Learning Mathematics in a Mobile App-Supported Math Trail Environment - Cahyono, Adi Nur
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This brief presents the results of a study on the development of the mobile app-supported math trail program for learning mathematics. This study is a part of the MathCityMap-Project, a project of the MATIS I Team from IDMI Goethe-Universität Frankfurt, Germany, that comprises math trails around the city that are supported by the use of GPS-enabled mobile phone technology. The project offers an activity that is designed to support students in constructing their own mathematical knowledge by solving the prepared mathematical tasks on the math trail and interacting with the environment,…mehr

Produktbeschreibung
This brief presents the results of a study on the development of the mobile app-supported math trail program for learning mathematics. This study is a part of the MathCityMap-Project, a project of the MATIS I Team from IDMI Goethe-Universität Frankfurt, Germany, that comprises math trails around the city that are supported by the use of GPS-enabled mobile phone technology. The project offers an activity that is designed to support students in constructing their own mathematical knowledge by solving the prepared mathematical tasks on the math trail and interacting with the environment, including the digital environment.

The brief focuses specifically on the development of a model for a mobile app-supported math trail programme and the implementation of this programme in Indonesia. It offers both an empirical exploration of its implementation as well as critical assessment of students' motivation in mathematics, their own performance, as well as teachers' mathematics beliefs. It concludes with a future-forward perspective by recommending strategies for implementation in schools, among the general public of the existing math trails (including its supporting tool). It also discusses strategies for developing and designing new trails and suggests further research in other geographical regions and contexts for continued project development and implementation. Learning Mathematics in a Mobile App-Supported Math Trail Environment articulates an innovative and exciting future for integrating real mathematical tasks and geographic and digital environment into effective mathematics education.

  • Produktdetails
  • SpringerBriefs in Education
  • Verlag: Springer / Springer International Publishing / Springer, Berlin
  • Artikelnr. des Verlages: 978-3-319-93244-6
  • 1st ed. 2018
  • Erscheinungstermin: 23. August 2018
  • Englisch
  • Abmessung: 235mm x 155mm x 8mm
  • Gewicht: 242g
  • ISBN-13: 9783319932446
  • ISBN-10: 3319932446
  • Artikelnr.: 52510019
Autorenporträt
Adi Nur Cahyono is a Lecturer in the Department of Mathematics at Semarang State University in Indonesia. He completed his PhD in the Institute for Mathematics and Computer Science Education at the Johann Wolfgang von Goethe University in Frankfurt am Main, with a special research focus on the didactics of mathematics. He has presented and published several papers in his research area in national and international forums and scientific journals.
Inhaltsangabe
Adi Nur Cahyono

About the author

Dr.rer.nat. Adi Nur Cahyono, S.Pd., M.Pd. was born on 11 March 1982 in Banjarnegara, Central Java, Indonesia. In 2000, he completed his secondary education at Senior High School in Karangkobar, Banjarnegara, and started his university studies in Mathematics Education at Universitas Negeri Semarang (UNNES), Indonesia, where he obtained a bachelor degree in 2004. He pursued a master's degree in Mathematics Education at Universitas Negeri Semarang in 2006 and graduated in 2008. Beginning in 2005, he worked as a senior high school mathematics teacher for three years, and in 2008 he worked as a lecturer in mathematics education in an institute of teacher training and education science for one year. In 2009, he started a new job as a civil servant lecturer at the Department of Mathematics of the Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang.

He also has experience as an academic staff member at the Centre of Development of Education Media (PPMP), Universitas Negeri Semarang, and as a reviewer of Interactive Educational Multimedia Production at the Department of ICT Development for Education (BPTIKP), Central Java, Indonesia. He teaches mathematics education, especially geometry and the use of ICT in Mathematics Education, and he has participated in several research projects in these areas. He has presented and published several papers in his research area in national and international forums and scientific journals. In 2006, he was recognised as the winner of a competition of teachers with smart ideas held by Citibank Indonesia and the Indonesian Hope Foundation.

In 2013, he was awarded a PhD scholarship from the Islamic Development Bank (IDB), Jeddah, Saudi Arabia, through an IDB-UNNES PhD fellowship program. In the same year, he started his PhD study at the Institute for Mathematics and Computer Science Education, J. W. v. Goethe- University Frankfurt am Main, Germany, under the supervision of Prof. Dr. Matthias Ludwig from Goethe Universit Frankfurt and Professor Marc Schaefer, Ph.D from Rhodes University, South Africa. His PhD research focused on the MathCityMap-Project for Indonesia. In 2017 he was awarded a doctoral degree in Natural Sciences (Dr.rer.nat.) in the speciality of Didactics of Mathematics after he furnished evidence of his ability in regularly conducted doctoral proceedings through his dissertation entitled "Learning mathematics in a mobile app supported math trail environment". In the same year, he resumed his position as a lecturer at Universitas Negeri Semarang to teach in the Undergraduate Program and Postgraduate Program of mathematics education.

Die Deutsche Nationalbibliothek verzeichnet diese Publikation

in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://d-nb.info/1137348240 abrufbar.

Learning mathematics in a mobile app-supported math trail environment

Springer

Adi Nur Cahyono

Learning mathematics in a mobile app-supported math trail environment

Springer

Adi Nur Cahyono aus Banjarnegara (Indonesien)

E-mail: cahyono@math.uni-frankfurt.de/ adinurcahyono@mail.unnes.ac.id

Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) angenommen vom Fachbereich 12 (Informatik und Mathematik) der Johann Wolfgang Goethe-Universität in Frankfurt am Main, 2017.

D30

Dekan: Prof. Dr. Andreas Bernig Erstgutachter: Prof. Dr. Matthias Ludwig

Zweitgutachter: Prof. Marc Schäfer, PhD. (Rhodes University, South Africa)

Datum der Disputation: 26. Juni 2017

Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://d-nb.info/1137348240 abrufbar.

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 educational process can be useful as a tool for learning mathematics. Through this process, learners have the opportunity to reconstruct the mathematical experience and gain new mathematical knowledge. Furthermore, encouragement is needed to motivate 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 countries to raise public

awareness of mathematics. For instance, in an effort to communicate 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 challenges, 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 mathematics. The project offers an activity that is designed to support students in constructing their own mathematical knowledge by solving the prepared mathematical tasks on the math trail and interacting with the environment, including the digital environment.

