The Hypothetical Learning Trajectory on Research in Mathematics Education Using Research-Based Learning

This study aims to create a learning trajectory on research in mathematics education using design research methodology to enhance research and academic writing skills for pre-service mathematics teachers. The fourteen pre-service mathematics teachers during 5 months period from one higher education institution in Tangerang – Indonesia was collected. The design research method was carried out in three phases: preliminary design phase, teaching experiments phase, and retrospective analysis phase. Initial data analysis of 14 pre-service teachers’ research and academic writing skills was conducted in six stages and the learning trajectories on this topic was identified. The fourteen pre-service teachers were divided into 7 groups and research independently to produce seven scientific articles. The six articles were published in the proceedings of Konferensi Nasional Matematika (National Congress of Mathematics) XVII 2014 and one article was published in the Elemen Journal Vol. 1 No. 1.

Several studies indicated that undergraduate students faced difficulties in writing thesis, affecting the length of their study (Bangun, Irmeilyana, & Andarini, 2011;Fathonah, Wahyuningsih, & Wahyuningsih, 2011;Firmansyah, 2014;Prahmana, 2014;Santosa, Wiyanarti, & Darmawan, 2009).In Indonesia, undergraduate students are required to write a thesis as part of their research training (PERMEN No. 49 Tahun 2014).The completion rate usually takes up 2 to 4 semesters.Limited knowledge of methodology, the capacity of research advi- sors, limited research training and experience in academic writing and low-involvement of students to resolve their problems were identified as main source of difficulties (Firmansyah, 2014;Fathonah, Wahyuningsih, & Wahyuningsih, 2011;Puspitasari, 2013).Difficulties in academic writing is also due to lack of motivation, anxiety, and language constraints (Rahmiati, 2014).Therefore, research and academic writing skills are accepted as important skills in the quality of learning of academic training.
Indonesian Directorate of Higher Education Institution to encourage more research and publications by students including undergraduate students issued a policy (PERMEN No. 49 Tahun 2014).Furthermore, the National Standard Qualification (Tim Penyusun KKNI Dikti, 2013) requires students to publish their research in a reputable national journal (acknowledged by KKNI level 6).On the other hand, some researchers have documented the success of research-based learning to enhance students' skills in conducting research (Widayati et al., 2010;Waris, 2009;Umar et al., 2011;Webb, Smith, & Worsfold, 2011;GIHE, 2008;University of Adelaide, 2009), but the greater part of them are still focused on the students who come from non-education department.
Willison & O'Regan ( 2007) developed six research skill indicators that are classified into 5 levels of research.Furthermore, Dowse and Howie (2013), conducted within the framework of design research, sought to design and develop an academic research writing intervention.Prahmana (2014) identified that the learning process at the university did not offer enough support for students to develop their academic writing skills.Therefore, this study aims to create a learning trajectory on research in mathematics education using design research methodology to enhance research and academic writing skills for pre-service mathematics teachers.Based on the problems mentioned, the success of the learning activities to improve pre-service teachers' skills is investigated in research question as follows, "To what extent do the learning trajectory on research in mathematics education in assisting pre-service mathematics teachers to enhance their research and academic writing skills?" Research-Based Learning (RBL) Boud & Feletti (1998) mention six principles which should guide the implementation of RBL, namely multiplicity, activeness, accommodation and adaptation, authenticity, articulation, and timelessness.Furthermore, Neo (2003) also mentions the six principles by using different terms, namely constructivism, contextual learning theory, discovery learning theory, information-process learning orientation, cooperative learning theory, and self-determination theory.RBL activity starts from identifying the problem, extracting knowledge and skills, solving the problem or application, and concluding with reflection (Farkhan, 2008).This is supported by Poonpan & Suwanmankha (2005) which states that RBL involves students in constructing knowledge with the five stage

