Methodology
Hallinger et al (2011) articulated in the research that IB schools confront the major issue in the transitioning process from MYP to DP for the continuum of mathematics. Therefore, the main focus of the study was to minimize the expectation gap in transitioning through horizontal and vertical curricular planning, as the official organization of the International Baccalaureate suggests. The study sought to examine how IB school ensures a smooth transitioning from the Middle Years Program to the Diploma Program through the past years’ results of recently graduated students of mathematics of both Middle Year and Diploma Year programs, interviews, and surveys. The research study utilized a mixed method approach to minimize the expectation gap in IB school for the seamless transition process from IB mathematics programs, including the Middle Years Program to the Diploma Program incorporating both qualitative and quantitative methods. A survey of 20 participants of IB MYP and IB DP teachers of the language of mathematics using the purpose-built questionnaire for getting their perception of the continuum of mathematics in DP provided the quantitative data that allowed the researcher to draw comparisons and inferences. Moreover, past exam results of students of IB MYP and IB DP also provided the quantitative data approach to address the concern about the potential expectation gap in IB schools. The qualitative data collected for the study involved interviews of recently graduated students from IB middle years and diploma programs as well as IB teachers, coordinators, and counsellors of the department of mathematics.
The Methods of Data Collection
Type of Data Collected
The primary data collection method was used to gather, record, measure, and analyze accurate data from a variety of reliable and relevant sources for both quantitative and qualitative methods. The method adopted in the study for data collection included the survey method, interview method, and observation method to identify the expectation gap in the continuum of the language of mathematics from MYP to DP in the International Baccalaureate School. The mixed methods methodology was solely to identify, measure, and analyze problems in a smooth transitioning process, answering the research questions, testing hypotheses, and evaluating the outcomes so that probabilities and trends can be forecasted (Long and Richards, 1987).
Data Collection Tools
The underlying need for data collection was to minimize the expectation gap in IB school by capturing quality evidence for the smooth transition problem that both programs for mathematics posed. Collection of data was done from surveys, one-on-one interviews of IB MYP and DP students, as well as IB mathematics teachers and reviewing of past final examinations of recently, graduated students from the selected IB school. These tools were taken as the primary data collection method to emphasize how the collected data was used and what explanations the collected data and the related data collection tools would generate to determine the analytical approach and methodology applied by the researcher in the study.
Sample Selection
The researcher used both qualitative and quantitative research methods to get data through observation methods from both MYP and DP Mathematics programs’ students and teachers of the IB school selected for the study. Students from both the mathematics programs were selected who had already completed their graduations through external assessments and examinations. The first step of sample selection was to select random senior students from both programs to record their responses, the second step was to interview MYP and DP mathematics teachers of IB school, the third step was to conduct the survey based on purpose-built questionnaires, and the fourth step was to analyze students’ examinations and assessments to assess how smooth the transition was from Middle Years to Diploma Program in the selected International Baccalaureate school for conducting the research. All the data and samples collected were recorded and analyzed under the supervision of IB moderators to have different ranges of responses and judgments regarding the transition process. The scores from the Middle Years Math program were assessed on the basis of four criteria: knowing and understanding the basic math ideas and concepts, investigating different patterns to solve particular problems, communicating mathematical concepts in the classroom tasks, and application of the language of mathematics for solving problems in real-life contexts (IB, MYP, 2020). The researcher relied on the level of students’ consistency in their internal and external examinations from each criterion to effectively evaluate the outcomes of smooth transitioning from MYP to DP mathematics in IB school (Walker et al., 2014). However, the scores for final examinations of the IB Diploma Program were taken and analyzed from the average of each senior student’s internal and external assessments.
Participants of the Study
The participants of the study were students of the language of Mathematics from Middle Years and Diploma programs who had already taken the examinations in the past years. Their scores in the final examinations of mathematics were calculated and compared to their level of achievements to explore how effective was the transition process. Moreover, interviews of recently graduated students from the selected IB school were conducted randomly in both programs, interviews of 20 teachers were also recorded, and their transcripts were thoroughly analyzed to measure the effectiveness of a smooth transition from the MYP to the Diploma Program (International Baccalaureate Organization, 2010). All the participants of the study including teachers and recently graduated IB students of Middle Years and Diploma Programs, were volunteers who contributed effectively to the data collection for the research through interviews and surveys. The survey questionnaire was used to determine the strengths and difficulties students and teachers faced during their work or study at the IB school regarding the transition from MYP to DP mathematics and was used as the screening instrument to identify and minimize the expectation gap (Goodman, 1997).
