Marja van den Heuvel-Panhuizen
For approximately the last 25 years, much time and effort has been invested in the development and implementation of Realistic Mathematics Education (RME). As of today, this process is still unfinished. Certain aspects of the curriculum still require further examination, and a number of important questions yet remain with regard to the implementation of RME in educational practice. Consequently, the RME theory, which includes the overarching and connecting principles that guide decisions in classroom practice, is still in a process of development as well.
RME takes the perspective of mathematics as a human activity, while focusing on meaningful applications. An important role in RME is played by the students who, by using contexts and models, can pass through various levels of mathematization and thereby develop their own mathematics. The idea that assessment constitutes an important part of education was expressed early on in the development of RME.
In spite of the battle waged by the proponents of RME against assessment, the quantifiability of learning results was never discussed (Freudenthal, 1978a), nor was assessment within RME ever dismissed (Treffers, 1983). The idea that assessment constitutes an important part of education was expressed early on in the development of RME.
It should be noted that assessment is not viewed here in the narrow sense of determining what the student has learned, but that it is also regarded from the viewpoint of educational evaluation and educational development. Another striking aspect is the important role played by the teacher. Moreover, that assessment is not only intended for looking back, but also for looking forward. Another aspect that soon arose was the preference for observation as a method of assessment.
Assessment in RME not only evaluates a student’s acquisition of certain skills, but also attempts to acquire as complete a picture of the student as possible. This is yet another reason for this predilection for observation:
“Observations, even though they are mere impressions caught by the expert teacher during a lesson, can provide a rather complete picture of the learning process” (Ter Heege, 1978, p. 82).
It should be noted that assessment is not viewed here in the narrow sense of determining what the student has learned, but that it is also regarded from the viewpoint of educational evaluation and educational development.
The consequence of focusing on discontinuity is that the observation must then be continuous (Freudenthal, 1978a). Freudenthal (1985) even suggested that the educational process be seen as a permanent process of assessment, in which the teacher must constantly sense what the next step should be. One effect of emphasizing this approach to assessment, therefore, is the integration of education and assessment. In RME, in fact, the instructional activities and the instances of assessment go hand in hand (Ter Heege and Goffree, 1981). This integration is expressed most clearly in the ‘test-lessons’ (Ter Heege and Treffers, 1979).
Another striking aspect is the important role played by the teacher. , the teacher who conducts the daily observations (Treffers (ed.),1979). Observing, administering tests, diagnosing and providing remedial work are all simply part of skilled teaching (Ter Heege and Treffers, 1979). Even assessment development is regarded primarily as the teacher’s domain, because it constitutes a significant moment of reflection on the instruction given.
An adapted method of assessment was gradually developed in The Netherlands in the wake of the development of RME. This means that assessment, like education: must regard mathematics as a human activity, while focusing on meaningful applications. Moreover, as in education, an important role in assessment is played by the students who, by using contexts and models, can pass through various levels of mathematization and thereby develop their own mathematics (see Section 1.1.2). In other words, if assessment is to be appropriate to RME, then it must be tailored to the three pillars of RME, to wit: the viewpoints on the subject matter, on how instruction should be given, and on the manner in which learning processes progress. Together, they determine what, why, and how assessment occurs.
Assessment within RME means: didactical assessment
The assessment most appropriate to RME can best be described as ‘didactical assessment’. This assessment is closely linked to the education, and all aspects of it reveal this educational orientation. This means that the purpose of the assessment as well as the content, the methods applied and the instruments used are all of a didactical nature.
The purpose is didactical
Assessment within RME is primarily assessment on behalf of education. Its purpose is to collect certain data on the students and their learning processes, in order to make particular educational decisions. These decisions may involve all levels of the education and may vary from local decisions on suitable instructional activities for tomorrow’s mathematics lessons, to broader decisions on whether to pass or fail, on which students need what extra assistance, on whether or not to introduce something new, on a given approach to a given program component, or on whether to take certain large-scale measures regarding the design of the mathematics education
Characteristic of RME, moreover, is the bilateral nature of this focus on improvement. Not only must assessment lead to good education, but it must simultaneously improve learning by giving the students feedback on their learning processes.
The content is didactical
Choosing didactical assessment means that the content of the tests is closely linked to the prevailing viewpoints within RME on the subject of mathematics and to the goals aspired to by the education. This implies that the assessment may not be restricted to particular easily assessed isolated skills, but, instead, that the entire range of goals must be covered, both in breadth (all curriculum components and the links between them) and in depth (all levels of comprehension)
The procedures are didactical
This didactical nature is clearly recognizable once again in the procedures applied in RME assessment. The most distinctive procedure in this respect is the integration of instruction and assessment. integration of instruction and assessment also means that assessment will play a role during each phase of the teaching and learning process. Moreover, it implies that assessment will look forward as well as backward. Looking backward involves determining what the students have learned, in the sense of educational results.
The tools are didactical
Because RME requires as complete a picture of the students as possible, assessment in RME involves using an extensive variety of tools for collecting the necessary information. The closer these tools lie to the education and its goals the better, as they will then produce information that can be applied directly to education.
Suggestions for improving assessment
Assessment within RME means: the problems play a crucial role. In addition, RME assessment require a problem that must be meaningful and informative. The method of assessment must be appropriate to the educational practice and must be able to be conducted within it. The suggestions for improving assessment offered by proponents of RME are, on the one hand, closely connected to the RME preferences regarding assessment and, on the other hand, are the mirror image of the RME objections to the existing tests. Here are the suggestions reflected the standpoint of subject matter content and of the learning child
- help teachers observe
- use observation as a point of departure for test development
- conduct discussions with the students
- place more emphasis on formative assessment
- conduct domain analyses and improve the goal description