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 submitted for the degree of Doctor rerum naturalium (Dr. rer. nat.) at Faculty 12 (Computer Science and Mathematics), Goethe University 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 University 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, March 2017 Adi Nur Cahyono

Acknowledgements

This thesis is the result of my PhD study at the Institute of Mathematics and Computer Science Education, Goethe University Frankfurt (GUF), Germany. It was implemented 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 University Frankfurt, Germany), who has supported 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 scholarship 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 deeply indebted to the teachers and students in Semarang, Indonesia who participated in my studies. 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 Republic Indonesia 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 dissertation 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.

Zusammenfassung

Das MathCityMap-Projekt ist ein Projekt der Arbeitsgruppe MATIS I des IDMI der Goethe-Universität Frankfurt. Es ist ein Projekt innerhalb des Math-Trail- Programms, das durch den Einsatz mobiler Technologie unterstützt wird. Die vorliegende Studie untersucht dieses Projekt speziell in Indonesien. Es wurde mittels folgendem Forschungsdesign durchgeführt und fand in einer vorbereitenden und drei nachfolgenden Phasen statt (eine Entwurfsphase, eine kleine Pilotversuchsphase und eine groß angelegte Feldversuchsphase).

Die Ziele dieser Studie konzentrierten sich auf das Design einer App und von Math-Trails rund um die Stadt, die Umsetzung des App-unterstützten Math-Trail-Programms in Indonesien und insbesondere die Untersuchung der Auswirkungen auf die Mathematik-Motivation und - Leistung der Schüler und auf die mathematische Überzeugungen der Lehrer. Die Ergebnisse dieser Studie und der Beitrag zur Entwicklung des MathCityMap- Projektes werden in dieser Arbeit vorgestellt.

Diese Studie wurde in einem theoretischen Rahmen, basierend auf der konstruktivistischen Theorie in der Mathematikausbildung, durchgeführt. Dabei wird davon ausgegangen, dass die Schüler im Mathematiklernprozess

ihr mathematisches Wissen aktiv erweitern, indem sie neu gewonnene Informationen mit ihrem bisherigen Wissen verbinden. Lehrer fungieren als Vermittler und sollen in der Lage sein, mathematische Probleme vorzubereiten und den Schülern Anleitung oder Unterstützung bei der Problemlösung zu bieten. Um diese didaktische Situation zu verwirklichen, muss eine besondere Mathematik- Lernumgebung entworfen werden.

In dieser Studie wurde eine Lernumgebung mit dem Math- Trail-Konzept als Grundidee entwickelt. Ein Math-Trail ist ein Pfad, bestehend aus einer Reihe von Stationen, an denen die Schüler Mathematik im Freien betreiben und entdecken können. Die Idee der klassischen Math-Trail- Projekte sind nicht neu, aber die Kombination dieses etablierten Outdoor-Bildungskonzepts mit dem Einsatz neuester Technologie ist es. Wir zeigen in dieser Studie dass der Einsatz von Mobiltechnologie im Freien das Potenzial hat, den Mathematik-Lernprozess zu unterstützen.

In der Designphase wurde die GPS-fähige App speziell für den Einsatz in Indonesien unter Berücksichtigung der lokalen Situationen, Bedingungen und Bedürfnisse entwickelt. Es handelt sich um eine native Android-App, welche folgendes anzeigt: die mathematischen Trailrouten/Karten einschließlich der Standortkoordinaten der mathematischen Trailaufgaben und der aktuellen

Benutzerposition, die authentischen mathematischen Probleme, die Informationen über das benötigte Werkzeug zu den Problemlösungen, die Hinweise (falls vom Benutzer angefordert) und die Rückmeldung über die eingegebenen Antworten. Die App zeigt auch die Kurzinformationen zum Objekt.

Die App wurde mit der MIT App-Inventor-Software speziell für MathCityMap. Indonesia erstellt und läuft auf Handys mit Android-Plattform. Neben der App wurden in dieser Phase auch 87 Aufgaben von Mathematiklehrinnen und Lehren die durch einen Workshop geschult wurden entworfen; die Aufgaben wurden 13 Math-Trails in verschiedenen Regionen der Stadt Semarang zugeordnet. Es gibt 6-8 Aufgaben für jeden Trail, mit verschiedenen mathematische Themen in einer sicheren Umgebung. Die entworfenen Trails führen durch über Schulgelände, Stadtparks, Märkte, aber auch zu historischen Gebäuden, Touristenattraktionen und anderen Orten.

Die Math-Trails und die Aufgaben wurden in das MathCityMap-Portal hochgeladen, so dass die Benutzer über die App darauf zugreifen können. Trail-Walker brauchen etwa zwei Stunden, um einen Trail zu erkunden (ca. 1-2 km Länge) und die Aufgaben auf diesem Trail zu lösen. Die entworfenen Math-Trails und die App bestanden zuerst den Evaluierungsprozess durch Validierung der Experten und einer Pilotphase mit einer kleinen Gruppe von Schülern und Lehrern. Einige Aufgaben wurden

aussortiert; die positiv evaluierten Aufgaben wurden für die nächste Phase verwendet.

Die groß angelegte Versuchsphase wurde in den Jahren 2015 und 2016 mit Schülern und Lehrern aus neun Sekundarschulen durchgeführt. Für jede Schule waren zwei Klassen (ca. 30 Schüler/Klasse) an dieser Studie beteiligt, eine Klasse als Versuchsgruppe und eine Klasse als Kontrollgruppe. Beide Gruppen in jeder Schule wurden von der gleichen Lehrperson mit gleichem Thema und Lehrstoff, aber mit unterschiedlichen Interventionen, unterrichtet. In der Versuchsgruppe wurden das Lehren und Lernen der Mathematik mittels App-unterstütztem Math-Trail-Programm durchgeführt. Die Schüler der Kontrollgruppe wurden auf dem herkömmlichen Weg unterrichtet.

