends and their teacher


ISBN 9786021570425 MATH-167

8. Relevance. Teachers design classroom activities that are relevant to students‘ interest and

concern

The data were analyzed by watching the video for several times and transcript all conversation

during lesson then compared the transcription to the observers‘ field note.

3. Results and Discussion

Teacher introduced the real life problem for starting her lesson as presented in the figure 1

below.

Figure 1. The arrangement of chairs problem

This study explains an example of evidence for each characteristic of democratic classroom in

teaching multiplication.

Characteristic 1: Active participation

Teacher introduced problem by shown the picture of chairs arrangement. The teacher engaged

students to participate actively in understanding problem as the script below.

Teacher : Ok, where do we usually see this chair arrangement?

Am : At Economic Faculty.

Teacher : Anywhere else?

Af : At Markaz [an Islamic community]

Teacher : At Markaz. If the chairs [arrangement] are like this [point the picture] can we reach

this chair [the middle chair]?

Students : No

Teacher : Is it difficult?

Students : Yes.

Students : No.

Teacher : It is difficult, isn‟t it? So, can we separate them? This is how we separate them

[pointing at the chair arrangement in the classroom].

Isn‟t it?

The picture is about the arrangement of chairs in a hall. There are 5 rows of chairs,

each row consists of 16 chairs.

Is it enough chair for 90 people?

How do you arrange the chairs so that people can find their seat quickly?

How do you calculate the number of chair based on your arrangement?


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Students : (Nodding)

Teacher : We want to count the chair, right? But we separate them in order to be able to count

them more easily. Then, we can use multiplication.

The teacher implemented question-answer method to encourage the students in understanding

the problem. All of students paid attention to the teachers‘ question. Most of them answered the

question in chorus. Then the teacher gave 80 small white stones to each group as representations of

the chairs. The teacher asked the students to arrange them on their tables and the students put rulers

or pens aisle among stone arrangements. All of the groups arranged the stone well but they did not

write the multiplication to count all of stones. Therefore, the teacher facilitated the students when

they solved the given problems. Dialogue below is one example of the conversation.

Teacher : Okay, now, this is sixteen multiplied by … ?

Sixteen, sixteen, sixteen, sixteen, sixteen.

What is the total? How do we write the multiplication?

Students : [No answer]

Teacher : [Asking one of students] How do we write the multiplication Af?

Af : [No answer, it seems that he was thinking]

Teacher : Am, how should we write the multiplication?

Am : [Acting as if he had gave up]

Students : [Together] Sixteen times five.

Teacher : What? Sixteen times five?

Kh : Five times sixteen.

Teacher : Five times sixteen.

What is the correct answer?

Students : Five times sixteen.

Teacher : Five times sixteen. Ok, so, do we agree on five times sixteen?

As can be seen in the conversation above, the teacher tended to accept the students‘ answer,

whether it was true or false. When the students gave incorrect answer, the teacher did not directly

reject the answer, but asking for clarification from the student until they came up what the right

answer was. Then the teacher came to groups. None of the groups was successful in using the stone

arrangement to help them get the number of stone from 5x16. The teacher asked the students to pay

attention to how to find the result of 5×16based on stone arrangement. The teacher gave an

example on the board as shown in the following dialogue.

Teacher : If I give seven stones in this group [the group on the left side of the aisle], five times

seven. How many stones remain in this group [the group on the right side of the

aisle]?


Teacher : How many stones remain?

We already got seven. How many remain?


Teacher : (Walking toward the students) Hello.. How many do we get left? How many?

Sulthan : Nine.

Teacher : How many is it?

Sulthan : Nine.

Teacher : Yes, nine. So it is five times …?

Students : Nine.

Teacher : (Writing on the board 5×7 = 35

5×9 = 45 +

80

You can continue your work in many ways


ISBN 9786021570425 MATH-169

The role of teacher in learning multiplication is to be a facilitator rather than an authoritarian

(Korkmaz and Gümüseli, 2013; Tse in Ahmad et al., 2014). This learning environment have

practiced by Kubow and Kinney (2000) to develop democratic skills to middle school teachers for

eight-day institute in Hungary, the instructors at the institute moderated discussion and to be

facilitators.

Another effort made by the teacher to foster students‘ active participation in teaching

multiplication was to give a reward. At the end of the lesson, the teacher provided ―star‖ for the

students who were active during the lesson. These activities in line with Kubow and Kinney

(2000), which is give feedback for participants.