Design of the Study
The interviews of teachers as well as students of mathematics in international baccalaureate schools, scores of MYP mathematics final examinations, and surveys were used as independent variables to minimize the expectation gap in IB school while exploring the continuum of mathematics in the smooth transitioning process from middle years to the diploma program. The final result of each MYP mathematics student was judged and recorded by each criterion to assess the smooth transition from MYP to DP mathematics. The design of the study was to evaluate whether the preparation of the MYP curriculum was sufficient to prepare students to join the Diploma Program in mathematics (Daly et al, 2012). Teachers were interviewed individually, and their subjective opinions and experiences were recorded. Responses were not of any significant difference as teachers for both programs were the same, highly qualified, and trained in their respective fields of the language of mathematics (Perry et al., 2018). The DP scores of mathematics were used as the dependent variable as the course had rigid weights of assessments to set the final score of the program with no specific criterion. Moreover, the assessments of Diploma Program mathematics were assessed under the supervision of IB moderators of the school in order to evaluate the validity of teachers’ responses and judgments they presented in the interviews regarding the continuum of the language of mathematics and related fields in the Middle Years program to the DP mathematics in IB school (International Baccalaureate Organization, 2015).
Calculation of Selected Data
After the collection of data through both quantitative and qualitative methods to research, the next step was the calculation of data based on the criteria for MYP so that outcomes for both Middle Years and Diploma programs could be compared and calculated. The scores of MYP mathematics from the criterion of knowing and understanding the basic mathematical ideas and concepts were compared with DP mathematics internal examination 1. Secondly, the Scores of MYP mathematics from the criterion of investigating different patterns to solve particular problems were compared against scores of DP mathematics 2nd internal examination. Thirdly, the scores of MYP mathematics from the criterion of communicating mathematical concepts in the classroom tasks were compared against the average external examination of DP mathematics. Fourthly, the scores of MYP mathematics from the last criterion of MYP to analyze how effectively students were able to apply the language of mathematics for solving conceptual mathematical problems in real-life contexts were taken against the DP mathematics criterion of final examination scores to be compared for the accumulation of final scores. All these scores were accumulated, compared, and analyzed under the surveillance of IB moderators for the assessment scores of both MYP criteria and DP internal and external assessments. The researcher compared and analyzed all the sets of MYP and DP criteria on the basis of regression values. It was suggested that if the analysis of the designed sets of MYP and DP approached a +1-regression value, it was taken as the successful and smooth transition from the Middle Years to the Diploma Program for the continuum of mathematics. However, if the regression value of the analysis approached 0, then the transition suggested that the curriculum of the Middle Years program needed to be revamped to achieve the desired results in its system of assessments.
Ethics of Study Referencing BERA Guidelines
Justification of Research Methodology
Nature of Theoretical Knowledge
The theoretical knowledge of the study aims to connect the researcher of the study to the existing knowledge that is relevant to the research topic or problem assumption. Articulating the problem assumption of the research study permits the researcher an intellectual transition from describing a phenomenon in a simple manner to addressing questions of what, why, and who in order to generalize about diverse aspects of that phenomenon. A theoretical framework, in this regard, helps to identify the limits to those generalizations that specify key variables in the research to influence and highlight the relevant guided theory to be examined under different circumstances. The reason why the present research study used evaluation of the theoretical knowledge students were taught in the Middle Years Program and Diploma Program through their assessments and final examinations was to conduct fundamental or basic research through investigation on a certain particular event of the transition process from MYP to DP for minimizing the expectation gap that under study existed in the International Baccalaureate School (Tampubolon, 2017). The theoretical knowledge of this study has also limited the scope of the relevant data to facilitate the understanding of the variables and concepts by defining the particular framework and focusing on certain specific variables such as to minimize the expectation gap in the IB school that the researcher collected data for through different data collection tools. Moreover, the theoretical viewpoints or framework of the research builds new knowledge through the understanding of variables by challenging and validating problem assumptions that exist under the study.
Consideration of Different Research Methodologies
The consideration of different research methodologies to facilitate the collection of data prior to the data collection approach, fieldwork, cultural or social context of the study, ethical issues, adequacy of the sampling method, and practical skills to conduct the research is a crucial approach. The present study utilized both approaches to collecting data; qualitative and quantitative research through a mixed method approach including survey, interviews, and observation methods for data collection, interpretation, and analysis to address methodological issues as the most significant quality criterion of research. The methodological consideration for the qualitative research method in the study was to identify the theme of minimizing the expectation gap through data collection tools and patterns under the interpretative phenomenological approach to analysis (Curry et al., 2009). On the other hand, the methodological consideration for the selection of the quantitative research method in the study was to answer the problem question or the designed objective to determine the kind of data collected through the study and the analysis that needs to be conducted. This consideration of research methodology is influenced by numerous factors in the quantitative method in mixed methods research including the specific expertise of the researcher, resources, scope of work, and the availability of the research design to confirm a hypothesis (Pluye et al, 2009).