Im App-unterstützten Math-Trail-Programm wurden Gruppen von 5-6 Schülern gebildet. Die Aktivitäten wurden während der normalen Schulzeit in etwa 2 x 45- minütige Abschnitten durchgeführt, mit einer kurzen einführenden Erklärung der Regeln und Ziele durch die Lehrer. Die Gruppen begannen dann ihre mathematische Reise von unterschiedlichen Aufgabenorten aus damit nur jeweils eine Gruppe an einer Aufgabe arbeitet. Während die Gruppen den Trail abwanderten, beobachteten und überwachten Forscher und Lehrer die Aktivitäten der Schüler, unterstützten diese aber nicht, da alle notwendigen

Informationen mittels der App verfügbar waren.

Mit Hilfe der App folgen die Schülergruppen einer geplanten Route, finden die Aufgabenorte und lösen das mathematische Problem vor Ort, und gehen dann zur nächsten Aufgaben weiter. Im Anschluss wurde mit allen Schülern der Klasse eine Nachbesprechung durchgeführt. Um Schülermotivation zu erfassen wurden Fragebögen (Situational Motivation Scale/SIMS) vor und nach den Aktivitäten verteilt, Ebenso wurden die mathematischen Überzeugungen (Beliefs) der Lehrer erfasst. Um den Lernfortschritt zu messen wurden individuelle mathematischen Tests erstellt und vor und nach den Aktivitäten durchgeführt. wurden.

Das Ergebnis der SIMS zeigt, dass die Art der Motivation der Schüler, sich zu engagieren, verschieden ist. Es hat sich gezeigt, dass alle Schüler einen positiven Self-Determined Index (SDI) besitzen. Dies bedeutet, dass ihre Motivation stark selbstbestimmt, bzw. eine verinnerlichte Motivationsform war. So waren intrinsische Motivation (IM) und identifizierte Regulierung (IR) dominannter als externe Regulierung (ER) und Amotivation (AM). Die Schüler empfanden die Aktivität interessant oder angenehm (ein Indikator für IM) sowie aussagekräftig oder wertvoll (ein Indikator für IR). Sie beteiligen sich an den Aktivitäten aus Eigeninteresse/Vergnügen/Zufriedenheit, und sie betrachteten ihre Teilnahme als ihre eigene Entscheidung.

Bei offene Anschlussfragen zum SIMS- Fragebogen berichteten die Schüler, dass sie an den mathematischen Outdoor-Aktivitäten Spaß hatten und interessiert an der Verwendung von moderner mobiler Technologie beim Lernen von Mathematik sind. Sie berichteten auch, dass das Lernen von Mathematikanwendungen in der realen Welt für sie wertvoll und sinnvoll war. Das SIMS-Ergebnis zeigt auch, dass es vor und nach der Teilnahme an diesem Programm einen signifikanten Unterschied in der Orientierung der Schülermotivation gab. Es gab eine Veränderung von extrinsisch motiviert hin zu mehr intrinsisch motiviert. Bemerkenswert ist auch, dass es diese intrinsische Motivation nicht auf den Neuigkeitseffekt zurückzuführen ist, da die Werte im zweiten Jahr der Studie sich nicht signifikant geändert haben.

Es zeigte sich ebenfalls, dass die Intervention die Leistungen der Schüler in Mathematik beeinflusst hat. Um die Wirkung der Intervention auf die Mathematikleistungen der Schüler zu bestimmen, wurden die Schülerresultate von Experimentalgruppe und Kontrollgruppe statistisch überprüft. Die Ergebnisse zeigen, dass der mittlere Leistungszuwachs der 272 Schüler in der Experimentalgruppe signifikant höher war als die der 248 Schüler in der Kontrollgruppe. Das zeigt, dass die Intervention mit diesem Programm die Leistung der Schüler in Mathematik erhöht hat.

Da der Lehr- und Lernprozess mit den Einstellungen der Lehrer verknüpft ist, beschäftigte sich diese Studie auch mit dem Einfluss des MathCityMap-Programms auf die mathematischen Überzeugungen der Lehrer im Zusammenhang mit ihren Strategien zur Förderung der Motivation der Schüler, sich in Mathematik zu engagieren. Bei den Lehrpersonen war zu erwarten dass durch die Fokusgruppen-Diskussion, Lehrerfortbildungen (Workshop zur Aufgabengestaltung) und die Einbeziehung in den Beobachtungsprozess ein Einfluss auf die mathematischen Überzeugungen stattgefunden hat Ein Pre-Posttest-design zeugen, dass es einen Wechsel der mathematischen Überzeugungen, von traditionell orientiert hin zu mehr forschungsorientiert gab.

Lehrer, nachdem sie an diesem Programm beteiligt waren, mehr von Folgendem überzeugt wurden: Mathematik ist ein Werkzeug zum Denken, das Ziel der Schüler ist es zu verstehen, die Schüler sollten eine Autonomie haben, Mathematikfähigkeit ist offen für Änderung, und die Schüler werden sich in Mathematik engagieren wollen, wenn die Aufgaben interessant und herausfordernd sind. Es gab auch einen signifikanten positiven Effekt der mathematischen Überzeugungen bei forschungsorientierten Lehrern auf die intrinsische Motivation der Schüler. Lehrer berichteten auch, dass durch die Nutzung der mobilen App es erleichtert wurde, Outdoor-Lehr- und Lernprozess zu gestalten.

Zusammengefasst konnte mit dieser Arbeit gezeigt werden, dass durch die für diese Studie entwickelte App und den dazu passenden Trail-Designprozess mehrere Math-Trails in der Stadt Semarang installiert werden konnten. Empirische Studien zum Einsatz der App und der Trails zeigen, dass die Studierenden waren sehr intrinsisch motiviert, sich in Mathematik zu engagieren. Sie haben durch diese Aktivitäten mathematische Erfahrungen gesammelt. Infolgedessen wurde ihre Leistung in der Mathematik verbessert. Der Einfluss dieses Programms auf den Wechsel der mathematischen Überzeugungen der Lehrer hat zu diesen Ergebnissen beigetragen. Wir empfehlen, dass Schulen und Öffentlichkeit die vorhandenen Math-Trails (einschließlich der unterstützenden Werkzeuge) nutzen oder neue Trails entwerfen, indem sie dem in dieser Studie angewendeten Entwicklungsmodell folgen. Weitere Untersuchungen sind für die Projektentwicklung und -umsetzung in anderen Orten/Städten mit anderen Situationen und auch anderen Studienaspekten und -bereichen notwendig.

