In Realistic Mathematics Education, we always hear term “mathematizing”. Interestingly, Freudenthal sees this as a general activity which characterizes both pure and applied mathematics. When setting “mathematizing as a goal for mathematics education, this can involve mathematizing mathematics and mathematizing reality.
Freudenthal uses the word “mathematizing” in a broader sense than simply an indicator of the process of recasting an everyday problem situation in mathematical terms. In Freudenthal’s view, mathematizing relates to level-raising – in mathematical sense. Level-raising is obtained when we promote features that characterize mathematics, such as generality, certainty, exactness, and brevity. In order to clarify what we mean by mathematizing, we can look at strategies we use to promote these mathematical characteristics:
ü For generality: generalizing (looking for analogies, classifying, structuring);
ü For certainty: reflecting, justifying, proving (using a systematic approach, elaborating and testing conjectures, etc);
ü For exactness: modeling, symbolizing, defining(limiting interpretations and validity);
ü For brevity: symbolizing and schematizing (developing standard procedures and notations).
In RME, mathematizing mainly involves generalizing and formalizing. Formalizing embraces modeling, symbolizing, schematizing and defining, and generalizing is to be understood in a reflective sense.
Freudenthal suggest that mathematizing is the key process in mathematics education for two reasons.
Firstly, mathematizing is not only the major activity of mathematicians. It is also familiarizes the students with a mathematical approach to everyday life situations. Here we can refer to the mathematical activity of looking for problems, which implies a mathematical attitude, encompasses knowing the possibilities and the limitations of a mathematical approach, knowing when a mathematical approach is appropriate and when it is not.
Secondly, the reason for making mathematizing central to the mathematics teaching relates to the idea of reinvention. In mathematics, the final stage is formalizing by way of axiomatizing. The end point should not be the starting point for the mathematics we teach. Freudenthal argues that starting with axioms is an anti-didactical inversion; the process by which the mathematicians came to their conclusions is turned upside down in education. He advocates mathematics education organized as a process of guided reinvention, where students can experience a (to some extent) similar process as the process by which mathematics was invented.
Sumber: Gravemeijer, Kueno. 1994. Developing Realistic Mathematics Education. Freudenthal Institute, Utrecht.