Koeno Gravemeijer



In recent years design has again begun to attract interest. It is no longer a direct attempt to find prescriptive models for improving the quality of design process but has become design as a research method. More researchers are setting out along the path of constructional research. One of them is developmental research. It should be able to provide more direct foundation. If developmental research is to fulfill this function, then both the substance and product of research must be clear.

Developmental research is not after all, a strict regulated methodology but, rather a manner of working that has grown through being put into practice. Only by reflecting on such practice can take a shape of method. Furthermore theory-guided bricolage was used to characterize developmental research in practice. In the end, the basic of philosophy of mathematics as human activity also has its roots in actual practice.

  1. 1.      Evaluation research

Two decades of developmental research whose guideline was the principle or realistic mathematics education have eventually led to the development of a domain specific theory for realistic mathematics education. The realistic instruction theory can be evaluated by examining the results achieved using realistic mathematics textbooks. The results give rise to some debate. When the theory behind the mathematics textbook series is at issues, the discussion becomes even more complex. However, with some of argument and example of researchers, it is clear that the textbook can play an important role.

Evaluation research repeatedly reveals a lag between the intentions and implementation of realistic mathematics education (RME). The RME theory will lose much of its practical significance. Evaluation research may well offer an indirect assessment of the instructional theory, but this does not make the results any less important.


  1. 2.      Internal legitimization

Being a combination of development and research, developmental research has a dual function that would like to refer to as production and justification. The emphasis is the legitimization aspect. The result of developmental work is a prototypical course. The result is a description of the source on meta-level (a local instruction theory) and a justification.

How is the educational theory legitimized? In the first place, through the collected developmental research, Prototypes are based or generalization of choice. In addition, the communal learning process of the realistic community provides a second legitimization.


  1. 3.      Developmental research clarified

In principle, developmental research offers the potential for more direct manner of evaluation. There is a room within the broad concept of educational development for different types of research: developmental research, implementation research and curriculum evaluation. Each can have its own function and its own research design and method.


–          Heuristic and design principles

Developmental research is a creative process in which implicit knowledge plays an important role. Before researchers dive into cyclical process on invention, experimentation and reflection, they will make an analysis of situation. Along this analysis, a general concept of a course must develop before the actual experiment can begin.  They can use the theory of RME by applying the central principle namely: the reinvention principle, the didactic phenomenology and the mediating models.

–          Theory-guided bricolage

Theory-guided bricolage was used to describe developmental research. The goal of it is to develop domain-specific instruction theory, but without deadline involved. Theory development is seen as ‘a never ending story’.

Theory-guided bricolage was also as the basis for theoretically based preliminary design. The theory as a means of guiding assumes more significance, particularly for developmental research. It plays important rule in early phase of textbook development. Now, it is the overall design of course that acquires a pronounced constructional character in developmental research.

Theory-guided bricolage on micro-level. Although the experiment does start with overall preliminary design, this is expanded an adapted in cyclical process of inventing, testing, and reflecting on educational activities. One might call this a small-scale empirical cycle. Freudenthal (1988) speaks in this context of ‘thought-experiment’ and ‘educational-experiment’

–          Criteria

Criteria used by researchers to make assessments and to carry out adjustment are taken from theory for RME. In practice, they flow from the heuristics outlined above. Related criterion is that the reinvention path not only be traveled upward but also downward. This is the summary of the criteria:

  1. Reflection of learning path in student’ solution
  2. Longitudinal and transversal dispersion of solutions
  3. Bottom-up problem solving
  4. Use of footholds offered by the context
  5. Situation-specific solutions with vertical perspective
  6. Applicability
  7. Naturalness, vertical power and breadth of application of models
  8. Spontaneous abbreviations
  9. Shift from context-bound to solution-focused
  10. flexibility

–          Evaluation

The realistic core is translated into criteria. During the development of prototype, the findings are evaluated against these criteria.


  1. 4.      External persuasiveness

Developmental research can be seen as the researchers’ learning process. That’s why it is so difficult to transfer the yield of developmental research. In answering that problem it may be helpful for developers to describe their ‘starting theory’ from beginning of the research. If it succeeded in objectifying the answer, developmental research could be considerably reinforced. Another way to increase the persuasiveness of developmental research is to broaden the theoretical base.

–          Objectification

At the first glance, the sole point of objectification would appear to be reinforcement of empirical base. At least as important, however, is the objectification of the interpretation (or analysis) of the empirical data. In developmental research we find, namely, crucial moments which the researchers experience as ‘Aha-Erlebniseen’. This Aha-Erlebniseen has a great deal to do with the reference framework of the person involved. Alongside the objectification of the analysis or interpretation of data, I also mentioned the objectification of the empirical observations themselves.

–          theoretical basis

The power of persuasiveness of developmental research will increase as the research results become more embedded in a broad theoretical framework. It means that the researcher demonstrates particularly in the documentation how the research result relates to generally accepted theories. The realistic instruction theory indicates how instruction can be developed that enables the independent construction of knowledge and focuses it as well.


  1. 5.      Conclusion

The above is an outline of developmental research and of how it is related to other sorts of research. Developmental research has function as internal legitimization of local and domain-specific instruction theories within the circle of realistic oriented researchers. This extensive analysis of developmental research can be justified by the practical and theoretical significance of such research. Furthermore, the analysis shows the remarkable character of this type of research. In summary, we can say, it evolutionary, stratified and reflexive.

The Dutch developmental research in the area of mathematics education has, after all, resulted in theory forming and instructional materials which have received international attention.



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