Abstract:

Student engagement and meaningful interaction remain persistent challenges in online mathematics courses, particularly in College Algebra (CA) and Quantitative Reasoning (QR). This study presents the design, implementation, and evaluation of the PMI–Q (Pluses, Minuses, Interesting points, and Questions) activity, an instructional strategy grounded in constructivist and constructionist learning frameworks. Adapted from OnCourseWorkshop.com – a large repository of effective teaching and learning strategies – the PMI–Q activity is designed to foster three-way interaction among students, instructors, and course content while promoting critical thinking, problem-solving, communication, and self-reflection.

In this activity, students create and present original mathematical problems, explain underlying theory, and engage peers through structured discussion prompts and reflective writing. The approach emphasizes student-generated content, collaborative learning, and metacognitive reflection.

A mixed-methods study was conducted across six online courses (n = 116) between 2019 and 2024 using a pre–post survey adapted from the Student Assessment of Learning Gains in Mathematics (SALG–M) instrument. Results indicate notable increases in student interest, confidence, communication skills, and engagement. For example, the percentage of students reporting high or very high confidence in their mathematical ability increased from 82% to 91%, while confidence in communicating mathematical ideas rose from 91% to 96%. Gains were also observed in students’ willingness to seek help, share ideas, and develop independent problem-solving strategies.

Findings suggest that the PMI–Q activity effectively enhances student engagement and learning outcomes in online mathematics courses by promoting active participation and deeper cognitive processing. The flexible structure of PMI–Q also allows for adaptation across disciplines and instructional formats. Implications for course design, student engagement strategies, and future research on interactive online learning are discussed.

Keywords:

Student Engagement, Three-way Interaction, Problem Solving, Critical Thinking, Learning Gains, Metacognitive Reflection, Active Learning, Effective Teaching.