Academic Writing Skills
Academic writing skills can be interpreted as the skill to produce a paper under standard rules and using a particular scientific method (Supriyadi, 2013;Rahmiati, 2014).Writing a scientific paper has several stages and procedures such as looking for ideas by reading, observing, conducting research, conducting experiments, finding the data, and supporting theory and further writing down the results (Rahmiati, 2014).Suparno (2012) provides general steps in writing a scientific article, namely developing the ideas, planning the text, developing paragraph, writing draft, and finalization.Furthermore, Supriyadi (2013) describes 13 stages in writing a good scientific paper.There are (1) understanding the nature of scientific paper; (2) understanding the difference between scientific paper and non-scientific paper; (3) identifying topics; (4) limiting the topic; (5) formulating the title of scientific paper; (6) formulating the problem of scientific paper; (7) formulating the thesis of scientific paper; (8) framing the scientific paper; (9) developing ideas and paragraphs groups; (10) quotation processing; (11) using the standard language in the scientific paper; (12) writing a list of references; and (13) editing the paper.In addition, scientific paper must also meet the rules of writing scientific language, such as the use of standard grammar, word choice, and the effectiveness of writing (Zulkarnain, 2012).All stages and requirements led to students having difficulty in writing a scientific papers (Yuniawan & Wardani, 2008;Sudiati & Nurhidayah, 2008;Ulfah et al., 2013).Therefore, it takes a special treatment at every stage by controlling every stage through certain indicators in order to produce the skills to write a good scientific paper.
The Hypothetical Learning Trajectory (HLT) in this study has several learning goals expected to be reached by the students.To reach the goals formulated, researcher designs a sequence of instructional learning for research in mathematics education to enhance research and academic writing skills (Figure 1).

Method
This study uses a design research as research method, which is an appropriate way to answer the research questions and achieve the research objectives that start from preliminary design, teaching experiments, and retrospective analysis (Prahmana, 2013).Design research is a methodology that has five characteristics, namely interventionist nature, process oriented, reflective component, cyclic character, and theory oriented (Akker et al., 2006).Design research is a cyclical process of thought experiment and instruction experiments to implementation (Gravemeijer, 2004).There are two important aspects related to design research.They are the Hypothetical Learning Trajectory (HLT) and Local Instruction Theory (LIT).According to Freudenthal (in Gravemeijer and Eerde, 2009), students are given the opportunity to build and develop their ideas and thoughts when constructing mathematics.Teachers can select appropriate learning activities as a basis to stimulate students to think and act when constructing mathematics.Gravemeijer states that the HLT consists of three components, namely (1) the purpose of mathematics teaching for students, (2) learning activities, devices or media used in the learning process, and (3) a conjecture of understanding the process of learning how to learn and strategies students that arise and thrive when learning activities are done in class (Gravemeijer, 2004).The fourteen pre-service mathematics teachers during 5 months period from one higher education institution in Tangerang -Indonesia was collected.The design research method was carried out in three phases: preliminary design phase, teaching experiments phase, and retrospective analysis phase.Initial data analysis of 14 pre-service teachers' research and academic writing skills was conducted in six stages and the learning trajectories on this topic was identified.This study consists of three steps done repeatedly until the discovery of a new theory that a revision of the theory of learning is tested (Figure 2).

Method
Th is study uses a design research as research method, which is an appropriate way to answer the research questions and achieve the research objectives that start from preliminary design, teaching experiments, and retrospective analysis (Prahmana, 2013).Design research is a methodology that has fi ve characteristics, namely interventionist nature, process oriented, refl ective component, cyclic character, and theory oriented (Akker et al., 2006).Design research is a cyclical process of thought experiment and instruction experiments to implementation (Gravemeijer, 2004).Th ere are two important aspects related to design research.Th ey are the Hypothetical Learning Trajectory (HLT) and Local Instruction Th eory (LIT).According to Freudenthal (in Gravemeijer and Eerde, 2009), students are given the opportunity to build and develop their ideas and thoughts when constructing mathematics.Teachers can select appropriate learning activities as a basis to stimulate students to think and act when constructing mathematics.Gravemeijer states that the HLT consists of three components, namely (1) the purpose of mathematics teaching for students, (2) learning activities, devices or media used in the learning process, and (3) a conjecture of understanding the process of learning how to learn and strategies students that arise and thrive when learning activities are done in class (Gravemeijer, 2004).Th e fourteen pre-service mathematics teachers during 5 months period from one higher education institution in Tangerang -Indonesia was collected.Th e design research method was carried out in three phases: preliminary design phase, teaching experiments phase, and retrospective analysis phase.Initial data analysis of 14 pre-service teachers' research and academic writing skills was conducted in six stages and the learning trajectories on this topic was identifi ed.Th is study consists of three

