mediante la cual se conoció y aceptó la renuncia del presidente

A decision concerning methodology entails a consideration of one’s own view of social reality and this requires a discussion of two important concepts: ontology and

epistemology. There are two opposite views concerning the nature of social science, both of which adopt very different ontological and epistemological assumptions: the traditional view (objectivist) and the interpretive view (subjectivist). The former regards social sciences and

natural sciences as having the same ability to ‘discover the universal laws’ (Robson, 2002, p. 5), while the latter focuses on the description and explanation of people’s different

behaviours rather than objects.

The objectivist approach holds a static view (also called standard view) of social science. Knowledge is assumed to exist outside of the knower as an independent existence, which is ‘hard, objective and tangible’ (Cohen et al., 2011, p. 6). It separates facts from values, and is known as positivism (Robson, 2002). Therefore, this ontology follows from an absolutist epistemology which has four characteristics: cause-and-effect thinking; select variables to interrelate; observations and measures; and theory verification (Creswell & Clark, 2007). Therefore, in a similar way to natural science or physical science, the objectivist view focuses on what we can see to uncover social laws (Johnson &

Onwuegbuzie, 2004). However, few studies in social science would take this extreme view as it implies that data is time-, context- and value-free. Therefore, post-positivism as an

extended approach emerged in the middle part of the 20th century. Post-positivism admits the limitations of research, especially from the researcher’s perspective, such as the values they hold may result in research biases. But post-positivism still insists on scientific reasoning. From this objectivist approach, quantitative methods are applied extensively, mainly

emphasising deduction and confirmation. Experiments and surveys are the main methods of quantitative research (Bryman, 2003). For example, an experimental group and a control group are used to examine the impact of independent variables on dependent variables, in the form of quasi-experiments in the educational research area. Surveys or tests by random sample are able to generalise the results to the entire population. The validity and reliability of the test or survey could be confirmed and improved through piloting. However, a

problematic issue with these methods is the possibility of unrepresentative or skewed sampling (Cohen et al., 2011).

Subjectivism. At the opposite extreme, subjectivism argues that reality is value-

bound and socially constructed, because the context legalizes the claimed truth. That is, knowledge can only be based on individual experience, as empirical knowledge. There is no external reality; however, reality is what the individual makes sense of. The epistemology of subjectivism has become known as constructivism or interpretivism. Advocates of

subjectivism insist that value-free generalizations are impossible and inadvisable (Johnson & Onwuegbuzie, 2004). Meaning is shaped by social interaction with others and from their own personal histories (Creswell & Clark, 2007). The ontology, called nominalism, suggests ‘there is no truth and facts’ and are ‘all human creations’ (Easterby-Smith, Thorpe, & Jackson, 2012, p. 19). This dynamic view of ontology, which leads to a fallibilist

epistemology, sheds light on individual experience to explore or interpret the reality, rather than seeking external reasons and universal laws to explain the world. Within the fallibilist epistemology, illustration is more important than proof (Cohen et al., 2011). This leads to grounded theory that aims to understand how individuals create, modify and interpret their world. From this subjectivist approach, qualitative methods such as interviews could explain the reality from multiple perspectives by understanding a small group of people in-depth. The reliability and validity of the research ‘rarely seems appropriate or relevant’ to qualitative research (Kirk, 1986, p. 14).

Each of the two extreme views holds an absolute approach to the real world, either purely emphasising on the proven unique truth or merely focusing on subjective personalised judgement. That is, objectivism tends to accept existing facts in real-world situations but excludes the function of individuality as it continues to build up the facts and meaning of this world. By contrast, subjectivism focuses on meaning or subject consciousness of the world but neglects the power of external structures in society. These two styles explore and understand social reality with two opposing lenses (Cohen et al., 2011).

Critical realism. Both objectivism and subjectivism have advantages and

disadvantages. However, a combination of the two reflects the view of social reality that is taken in this study, namely a realist view. Between these two poles, critical realism adopts a middle ground (see Figure 18), as embracing both the existing knowledge and the importance of the context of justification. It represents the theoretical foundation of this research.

Figure 18. Critical realism as a middle ground between objectivist and subjectivist views Specifically within the area of education research, critical realism has been proposed as the pragmatic approach. Pragmatists advocate that truth is ‘what works’ (Robson, 2002, p. 43) and this provides the best workable solution as using both qualitative and quantitative research (Johnson & Onwuegbuzie, 2004). It leads to and is consistent with a mixed-method approach for breadth and depth of understanding of social research. Mixed methods, which encourage multiple views of the world, effectively address the complexity of social research problems (Creswell & Clark, 2007).

My choice of research methodology, critical realism, is widely reflected by my view of mathematical concepts in schools. As I have previously discussed, although the concept of function has been socially developed within learning in schools, the absolute knowledge exists in the curricula, relevant textbooks and other teaching materials. As the learning object, knowledge is regarded as a static reality. That is, the presented information or resource that is required to be obtained by students. On the one hand, this study is going to discover the ‘objective’ differences in knowledge levels of the national curricula, the textbooks, and student performance. Within this, however, the different requirements of knowledge of the

Objectivist Subjectivist

curriculum in each country, to a large extent, show the divergent values of certain knowledge. Though these values have been influenced by a strong cultural and historical background, the context is also related to the process of teaching and learning, and views of the teachers. Therefore, a possible compromise, namely the pragmatic approach of realism, would be suitable in order to comprehend both what the differences are and the mechanisms behind performance, namely how these differences occur.

The chosen methodology also fits with my view of comparative education, laying stress on descriptions and explanations of the quantitative data as it will be discussed in the next section. This view is also built on the fundamental importance of comparison to understand other societies (Stenhouse, 1979).