Presented by:

**Christa Kaune**, Institute for Cognitive Mathematics, University Osnabruck, Germany, and

**Edyta Nowinska**, Intitute for Mathematics Didactics, A. Mckiewicz University in Poznan, Poland

in a general lecture conducted in Sriwijaya University on 30th July 2013.

The issue of contractual arithmetic in Indonesia was firstly introduced by Christa Kaune and team from Osnaburck University. Prior to the proposal of this approach, researches which focused on mathematical cognition had been conducted in several secondary schools in Yogyakarta and Nusa Tenggara Timur.

As the result, the idea was formulated to transform from head-to-head learning style into teaching mathematics for undertstanding. This approach does concern on the cognitive styles with three main steps, namely, generating argumentation, explanation, and prediction and justification.

What mainly backgrounded this concept to appear was the existence of several concepts in mathematics which was quite hard to deliver within a real context. Therefore, axiomatic approach is employed, that is, to condition a certain convention to be produced based on previous proveable mathematical ideas.

In order to reach the convention, microworld is made (we call it the first contract, containing rules which would be applied during the activities). The microworld itself is almost similar with the context in RME. However, the rules in the microworld should be re-emphasized and re-introduced in the beginning (considering its unfamiliarity).

For example, in explaining operation of containing negative numbers, ‘microworld banking’ could be first formed, with rules: (-) for debit, (+) for credit, (addition) for pay in/deposit, (subtraction) for pay out.

So, in case Mr. A has Rp.350.000,00 in debit and withdraws Rp.400.000,00 could be represented as (-350.000)-400.000=(-750.000).

At the end of the lesson, a contract is made. The contract has been in mathematical forms containing variables.

Christa Kaune and Edyta Nowinska with the big family of PPs. Matematika, Sriwijaya University

From left to right (Edyta Nowinska, Christa Kaune, Zulkardi)

Collaborative research agreement

#the post based on my own understanding toward the lecture. This is to introduce the issue only and is not suggested for a reference.

#for further investigation, you may search and find other references.

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