In different fields

Part of the importance of methodology is reflected in the number of fields to which it is relevant. They include the natural sciences and the social sciences as well as philosophy and mathematics.

Natural sciences

The dominant methodology in the natural sciences (like astronomy, biology, chemistry, geoscience, and physics) is called the scientific method.[8][58] Its main cognitive aim is usually seen as the creation of knowledge, but various closely related aims have also been proposed, like understanding, explanation, or predictive success. Strictly speaking, there is no one single scientific method. In this regard, the expression "scientific method" refers not to one specific procedure but to different general or abstract methodological aspects characteristic of all the aforementioned fields. Important features are that the problem is formulated in a clear manner and that the evidence presented for or against a theory is public, reliable, and replicable. The last point is important so that other researchers are able to repeat the experiments to confirm or disconfirm the initial study.

For this reason, various factors and variables of the situation often have to be controlled to avoid distorting influences and to ensure that subsequent measurements by other researchers yield the same results.

The scientific method is a quantitative approach that aims at obtaining numerical data. This data is often described using mathematical formulas. The goal is usually to arrive at some universal generalizations that apply not just to the artificial situation of the experiment but to the world at large. Some data can only be acquired using advanced measurement instruments. In cases where the data is very complex, it is often necessary to employ sophisticated statistical techniques to draw conclusions from it.

The scientific method is often broken down into several steps. In a typical case, the procedure starts with regular observation and the collection of information. These findings then lead the scientist to formulate a hypothesis describing and explaining the observed phenomena. The next step consists in conducting an experiment designed for this specific hypothesis. The actual results of the experiment are then compared to the expected results based on one's hypothesis. The findings may then be interpreted and published, either as a confirmation or disconfirmation of the initial hypothesis.

Two central aspects of the scientific method are observation and experimentation. This distinction is based on the idea that experimentation involves some form of manipulation or intervention.

This way, the studied phenomena are actively created or shaped. For example, a biologist inserting viral DNA into a bacterium is engaged in a form of experimentation. Pure observation, on the other hand, involves studying independent entities in a passive manner. This is the case, for example, when astronomers observe the orbits of astronomical objects far away.[64] Observation played the main role in ancient science. The scientific revolution in the 16th and 17th century affected a paradigm change that gave a much more central role to experimentation in the scientific methodology.

This is sometimes expressed by stating that modern science actively "puts questions to nature".

While the distinction is usually clear in the paradigmatic cases, there are also many intermediate cases where it is not obvious whether they should be characterized as observation or as experimentation.

A central discussion in this field concerns the distinction between the inductive and the hypothetico-deductive methodology. The core disagreement between these two approaches concerns their understanding of the confirmation of scientific theories. The inductive approach holds that a theory is confirmed or supported by all its positive instances, i.e. by all the observations that exemplify it.

For example, the observations of many white swans confirm the universal hypothesis that "all swans are white".

The hypothetico-deductive approach, on the other hand, focuses not on positive instances but on deductive consequences of the theory.

This way, the researcher uses deduction before conducting an experiment to infer what observations they expect.[72][8] These expectations are then compared to the observations they actually make. This approach often takes a negative form based on falsification. In this regard, positive instances do not confirm a hypothesis but negative instances disconfirm it. Positive indications that the hypothesis is true are only given indirectly if many attempts to find counterexamples have failed.

A cornerstone of this approach is the null hypothesis, which assumes that there is no connection (see causality) between whatever is being observed. It is up to the researcher to do all they can to disprove their own hypothesis through relevant methods or techniques, documented in a clear and replicable process. If they fail to do so, it can be concluded that the null hypothesis is false, which provides support for their own hypothesis about the relation between the observed phenomena.

Social sciences

Significantly more methodological variety is found in the social sciences, where both quantitative and qualitative approaches are used. They employ various forms of data collection, such as surveys, interviews, focus groups, and the nominal group technique.

Surveys belong to quantitative research and usually involve some form of questionnaire given to a large group of individuals. It is paramount that the questions are easily understandable by the participants since the answers might not have much value otherwise. Surveys normally restrict themselves to closed questions in order to avoid various problems that come with the interpretation of answers to open questions. They contrast in this regard to interviews, which put more emphasis on the individual participant and often involve open questions. Structured interviews are planned in advance and have a fixed set of questions given to each individual. They contrast with unstructured interviews, which are closer to a free-flow conversation and require more improvisation on the side of the interviewer for finding interesting and relevant questions. Semi-structured interviews constitute a middle ground: they include both predetermined questions and questions not planned in advance.