Characteristic 2: Avoidance of text book oriented instruction

The lesson was based on an open-ended problem about arranging chairs to represent

multiplication of 5×16, which was not taken from the textbook. During the lesson, the teacher and

students did not focus on the textbook. Through the problem, the students worked collaboratively

with their group members to re-arrange the chairs so that they could find many representations of

multiplication that had the same result as 5 × 16. By using 80 small white stones as tools to

represent the chairs, the students made some ‗aisles‘ between those ‗chairs‘ and then wrote down

the multiplications for those arrangements. Thus, the students used their own strategy to solve the

problem. Figure 2 below showed how some students put their pencils and rulers between the stones

as representation of ‗aisles‘.

Figure 2. One group‘s strategy to arrange chairs

Characteristic 3: Reflective thinking

During the lesson, the teacher asked the students to think critically to represent the result of

5×16 in many ways by using manipulative. Teacher asked students to give reason whether their

answer was correct. The following conversation is one of examples when the teacher encouraged

the students to do reflective thinking.

Teacher : Multiplication, what is the multiplication [representation of the number of chair for

each group in multiplication symbol]?

Oh, too many „aisles‟you have!

Mz : For „aisles‟, is it Ok?

Students : It is ok for three, one , or two [„aisles‟]

Teacher : Put like this, like this [move a pen in horizontal position to vertical one]

Mz : Are you ready? Ready? [students put something for each „aisles‟]

Teacher : Are you ready? Why do you have too many „aisles‟?

How do you calculate the number of chair?


ISBN 9786021570425 MATH-170

Teacher asked students in group to give reason of their work whether their choice was the best

position of ‗aisles‖ between those ‗chairs‘ so that students can calculate the number of chairs

easily. Then, teacher asked the students from the other group about which multiplication was

incorrect to check their work as dialogue below.

Teacher : [Come to Ys and Fs group]. Ok, this is the same. Pay attention to this [teacher

circle the first strategy, on the left side of figure 3]

This one [the second strategy, on the right side of Figure 3]. This is the correct

one.This number [circle 5 and 11] are different. The same number for what? [for

multiplyer or multiplican]

Figure 3. Student did not split multiplication consistently

In teaching multiplication, teacher posed some reflection questions to students to arrange the

chairs and their ‗aisles‘ so that the students wrote the multiplication symbol for each group of

chairs, rather than the teacher gave the final solution to students. The students were active to

construct their mathematical concept through reflective thought (van de Walle, 1990: 32).

Implementation of reflective thinking according to Kubow and Kinney (2000) could be asked

students to pay more attention all their friends‘ response in class discussion and asked individual

response about the activities they engaged in. In teaching multiplication, teacher did not give

opportunities to students for communicating their feeling after completion of activities about

arranging chairs. It was not enough skill for students to develop democratic interaction.

Characteristic 4: Student decision-making

The teacher asked the students to make a decision about their solution to solve chairs

arrangement problem related to multiplication. During lesson for implementation of democratic

classroom, Kubow and Kinney (2000) provided participants to make their own decisions including

the way to solve problem.

Teacher in this research asked students to discuss the classroom rules and its sanction, as the

dialogue below.

Teacher : Ok, do we agree?

Students : Yes.

Teacher : What will we do to people who do not obey our agreement?

Fh : Standing up on one foot like this [demonstrating how to stand], Ma‟am.

Teacher : How about that? Do you agree?

Students : No.

Teacher : No. So what is the sanction?

Am : Like this [standing up with his two hands crossed and holding his ears]

Sl : Dancing, Ma‟am.

Teacher : Dancing. Agree?

Students : Agree.

Teacher : Agree.

After the rule has been decided, the teacher and the student applied it so that the students

became more discipline. Sometimes, when the teacher needed students‘ attention, she reminded

students about the rule ―red flag‖ it means students have to keep silent and pay attention to her.


ISBN 9786021570425 MATH-171

Teacher : It‟s red flag. Listen.

Students : [Not paying attention to the teacher]

Teacher : Hallo, when I raise red lag, no one talks

Students : Sit neatly.

An effective classroom management is depending on the teacher‘s capability to overcome

annoyance and disciplinary problems (Koinin in Tal, 2010). Students involved in decisions about

classroom rules and sanctions (Korkmaz and Gümüseli, 2013, Ahmad et al., 2014).

