Conceptions, in the mathematics education research, address a mental structure including beliefs, concepts, mental images, and meanings (Philipp, 2007). Most of the studies on doctoral students’ conceptions do not provide much information on how they refer to the construct of ‘conceptions.’ Meyer, Shanahan, and Laughksch (2005) state the conceptions of research as “reflected as (variation in) the contextualized beliefs, ideas, or understandings of postgraduate students who are actually engaged in various forms of research” (p.227).
Meyer (2007) addressed that postgraduate research was a learning process. In this process, new knowledge was created through an interaction of research processes and prior knowledge of research, which were influenced by conceptions of research. He stated that while research processes addressed generic or discipline-specific elements within the production of research, prior knowledge of research included the ways of creation of a new knowledge in the discipline.
This prior knowledge of research, in turn, influenced conceptions of research when individuals were involved in the research process. Therefore, conceptions of research were likely to be context and/or discipline specific because of the specific research processes and prior knowledge of research (Meyer, Shanahan,
& Laughksch, 2005; Stubb, Pyhältö, & Lonka, 2012).
Research on conceptions of research has focused on undergraduate and graduate students, doctoral supervisors, and senior researchers and has employed qualitative and quantitative approaches in a wide array of disciplines and fields.
The most widely expressed conceptions have been knowledge orientated in terms of gathering, exploring, discovering, or validating knowledge as well as problem solving (Akerlind, 2008; Brew, 2001; Meyer, Shanahan, & Laughksch, 2005; Pitcher, 2011; Stubb, Pyhältö, & Lonka, 2012). Research has also been conceptualized as a personal journey where researchers have investigated their interests and developed own understandings (Akerlind, 2008; Brew, 2001; Stubb, Pyhältö, & Lonka, 2012) or as a job to do especially by doctoral students in natural sciences or medicine (Stubb, Pyhältö, & Lonka, 2012). Conceptions of being a
researcher, on the other hand, have received less attention among researchers.
Being a researcher was conceptualized among academics from a wide range of research areas as fulfilling academic requirements, establishing oneself in the field, developing oneself personally, and enabling a broader change (Akerlind, 2008). These conceptions seemed to be parallel to the conceptions of research stated earlier.
The stated conceptions of research and of being a researcher, however, have not specifically addressed conceptions of doctoral students studying in the field of mathematics education. Doctoral students have relatively shorter duration of research experience and are still considered in the process of developing conceptions of research and of being a researcher in the field of mathematics education. Understanding conceptions of research and of being a researcher may provide a baseline for training programs focusing on researcher skills such as developing critical thinking and multiple perspectives, and distinguishing between judgments based on evidence or speculation (Meyer, Shanahan, &
Laugksch, 2005).
Doctoral students’ conceptions are likely to reflect the research context they work in. An analysis of completed dissertations and theses in the field of mathematics education in Turkey has revealed that more than half of the graduate research in the last decade focused on issues of teaching mathematics, learning mathematics, methodological issues, mathematics teacher education, and mathematics curriculum (Baki, Güven, Karataş, Akkan, & Çakıroğlu, 2011) supervised by mathematics education researchers with mathematics or mathematics education background (Sriraman, 2010). Therefore, Turkish mathematics education doctoral students’ conceptions are likely to be influenced by these past studies, the local and national research context, and their supervisors’ research fields and priorities.
Methodology
Context
The study was conducted in the context of the doctoral program in Elementary Education focusing on issues of teaching and learning at all levels in the fields of mathematics, science, and early childhood education. Students with related backgrounds can pursue their studies in this program either after getting a Master’s degree by taking 21 credits or a B.S. degree (integrated program) by taking 42 credits. The program required students with Master’s degree to take an advanced course on research methodologies and dissertation credits in addition
to five elective courses. Students without Master’s degree should also take research methodologies, statistics, and seminar courses. Doctoral students pass a doctoral comprehensive examination (which is administered twice a year – May and November) after or during the completion of their coursework within the first five semesters. They defend their doctoral dissertation proposal six months after they pass the examination to a dissertation committee and report their progress to this committee every six months. They defend their dissertation to their doctoral dissertation examination committee and are awarded by the Ph.D.
degree upon a successful defense.
The language of instruction and dissertations is English in the program. The department had 12 faculty members and four of them were working in the field of mathematics education at the time of the study.
Participants
The study was announced to all mathematics education doctoral students in the program (i) who pursued their degrees after getting a M.S. degree; and (ii) who were in the integrated program and passed the doctoral comprehensive examination. Among the 20 contacted students, 10 (9 females and 1 male) accepted to participate. All of the participants had their Master’s degrees and had taken research methodologies and statistics courses during the Master’s studies.
Three participants had not taken the advanced course on research methodologies.
Two of the participants were writing their dissertations. One participant has passed the doctoral comprehensive examination and the others were in their first four semesters of the program. Seven participants were graduate assistants, five of which with contracts with other universities as future faculty members, one at another university, and one at the program department. One participant was working as an elementary mathematics teacher trainer in a private school and two were unemployed, one of which had previously worked in the department for six years.