Results
The results of this study indicate that learning trajectory on research in mathematics education have a very important role in assisting pre-service mathematics teachers to enhance their research and academic writing skills.The learning activities start from (1) dividing 14 pre-service mathematics teacher into seven groups to do research independently, reviewing mathematics education journal, searching and observing the current problem issue in mathematics education, and making research question; (2) designing and doing research based on observation results to answer the research question; (3) collecting and analyzing the research data and also making the conclusion; (4) searching the conference event, submitting the research abstract, and attending also to this event; and the last, (5) writing full paper based on the research result and publishing that paper in proceedings or journal as a part of dissemination stage.Furthermore, students collect all research process portfolio and give them research and academic writing skills questionnaire as one of evaluation process in this learning activities.As a result, students were able to do research, write scientific paper, and publish it seen from the research results in the end of activities.There are seven scientific articles that published in the proceedings of Konferensi Nasional Matematika XVII 2014 (six scientific paper) and the Jurnal Elemen Vol. 1 No. 1 (one scientific paper).For more detail, the researcher will discuss the results of the learning process on research in mathematics education, which is divided into three stages namely preliminary design, teaching experiments, and retrospective analysis.

Results
Th e results of this study indicate that learning trajectory on research in mathematics education have a very important role in assisting pre-service mathematics teachers to enhance their research and academic writing skills.Th e learning activities start from (1) dividing 14 pre-service mathematics teacher into seven groups to do research independently, reviewing mathematics education journal, searching and observing the current problem issue in mathematics education, and making research question; (2) designing and doing research based on observation results to answer the research question; (3) collecting and analyzing the research data and also making the conclusion; (4) searching the conference event, submitting the research abstract, and attending also to this event; and the last, (5) writing full paper based on the research result and publishing that paper in proceedings or journal as a part of dissemination stage.Furthermore, students collect all research process portfolio and give them research and academic writing skills questionnaire as one of evaluation process in this learning activities.As a result, students were able to do research, write scientifi c paper, and publish it seen from the research results in the end of activities.Th ere are seven scientifi c articles that published in the proceedings of Konferensi Nasional Matematika XVII 2014 (six scientifi c paper) and the Jurnal Elemen Vol. 1 No. 1 (one scientifi c paper).For more detail, the researcher will discuss the results of the learning process on research in mathematics education, which is divided into three stages namely preliminary design, teaching experiments, and retrospective analysis.

Preliminary Design
At this stage, the literature study on research-based learning, research skill, and academic writing skill was conducted by researcher including develop learning design and skills indicators.Furthermore, researcher conducted observations in undergraduate student, designing hypothetical learning trajectory (HLT), as shown in Figure 1.A set of activities for learning research in mathematics education has been designed based learning trajectory and thinking process of students who hypothesized and also discussed about learning trajectory and all indicator with Prof. Dr. Darhim and Dr. Nancy Susiana as an expert validator.Th e instruction set of activities has been divided into six activities that have been completed in 10 meetings that has been discussed above.

Teaching Experiment
At this stage, the learning activities that have been designed in the preliminary design stage was tested by researcher.Th ere are the student activity of dividing 14 pre-service mathematics teacher into seven groups to do research independently, reviewing mathematics education journal, searching and observing the current problem issue in mathematics education, and making the research question.Next, all groups design and research based on observation results to answer the research question.Aft er that, they collect and analyze the research data and also making the conclusion.Furthermore, lecture and all groups were searching the conference event and submitting the research abstract to this event.Lastly, they written full paper guided by the lecture based on the research result and published that paper in proceedings or journal as a part of dissemination stage.To see the response of the students during the learning process, researcher give them research and academic writing skills questionnaire and also collect all research process portfolio as one of evaluation process in this learning activities.