Characteristic 5: Open-ended problem

As described in characteristic 2, the problem proposed in this lesson was an open-ended

problem. The teacher asked the students to solve the problem in any ways as can be seen in the

following dialogue.

Teacher : Now, every group gets one pouch of stones.

Pretend that the stones are chairs. Arrange it.

What is the rule? How many rows should there be?

Student : Five.

Teacher : Five. So, in a line there are how many chairs?

Student : Sixteen.

Teacher : Ok.

With only a small help from the teacher, the students could produce many multiplications from the

arrangement they made as can be seen from the following figures.

Figure 4. Students producing many multiplications as representation of the chair arrangement

Open-ended problem provide students to develop their own mathematics problem solving

(Kroesbergen & van Luit, 2002). Students were able to find the result of 5×16 in many ways of

splitting rather than using standard algorithm of multiplication. To implement democratic

classroom in school practice during eight-day institute for teachers, Kubow and Kinney (2000)

delivered the controversial issues as open-ended problem so that the participants solve them in

multiple perspective. Teachers discussed the similarities and differences of democratic attitude in

national curriculum and school practice.

Characteristic 6: Individual responsibilities

Through an open-ended problem, the students had responsibility to come up with many

strategies to split the multiplication of 5 × 16 so that it became easier to get the result. The teacher

reminded students to finish their work immediately. She informed that she would give ‗star‘- a

shaped like a star on a piece of paper- as a feedback to student who finished their work creatively.

Teacher : Come on, who finish faster gets two stars.

Have you got the result?.


ISBN 9786021570425 MATH-172

Come on.. Come on..

Students : [Continuing working in their groups]

Teacher : Okay, who finish faster will get two stars.

The group who finish faster get two stars.

Come on, you have ten more minutes. I want to see your result.

During the group discussion, the students felt responsible to finish their work, thus they asked

the teacher to give them extra time to finish the work.

Teacher : [Giving comments to one group‟s work]

Yes. Oh, do you want to try it another way?

Sl : Yes [moving his pencil]

Teacher : Ok, but the time is over.

Students : Give us a moment, Ma‟am. Give us a little more time.

Teacher : What? Do you need more time?

Ok, five minutes. Hurry up.

Students were passionate to find many ways to split 5 × 16. They were responsible to solve the

open-ended problem. Responsibility of the students to finish their work is one part of democratic

classroom objective; it aims to increase the independence and self-confidence of students (Kubow

and Kinney, 2000; Korkmaz and Gümüseli, 2013; Topkaya &Yafuz, 2011). In this research, each

student contribute to share her/his ideas for arranging chairs to their partner in group then one

member of group collect all of possibilities to get the result of 5×16 in many ways of splitting.

They wrote their ideas on the poster paper. Then teacher hung each paper poster of group on the

wall. Nevertheless, there is one of seven group find the result of 5 × 16 using trial and error for

many times as figure 5 below.

Figure 5. Students use trial and error strategy to find the result of 5 × 16

Teacher guided them to understand the problem. Then, that group found only one way to get

the result of 5 × 16, which is

5 × 5 = 25

5 × 10 = 50

5 × 1 = 5

80

After all of paper hung on the wall, teacher gave feed back to each group and reminded all of

group to find the result of 5 × 16 effectively and shortly.

Characteristic 7: Recognition of human dignity

As previous classes, the students were allowed to choose their own seat when entering the

classroom. They sat in pair of boy (B) or pair of girl (G). Figure 6 shows the illustration of

students‘ seat arrangement in the classroom. There were 15 boys and 14 girls at that class.


ISBN 9786021570425 MATH-173

Front

Figure 6. The position of students‘ group in the classroom

The teacher asked the students to sit in groups consisting of students sitting near one another

to save time. Therefore, some groups are consisted only male, some only females and the others

both. The way the teacher instructed the students to sit in groups is represented by the following

conversation.

Teacher : Now please sit in groups.

You have two minutes to make your groups.

Teacher : [Helping students sitting in groups]

St : Ms. Cut. [Yh] please join us in this group.

Teacher : What‟s about here? Oh, alright, here [St‟s group] say Yh.

Yh : (Moving his chair to the front, to St‟s group)

Mz : Join is here! [in his group].

Teacher : Where do you want to sit Yh? Here [St‟s group] or there [Mz‟s group] ?

Which one would you like to choose?

Yh : Here is fine [in St‟s group].

Teacher : Okay.

