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Non Positivist Approach Research Papers

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The first article is about a horizontal (across countries) comparison between mathematics textbooks, while the second one is a vertical (across time) comparison between genealogically related religious texts.

I have chosen the articles in this paper based on my research interest in the history of textbooks. I intend to study how textbooks have evolved over time and to connect their change of content and language to the culture of the authors as well as of their target audience. It is my position that content of the textbooks is determined by the environment it which they arose. However, this relationship is not a simple cause and effect one, but rather a complex web of historical and cultural ties. I propose that by analyzing the content of the textbook in light of its antecedents and the cultural setting of the author and the students we can obtain additional insight into the choice of topics of a book as well as the manner in which they are presented and explained to the readers. Those issues are of great relevance to the study of curriculum.

In the first article the authors study mathematics textbooks from Japan, a country well know to be among the top in mathematical education, and from the USA, a country where mathematics education is considered by most to be unsatisfactory. I have chosen this research article because the background of this investigation is the cultural difference between Japan and the United States.

While not explicitly stated, an attuned reader will connect their findings to the business oriented culture of the USA, where social programs and their funding have their raison d’être as subservient to the capitalistic economic system. As the preceding observation on the absence of any social comment has already indicated, the article is a clear example of positivist research. I will show this more organically in this paper.

I claim that the second article is an example of a non-positivist research paradigm. The methodology of the article is the historical method and thus does not closely fit any of the paradigms discussed in Merriam (1991) and Gough (2000). However, based on Gough (2000, Table 1) and other reasons which I will offer in this paper, I tentatively place it close to the constructionist (or constructivist) paradigm.

Example of the Positivist Research Paradigm

Richard E. Mayer, Valerie Sims, and Hidetsugu Tajika (1995). A Comparison of How Textbooks Teach Mathematical Problem Solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460.


This article is an example of the positivist paradigm as I will try to show by analyzing its content. The article presents a study of a cross-national comparison of textbooks. The three authors analyzed seventh-grade Japanese and U.S. mathematical textbooks. Mayer et alii discovered that Japanese textbooks contain more relevant illustrations than comparable books in the U.S.. Conversely, the U.S. textbooks devoted 19% of space to irrelevant illustrations, while Japanase textbooks only devoted space to relevant illustrations.


The authors claim that their research was able to find an objective understanding of part of the real world, in this case mathematics textbooks. According to Merriam (1991, p. 44) the positivist worldview assumes “a single, objective reality – the world out there – that we can observe, know, and measure.” In addition, Gough (2000, Table 1) defines the positivist ontology as “Stable external reality. Law-like.” Several statements by the researchers reflect this position, for example on page 447 “The instructional lesson is much longer in Japan than in the U.S…. ”Hence, we can see that the authors of this article operate according to the positivist paradigm.`


The epistemology of the authors is clearly in line with the positivist paradigm, that is, using the scientific method we can unambiguously discover an aspect of reality. The authors state on page 447 “Worked-out examples and concrete analogies are more common in Japan than in the U.S.” This is a categorical and general statement, which implies the belief by the authors that they are able to objectively identify a universal reality. As we have seen in the previous citation of Merriam (1991, p. 44) this paradigm posits that reality can be ‘observed, known, and measured.’ Gough (2000, Table 1) describes this epistemology as performed by an objective, detached observer.” The researchers used on page 445 the expression “independent raters,” which is in line with Table 1.


The methodology used by the authors is the scientific method. The authors wrote “To conduct a quantitative analysis of the . . . ,” on page 445. The key word is ‘quantitative.’ There were some subjective parts to the procedure, which is the categorization of a lesson into parts. However, the researchers tried to be as objective as possible in order to be faithful to their positivist paradigm by using “independent raters” who “resolved conflicts by consensus” “To ensure consistency” hence “there were no unresolved disagreements between the raters” (page 446).

The researchers make an explicit claim to their methodology by stating “Given the objective nature of these measurements,” Again, notice the keywords ‘objective’ and ‘measurement.’ These statements match the previously mentioned one by Merriam (p. 44), “. . . we can observer, know and measure.” and Table 1 of Gough (2000), “Experimental, quantitative, hypothesis testing.”


While it is not often mentioned, the positivist paradigm does have an axiology, a value system that is integral to its paradigm and without whom it could not function. Positivist research values honesty and personal integrity more than anything else. That is because these values have the function of creating an environment of “trust.” That is, we can trust that what we read in a research journal corresponds to “reality.”

The ultimate purpose of the positivist research paradigm is that there is an objective reality that can be investigated with the expectation that we will obtain an understanding of reality that we can trust (here is that word again) to be an as close as possible representation of it. Anything that threatens this understanding of reality is considered a grave infraction of the paradigm, and, consequently, its perpetrators are almost always ostracized from the positivist research community.

Foremost, there needs to be an honest representation of the “facts.” The experiment and its results have to be exactly as described in its publication. Indeed, he researcher must be able to produce the raw data in the form of printouts, data sheets, laboratory notes, etc., when requested. However, this is a rare event since the positivist research community values “trust.”