Table of Contents

Cover............................................................................ i

Preface........................................................................ iii

Acknowledgemens....................................................... vii

Zusammenfassung (German-Summary)........................... xi

Table of Contents....................................................... xix

Chapter 1. Introduction................................................. 1

1.1. Background of the study.......................................... 1

1.1.1. What is the problem?....................................... 5

1.1.2. Can the mobile app-supported math trail programme offer a solution? 9

1.2. Design of the study............................................... 13

1.2.1. Topic of the study........................................... 13

1.2.2. Aims of the study............................................ 14

1.2.3. Research questions......................................... 16

1.2.4. Approach of the study..................................... 19

1.2.5. Phases of the study......................................... 21

1.3. The book's structure.............................................. 25

Chapter 2. Theoretical Background................................ 29

2.1. Constructivism in mathematics education................. 30

2.2. Students' motivation in mathematics....................... 38

2.3. Students' performance in mathematics..................... 41

2.4. Teachers' mathematical beliefs............................... 45

2.5. Didactical situation in mathematics.......................... 47

2.6. Outdoor mathematics education.............................. 52

2.7. Technology in mathematics education...................... 64

2.8. Conceptual framework of the study......................... 71

Chapter 3. The MathCityMap Project............................ 75

3.1. The concept and the goals of the project................... 76

3.2. Components of the project..................................... 77

3.2.1. Mathematical outdoor tasks............................. 77

3.2.2. Mathematical city trips................................... 80

3.2.3. Map-based mobile app.................................... 83

3.2.4. MathCityMap community................................ 87

3.3. Technical implementation of the project................... 89

3.3.1. Steps of preparation........................................ 89

3.3.2. Settings of the activity..................................... 90

3.3.3. Evaluating and publishing the activity.............. 92

Chapter 4. Designing the mobile app-supported math trail environment in Indonesia 93

4.1. Indonesian secondary school mathematics

education.................................................................... 93

4.1.1. A brief profile of Indonesia.............................. 94

4.1.2. Education system in Indonesia......................... 96

4.1.3. Indonesian secondary school mathematics curriculum 98

4.2. Design of the mobile app-supported math trail programme for Indonesia 101

4.2.1. Design of the rules of the activity.................... 106

4.2.2. Design of the mobile app............................... 110

4.2.3. Design of the math trails............................... 127

Chapter 5. Evaluating the potential effects of a mobile app-supported math trail programme: An exploration study in Indonesia.................................................................. 151

5.1. Method.............................................................. 151

5.1.1. Approach..................................................... 152

5.1.2. Participants, situations, activities and procedures 152

5.1.3. Data collection and analysis.......................... 154

5.2. Results............................................................... 158

5.2.1. What was the initial condition of the students like? 159

5.2.2. How has the programme been running?........... 163

5.2.3. How did the students work?........................... 164

5.2.4. Why do students engage in this programme?. 168

5.2.5. What mathematical experience do they get after having engaged in this programme? 184

5.2.6. Does the intervention promote students' performance in mathematics? 199

5.2.7. How does the project affect teachers' mathematical beliefs? 202

5.3. Discussion.......................................................... 208

Chapter 6. Conclusions and recommendations............... 219

6.1. Conclusion......................................................... 219

6.2. Recommendations............................................... 240

References................................................................ 243

Chapter 1

Introduction

This book reports a study on the development, implementation and evaluation of a mobile app-supported math trail programme in Indonesia. As an introductory chapter, this chapter contains the background of this research, including the problems that underlie the need for this research, and the solution offered through this study. The design of the study, including the topic, aims, questions, approach and phases of the study, is described in detail in this chapter. To facilitate an understanding of the flow of the study, a concept map is also presented in this part. The structure of this book is then outlined in the last section of this chapter.

1.1. BACKGROUND OF THE STUDY

Mathematics plays a role in daily life - both individual and social - and in professional life. People, therefore, must be able to apply basic mathematics in their everyday lives, a skill that the Organisation for Economic Cooperation and Development (1999) termed "mathematics literacy". In an educational context, mathematics activities should offer the chance for students to experience mathematics as a

meaningful subject that can be understood well (Freudenthal, 1991).

Furthermore, Ojose (2011) suggests that students should be provided with real-world situations that are relevant to their position as citizens or their concern area. Such situations can be experienced by mathematics students outside the classroom (Dubiel, 2000). This approach can show students that mathematics is all around them and not merely in textbooks. Bringing mathematics outdoors can provide an opportunity for students to experience mathematics in real-world situations.

In some countries, interest in the development of outdoors and adventure education programmes has increased (Fägerstam, 2012). Various activities outside the classroom have been specifically designed to increase student engagement. Integrated programmes have also been developed to combine learning outside the classroom with traditional learning in the classroom. In mathematics, one of the outdoor educational programmes that have been elaborated is the math trail programme. This programme is not purely an outdoor activity, as it can also be conducted indoors, but it can be used as one alternative to encourage students to learn mathematics outside the classroom.

The math trail programme, which is a pathway to discovering mathematics, was created as a medium for experiencing mathematics in relevant applications (Shoaf,

Pollak, & Schneider, 2004), namely communication, connections, reasoning and problem solving (National Council of Teachers of Mathematics, 2000). In a math trail, students can simultaneously solve mathematical problems encountered along the path, make connections, communicate ideas and discuss them with their teammates, and use their reasoning and skills in problem solving.

Dudley Blane and his colleagues first developed a math trail by blazing trails in the centre of Melbourne as a family holiday activity (Blane & Clarke, 1984). The programme was then strengthened when some schools took advantage of the trails by integrating them into their mathematics learning programmes. The success of this idea allowed this programme to be adapted and applied in different places, and math trail projects subsequently emerged in various cities, such as Vancouver, Boston, Philadelphia and San Francisco (Richardson, 2004).

Although the math trail project is not new, the idea of an outdoor education programme supported by mobile technology appears to be new. This idea is facilitated by the fact that in recent years, developments in mobile technology and mobile phone use have improved significantly (Cisco, 2016; Lankshear & Knobel, 2006). These improvements were followed by many mobile phone applications (apps), including those intended for use in outdoor activities, such as Endomondo® for outdoor sports. In learning activities, Wijers, Jonker, and Drijvers (2010)

suggested that mobile devices could be employed to promote learning outside the classroom.

