The Identification of Aspects and Grundvorstellungen in the Learning Process of the Function y=ax²: Based on the Mathematics Textbook for Grade 9

Abstract

The purpose of this study is to identify Aspects and Grundvorstellungen in the learning process of the function y=ax² and obtain suggestions for teaching the function y=ax². For this purpose, we list implications through an identification of the Aspects and Grundvorstellungen, and give an explanation based on the mathematics textbook. As a result, we demonstrate the usefulness of Aspects and Grundvorstellungen. The focus on Grundvorstellungen allows us to make a concept image not only about content within mathematics, but also about content outside of mathematics. The relationship between Aspects and Grundvorstellungen points out some teaching considerations in the process of learning the function y=ax². It is also clear that other Grundvorstellungen are affected by the link of Aspects to Grundvorstellungen. A future task is to take into account the descriptive Grundvorstellungen. In this paper, we have focused only on the normative (prescriptive) Grundvorstellungen.