Reason for Choosing Research Methodology
The pivotal rationale for choosing a mixed method research methodology was what was suggested by Greene et al. (1989) Johnson and Onwuegbuzie (2004) cited in their research “Mixed methods research: A research paradigm whose time has come” that there are five important rationales to conduct the mixed methods research methodology in the research study including initiation, complementarity, development of results from the other research method, triangulation, and expansion of the variables for obtaining the distinct range of outcomes. The triangulation poses the confirmation of results through different methods; the process of complementarity elaborates, enhances, and clarifies results that are deduced from one method for the stimulation of another method used in the research study. The development approach of using a mixed method shapes the other method through the result of one method, the expansion approach expands the range of research for obtaining results from different lines of inquiry, and the initiation rationale for conducting the mixed method approach is where new research questions are stimulated through obtaining new and different insights into the research topic. The present study is based on the triangulation approach of Greene et al. (1989) cited by Johnson and Onwuegbuzie (2004) for the confirmation of a smooth and seamless transition process from MYP to DP mathematics to investigate the expectation gap in the International Baccalaureate School and the identification of ways to minimize that gap. The triangulation approach requires a researcher to not just amalgamate the corroboration of data collected through different methods in the mixed method research methodology approach but rather focus on how the data would be collected, findings would be analyzed, research questions or problem assumptions would be answered, and the result is being combined. Moreover, the mixed method research methodology in the study dictates what type of data collection methods and tools would be used or employed that are capable of meeting the objectives of the study that underpin the research. Mixing different methods of data collection and analysis techniques in the research allowed the researcher of the study to put findings in context gathered through quantitative and qualitative research methods and to add richer details to the conclusions of the study. Using different research methods through mixed method research methodology in order to collect data on the same research subject enabled the researcher to make the results of the study more credible so that the expectation gap in the continuum of mathematics from the Middle Years Program to the Diploma Program could be minimized in the IB school (Johnson and Onwuegbuzie, 2004).
Nature of Research Methodology
The nature of the mixed methods research methodology opted for the study was a research design with methods of inquiry into the continuum of mathematics through the smooth transition process from MYP into DP with philosophical assumptions to minimize the expectation gap in International Baccalaureate School. The mixed methods approach in the research is regarded as a methodology that involves philosophical assumptions along with methods of inquiry to guide the researcher about the direction of how to collect the data and analysis of the collected data through quantitative and qualitative approaches during many phases of the research phenomenon (Bashir et al., 2017). The central premise of the mixed methods research methodology is to focus on the collection, accumulation, and analysis and use both qualitative and quantitative approaches in combination. The mixing of both qualitative and quantitative data provides the researcher with enough knowledge and information collected through different sources to conduct the research with a better understanding of the research problems and gaps in the research in a single study or series of research studies through a range of concurrent and sequential strategies.
Purpose of Research Methodology
The research methodology of the study facilitates the conceptual basis for collecting, designing, analyzing, and investigating the data collected through different tools such as survey method, observation method, interview method, questionnaire method, etc., in order to investigate relationships and problem assumptions within a social system. The purpose of research methodology is to serve the ways of discerning certain specific facts to evaluate or prescribe solutions to the research problems among the accumulated knowledge. The point of the mixed method research methodology is to comprehensively justify how the researcher has designed the research and how a specific approach to research methodology would address the thesis question by using different data collection tools in order to get diverse perceptions and observations (Tashakkori and Creswell, 2007). The overall goal of choosing a mixed methods research methodology was to combine the elements of qualitative and quantitative research in order to expand the research to contribute the new component to already published literature. The mixed method approach in this study would strengthen the study’s conclusion in achieving a more seamless and successful transition from Middle Years Program mathematics to Diploma Program mathematics for the continuum program in the Mathematics Department. The approach would also analyze the correlation between both the IB mathematics programs to revamp the curriculum of MYP in case the results of the study reveal no successful transition (Walker and Lee, 2018).