Retrospective Analysis
As a result, all activities which have been designed can be used to answer the research question above.Th e fourteen pre-service teachers were divided into 7 groups and conducted research independently to produce seven scientifi c articles.Th e six articles were published in the proceedings of Konferensi Nasional Matematika XVII 2014 and one article was published in the Jurnal Elemen Vol. 1 No. 1.For more details, the results of the learning process on research in mathematics education will be discussed.Th e activities are as follows: Learning trajectory which has been designed in Figure 1 is the activity undertaken in this study to guide students doing research and writing scientifi c paper as a their research result by using research-based learning.So that, researcher designed an activity that make students review journal and fi nd "hot" issue in mathematics education.Th is activities start from dividing all students into 7 groups and conduct research independently.Th e goal is that students are able to design learning trajectory for their research (Figure 3).

Fig. 3. One of the student's learning design for her research
2. Furthermore, all groups collected research data based on their research and analyzed that data a lso made the conclusion.Next, they are looking for the conference and submitting their research abstract his event as a part of dissemination of their research (Table 1).Furthermore, all groups collected research data based on their research and analyzed that data and also made the conclusion.Next, they are looking for the conference and submitting their research abstract to this event as a part of dissemination of their research (Table 1).2. Furthermore, all groups collected research data based on their research and analyzed that data and also made the conclusion.Next, they are looking for the conference and submitting their research abstract to this event as a part of dissemination of their research (Table 1).
Table 1.All research abstracts that have been submitted to Konferensi Nasional Matematika 3. Next, full paper based on the research result and feedback from all participants in conference that had been seen their present was written by all groups and guided by their lecture.
4. Lastly, they submit that paper in proceedings or journal.As the result, students were able to publish the research results in the end of activities.There are six scientific articles that were published in the proceedings of Konferensi Nasional Matematika XVII 2014 (Team 2-7) and one scientific paper in the Jurnal Elemen Vol. 1 No. 1 (Team 1) as a product of this research (research and academic writing skills).
5. The retrospective analysis occurred in the first cycle showed that these pre-service teachers were on the level 1 and 2, based on research skill indicators developed by Willison and O'Regan (2007).Further research analysis will be needed to revise the HLT which will be then tested back in the next cycle (further research).
Next, full paper based on the research result and feedback from all participants in conference that had been seen their present was written by all groups and guided by their lecture.
Lastly, they submit that paper in proceedings or journal.As the result, students were able to publish the research results in the end of activities.Th ere are six scientifi c articles that were published in the proceedings of Konferensi Nasional Matematika XVII 2014 (Team 2-7) and one scientifi c paper in the Jurnal Elemen Vol. 1 No. 1 (Team 1) as a product of this research (research and academic writing skills).
Th e retrospective analysis occurred in the fi rst cycle showed that these pre-service teachers were on the level 1 and 2, based on research skill indicators developed by Willison and O'Regan (2007).Further research analysis will be needed to revise the HLT which will be then tested back in the next cycle (further research).

Discussion
Th is study creates a learning trajectory on research in mathematics education using design research methodology (Gravemeijer and Cobb, 2013) to enhance research and academic writing skills for pre-service mathematics teachers.Initial data analysis of 14 pre-service teachers' research and academic writing skills were conducted in six stages and the learning trajectories on this topic were identifi ed.Th e fourteen pre-service teachers were divided into 7 groups and conducted research independently to produce seven scientifi c articles.Th e six articles were published in the proceedings of Konferensi Nasional Matematika XVII 2014 and one article was published in the Jurnal Elemen Vol. 1 No. 1. Th e retrospective analysis occurred in the fi rst cycle showed that these pre-service teachers were on the level 1 and 2, based on research skill indicators developed by Willison & O'Regan (2007).Further analysis will be needed to revise the HLT which will be then tested back in the next cycle.Open Access.Th is article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
, t. 123, Nr. 3 steps done repeatedly until the discovery of a new theory that a revision of the theory of learning is tested (Figure2).

Fig. 3 .
Fig. 3.One of the student's learning design for her research