Developing LTBI for addition and multiplication rules in probability theory with realistic mathematics education

Abstract

There were three components on a hypothetical learning trajectory (HLT) developed in this paper, namely: (1) the learning goal, (2) the learning activities, and (3) the way of students' thinking and learning. A learning trajectory based instruction (LTBI) was defined as a teaching and learning trajectory using HLT for instructional decisions. In this paper, the researcher will present a LTBI using Realistic Mathematics Education approach which helps mathematics education students following the Probabilistic Theory course to construct (1) the addition rule, and (2) the multiplication rule. The type of the research was the design research developed by Gravemeijer and Cobb. There were three phases in the research development, namely (1) the design preparation, (2) the design trial, and (3) the retrospective analysis. The researcher exposure in this paper was limited to the first stage of the design research developed by Gravemeijer and Cobb. As the products developed in this paper was limited to LTBI, so to construct a local instructional theory (LIT) for the sum and multiplication rules, the researcher needs to implement this LTBI in the classroom learning process.