However, to date, most mobile technology apps for mathematics learning have only been employed in regular teaching settings (Trouche & Drijvers, 2010). Thus, it is necessary to explore the potential of mobile technology for teaching and learning mathematics, including for use in outdoors mathematics learning, and in so doing, engage students in meaningful mathematical activity. The combination of reality and virtual reality is expected to contribute to student engagement (Schwabe & Göth, 2005; Wijers et al., 2010).

This point is used as the basis for the development of the MathCityMap project. The project is a programme of math trails that are facilitated by the use of mobile phone technology and use special mathematical tasks (Cahyono & Ludwig, 2014; Jesberg & Ludwig, 2012). The project offers the opportunity to experience mathematics in the environment by arranging educational tasks in several locations around the city. Through a mobile phone app- supported mathematical activity, learners in groups find the task locations by tracing a planned math trail and solve mathematical problems encountered along the path.

The project aims to develop math trails and supporting tools, such as a web portal and a mobile phone app, and then share the project with the public (especially students).

This approach is expected to have the potential to encourage students to be actively involved in mathematics and promote student motivation to engage in mathematical activity. During their involvement in each activity and their interaction with the environment, students have the opportunity to construct their own mathematical knowledge. As a result, this will achieve the primary target of improving their performance in mathematics.

Referring to these basic ideas and objectives, as a part of the MathCityMap project, the model of the mobile app- supported math trail programme was then developed. The implementation of this programme in Indonesia tailored to that country's situation was also studied scientifically. It was motivated by several problems in the field of mathematics education, especially in Indonesia.

1.1.1. What is the problem?

Public understanding of mathematics is often unsatisfactory, and only a small number of students enjoy participating in maths during the school day (Behrends, 2009, p. 1). At school, and globally, mathematics is sometimes perceived as a difficult and abstract subject. Internationally, by the eighth grade, only about a quarter of students enjoy learning mathematics (Mullis, Martin, Foy, & Arora, 2012, p. 325). This issue is a worldwide phenomenon, but given the unique aspects of each country, in this study we restrict ourselves to focusing on the issue in Indonesia.

In Indonesia, the percentage of students who report being happy at school is high in comparison with other countries (Organisation for Economic Cooperation and Development, 2013). However, Hadi (2015) reported that "most students fear mathematics, tend to skip mathematics subjects, and are happy when the mathematics teacher is not able to come to class" (p. 1).

In addition, based on the TIMSS 2011 results in mathematics, only approximately 20% of Indonesian eighth-grade students like learning mathematics and only 3% are confident in their abilities in maths (Mullis et al., 2012). In general, mathematics involves learning a lot of processes and formulae that appear to be not only unconnected with each other but also irrelevant to students' lives (Education, Audiovisual and Culture Executive Agency, 2011).

Students appear to be less motivated to learn mathematics. This problem is serious because if we refer to the results of Hattie's (2009) meta-analysis, students' motivation and attitude toward mathematics and science are related to their performance in those subjects. In a synthesis of over 800 meta-analyses relating to achievement, 288 studies reported that attitudes toward mathematics and science were related to mathematics and science achievement (Hattie, 2009, p. 50).

From six meta-analyses (327 studies involving 110,373 people), Hattie concluded that motivation has a significant positive effect on achievement. Hattie's effect size of student motivation was d = 0.48. This means that the influence was labelled as being in the "zone of desired effects". Therefore, we assume that the above conditions have an impact on the low performance of Indonesian students.

Nationally, overall, Indonesian secondary school student performance has improved significantly. For mathematics, between 2004 and 2006, the average examination score rose from 5.0-6.2 to 6.8-7.6 (EFA Secretariat Ministry of National Education of RI, 2007). However, based on the data from the UNESCO International Bureau of Education (2011), Indonesian students still rank low in international standardized tests. Since PISA 2000, the trend has shown no significant increase or decrease and has tended to stagnate at low performance values (Baswedan, 2014).

PISA 2012 ranked Indonesian students aged 15 years 64th out of 65 countries, with a score of 375 for mathematics. PISA 2012 examines how well students can perform with the knowledge they possess (Organisation for Economic Cooperation and Development, 2013). Similarly, in TIMMS 2011, the mathematics achievement of Indonesian eighth-grade students was ranked 38th out of 42 countries, with a score of 386 in comparison to an average score of 500.

Further, PISA 2012 found that 75.7% of students were unable to reach level 2. This indicates that Indonesian students were unable to extract the relevant information for a given task or use basic algorithms to answer questions. Students also had difficulty solving realistic problems, especially in geometry. In the national exam in 2012, the average score of junior high school students in mathematics was 5.78 out of a maximum of 10, and mastery of geometry was below 50% (Kementerian Pendidikan dan Kebudayaan RI, 2013).

The World Bank (2010) reported that an ineffective learning process contributes to the low quality of graduates from Indonesian secondary schools. Previous studies indicated that several factors may affect quality, such as an increased focus on theory and routine learning, a focus on external examinations, administrative demands, textbook- based teaching and learning, and a crowded curriculum (Marsigit & Rosnawati, 2011; Sembiring, Hadi, & Dolk, 2008).

The natural next question, therefore, is how to improve Indonesian students' motivation in mathematics in an effort to promote their performance in mathematics. One expected approach concerns the implementation of the mobile app-supported math trail programme. Conceptually, this programme is intended to address

problems similar to those encountered in Indonesia, as described above.

1.1.2. Can the mobile app-supported math trail programme offer a solution? Mathematics can be found everywhere and is experienced in everyday situations. The environment provides unlimited sources and ideas for teaching and learning mathematics. Students need to connect with the subject through meaningful activities, such as by implementing abstract mathematical concepts in real-life situations. The math trail programme provides opportunities in this regard. Supported by the use of mobile phone technology, in this project, math trails were designed around the city and offered opportunities to encourage student involvement in meaningful mathematical activities by utilizing the advantages of the latest technology.

