Open modelling problems: cognitive barriers and instructional prompts

Abstract

AbstractOpen mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these problems is that information that is essential for solving the problems is missing. In the present study, we aimed to analyze students’ cognitive barriers while they solved open modelling problems, and we evaluated the effects of instructional prompts on their success in solving such problems. A quantitative experimental study (N = 263) and a qualitative study (N = 4) with secondary school students indicated that identifying unknown quantities and making numerical assumptions about these quantities are important cognitive barriers to solving open modelling problems. Task-specific instructional prompts helped students overcome these barriers and improved their solution rates. Students who were given instructional prompts included numerical assumptions in their solutions more often than students who were not given such prompts. These findings contribute to theories about solving open modelling problems by uncovering cognitive barriers and describing students’ cognitive processes as they solve these problems. In addition, the findings contribute to improving teaching practice by indicating the potential and limitations of task-specific instructional prompts that can be used to support students’ solution processes in the classroom.