Academic journal article The Mathematics Enthusiast

The Role of Theory When Studying Epistemological Characterizations of Mathematics Lecture(r)s

Academic journal article The Mathematics Enthusiast

The Role of Theory When Studying Epistemological Characterizations of Mathematics Lecture(r)s

Article excerpt

Introduction and background

The study presented in this paper is a contribution to the scientific discussion about the role and use of theory in mathematics education research. In particular, focus is here on the use of and comparison between different types of theories and frameworks, which is discussed primarily through the example of an empirical study examining what types of messages about mathematics are conveyed in lectures. The main purpose of this paper is to examine how different types of theories and frameworks can affect different parts of the research process.

The role of theory in research

In research, the use of theory is an important and frequently discussed issue. When publishing research reports, it is most often a demand that you should relate to a theory. This centrality of theory is also evident from how different researchers describe the relationship between research and theory. Silver and Herbst (2005) discuss a general function of theory when they place it in the centre of the scholarship triangle, which consists of research, problems, and practice, where theory functions as a connection between all three parts of the triangle. Lester (2005, p. 458) describes four general purposes of using a research framework (later I discuss relationships between similar notions such as theory and framework); to give structure to a research study, that a framework is always needed for data to make sense, to come further than common sense, and in order not to be limited to finding answers to local problems. Also Niss (2006, 2007) describes different general purposes and functions of a theory, for example to predict or explain phenomena, to organize observations and interpretations into a coherent whole, and to give a methodology for empirical studies.

The descriptions above are from a general perspective, but if we think more specifically about the different parts of a research study it could be of interest to, as Bergsten (2008, p. 190) does, ask how "a theoretical basis adopted for a study influence the nature of the purpose, questions, methods,

evidence, conclusions, and implications of the study". This highlights the potential of a theory to affect all parts of a research study. However, for a specific study it might be that some choices in some parts of the study are not based on a given theory and there are also "numerous cases where [...] the research is carried out without really involving the theory which is being invoked" (Niss, 2006, p. 9).

The diversity of theories

If theory does, or should, play a central role in all or many parts of a research study, how should we handle the situation when different studies that focus on the same phenomenon use different types of theories? One problem can then be to build new research on previous research if different theories are used, since:

Taking isolated research results at face value, without relating them to the conditions and constraints of the research processes behind them, provides no criteria or bases for relating them to other seemingly contradictory or similar results. (Bergsten, 2008, p. 189)

To relate results to the theory that has been used in the process of producing these results is therefore an important aspect. However, it is not necessarily the case that research based on different theories, which can even be partially contradictory, produces results that are impossible to combine in some way, for example if the contradictory parts of the theories are not relevant for the studies in question. As previously mentioned, it can also be that the parts of specific research studies that are compared are not dependant on the given theory. This relationship is also highlighted by Prediger's (2008, pp. 284- 285) conclusions from a comparison between researchers' use of different theories: "the theoretical base alone did not completely predetermine their conceptualizations", showing that "research practices and theoretical bases of course are strongly connected, but it would be a misleading simplification to propose a direct causal or deterministic connection". …

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