This programme has the math trail concept at its core. A math trail is a planned pathway that consists of a series of stops at which students can explore mathematics in the environment (English, Humble, & Barnes, 2010; McDonald & Watson, 2010; Shoaf et al., 2004). Students find and solve real problems related to mathematics in real situations and connect mathematics with other disciplines.

Math trail tasks are created in several locations and then collected in a database. During the implementation phase, the tasks can be selected and grouped into a math trail route

based on the conditions and objectives. The tasks, their locations and directions to these sites, as well as the route and the tools required for problem solving, are provided in a trail guide, which is a scale map of the trail.

With the rapid development of technology, it is possible to collect the tasks and design a trail guide based on a digital map through a portal. Teachers can arrange the math trails in a web portal, and students can access the trails with the help of GPS-enabled mobile devices or use a paper version of the trail guide. In this project, we designed a web portal and a mobile phone application to support the math trail programme.

Using mobile devices is a familiar practice to all social and economic groups. In fact, in recent years, rapid developments have occurred in the scope, uses and convergence of mobile devices (Lankshear & Knobel, 2006) used for computing, communications and information. Within the next five years, it is estimated that the total number of smartphones will account for nearly 50 per cent of all global devices and connections (Cisco, 2016, p. 3).

As in other countries around the world, the rapid development of mobile technology has also occurred in Indonesia. Indonesia is amongst the top five countries worldwide in terms of the number of mobile phone users, with growth in 2012 reaching 60% (Prayudi & Iqbal,

2013). The same authors also reported that the percentage of market share in 2012 was 68.8% Android, 18.8% iOS, 4.5% BlackBerry OS, 3.3% Symbian, 2.5% Windows Phone, 2.0% Linux and 2.1% others. The World Bank Group (2015) reported that mobile cellular subscription in Indonesia in 2012 was 319,000,000 or 126.18 per 100 people.

Using mobile technologies is also common practice in learning activities, and these technologies offer advantages in terms of learning opportunities. The National Council of Teachers of Mathematics (2008) stated that technology has the potential to be a fundamental tool for mathematics learning. O'Malley et al. (2003) called the learning process in which learners take advantage of this approach "mobile learning". One of the benefits of mobile learning is the opportunity to place learning outdoors in the real world. Mobile devices have the potential to integrate the characteristics of effective learning, such as situated realistic learning, motivational power and teamwork (Wijers et al., 2010). Thus, mobile learning enables learners to build knowledge and construct their understanding in unusual settings (Winter, 2007).

The math trail is the core of the activities in this project, and mobile technology is used to support these activities. This shows that this project combines real and virtual environments. According to Schwabe and Göth (2005), this combination might contribute to the improvement of

student engagement. When students are highly motivated to engage in mathematics, they are interested in, and enjoy spending more time, learning and solving mathematical tasks. Such students tend to be more persistent in solving mathematical problems (Lepper & Henderlong, 2000). Enjoyment and persistence in learning mathematics and positive views concerning the value and relevance of mathematics learning can lead to engagement with mathematics (Attard, 2012). Rigby, Deci, Patrick, and Ryan (1992) reported that student engagement in learning processes has a positive impact on their understanding of new knowledge and their flexibility in using new information.

Thus, theoretically, the concept of the mobile app- supported math trail programme offers several benefits for solving the current problems in the field of mathematics education, especially in Indonesia. We felt that if it were carefully designed and integrated into an intervention, the programme developed in this project could increase students' motivation to engage in the mathematics learning process. As a result, in line with the results of Hattie's (2009) meta-analysis, it will have an impact on improving their performance in mathematics. However, the design and implementation of the teaching and learning programme are also related to teachers' attitudes toward the programme and their practices in the classroom. Thus, it is also important to address teachers' mathematical

beliefs related to their strategies in fostering students' motivation to engage in mathematical activity.

1.2. DESIGN OF THE STUDY

The conceptual idea described above must be studied scientifically to develop a theory, translate the theory into a model of an educational programme, implement the programme and evaluate it through an empirical study. This need prompted us to carry out this study.

1.2.1. Topic of the study

This PhD study researches the development of the model of the mobile app-supported math trail programme and its implementation in Indonesia. The implementation in this study also includes an empirical study to explore the impact of the programme developed on student motivation in mathematics, their performance in mathematics and teachers' mathematical beliefs. The programme was developed and implemented primarily for school activities as part of the process of teaching and learning mathematics, so the programme was developed in accordance with the school mathematics curriculum in Indonesia. Since the area of school mathematics is too broad to be investigated in the framework of this study, it must be restricted to an area that is relevant to the issues mentioned in the part of the background of this study. Therefore, the programme was implemented particularly for lower secondary school or

junior high school level (for all grades and for all mathematics topics).

As a pilot study, we implemented and studied empirically the programme for secondary schools in the city of Semarang, Indonesia from 2013 to 2016. It was carried out in cooperation between the two countries through two institutions, namely IDMI Goethe-Universität Frankfurt in Germany and FMIPA Universitas Negeri Semarang in Indonesia, and in collaboration with the Department of Education of the city of Semarang to implement the project in nine schools in the city. Semarang is not representative of Indonesia as a whole but has unique characteristics as a town and includes high-, middle- and low-level schools. Both urban and rural schools are also found in this region, which has hills and seaside areas, while the economic level of citizens varies. Thus, the implementation of the programme in this city is expected to provide a large amount of information and to serve as a model for the development and implementation of the programme in other cities in Indonesia, which is rich in diversity.

1.2.2. Aims of the study

This study consisted of two phases, namely: (1) the developmental phase and (2) the implementation and empirical study phase. These two phases were preceded by a preliminary phase. The first phase was aimed at developing a model of a mathematics educational

programme grounded in the basic idea and objectives of the MathCityMap project. The basic idea of the MathCityMap project is to set up mathematical problem-solving activities in outdoor situations following the concept of the math trail and supported by the use of mobile technology. The programme offers the opportunity for learners to construct their own mathematical knowledge during their interactions with the environment.

Therefore, the programme was developed within a framework informed by constructivism in mathematics education and built using some basic concepts, such as the concept of the math trail and the use of mobile technology in mathematics education. From this theoretical framework, the model of a mobile app-supported math trail activity was formulated. This model includes the concept, objectives, components and technical implementation of the programme and its evaluation.