Furthermore, all input has to be credited. That is, positivists detest plagiarism. Also, as less important, but still part of its value system, existing literature on the research topic has to be acknowledged. Previously, this was not a requirement. This was not due to any dishonesty on the part of the scientists and scholars, but rather on the understanding that the educated reader would recognize these references. It was a form of validation of belonging to a select group of people who would ‘get it’. Ironically, the presence of explicit references in a text was considered to be a ‘courtesy’ for the ignorant. Of course, previously the relevant literature was minuscule and thus it was quite feasible for a scientist or scholar to know it all. Moreover, all educated people would be able to read Latin, Greek, and French, and many also German.

In summary, positivist ethics is very strict about any form of intentional misrepresentation of experimental research and about plagiarism. Usually, severe sanctions are applied to those that violate its ethical system.

Positivist researchers also give value to preciseness and rigorous logic. The first is important due to the belief that reality can be studied only by making measurements, thus the more precise they are the more accurately we are discovering reality. Rigorous logic is certainly not only appreciated by those who use the scientific method. Indeed it is fundamental also in mathematics and philosophy, which are strictly speaking not scientific enterprises.

Ultimately, positivist researchers believe that the pursuit of knowledge has an intrinsic value that is independent of any utilitarianism, that is, the increase of knowledge is a meritorious enterprise by itself. Often, when researchers apply for grants or other resources they will appeal to the social, if not economical, value of their research. However, that is often the public face of the scientific enterprise. Among peers scientists do mostly dispense with any reference to any practical use of their findings and merely present their additive contribution to scientific knowledge.

Certainly, this attitude is less prevalent among the applied sciences, e.g. medicine as applied biology, engineering as applied physics and chemistry, and education as applied psychology. In those fields the tension between ‘pure’ and ‘applied’ research is more visible. Nonetheless, pure research in these supposedly applied fields is often accepted based on the tacit understanding that sooner or later an application for this particular line of research will be found.

It seems that positivist research, while it does not apologize itself as the cure to all ills of the world, still believes that results of its activities will positively contribute to human welfare. Nowadays, this attitude is most apparent in medical and energy research. With reference to the article in question, the authors state on page 458 “Ultimately, the practical goal of this study is to provide suggestions for the improvement of textbooks. . . ” It is evident thus that Mayer et al. consider the value of their work extend beyond the mere increase of knowledge and is intended to bring a positive contribution to society.

Example of a Non-Positivist Research Paradigm

Matthias Klinghardt (2008). The Marcionite Gospel and the Synoptic Problem: A New Suggestion. Novum Testamentum, 50, 1-27.


I chose this article because it has the potential of being an important step in a paradigm shift in a significant historical investigation. About 200 years ago historical research in Germany established that there is a ‘genealogical’ relationship between the first three canonical gospels, Matthew, Mark and Luke. An example of this relationship is the following string of six words:

kerússon báptisma metanoías eis áfesin hamartiôn

In English “preaching a baptism of repentance for the forgiveness of sins.” This string of words is identical in Mark 1:4 and Luke 3:3. Moreover, the string is part of the narrative and not of any quote. That means it is editorial and thus for sure composed by the authors themselves. The only logical explanation is textual copying. That is, one author had another text in front of him which he copied into his own text.

Once this was realized, historians have been trying to establish the specifics of this literary relationship. The awareness of this relationship, as well as its investigation is called the “Synoptic Problem.” Since then, several hypotheses and theories have been proposed to solve the synoptic problem. The most popular one is the “Two Source Hypothesis.” This is the theory that is present in the textbooks and taught at universities. It is the ‘academic’ and ‘respectable’ theory.

However, there is an alternate theory, called the Farrer-Goulder Theory that has some popularity in the UK. One of its strengths is that it requires fewer assumptions and thus would be favored by Occam’s Razor. Historical discourse regarding these two theories has focused so far on the argument from best explanation. This argument states that the theory with the greatest explanatory power as well as with the least amount of anomalies (see Kuhn, 1996) is the preferred one.

However, both anomalies and explanations are close to impossible to quantify and thus the historians have reached an impasse.

This article proposes a third theory that, at least according to the author, would lack all anomalies of the previous theories, require fewer assumptions, and explain all the available data.


I deduce that the ontology of the author is realism, something specific really happened in a certain place at a certain time. Statements such as “the arguments . . . are convincing” and “I consider the Markan priority to be well substantiated. . . ” (p. 2) point to this belief. However, it is not the realism of the positivist paradigm. It does not fit the definition of positivist ontology of Gough (2000, Table 1), “Stable external reality. Law-like.” Historical events do not follow laws and certainly are not stable. Neither does it follow the descriptions of Merriam (1991), “. . . reality . . . that we can observe, know, and measure.” Historical events can not be observed nor measured. Historical events are re-constructed by historians. While this sounds close the constructionist ontology (Gough2000, Table 1), historians like still to think in absolute terms. In our case, Mark was the first gospel or not, a clearly binary statement. However, as we will see here, the answer can only be obtained by historians interpreting data. The farther back we go in time, the less complete the data (historical records) and thus the less certain the conclusions of historical research. All researchers do interpret data, even positivist ones, however, historians have a much larger discretionary activity in their research than scientists do. To have an idea of this situation notice the variety of answers to questions such as the cause(s) of the fall of the Roman Empire in the west, the cause of the crusades, how did Hitler rise to power, and so on.


