Proportional Reasoning and Belief of Pre-Service Mathematics Teachers: The Use of Modified Authentic Investigation Activities (AIA) Model

Proportional reasoning is fundamental for students as a part of higher-level mathematical reasoning. It is not only fundamental for students to learn mathematics but also important for teachers and pre-service mathematics teachers having a good capability in proportional reasoning because it can lead them to teach better mathematics. This study aims to analyze the implementation of Authentic Investigation Activity (AIA) model for enhancing proportional reasoning and beliefs of pre-service mathematics teachers. This is an experimental study with pre-test and post-test design. The population of this study are second year of pre-service mathematics teachers in mathematics education department of Garut District, West Java Province, Indonesia. Using random cluster sampling are 70 pre-service mathematics teachers as the sample of the study for both. The instrument in this study is a set of test that constructed for measuring the proportional reasoning of pre-service mathematics teachers and a set of the questioner for measuring mathematical beliefs of pre-service mathematics teachers. The proportional reasoning test consisted of six essay problems in the topic of ratio and proportion with three indicators: 1) differentiating proportional and nonproportional situation; 2) understanding the mathematical relationship in the proportional situation; and 3) solving the various problem in the proportional situation. The data were analyzed quantitative using a t-test and Mann-Whitney U test. The result of the study indicates that the AIA model can enhance the proportional reasoning of pre-service mathematics teachers especially in terms of differentiating proportional and non-proportional situation and understanding mathematical relationship in the proportional situation but not in solving the various problem in the proportional situation. However, the AIA model gives similar result for mathematical beliefs of pre-service mathematics teachers.