Students may apply for doctoral programs in Turkey without an explicit research interest and/or a funded project. Their doctoral research is generally supported by the Graduate School of Social Sciences in terms of expenses once during their studies. They may participate in research other than their doctoral research not necessarily with financial benefits under the guidance of a faculty member.
Students who are working as graduate assistants at public universities are paid a monthly salary on 12-month contracts and their primary duties are generally teaching related.
Data Collection
Participants were asked to complete two tasks in the beginning of April 2012. The first task was an open-ended questionnaire with 19 major items asking doctoral students about their views of conducting research and of being a researcher in the field of mathematics education, future plans for research after completing their doctoral studies, and reflections on and evaluations of the mathematics education research in Turkey. The second task asked participants to develop a career plan considering their current research interest, future research plans, and anticipated problems at their future universities. Two tasks were initially piloted for language, clearness, and comprehensiveness with a mathematics education doctoral student at another department in the same faculty. Final versions of tasks were sent to participants via e-mail and they were given one week to respond and send their responses back in the same way.
Participants’ responses were initially analyzed for conceptions of research and being a researcher in the field of mathematics education with focus on the role of the researcher, the research methodology, knowledge and skills needed for being a researcher, future plans, and future problems. Then, participants were invited to a one-day workshop developed through the findings of the initial analyses two weeks after they sent their responses. The responses were clustered around similar views and the aim of the workshop was to help participants to think about, discuss, clarify, and expand their views of conducting research and of being a researcher in the field of mathematics education. We also aimed to help them develop a more critical perspective on the conceptions and practices in the field. The participants discussed most of the questionnaire items in three groups in the first phase and were asked to write their group-agreed responses as well as different responses in the group. Then, all groups announced and discussed their responses facilitated by researchers. Extensive notes were taken through the workshop by the researchers. The aim of the second phase was to help participants develop more realistic career plans in the light of their discussions in the first phase.
Data Analysis
Data of the study were participants’ written responses to open-ended items in the questionnaire before the workshop, their group responses to some of the selected questions during the workshop, and notes taken by researchers during the workshop discussions. Data analysis process employed thematic analysis steps (Braun & Clarke, 2006), which were guided by research questions and data in a more flexible way. Data were first read by researchers several times, common
issues were detected among the responses, and an initial list of codes was generated. Coded data were clustered in potential themes. While conceptions of research and of being a researcher were themes driven by the research questions, conceptions related to the quality of the research was revealed as another theme during the analysis. The themes were reviewed through the codes and data, and finalized. Conceptions of research included purposes and outcomes of research and mathematics education research, audience of research, and research methods.
Conceptions of quality of research included research process and capacity of research. Conceptions of being a researcher comprised researcher’s knowledge and skills of researchers and their values and attitudes.
Findings
Conceptions of Research
In general, participants’ conceptions of research in their written responses before the workshop mostly focused on the potential of closing a possible gap in the field, identifying possible problems objectively, and exploring people’s ideas about the problem, as well as developing solution strategies for these problems.
Contributing to the knowledge base and theories in the field and to the society were other reasons for conducting research. A doctoral student stated that:
Research is conducted for the purpose of serving science and society by providing new theories and products through investigation, and if necessary, evaluation of the existing research and theories.
The fundamental purpose of conducting mathematics education research was to improve the quality of mathematics instruction in schools by identifying and solving problems and removing gaps. Investigating factors affecting student achievement and teacher effectiveness in school mathematics was also one of the major purposes: “[Mathematics education research is conducted] in order to investigate the problems in the system […], to provide ideas for what could be done for a better mathematics instruction, and to produce solutions.”
Participants elaborated more on the purposes of mathematics education research in the workshop. The nature of knowledge produced through the research was important while conducting mathematics education research.
Doctoral students addressed that research should contribute to the mathematics education field through producing scientifically valid and reliable knowledge for the mathematics education. In this sense, evaluating existing programs and implementations in schools and research in the field was important. Specifically,
the validity of international research findings, education programs, and school based implementations in the Turkish context should be evaluated through the research. Understanding the nature of successful implementations was also considered as a focus of the research. One of the groups stated this in their written notes in the following way:
[Mathematics education research] is conducted in order to determine the existing situation in the mathematics education. [...] Research is conducted both for successful and unsuccessful situations. If unsuccessful, [research is conducted] to figure out the problem. If successful, then [the reason for success are investigated].
One of the groups also claimed that the research should raise the awareness about the undervalued issues in mathematics education and address research trends in the field. The contribution to society, teachers, students, and the theory in the mathematics education was also emphasized by all groups. The interesting issue in doctoral students’ responses was that they did not specifically state the teacher education as an issue in the field of mathematics education although most research was conducted on teacher education issues in the department including some participants’ Master’s theses.
We were particularly concerned about how doctoral students conceptualized the audience of the mathematics education research. Questionnaire and workshop responses to the related item did not differ. Participants stated that research in mathematics education should have contribution to teachers’ development and should inform people involved in this field, such as teacher educators and teachers themselves. They also mentioned that research should inform people who were responsible for quality of instruction in schools, such as curriculum developers and teachers. They argued that students were influenced by the research findings rather indirectly. Despite our request for a list of priority, most of our participants claimed that groups they mentioned had equal importance.