The author uses the historical method which, as shown in the previous section, assumes that there is a single truth just like in positivism. However, since all that can be investigated are historical data, the confidence that the historians have depends on the quality and quantity of the historical data.

Based on Table 1 of Gough, we can see that the epistemology of the historians has elements of both the positivist and constructionist paradigms. The historian aims to be an “objective, detached observer,” however to be so he or she has to be “suspicious” of the texts under examination. The political and ideological setting of the author determines the content of the texts. In our case, it is impossible to understand the texts of the New Testament without recognizing that they are the product of a furious political strife between the four main divisions of Christianity in the 2nd century, Orthodox-Catholic, Marcionite, Gnostic, and Jewish-Christian. The victors (re)write the history of this conflict, in our case the Orthodox-Catholic Church.


The methodology used by the author is the historical method, not the scientific method nor active participation. The scientific method requires performing experiments in controlled conditions that are replicable by others. Obviously this is not possible in historical research. Likewise, active participation is impossible for obvious reasons.

The historical method and the scientific method often use the same technology. That is, they will use laboratory analysis, statistical analysis, computerized databases, and so on. The great difference is that historians can not set up experiments and can not generate new data, but have to depend on what is available as far as archaeological artifacts, manuscripts, inscriptions and so on. Similarly, historians can not interview the authors of the texts, neither survey their original audience.

These limitations are apparent from the following statements of the author: “Although no copy of Mcn has survived, . . . ” (p. 5); “one restriction must be kept in mind: Mcn’s text is not completely recoverable.” (p. 11); “Since there is no hint whether this material is derived . . . ” (p. 25).

One of the consequences of this situation is that the same set of necessarily incomplete data can be interpreted in several different ways. The sparser the data, the greater the chance of conflicting theories. Furthermore, it is not possible to know what all the missing data are. In the case of the scientific method other experiments can be performed, more data can be collected to settle these differences. Interpretivist researchers can interview or survey again the subjects of their investigation. By its own nature, none of this is possible with the historical method.

Briefly, the historical method consists of External Criticism, the study of authenticity and provenance; Internal criticism, the study of historical reliability; and Synthesis, which is historical reasoning. The latter uses the Argument to best explanation, Statistical inference, and the Argument from analogy (McCullagh, 1984; Garraghan 1946; Shafer, 1980). Again we can notice a similarity to the constructionist paradigm whose methodology is described by Gough (2000, Table 1) to consist of deconstruction, textual analysis and discourse analysis.

It should be noted that the author of this research article arrives to completely different, if not opposite, conclusions from the prevailing theory without using any additional data. Both theories use the same data set, the distinguishing factor being the differing interpretation of the same data. This is clearly evinced from “Subject to the condition that Mcn was prior to Luke and thus ought to be included in the discussion of the synoptic relations, the whole picture changes considerably. It is the contention of this paper to explore some of the consequences of this perspective for the synoptic problem” (p. 7).

The author completely reverses one of the basic assumptions of both prevalent synoptic theories (Two Source and Farrer-Goulder). This reversal is not based on any new data, but on a new way of looking at, understanding, interpreting the same data.


The issue of values has been, and still is, decisive in the acceptance and popularity of a certain synoptic theory. For many the purpose of the study of the history of the documents comprising the New Testament has been to support traditional ideologies. The historical statement that the all canonical gospels preceded the non-canonical ones was in line with these ideologies. The alternative theory proposed by Klinghardt makes a canonical gospel, the Gospel of Luke newer, and worse dependent on, a non-canonical gospel, the Gospel of Marcion. Ironically, all New Testament historians, even those who do not profess to follow any ideology will been taught by or read books written by those who directly or indirectly were adhering to an ideology. This makes the study of this field of history so difficult: ideological influence is both pervasive and unrecognized.


Garraghan, G. J. (1946). A Guide to Historical Method. New York: Fordham University Press.

Gough, N. (2000). Methodologies under the microscope. Paper presented at DUPA research conference.

Kuhn, T. S. (1996). The structure of scientific revolutions (3rd ed.). Chicago: University of Chicago Press.

McCullagh, C. B. (1984). Justifying Historical Descriptions. New York: Cambridge University Press.

Merriam, S. B. (1991). How Research Produces Knowledge. In J. M. Peters & P. Jarvis (Eds.), Adult Education (p. 42-65). Lanham, MD: Jossey-Bass.

Shafer, R. J. (1980). A Guide to Historical Method. Boston: Wadsworth Publishing.

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