ICEBERG Structure for Mathematics Learning Process II - Ethnomathemaitcs Reflection

ICEBERG Approach in Realistic Mathematics

Mathematics is abstract, I admit that. Until now I still think that mathematics is complicated and always become the ‘unseen’ thing. If I, the university student, still think mathematics is abstract thing, then how about children in elementary school and junior high school? Maybe they will think that mathematics is from the outer-space.

Realistic mathematics divides mathematics itself into four kinds: concrete mathematics, concrete model, formal model, and formal mathematics. Concrete mathematics is the lowest mathematics because we use a concrete object to deliver the material. The highest is, of course, the formal mathematics. Formal mathematics is used in university, used by mathematicians. We can say that formal mathematics is the abstract one.

To facilitate students to understand the material, teacher can use the ICEBERG method. Here is the construction of ICEBERG.

The floating capacity represents the mathematics learning we use in elementary school, junior high school, and senior high school. Concrete mathematics is given by teacher. This kind of mathematics is the mathematics world orientation, which means mathematics is always relevant with our daily life. In learning fraction teacher uses examples like this picture.

Cake or maybe pizza can show the functions of fraction. This is one of the examples we can found in our daily life. Concrete model is like when we try to convert the material from our daily life into other models. For example like this.

This figure can show us the same concept in concrete mathematics, but we make it more formal. Then for concrete model we can make line that shows the measurement of fractions. For example is the figure shown below.

The top of ICEBERG shows the formal mathematics, the most confusing part of mathematics. This part shows the pure mathematics. There are not many people becomes a pure mathematicians, but there are many of them becomes a mathematics teacher. Mathematics teachers cannot use formal mathematics because they teach pupils with different ability to absorb the material. Pupils still need help on mathematics, and the teacher gives the helps by giving rational problems so they could understand the material.

If teacher gives formal mathematics to pupils, especially elementary students, then it will be a disaster for children. Their thought will destroyed by mathematics. They will not like the mathematics, even though mathematics is needed in every know ledges. They will not give any attention to mathematics unless the teacher gives the material step by step, using the ICEBERG construction.

Study ethno mathematics has same way with study mathematics in general. If students ready for the lesson, then they will totally absorb the knowledge. Ready signed with happiness when study, study with joy, and no burden. If students don’t ready, then it will become a disaster for their mind set. Unready signed with no happiness when study and reject the knowledge.