Chapter 3: Methodology
3.1 Methods
This research applied the mixed methods design. Mixed-methods research is defined by Teddlie and Tashakkori (2011) as an inquiry that is conducted by “selecting and then synergistically integrating the most appropriate techniques from a myriad of QUAL, QUAN, and mixed methods” (p. 286). The method used in this study was based on a quantitative and qualitative (QUAN-Qual) model that is also known as an explanatory mixed methods design (Gay, Mills & Airasian, 2012; Mills & Gay, 2019).
More specifically, it is represented using the symbol as “QUAN qual” (deductive- sequential design, where the core component is quantitative and the supplemental component is qualitative) (Schoonenboom & Johnson, 2017). Kansteiner (2020) indicated that the Schoonenboom and Johnson (2017) approaches have been widely accepted because it is said to have many advantages ranging from philosophical positions to the question of method. This type of mixed-methods research is quantitatively dominated in which one relies on a quantitative, post-positivist view of the research process while recognizing at the same time that adding qualitative data and approaches is likely to be useful as it can expand understanding the quantitative data (Kansteiner, 2020; Schoonenboom & Johnson, 2017). Green (2007) lists five
main purposes for mixed methods research; triangulation, complementarity, development, initiation, and expansion. This research seeks to achieve the complementarity purpose as the qualitative data clarify and elaborate on the data of the quantitative portion and seek to enhance the MEP.
The main method used in this research was the quasi-experimental design. This quantitative method is used to fulfill the intention of this research to learn about the effect of the enrichment program on the students’ mathematical literacy. A quasi- experimental study was conducted based on groups of nonequivalent pretest-posttest design. A quasi-experimental design is chosen to fulfill the purpose of this study as it seeks to establish a cause-effect relationship between two or more variables (Gay, Mills & Airasian, 2012; Mills & Gay, 2019). The experimental groups were identified and enrolled in the math enrichment program. Results were compared with results from control groups who were not enrolled in the MEP.
Additionally, this study applied the survey design method to study the effect of the enrichment program on the students’ motivation. The qualitative part of this mixed- methods study came from the perceptions survey to understand the students’
perceptions of the math enrichment program. The use of the student survey to gain insight into students' perceptions was an additional design strength. Allowing students to complete an anonymous survey provided valuable data from those who enrolled directly in the math enrichment program to improve their mathematical literacy. This data was collected in a non-threatening, inexpensive way, and could be used to compare students' perceptions with actual results.
Internal validity is the degree to which the observed differences in the dependent variable are direct results of the treatment of the independent variable, not
some other variables (Gay, Mills & Airasian, 2012; Mills & Gay, 2019). This study did not control many of the confounding variables that have been shown to affect student achievements such as differences in teachers’ pedagogy, language barriers, individual learning styles, and the instructional methods. Thus, the complexity of teaching and learning styles and inability to manipulate different aspects of the program addressed the various aspects of the program to distinguish differential effects were threat the internal validity. However, the nature of the MEP focused on communication and sharing of ideas during solving problems together. This nature was agreed upon it with teachers who implemented the MEP with their students as part of the PBL and CTL.
Random selection of group participants is argued to be the best way to control several external variables simultaneously and to ensure equivalency in groups (Gay, Mills & Airasian, 2012; Mills & Gay, 2019). Therefore, the lack of randomization of the participants was one of this study’s weaknesses. However, in an attempt to limit the effect of the lack of randomization of the participants, the researcher randomly assigned the experimental and the control groups as whole classes in each of male and female schools. Moreover, both schools were chosen from Al Ain, the same city, besides MEP was implemented only for grade 10 Advanced as a selected criterion.
Thus, since there was no control over the previously mentioned variables, the events must be interpreted carefully because the cause-and-effect relationship might not be the ones that it appeared to be (Gay, Mills & Airasian, 2012; Mills & Gay, 2019).
The external validity or generalizability of the study was limited by the possible effect of pre-testing. Pretest-posttest designs are widely used in behavioral research, primarily to compare groups and/or measuring change resulting from experimental
treatments (Gay, Mills & Airasian, 2012; Mills & Gay, 2019). To increase the generalizability of the study by limiting the researcher's influence on participants, the experimenter's influence was controlled by selecting both experimental and control female groups that were taught by the same teacher in addition to selecting experimental and control male groups that were taught by one teacher as well. The researcher was only involved in the pilot study application. The testing effect was minimized because two months were separating the administration of pretest and posttest.
The essential strength of mixed-methods design was that it would not be possible without the synergy between quantitative and qualitative research. The mixed-methods design allowed the researcher to use more than one approach to analyze research questions. Quantitative statistical data could be described by the insight of personal survey questions. Another positive feature of this research revolved around action research with the professional implications of the learning community and educational decisions. Action research in education is based on a systematic survey in the teaching and learning environment that will influence a positive change in the school environment (Gay, Mills & Airasian, 2012; Mills & Gay, 2019). This will allow stakeholders to make informed decisions to improve students’ mathematical literacy.
The General and Advanced streams are dominant in most secondary schools.
Depending on the students’ performance, they can choose either to remain in the general stream or to join the advanced stream. In both, general and advanced streams students will continue Grades 10, 11 and 12. The key difference between the general stream and the advanced stream is the range of scientific subjects. Students in the
advanced track will receive more in-depth instruction in mathematics and sciences than those in the general track. Thus, most high achiever students choose the advanced stream.