The second phase was aimed at implementing the programme in Indonesia tailored to the local situation. It included the evaluation of its implementation by conducting an empirical study. Through an exploration study, the potential of the programme for eliciting engagement in meaningful mathematics teaching and learning activities was explored. Decisive factors that affect students' motivation to engage in mathematics and their performance in mathematics were also examined in this study. Furthermore, because teaching and learning

processes are linked with teachers' attitudes, this study also considered the effects of the project on teachers' mathematical beliefs. Thus, teachers' mathematical beliefs related to their strategies in fostering students' motivation to engage in mathematics education through the implementation of the programme were also investigated in this study.

1.2.3. Research questions

Taking into consideration the aims of the research, the three central research questions of this study were clarified. The first question was:

1. How can the mobile app-supported math trail programme promote students' motivation to engage in mathematics?

The meaning of the keywords of this question are as follows. First, the question starts with the words "how can". This phrasing indicates that the question focuses on identifying the conditions and approaches that optimize the benefits offered by the programme. This programme is a "mobile app-supported math trail programme", which is a core of the MathCityMap project and was also theorized through this study.

"Engagement" leads this study to determine how students are actively engaged in this programme. The use of outdoor

activities supported by a mobile phone application is a strategy to engage students in the mathematics learning process. Because students' engagement in an activity is related to their motivation, it is necessary to investigate the nature of "students' motivation" to engage in such an activity. It is also important to determine the impact of this programme in "promoting" student motivation in mathematics and to investigate the differences in student motivation to engage in mathematics before and after the programme.

Furthermore, as a type of mathematics education programme, this programme focuses on "mathematics". It was designed to motivate students to engage in an activity that helps them to construct their own mathematical knowledge. Therefore, this study was also concerned with examining the impact of the programme on student performance in mathematics by answering the question:

2. Does an intervention with a mobile app-supported math trail programme enhance students' performance in mathematics?

The "intervention" in this study was performed by arranging a teaching and learning mathematics in which a "mobile app-supported math trail programme" was carried out. In line with the Indonesian school mathematics curriculum contents, "students' performance in mathematics" addressed in this study includes their mathematical ability and skill in understanding and

applying mathematics in solving problems. This question led to the findings on the effect of this intervention on student performance in mathematics. It is controlled by knowing whether the performance of the students involved in this programme is better than that of students learning in regular settings.

Furthermore, the arrangement of learning needs the support of teachers in their teaching practice. Thus, the study also intervened in teachers' mathematical beliefs, so the teachers' strategies in their teaching practices were in line with the concept and objectives of programmes developed through this study. The impact of the intervention was evaluated in the study by answering the question:

3. How do teachers' mathematical beliefs differ after being involved in the project compared with their initial beliefs?

This question addresses teachers' view of mathematics, and its teaching and learning, before, during and after involvement in the project. It led to the findings on "teachers' mathematical beliefs" and measured changes in those beliefs. The impact of the project on teachers' orientation - traditional or inquiry - was also associated with this question.

1.2.4. Approach of the study

This study globally followed a design research paradigm. Design research is also known as developmental research. This approach integrates research, development, implementation and dissemination and involves all participants (researchers, developers, teachers and practitioners) in dialogue in the field (Gravemeijer & Terwel, 2000). This work produces theories and prototypes that are theoretically and empirically founded and studied. Freudenthal (1968) described the principle of developmental research as follows:

experiencing the cyclic process of development and research so consciously, and reporting on it so candidly that it justifies itself, and that this experience can be transmitted to others to become like their own experience (p. 161).

Through this principle, Freudenthal suggested that the research experiences should be transferred to outsiders, such as teachers, who can then use the experiences as the basis of decisions when they implement them in their classroom to achieve their own goals according to the actual situation. This process shows that this kind of research fits into the pedagogical tradition (Gravemeijer & Terwel, 2000).

Van den Akker (1999) stated that developmental research is based on two objectives, namely the development of prototype products and the formulation of methodological suggestions for designing and evaluating prototype products. The prototypes produced in this study were the model of the programme, the math trail tasks and the mobile phone app. The aims of design research are to develop theories or models, instructional materials and an empirically grounded understanding of the work of the learning process (NCTM Research Advisory Committee, 1996).

Design research is particularly suitable in situations for which a full theoretical framework is not yet available; thus, hypotheses must still be developed, and some new teaching materials must be designed (Drijvers, 2003). To produce prototypes, it is necessary to establish criteria for their development. Nieveen (1999) offered three criteria that can be used: validity, practicality and effectiveness.

· The product meets the requirement of validity if the components are based on state-of-the-art knowledge and consistently linked to each other (internally consistent).

· Practicality is fulfilled when experts and practitioners claim that the prototype can be used and when the prototype can really be employed.

· The product meets the criterion of effectiveness when the students appreciate the learning programme and the desired learning takes place (P. 127).

Therefore, the products developed in this study must meet these requirements. The evaluation of the products was conducted through multiple phases in this study.

1.2.5. Phases of the study

According to Drijvers (2003), "Design research has a cyclic character: a design research study consists of a research cycle in which thought experiments and teaching experiments alternate" (p. 20). The development that occurs during the cycles can be characterized as ranging from qualitative formative to more quantitative summative.

Fig. 1.1 Layers of formative evaluation (Tessmer, 1993)

Following the layers of formative evaluation proposed by Tessmer (1993) reveals the progress from small-scale to large-scale evaluation (Fig. 1.1). This method requires mixing a qualitative formative method at the beginning of the study and a quantitative summative method afterward, using a quasi-experimental approach (Bokhove, 2011). Therefore, this study took place in one preparatory cycle and three subsequent cycles (prototypical design (CYCLE I), a small-scale field experiment (CYCLE II) and a large- scale experiment (CYCLE III)). This phase is shown in Fig. 1.2.

Fig. 1.2 Design research cycles within this study

The preparatory cycle involved the literature review, which led to the theoretical framework and the design of the prototypes. The focus of activity in this cycle was to conduct an in-depth review of the literature cross-checked with field experiences and existing data. The result is the theoretical framework for the development of the project

for implementation in Indonesia. The cross-checking process was completed through an exploration step that consisted of benchmarking, needs analysis and focus group discussion (involving experts and practitioners/educators).

