Effects of Problem-Posing Activities Using Goal-Free Problems on Elementary Students’ Affective Characteristics and Problem-Solving Beliefs in Mathematics

This study aims to examine the effectiveness of utilizing goal-free problem-posing activities, a learning strategy tool that reduces external cognitive load and enhances flexible thinking and transfer abilities, in elementary mathematics education. This is done by investigating their impact on students’ affective characteristics (interest, attitude, values, motivation, conation, and efficacy) and problem-solving beliefs (process, persistence, and challenge). To achieve this aim, a set of mathematical problem-posing activity sheets were developed and used in math classes. Specifically, three 5th-grade classes were randomly assigned to three groups: a goal-free problem-posing group (n = 22), a goal-given problem-posing group (n = 20), and a control group (n = 20), and they were engaged in 10 sessions focused on the mathematics problem-posing activities. Pre- and post-test scores on affective characteristics and problem-solving beliefs were compared across groups. Key findings indicate that the goal-free problem-posing activities was more effective than the goal-given problem-posing activities in promoting the value, conation, and efficacy associated with mathematics learning. Additionally, the goal-free problem-posing activities positively influenced process-oriented and challenge-related problem-solving beliefs. This study demonstrates that applying a goal-free problem-posing approach in mathematics can positively impact students’ problem-solving methods and attitudes, highlighting its potential as an effective instructional strategy in mathematics education.