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Abstract
This study examines the impact of problem posing on developmental mathematics students. Currently, students enter post-secondary institutions underprepared for college mathematics and are required to take developmental mathematics courses. Given their past challenges with mathematics, the students tend to have negative beliefs and attitudes toward mathematics. Despite these beliefs and attitudes, many developmental mathematics courses still teach the same content to the students in a lecture format; thus, reinforcing their negative perceptions about mathematics. Problem posing has been shown to engage students at all levels by allowing the students to build on their experiences. Based on a quasi-experimental design, this study investigated the impact of problem posing and the effect it had on developmental mathematics students' engagement, attitudes and beliefs, and mathematical proficiency. Developmental mathematics students engaged with a scaffolded approach to problem posing that drew on their personal interests and experiences to design word problems. The study shows that developmental mathematics students are willing to engage in problem posing in a meaningful way and appreciate the autonomy afforded in the process. The students constructed problems that built on contexts that were relatable to their everyday lives, like money and family, and special occasions such as Thanksgiving. This autonomy impacted attitudes on self-exploration and views of success, however, had limited impact on the students’ beliefs about instructional needs and scaffolding of the posing levels. Beliefs also hindered students from engaging with new tasks if they did not foresee successful outcomes. The students enjoyed engaging in problem posing if they found the contexts of the problems relatable to their everyday lives, resembled previously done tasks or familiar contexts and felt they would be successful if they engaged with the task. The students noted the high cognitive load when they engaged with problems where they were provided a context and asked to come up with their own numbers. Students with a deeper understanding of the content were more likely to persist with numerical free problems and show more growth. Students from the lowest performing group in the pre-test showed the greatest growth in the post-test. This study illustrates that problem posing can be a promising avenue for developmental mathematics students, especially those who may initially unperformed on entrance tests.