Bias and Variables in Research Methodology
The comparative weakness or bias in the research methodology chosen for the study was the smaller sample size due to the qualitative research method in mixed methods research methodology. Some bias of the study during the data collection phase for the researcher was the voluntary nature of participants as when interviewed, people were asked about their ideas, observations, beliefs, and experiences regarding working in the IB school by a small group of school staff and recently graduated students, it could not be taken as the practice on the whole. The participants of the study were volunteers from the IB school, so it was difficult to assume for the researcher whether the members of the Department of mathematics and the other group of students who volunteered for the research who recently graduated from the IB school followed the same practice. Therefore, it was a difficult task for the researcher to conduct a quantitative analysis for the small size sample of the teaching staff and students of the school selected for the study. Another variable of the research that could be the bias of the study was that grades are especially important in the International Baccalaureate School for the continuum of mathematics from MYP to DP. However, the staff of the department of Mathematics does not consider the bias of group grading in the MYP assessments, where the achievement rate of the individual candidate cannot be measured for future career opportunities. This approach of group grading in the IB school can create a cultural bias as the IB sets this bias in a context where an alternative idea of individualism poses a culture to determine individual selection decisions through the assessment outcomes while transitioning from the MY Program to the Diploma Program in the International Baccalaureate school (Benitez et al., 2022). IB culture expects that all students should work together like a prospective team for the completion of a task or an activity to enrich students’ interprofessional skills if they encounter any such situation in the future workplace (IBO, 2018). However, this negation of the idea of individualism in IB school’s criterion of group work seemed as bias in the study as the researcher found it impossible and difficult to identify the contribution and role of an individual to the whole group activity.
Mitigation of Biases in Research Methodology
In the mixed methods research methodology chosen for the study, the researcher crafted the contextualized insights of the qualitative data through detailed insights, whereas quantitative data crafted the externally generalizable and valid insights that mitigated the comparative weakness of a smaller sample size with a larger sample size in the quantitative study. In this way, the strength of one type of data collected to conduct the research often mitigates the weakness of the other data collection method in the study. The mixed methods research methodology in this study manifested certain different variables collected through different data collection types to obtain a complete picture of the construct in order to minimize the expectation gap for the continuum of mathematics through a smooth and successful transitioning process from MYP to DP in the International Baccalaureate School. The methodology aimed to avoid the bias associated with a single variable in the study, such as the performance of DP mathematics students in IB school in subjects related to the language of Mathematics, including Algebra, Geometry, Calculus, and Trigonometry as variables for the manifestation of mathematical ability.
Reliability and Validity of Research Methodology
In comparison with other types of research methodologies, mixed method research methodology is more reliable and valid as this approach to methodological issues ensures consistency across time and researcher through reliability and variability score through the validity of the data collected to be analyzed (Bryman et al., 2008). The method opted for the study was time-consuming yet strengthened the judgment based on different evidence and facts through different data collection tools and improved the casual inferences in hypothesis testing through observing the data convergence and divergence. The study offers reliable and valid responses to the research questions in a concise manner to the extent that if the same study is to be conducted with the same instruments, the results would be no different than the present study concluded for the minimization of the expectation gap in the continuum of the language of mathematics from MY Program to Diploma Program in the IB school. The survey and interviews were used as valid and reliable data collection tools that allowed the researcher for both quantitative and qualitative data to be captured for the study that centred on the research questions and objectives of the research.
Triangulation of Research Methodology
The present research study approached the triangulation method in the mixed methods research methodology to bring together all the findings collected from different tools and sources such as surveys, observation, and interviews for the research inquiry. The study opted for the research strategy of methodological triangulation to enhance the confirmability of findings in qualitative as well as quantitative research to enhance the credibility and validity of the findings. Howe takes on the disjunctive conception of the role of triangulation and various conceptions and roles of mixed methods research methodology that is assigned to both qualitative and quantitative research methods. He takes on the challenge of exploring qualitative and quantitative research methods and concludes that the quantitative research approach is for testing casual relationships in the research, whereas the qualitative research method is for the discovery of the findings of the study. Howe also states his insight about the biased nature of the participants of the study that people act in an intentional manner and the researcher can only capture the collective intentionality. This behavior of the participants of the study, according to Howe, leads to the construction of certain facts as well as challenges when the researcher combines the findings with certain specific skills, knowledge, and dispositions. He reaches the controversial conclusion that the role of qualitative research method in the mixed method methodology is providing casual explanations whereas the role of quantitative research method in the mixed methods approach research methodology is descriptive. The explanation for the triangulation in the qualitative interpretative method is that it answers the “why” question by putting the data collected through different data collection tools in the research to a more comprehensive explanatory framework (Towne and Shavelson, 2002). The triangulation approach through using multiple datasets and methods to address a research question, also helps to reduce bias that comes from using a single data collection method in the research. Therefore, for the qualitative research in the study, the researcher utilized a mixed methods approach to research methodology that refers to a similar idea of triangulation by the act of combining several research methods in the research to study the exploration of the continuum of mathematics from MYP to DP through the smooth transitioning process so that expectation gap in the IB school could be minimized.
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