The teacher asked the students to choose which group they wanted. The teacher did not

consider gender in making groups. Heterogeneity in terms of ability is also possible because where

the students sit were not due to their ability but it was due to students who first chose the seat.

The teacher also motivated the student to respect their friends‘ opinion. One of the situations

when the teacher asked students to respect their friend was quoted in the following conversation.

Teacher : Ok, look here.

Hello, Ft.. Listen to your friend [explanation].

Ok, look at Am [Am was solving a problem on the whiteboard].

In this research, students have allowed to choose their seat, their peer, and their group. It

means the teacher divided the group no gender bias. This is on example of anti-sexism as Korkmaz

and Gümüseli (2013) said. Students also be reminded to respect to their friends and teacher as well.

Here, teacher concern to the equity principle according to NCTM (2000). Students in the

democratic classroom solve mathematics problem in multi ways (Daher, 2012) so that students feel

highly appreciated in the class. Teachers should be practice how to recognize the democratic

society in the classroom (Topkaya &Yafuz, 2011) and to be model for students recognizing human

dignity in the classroom.

Characteristic 8: Relevance

The other characteristic of a democratic classroom is relevance (Kubow and Kinney, 2000;

Korkmaz and Gümüseli, 2013). The lesson should be relevant with the students. In this study, the

teacher proposed a chair-arrangement problem that was familiar to the students and they knew

B B

B B

B B

B B

B

B B

G G

G G

B B

G G

G G

G G

G G

B B

G G


ISBN 9786021570425 MATH-174

where and why people need to arrange chairs. Through this problem, the students became

enthusiastic to learn about the subject. The following dialogue shows how familiar the problem was

to students.

Teacher : Ok, where do we usually see this chair arrangement?

Am : At Economic Faculty [in university].

Teacher : Anywhere else?

Af : At Markaz [an Islamic community]

Teacher : At Markaz. If the chairs [arrangement] is like this [point the picture] can we reach

this chair [the middle chair]?

Is it difficult?

Students : Yes.

The content of curriculum should be have relation with students‘ experiences (Korkmaz and

Gumuseli, 2013) due to learning effect students‘ interest and students‘ interest effect learning

(Nyman and Emanuelsson, 2013: 116).

4. Conclusion

The teacher efforts to implement eight characteristicsof democratic classroom are as below.

Characteristics 1: Active participation

a. The teacher facilitated students in solving the problem given.

b. The teacher gave ‗star‘ for the students who were active during the lessons

c. The teacher accepted the students‘ opinion so that they felt free to express their opinion. The

students also respected their friends‘ opinion.

Characteristics 2: Avoidance of text book oriented instruction

The students solved open-ended problem given by the teacher. The problem that was about

arranging chair to represent multiplication 16×5 was not taken from Indonesian text book

Characteristics 3: Reflective thinking

Teacher asked students to give reason for their work and check it. Nevertheless, the teacher did not

give opportunities to students for communicating their feeling after completion of activities

because of limited time.

Characteristics 4: Decision-making

1) The teacher and the students compromised a new rules, such as:

a. Rule of red and yellow flag followed by its sanction.

b. The teacher would not come to groups that were noisy

2) The teacher and the students applied the rules so that the students became more discipline or

more quite to listen the teacher as below:

a) Remind the red flag rules .

b) Because students talk to each other in groups on the material, the teacher uses the ever-

agreed rules, namely the pat one, pat two, and pat three, so that the students silent

Characteristics 5: Open ended problem

The teacher proposed open-ended problem about arranging chairs as representation of 16×5 in

many ways, to get the result of 16×5

Characteristics 6: Individual responsibility

The students collaboratively determined the result of 16×5 in various ways. They asked teacher to

give them the extra time for writing their answer on poster paper

Characteristics 7 Recognition of human dignity

The teacher accepted students‘ opinion, so that the students felt free to deliver their opinion. The

students also respected their friends‘ opinion. Teacher allowed students to choose their seat in peer

and group. It is not bias gender.


ISBN 9786021570425 MATH-175

Characteristics 8: Relevance

Teacher showed arranging chairs problem related to multiplication. It is relevance to students‘

interest at primary school.

This study has some implications. First, the eight characteristics of democratic classroom help

teacher to manage their class optimally so that students will convenience to learn mathematics. It

implies to students understand mathematics deeply. Second, the eight characteristics of democratic

classroom are to practiced in classroom rather than to memorized them by teachers. Finally, teacher

educators from university need to work together with teachers in implement the characteristics of

democratic classroom. Both of teacher educators and teachers got the benefit. Teacher educator can

use the video of classroom activities related to democratic classroom for pre service teacher.