Structured interviews make it easier to compare the responses of the different participants and to draw general conclusions. However, they also limit what may be discovered and thus constrain the investigation in many ways.

Depending on the type and depth of the interview, this method belongs either to quantitative or to qualitative research. The terms research conversation and muddy interview

have been used to describe interviews conducted in informal settings which may not occur purely for the purposes of data collection.

Focus groups are a qualitative research method often used in market research. They constitute a form of group interview involving a small number of demographically similar people. Researchers can use this method to collect data based on the interactions and responses of the participants. The interview often starts by asking the participants about their opinions on the topic under investigation, which may, in turn, lead to a free exchange in which the group members express and discuss their personal views. An important advantage of focus groups is that they can provide insight into how ideas and understanding operate in a cultural context. However, it is usually difficult to use these insights to discern more general patterns true for a wider public.

One advantage of focus groups is that they can help the researcher identify a wide range of distinct perspectives on the issue in a short time. The group interaction may also help clarify and expand interesting contributions. One disadvantage is due to the moderator's personality and group effects, which may influence the opinions stated by the participants.

The nominal group technique is similar to focus groups with a few important differences. The group often consists of experts in the field in question. The group size is similar but the interaction between the participants is more structured. The goal is to determine how much agreement there is among the experts on the different issues. The initial responses are often given in written form by each participant without a prior conversation between them. In this manner, group effects potentially influencing the expressed opinions are minimized. In later steps, the different responses and comments may be discussed and compared to each other by the group as a whole.

Most of these forms of data collection involve some type of observation. Observation can take place either in a natural setting, i.e. the field, or in a controlled setting such as a laboratory. Controlled settings carry with them the risk of distorting the results due to their artificiality. Their advantage lies in precisely controlling the relevant factors, which can help make the observations more reliable and repeatable. Non-participatory observation involves a distanced or external approach. In this case, the researcher focuses on describing and recording the observed phenomena without causing or changing them, in contrast to participatory observation.

An important methodological debate in the field of social sciences concerns the question of whether they deal with hard, objective, and value-neutral facts, as the natural sciences do. Positivists agree with this characterization, in contrast to interpretive and critical perspectives on the social sciences.[19][85][86] According to William Neumann, positivism can be defined as "an organized method for combining deductive logic with precise empirical observations of individual behavior in order to discover and confirm a set of probabilistic causal laws that can be used to predict general patterns of human activity". This view is rejected by interpretivists. Max Weber, for example, argues that the method of the natural sciences is inadequate for the social sciences. Instead, more importance is placed on meaning and how people create and maintain their social worlds. The critical methodology in social science is associated with Karl Marx and Sigmund Freud. It is based on the assumption that many of the phenomena studied using the other approaches are mere distortions or surface illusions. It seeks to uncover deeper structures of the material world hidden behind these distortions. This approach is often guided by the goal of helping people effect social changes and improvements.

Philosophy

Philosophical methodology is the metaphilosophical field of inquiry studying the methods used in philosophy. These methods structure how philosophers conduct their research, acquire knowledge, and select between competing theories.

It concerns both descriptive issues of what methods have been used by philosophers in the past and normative issues of which methods should be used. Many philosophers emphasize that these methods differ significantly from the methods found in the natural sciences in that they usually do not rely on experimental data obtained through measuring equipment.[89][90][91] Which method one follows can have wide implications for how philosophical theories are constructed, what theses are defended, and what arguments are cited in favor or against.[53][92][93] In this regard, many philosophical disagreements have their source in methodological disagreements. Historically, the discovery of new methods, like methodological skepticism and the phenomenological method, has had important impacts on the philosophical discourse.

A great variety of methods has been employed throughout the history of philosophy. Methodological skepticism gives special importance to the role of systematic doubt. This way, philosophers try to discover absolutely certain first principles that are indubitable.[95] The geometric method starts from such first principles and employs deductive reasoning to construct a comprehensive philosophical system based on them.[96][97] Phenomenology gives particular importance to how things appear to be. It consists in suspending one's judgments about whether these things actually exist in the external world. This technique is known as epoché and can be used to study appearances independent of assumptions about their causes.

The method of conceptual analysis came to particular prominence with the advent of analytic philosophy. It studies concepts by breaking them down into their most fundamental constituents to clarify their meaning.

Common sense philosophy uses common and widely accepted beliefs as a philosophical tool. They are used to draw interesting conclusions. This is often employed in a negative sense to discredit radical philosophical positions that go against common sense.[91][102][103] Ordinary language philosophy has a very similar method: it approaches philosophical questions by looking at how the corresponding terms are used in ordinary language.

