Open modelling problems in mathematics teaching oriented towards self-regulation – open goal state (OModA-E)

Basic data for this project

Description

Open problems that can be solved by using different solution methods are an important part of the school curriculum in mathematics and science. One important type of open problem is related to the real world. Open real-world problems can be solved by constructing mathematical models and are known as open modelling problems. Prior research analyzed open problems that did not include all information that is essential for solving the problems. In this type of open problem, the initial state is open. In this grant application, we are going to analyze problems with open goal state. While solving the problems with an open goal state, different factors (e.g., temporal, and financial) can be considered to answer the question. In the project we will investigate the effects (1) of instruction that is focused on important barriers in solving problems with open goal state and (2) how the teaching of problems with open goal state affects students’ cognitive and motivational learning outcomes. We will carry out an experimental study to investigate the impact of instructions in a) how to identify solution-related factors in the goal state, b) how to set up a mathematical model, and c) how to interpret and validate mathematical results on students' solutions. Further, we will contrast two treatment programs in a quasi-experimental study and analyze the effects on interest and performance. In the first teaching program, students will solve modelling problems with an open goal state, and in the second teaching program, they will solve real-world problems with a closed goal state. The main aim of this application is to investigate students’ cognitive barriers while they solve modelling problems with an open goal state and to analyze the effects of interventions (instruction and teaching program) for problems with open goals state on students' performance. Further, we will analyze, how interventions in solving modelling problems with an open goal state will affect students’ cognitive and motivational development. This research will contribute to the overarching aim of getting new insights about dealing with open problems in instructional settings that are oriented toward self-regulation.