Untitled - RP2U Unsyiah
-
Upload
khangminh22 -
Category
Documents
-
view
0 -
download
0
Transcript of Untitled - RP2U Unsyiah
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
ISBN 9786021570425 MATH-165
OME-16 Implementation of Democratic Classroom in Teaching
Multiplication
Rahmah Johar*, Cut Khairunnisak, Suhartati
Syiah Kuala University, Banda Aceh, Indonesia
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
ISBN 9786021570425 MATH-166
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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?
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
ISBN 9786021570425 MATH-168
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]?
Students : [No answer]
Teacher : How many stones remain?
We already got seven. How many remain?
Students : [No answer]
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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?
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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.
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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?.
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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.
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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.
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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.
Proceedings International Conference on Mathematics, Sciences and Education, University of Mataram 2015 Lombok Island, Indonesia, November 4-5, 2015
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:
PrintPartnersIpskamp.