Navigating the Liminal Space: Strategies to Support Learners in Calculus at Chishinga Secondary School in Kawambwa District

Abstract

This study investigates the challenges and pedagogical strategies associated with calculus learning at Chishinga Secondary School in Kawambwa District, Zambia, focusing on the concept of “liminal space”, a transitional phase where learners grapple with difficult, transformative concepts that define their mastery of the subject. The research addresses three key questions: the factors influencing the emergence of liminal space in calculus, the specific barriers students encounter within this space, and the instructional strategies that can support students in overcoming these challenges. A mixed-methods approach was used, incorporating surveys, pre and posttests for 100 learners and, interviews with three (3) mathematics teachers to gain a nuanced understanding of the calculus learning experience. The findings reveal that both internal factors, such as prior algebra and trigonometry knowledge (foundational knowledge) and motivation, and external factors, like teaching methods and curriculum structure, contribute significantly to students experiences in the liminal space. Students frequently reported cognitive overload, misconceptions, and emotional challenges, including anxiety and frustration, particularly with threshold concepts such as limits, derivatives, and integrals. Teachers, too, observed that students often misunderstand these foundational ideas, which hinders their progress and affects their overall attitude toward calculus.The study identifies a range of effective instructional strategies for helping students navigate this challenging phase. Active learning, inquiry-based methods, and peer-assisted activities were found to enhance engagement and deepen understanding. Formative assessments and especially constructive feedback emerged as critical tools in identifying misconceptions and providing real-time guidance, while differentiated instruction and scaffolding were noted as essential in helping learners’ bridge foundational gaps. Additionally, the integration of technology and visual aids proved valuable in helping students visualize abstract calculus concepts, though equitable access remains a concern. This research underscores the importance of a student-centered, multifaceted approach that includes active engagement, regular assessment, individualized support, and collaborative learning environments. The findings provide actionable insights for educators, policymakers, and curriculum developers to enhance calculus instruction and support students in navigating the complexities of mathematical learning.

Keywords: Liminal space, calculus education, threshold concepts, formative assessment, Chishinga Secondary School.

DOI: 10.7176/JEP/16-9-11

Publication date:August 31^st 2025