Learning Mathematics in a Mobile App-Supported Math Trail Environment

148 Pages·2018·5.41 MB·English

by  Adi Nur Cahyono

SPRINGER BRIEFS IN EDUCATION
Adi Nur Cahyono
Learning
Mathematics in
a Mobile App-
Supported Math
Trail Environment
123
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Adi Nur Cahyono
Learning Mathematics
in a Mobile App-Supported
Math Trail Environment
Adi Nur Cahyono
Department of Mathematics
Universitas Negeri Semarang
Semarang, Jawa Tengah, Indonesia
ISSN 2211-1921 ISSN 2211-193X (electronic)
SpringerBriefs in Education
ISBN 978-3-319-93244-6 ISBN 978-3-319-93245-3 (eBook)
https://doi.org/10.1007/978-3-319-93245-3
Library of Congress Control Number: 2018945226
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Preface
Considering mathematics as a human activity, as in Freudenthal’s educational credo,
has led to the view of mathematics education as a process of doing mathematics that
results in mathematics as a product. As a human activity, mathematics is also an
activity of solving problems. Bringing problem-solving practice into the educa-
tional process can be useful as a tool for learning mathematics. Through this pro-
cess, learners have the opportunity to reconstruct the mathematical experience and
gain new mathematical knowledge. Furthermore, encouragement is needed to moti-
vate learners to engage in this process.
However, the current public understanding of mathematics and its teaching and
learning process is still not satisfactory. Many students do not enjoy engaging in
mathematics activities. Mathematics is also sometimes considered to be a subject
that is difficult, abstract and far from students’ lives, in terms of both daily life and
occupation. This problem leads mathematicians and mathematics educators to think
of ways to popularize mathematics among the public.
A variety of projects have been developed and implemented in numerous coun-
tries to raise public awareness of mathematics. For instance, in an effort to commu-
nicate mathematics to the public, in 2008, the German “Year of Mathematics” was
held successfully. One positive message from this event was “Du kannst mehr
Mathe, als Du denkst” (You know more maths than you think). This message
emphasizes the importance of working on the public’s views of what mathematics
is about and what mathematicians do. The event also focused on news and chal-
lenges, as well as images and jobs.
In the same spirit, the MATIS I Team from IDMI Goethe-Universität Frankfurt,
Germany, has also given attention to this subject by developing and implementing a
project called MathCityMap. This project comprises math trails around a city that
are supported by the use of GPS-enabled mobile phone technology. It aims to share
mathematics with the public (especially students), encouraging them to be more
involved in this field. The project offers an activity that is designed to support stu-
dents in constructing their own mathematical knowledge by solving the prepared
mathematical tasks on the math trail and interacting with the environment, includ-
ing the digital environment.
v
vi Preface
My PhD research is a part of the MathCityMap project. By following a design
research paradigm, it focused on the development of a model for a mobile app-
supported math trail programme and the implementation of this programme in
Indonesia tailored to that country’s situation. The implementation included a field
empirical study to explore its effect on students’ motivation in mathematics, their
performance in mathematics and teachers’ mathematical beliefs.
The results of the research are presented through my dissertation, which is sub-
mitted for the degree of Doctor rerum naturalium (Dr.rer.nat.) at Faculty 12
(Computer Science and Mathematics), Goethe-Universität Frankfurt, Germany. The
research described herein was conducted under the supervision of Professor
Matthias Ludwig at the Institute of Mathematics and Computer Science Education,
Faculty of Computer Science and Mathematics, Goethe-Universität Frankfurt,
between September 2013 and August 2016. These results have also been reviewed
by Professor Marc Schäfer, SARChI Mathematics Education Chair at Rhodes
University, South Africa.
Frankfurt, Germany Adi Nur Cahyono
March 2017
Acknowledgements
This brief is the result of my PhD study at the Institute of Mathematics and Computer
Science Education, Goethe-Universität Frankfurt (GUF), Germany. It was imple-
mented in collaboration with the Department of Mathematics, Semarang State
University (UNNES), Indonesia, and nine secondary schools in the city of Semarang
with the agreement of the Department of Education of the city of Semarang,
Indonesia. This study was funded by the Islamic Development Bank (IDB), Jeddah,
Saudi Arabia, through an IDB-UNNES PhD fellowship programme. It would not
have been possible without the support, guidance and help of many people around
me. Therefore, I would like to dedicate this section to acknowledging these
people.
First, I would like to express my sincere gratitude to my Doktorvater/ supervisor,
Professor Matthias Ludwig (Goethe-Universität Frankfurt, Germany), who has sup-
ported and guided me with his impressive knowledge and expertise. It was a great
opportunity for me to do my PhD research under his guidance. He guided me to see
things in a comprehensive and coherent way that was not only important for my
PhD work but will also be essential for my future professional life. He not only gave
me professional and academic support but also personal support. Thank you very
much for this experience, Professor Ludwig.
I am also indebted to Professor Marc Schäfer (Rhodes University, South Africa),
my second supervisor, for his valuable guidance and support. He gave valuable
feedback and input that stimulated me to further reflect on my own thought and
works. Thank you very much for your support, enthusiasm, knowledge and
friendship.
I would like to acknowledge the IDB and the PMU IDB-UNNES for the scholar-
ship I received. I would also like to express my gratitude to UNNES, the university
where I work as a lecturer, for giving me permission and encouragement to pursue
my doctoral degree in Germany.
During my PhD study, I received support and help from my colleagues at the
Institute of Mathematics and Computer Science Education, GUF (thanks to Phillip,
Xenia, Hanna, Sam, Jorg, Iwan, Martin and Anne), and the Department of
Mathematics, Faculty of Mathematics and Natural Sciences, UNNES. I am also
vii
viii Acknowledgements
deeply indebted to the teachers and students in Semarang, Indonesia, who partici-
pated in my studies. The completion of my PhD research would never have been
possible without their help and cooperation. I would like to extend my gratitude to
KJRI Frankfurt (General Consulate of the Republic of Indonesia in Frankfurt am
Main) and to all my friends during my stay in Germany.
Above all, I would like to express my immeasurable gratitude to my wife, Chatila
Maharani, for her love, understanding, unfailing encouragement and support.
Without her unconditional support, I would never have completed my study.
Although she was also busy with her doctoral study, she was always there whenever
I needed her. To my daughter, Calya Adiyamanna Putri, you are a great kid who
always cheerfully follows our journeys, and to my son, Arbiruni Neumain Cahyono,
our spring child, who was born in the busy time when I prepared this dissertation
submission. I dedicate this brief to the three of you. Special thanks to my parents
(Bapak Harjono and Ibu Rusmini), my parents-in-law (Bapak Suwignyo
Siswosuharjo and Ibu Nurhayati), my sisters, my brothers, my nephews and my
nieces, who have always supported and encouraged me.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 What Is the Problem? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Can the Mobile App-Supported Math Trail Programme
Offer a Solution? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Design of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Topic of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Aims of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.4 Approach of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.5 Phases of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 T he Book’s Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 T heoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 C onstructivism in Mathematics Education . . . . . . . . . . . . . . . . . . . . 17
2.2 Students’ Motivation in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Students’ Performance in Mathematics . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Teachers’ Mathematical Beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Didactical Situation in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Outdoor Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Technology in Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . 32
2.8 Conceptual Framework of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3 The MathCityMap Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1 The Concept and the Goals of the Project . . . . . . . . . . . . . . . . . . . . . 43
3.2 Components of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.1 Mathematical Outdoor Tasks . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Mathematical City Trips . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.3 Map-Based Mobile App . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.4 MathCityMap Community . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
ix