References

Ahmad, I., Said, H., Mansoq, S. S. S., Mokhtar, M., & Hasan, Z. 2014. How teacher moderates the

relationship between democratic classroom environment and student engagement. Journal

Review of European Studies, 6(4): 239-248

Armanto, D. (2002) Teaching Multiplication and Division Realistically in Indonesian Primary

Schools: A Prototype of Local Instructional Theory. Thesis University of Twente, the

Netherlands.Enschede: PrintPartnersIpskamp.

Bergen, O. K. &Pepin, B. 2013. Developing Mathematical Proficiency and Democratic Agency

through Participation-an Analysis of Teacher-Student Dialogues in a Norwegian 9th Grade

Classroom. In Kaur, B., Anthony G., Ohtani M., & Clarke, D. (Eds). Student Voice in

Mathematics Classroom a round the World. Rotterdam: Sense Publisher.

Barmby, P. & Harries, T., Higgins, S. (2009). The array representation and primary children‘s

understanding and reasoning in multiplication. Education Studies in Mathematics. 70: 217-

241.

Chamundeswari, S. (2013). Teacher Management Style and their influence on performance and

leadership development among students at the secondary level. International Journal of

Academic Research in Progressive Education and Development. 2 (1). 367-418

Daher, W. (2012). Student teachers‘ perceptions of democracy in the mathematics classroom:

Freedom, equality and dialogue. Pythagoras. 33(2) 2-11

de Lange, J. (1987). Mathematics, insight, and meaning. The Netherlands, Utrecht: OW& OC.

Dewey, J. (1916). Democracy and education. New York: Macmillan Inc.

Frid, S. (2001) Food for thought. The Australian Mathematics Teacher. 57(1). 12-16

Goos, M. (2006). Why teachers matter. Australian Mathematics Teacher. 62(4). 8-13

Johar, R. & Khairunnisak, C. (2013) Supporting Students in learning multiplication through

splitting strategy. In Proceeding th First South East Asia Design/Development Research

(SEA-DR) International Conference. Sriwijaya University, Indonesia. 344-354.

König, J. & Kramer, C. (2015, online first) Teacher professional knowledge and classroom

management: on the relation of general pedagogical knowledge (GPK) and classroom

management expertise (CME). ZDM the International Journal on Mathematics Education.

1-13

Korkmaz, H. E. &Gümüseli. (2013). Development of the democratic education environment scale.

International Journal of Education Sciences. 52(1) 82-98

Kroesbergen, E. H. & van Luit, J. E. H. (2002) Teaching multiplication to low math performers:

guided versus structured instruction. Instructional Science. 30. 361-378

Kubow, P. K. & Kinney, M. B. (2000) Fostering democracy in middle school classrooms: insights

from a democratic institute in Hungary. The Social Studies. 91(6) 265-271.

Mujib, A. & Suparingga, E. (2013). Upaya mengatasi kesulitan siswa dalam operasi perkalian

dengan metode Latis. In Prosiding Seminar Nasional Matematika dan Pendidikan

Matematika, Yogyakarta State University, 9 November 2013.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School

Mathematics. Reston, USA: NCTM.


ISBN 9786021570425 MATH-176

Nyman, R. & Emanuelsson, J. (2013) What do students attend to? Students‘ task-related attention

in Swedish setting. In Kaur, B., Anthony G., Ohtani M., & Clarke, D. (Eds). Student Voice in

Mathematics Classroom a round the World. Rotterdam: Sense Publisher.

Power, F. C. (1999 ) Education toward democracy: how can it be accomplished? Prospects. Vol

XXIX (2)

Tal, C. (2010). Case studies to deepen understanding and enhance classroom management skills in

preschool teacher training. Early Childhood Education Journal. 38. 143-152

Topkaya, E. Z. & Yafuz, A. (2011) Democratic values and teacher self-efficacy perceptions: a case

of pre-service English language teachers in Turkey. Australian Journal of Teacher

Education. 36(8) 32-49

van de Walle, J. (1990). Elementary school mathematic: Teaching developmentally. New York:

Longman

Zulkardi (2002) Developing a Learning Environment in Realistic Mathematics for Indonesian

Student Teachers. Thesis University of Twente, the Netherlands. Enschede:

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