The Rule of The Context
The curriculum of Mathematics is differenciated from many others by dominating place occupied by context problems, serving both as a source for conceptual mathematization and as a field for application of Mathematical concepts.
According to Trafers and Goffree, context problem in realistic Wiskobas-like instruction fulfill a number of function, there are: (1) concept forming: allow the students a natural and motivating access to Mathematics in the first phase, (2) model forming: the students supply a firm hold for learning the formal operations, procedures, notations, rules and they do together with other models had an important function as supports for thinking, (3) applicability: the students uncover reality as source and domain of application, (4) exercise of specific abilities in applied situations.
More importantly, there are three different uses of context problem in Mathematics. Firstly, the third order context use, the use of the context to introduce and develop a mathematical model or concept. It is the most significant use. Secondly, the second order context use, a real world problem presented to the students, and the student are expected to find the relevant mathematics, to organize and structure and solve the problem. In other words, no context at all. Finally, the first order context use, embed the mathematical operation in context. A simple transition from the problem to a mathematical problem is sufficient. The context in this situation is only used to camouflage the mathematical problem. This kind of problems are often found in traditional schoolbook.
Moreover, there are two remarks concerning the motivating aspect of contexts:
a. Artificial contexts are acceptable and motivating for younger students.
Context must be more realistic to be acceptable for older students.
b. The context can be motivating to all, one should offer a whole range of different contexts.
According to Kaiser, context is used in general improves motivation and interest in mathematics. If the teacher or the students learn a lot about the context, there are some possibilities conflict that will happen, for instance: conceptual conflict, a conflict within the individual about possible different solutions to a problem. Then sociocognitif conflict, as a result interindividual encounters, between students or students-teachers.
In addition, the famous controversial context is an exercise in which the rates of abortion in different countries were compared. The other one is the photo used to illustrate visually the acceleration in free fall.
On the other hand, a realistic context does not always mean that there has to be a direct connection to the physical world. One of the consequences for context use is to change the context often. One useful thing from motivating aspect is a way to minimize the differences in the real word perception of the students.
Some suggestions recommended to the teacher training and tradition in teaching are: there are some things that should be avoid as follows: context that are emotionally disturbing (defense, war, illnes, ethic affairs), artificial context, neutral context, too much background information of the students; that they should choose the context and edit the exercise in a way that stimulates interindividual actions.
Finally, one final remark must be made: there is a danger of a mathematical concept being too strongly, but it is no danger at all since the students who do not perform the required abstraction can work well with this context-bound idea.
Jzn, Jan de Lange. Mathematics, Insight and Meaning Teaching, Learning and Testing of Mathematics for the Life and Social Sciences. 1987.