In RME (Realistic Mathematics Education) a context plays an important role and distinguishes RME from other mathematics teaching approaches, such as the mechanistic and structuralist approaches. The use of contextual problems as the starting point in mathematics teaching will engage students in meaningful mathematical activities. According toTreffers and Goffree (de Lange:1987, de Lange 1995), contextual problem have number number of functions:
- Concept formation: In the first phase of a course, they allow the students natural and motivating access to mathematics.
- Model formation: Contextual problems supply a firm basis for learning the formal operations, procedures, notations, and rules, in conjunction with other models that function as important supports for thinking.
- Applicability: Contextual problems utilize reality as a source and domain of applications. In the other words, it means that the role of context in RME is not only as a source of conceptual mathematixation but also as a field of mathematical concepts. But not all contexts in the story problems can play these important roles.
- Practice the exercise: Contextual problems supply opportunities for developing specific abilities in applied situations.
According to de Lange (1987; 1995), there are 3 different types of context in RME when dealing with assessment:
1. No Context or second order context
De Lange in his article Assessment: No change without problems, took an example from standardize test from Poland which shows that the complex task without any context.
2. Camouflage context or first order context
The context in this situation is only used to ‘camouflage’ or ‘dress up’ the mathematical problem. In the other words, we need notation or symbol or algebra notation to solve the problem. For instance:
The growth factor of a bacterium type is 6 (per time unit). At the moment there are 4 bacteria.Calculate the point in time when there will be 100 bacteria.
Which one of the number sentences below could be used to solve the following problem? Bill weighed 107 pounds last summer. He lost 4 pounds and then gained 11 pounds. How much does he weigh now?
a. 107 – (4 + 1) = A
b. (107 – 4) + 11 = A
c. (107 + 11) + 4 = A
d. –4 + 111 = 107 + A
e. (107) – 11) + 4 = A
3. Relevant and essential context or third order context uses
Using context as starting point is the characteristic of this kind of context uses. In the other words, students can use real context to develop mathematics idea/concept. Context should be familiar to the students; be easy to imagine and recognize.
De Lange use the context of ‘growth’ in Exponential and logarithmic function of aquatic plants as starting point for introducing the concept of logarithms.
de Lange. Mathematics, Insight and Meaning Teaching, Learning and Testing of Mathematics for the Life and Social Sciences. 1987.
de Lange. Assessment: no change without problems.1995.