Many methods in philosophy rely on some form of intuition. They are used, for example, to evaluate thought experiments, which involve imagining situations to assess their possible consequences in order to confirm or refute philosophical theories.

The method of reflective equilibrium tries to form a coherent perspective by examining and reevaluating all the relevant beliefs and intuitions.

Pragmatists focus on the practical consequences of philosophical theories to assess whether they are true or false.

Experimental philosophy is a recently developed approach that uses the methodology of social psychology and the cognitive sciences for gathering empirical evidence and justifying philosophical claims.

Mathematics

In the field of mathematics, various methods can be distinguished, such as synthetic, analytic, deductive, inductive, and heuristic methods. For example, the difference between synthetic and analytic methods is that the former start from the known and proceed to the unknown while the latter seek to find a path from the unknown to the known. Geometry textbooks often proceed using the synthetic method. They start by listing known definitions and axioms and proceed by taking inferential steps, one at a time, until the solution to the initial problem is found. An important advantage of the synthetic method is its clear and short logical exposition. One disadvantage is that it is usually not obvious in the beginning that the steps taken lead to the intended conclusion. This may then come as a surprise to the reader since it is not explained how the mathematician knew in the beginning which steps to take. The analytic method often reflects better how mathematicians actually make their discoveries. For this reason, it is often seen as the better method for teaching mathematics. It starts with the intended conclusion and tries to find another formula from which it can be deduced. It then goes on to apply the same process to this new formula until it has traced back all the way to already proven theorems. The difference between the two methods concerns primarily how mathematicians think and present their proofs. The two are equivalent in the sense that the same proof may be presented either way.

Statistics

Statistics investigates the analysis, interpretation, and presentation of data. It plays a central role in many forms of quantitative research that have to deal with the data of many observations and measurements. In such cases, data analysis is used to cleanse, transform, and model the data to arrive at practically useful conclusions. There are numerous methods of data analysis. They are usually divided into descriptive statistics and inferential statistics. Descriptive statistics restricts itself to the data at hand. It tries to summarize the most salient features and present them in insightful ways. This can happen, for example, by visualizing its distribution or by calculating indices such as the mean or the standard deviation. Inferential statistics, on the other hand, uses this data based on a sample to draw inferences about the population at large. That can take the form of making generalizations and predictions or by assessing the probability of a concrete hypothesis.

Pedagogy

Pedagogy can be defined as the study or science of teaching methods.

In this regard, it is the methodology of education: it investigates the methods and practices that can be applied to fulfill the aims of education.

These aims include the transmission of knowledge as well as fostering skills and character traits.

Its main focus is on teaching methods in the context of regular schools. But in its widest sense, it encompasses all forms of education, both inside and outside schools.

In this wide sense, pedagogy is concerned with "any conscious activity by one person designed to enhance learning in another".

The teaching happening this way is a process taking place between two parties: teachers and learners. Pedagogy investigates how the teacher can help the learner undergo experiences that promote their understanding of the subject matter in question.

Various influential pedagogical theories have been proposed. Mental-discipline theories were already common in ancient Greek and state that the main goal of teaching is to train intellectual capacities. They are usually based on a certain ideal of the capacities, attitudes, and values possessed by educated people. According to naturalistic theories, there is an inborn natural tendency in children to develop in a certain way. For them, pedagogy is about how to help this process happen by ensuring that the required external conditions are set up.

Herbartianism identifies five essential components of teaching: preparation, presentation, association, generalization, and application. They correspond to different phases of the educational process: getting ready for it, showing new ideas, bringing these ideas in relation to known ideas, understanding the general principle behind their instances, and putting what one has learned into practice.

Learning theories focus primarily on how learning takes place and formulate the proper methods of teaching based on these insights.

One of them is apperception or association theory, which understands the mind primarily in terms of associations between ideas and experiences. On this view, the mind is initially a blank slate. Learning is a form of developing the mind by helping it establish the right associations. Behaviorism is a more externally oriented learning theory. It identifies learning with classical conditioning, in which the learner's behavior is shaped by presenting them with a stimulus with the goal of evoking and solidifying the desired response pattern to this stimulus.

The choice of which specific method is best to use depends on various factors, such as the subject matter and the learner's age.

Interest and curiosity on the side of the student are among the key factors of learning success. This means that one important aspect of the chosen teaching method is to ensure that these motivational forces are maintained, through intrinsic or extrinsic motivation. Many forms of education also include regular assessment of the learner's progress, for example, in the form of tests. This helps to ensure that the teaching process is successful and to make adjustments to the chosen method if necessary.