Based on the results of this activity, the specification procedure was defined and the technical requirements were developed, primarily as a foundation and guideline for designing prototypes. The results of this cycle are the guidelines for the technical implementation of the project in Indonesia, a guide to designing the prototypes. In addition, the research instruments based on the theory are also reviewed in this cycle to obtain research tools that are appropriate for the theory and the chosen situations.

The first intervention cycle focused on the prototypical design, such as the model of the programme including the activity rule, the design of math trails containing varied mathematical outdoor tasks and the design of the mobile phone app. The prototypes were designed based on the specifications and requirements defined in the previous cycle. In this cycle, the trails were created by the project team and also by the task contributors (teachers, educators and others), with reference to the guidelines and characteristics that were set in the previous cycle. The math trails were created by contributors through training and a workshop session. The mobile app to support the math trail programme was also created in this cycle by the app programmer of the project team. Activities took place until

the authors uploaded the tasks into the MathCityMap website portal.

In the second cycle, the prototypes were reviewed by experts (mathematics, mathematics education and mathematics educational multimedia), and a small-scale field experiment (simulation session) was carried out to determine how the prototypes would work. In this cycle, teachers and small groups of students performed math trail activities and tested the mobile app. It is necessary to see how the math trails run and how the app works. Here, teachers and a small group of students were involved. During this session, the researchers conducted observations and interviews. The prototypes were then revised based on the results of the review and simulation in this phase.

In the final cycle, we implemented the project in a large- scale class experiment and studied its effects. This cycle was carried out in several pilot studies by involving teachers and students from nine schools. The implementation consisted of an introduction session, a math trail run and a debriefing session. In this step, we explored how the math trails ran and how the application worked in all pilot studies, how the students performed and how motivated the students were to participate in the activity. We also investigated the attitudes and beliefs of teachers related to mathematics and this project. We then

analysed the data obtained in this step to answer the research questions, drawn conclusions and recommended (and criticized) some important points for the further development of the project.

1.3. THE BOOK'S STRUCTURE

This book consists of six chapters. These six chapters represent the main content and are preceded by a preface. The concept map of this study and its link to the content of each chapter of this book are illustrated in Fig. 1.3.

Chapter 1 is an introductory chapter. In this chapter, we present some background for this study, including the problems and solutions offered through this study. The topic, objectives, questions, approach and phases of this study are also described herein. At the end of this chapter, we outline the concept map of the study and the structure of the book.

Chapter 2 focuses on the theoretical background of the study. This chapter presents the results of a literature review relating to the study. The theory of constructivism in mathematics education linked with the concepts of student motivation in mathematics, students' performance in mathematics and teachers' mathematical beliefs is discussed in this chapter as the theoretical basis for the framework of the study. This section is followed by a discussion on some basic concepts that build on the idea of the study, such as the concept of mathematics trails and the

use of mobile technology in math trail programmes. From this theoretical background, the framework of the study was formulated.

Chapter 3 focuses on the MathCityMap project. The concept and goals of the project are formulated and the components of the project are also described. In reference to implementing the project, we also propose the technical implementation of the project in this chapter.

Chapter 4 describes the results of the development of the model of the mobile app-supported math trail programme for implementation in Indonesia. This chapter starts with a closer look at the situation in Indonesia and contains the results of designing a mobile app and math trails in the city of Semarang, as well as the rules of the activity.

Chapter 5 is a report on an exploration study of the implementation of the programme in Indonesia. This chapter describes the methodology and the procedures of the study. The impact of the programme on Indonesian secondary school students' motivation to engage in mathematical activity, their performance in mathematics and the teachers' mathematical beliefs are discussed in this chapter. At the end of this chapter, the results of this study are presented.

Chapter 6 is the concluding chapter. Here, we draw conclusions from the results obtained in this study and

provide recommendations for future activities and researches.

Fig. 1.3 The concept map of the study

Chapter 6

Conclusions and recommendations

In this final chapter, we review the detailed results of this study that were presented in the previous chapters from a more global perspective. The aim of this chapter is to draw conclusions regarding the results as the answers to the research questions stated in the first chapter. Recommendations are also given in the last section of this chapter. There are two kinds of recommendations, namely: a recommendation that the programme be implemented and recommendations for further studies on the MathCityMap project.

6.1. CONCLUSION

Mathematics plays an important role in daily life. However, the current public understanding of mathematics remains unsatisfactory. Many students do not enjoy mathematical activities and appear unmotivated to learn mathematics, while their attitudes affect their performance in mathematics. These problems have led mathematicians and mathematics educators to think of ways to popularize mathematics. A variety of projects have been developed and implemented in numerous countries to raise public

awareness of mathematics, one of which is the MathCityMap project, a project of the working group MATIS I IDMI Goethe University Frankfurt. It is a project of a math trail programme supported by the use of mobile technology.

The research on this project was carried out in multiple places and using multiple areas of study, including this PhD study. This work is a study on this project specifically in Indonesia. It was conducted by following a design research paradigm and took place in one preparatory phase and three subsequent phases (a design phase, a small-scale field experiment phase and a large-scale experiment phase). The aims of this study were focused on designing a mobile app and math trails around the city, implementing the mobile app-supported math trail programme in Indonesia and exploring its impact on students' motivation and performance in mathematics and on teachers' mathematical beliefs.

Because the MathCityMap project has not been theorized yet, this study was also concerned with formulating the concept of the MathCityMap project as a guideline for the implementation of this project, both in this study and other studies in the future. Therefore, in this study, the concept of the MathCityMap project was theorized. For the implementation of the project in Indonesia, the model of the mobile app-supported math trail programme was

developed; it was followed by designing the rules of the activity, the mobile app and the math trails around the city of Semarang. Then, the programme was implemented and studied empirically in nine secondary schools in the city of Semarang.

This study was conducted within a theoretical framework informed by constructivist theory in mathematics education. This view suggested that, in the learning mathematics process, students should actively construct their own mathematical knowledge by connecting new information they have gained with their previous knowledge. However, learners' engagement in an activity depends on their motivation. Sociocultural views state that learners need guidance as a sort of push for students to get started in their engagement in the learning process, and classroom social interaction also motivates them to engage