Doctoral students prioritized longitudinal, experimental, and qualitative methodologies in the field of mathematics education in their written responses. In the workshop, they additionally mentioned that review studies, action research, and mixed methodologies should be employed in mathematics education research. The emphasis on the longitudinal and in-depth studies was also apparent in their workshop responses such as “Longitudinal studies should be conducted especially when there is a new implementation in the education system in order to study them in the long-term” and “... Because previously identified problems and deficiencies may better be solved by these methodologies.”
Quality of a Research
Doctoral students’ written responses about the quality of research in the field of mathematics education addressed that the research should be planned and carried out thoroughly. The research process should produce valid, reliable, and significant knowledge, as well as applicable and realistic results for the field. Research should be methodologically sound and have a strong theoretical background. The context and researcher’s stance were important and should be acknowledged:
The research process should be well-structured. The topic should be worthy, the proper sample should be identified, the supports that could be received should be planned, [and] data collection tools should be determined previously. [The research topic] should be addressed as important in the literature, should have a theoretical background, should be free from bias, should be realistic, and should have a possible aim of finding a solution to a problem.
Analysis of the workshop discussions revealed that the capacity of research to direct further research was important for participants. They argued that the communication of findings should be clearly expressed so that stakeholders could make sense. Discussions addressed teachers as the group for which the findings of the research were less communicated and participants criticised researchers for not making their findings accessible to teachers.
We ignore the relative importance of the publication for the reader. The findings are presented only for the researchers, teachers may not have any information about [the findings].
Participants also argued that the quality of the research was evident in its potential to inform the contexts beyond the research context and its capacity to be published in highly respected journals.
the Mathematics education Researcher
Doctoral students’ conceptions of a mathematics education researcher were sought both in the questionnaire and in the workshop by means of the knowledge, skills, attitudes, and values that researchers should have. Written responses revealed that the mathematics education researcher should have up to date knowledge in the field, in the related literature, and in research methodologies. Having critical knowledge of the field was prioritized by some of the doctoral students: “First of all, [the researcher] should be competent in his/her field, have an idea about
the related studies, and be able to interpret and discuss them. He/she should be sensitive about how research is conducted.”
Participants pointed that being a reflective thinker and being objective in interpreting his/her own research were important characteristics of researchers.
In addition they argued that a researcher should be creative and foresighted:
… the basic skills that researchers should have are being able to inquiry and reflect. Mathematics education researcher should follow the new improvements and investigate their results. Meanwhile, he/she should evaluate these in order to improve his/her knowledge and skills. He/she should also reflect these in his/
her communities and relationships.
[The mathematics education researcher] should be creative, be able to observe problem situations or see the new problem situations within the existing research, should be able to investigate these [problems] through scientific methods, should use the mathematical language well, and should have the skill for verbal and written [communication].
Some of the participants gave a more detailed account of what they meant by the knowledge of the field. They argued that the knowledge of field in mathematics education would include mathematics content knowledge, pedagogical content knowledge, knowledge of pedagogy, and knowledge of theories and research in the field. Participants stated that a researcher should have skills to implement this knowledge into their research and be a problem solver.
In their written responses, participants’ conceptions of attitudes and values of a mathematics education researcher emphasized being open to improvement and the person’s willingness to contribute to the field. According to participants, a researcher should also be sensitive to ethical issues and have a concern for the society, as well as for his/her participants:
He/she should be open to new improvements and should aim to contribute to mathematics teaching and learning by communicating other people in the mathematics education field.
He/she should not consider the teachers, students, preservice teachers, and researchers as a “sample”, but see them as “human beings” and be aware of the fact that his/her research is affecting these people in some ways and [research]
is not mechanical. In short, he/she should value people… should have ethical principles in research.
He/she should not misinterpret the findings of his/her research. The findings may contradict with certain group’s [and individual’s] personal or financial gains. In this case, he/she should express the findings as they are. He/she should have the value that expressing the true findings contributes to the science and society instead of considering individual’s gains and power.
Participants addressed personality traits of a researcher such as being “disciplined and organized”, “patient”,” enterprising”, “collaborative”, “responsible”, and
“respectful” in their written responses. The mathematics education researcher should have developed effective research skills such as observation and written and oral communication as well as discussion and listening.
The most discussed issue in the workshop was patience and collaboration among mathematics education researchers. Doctoral students addressed that researchers tend to conduct rather short-term studies because long-term studies would require more patience and time taking procedures to be conducted. They stated that the lack of effective collaborative skills were a result of considering personal ambition and gains more than the benefit for the society.
Conclusion
The purpose of the current study was to investigate mathematics education doctoral students’ conceptions of research and of being a researcher. One of our intentions was to explore their beliefs, meanings, mental images, and ideas
The purpose of the current study was to investigate mathematics education doctoral students’ conceptions of research and of being a researcher. One of our intentions was to explore their beliefs, meanings, mental images, and ideas