2026 ASEE Annual Conference & Exposition

From Math Review to Numerical Methods Proficiency: Hybrid TBL and Lecture Approaches in a Materials Course

Presented at Materials Division (MATS) Special Session: How you teach it

Abstract submitted under: Special Session 2: “How you teach it”
Equipping students with the skills necessary for independent research is a crucial goal of graduate coursework, particularly in materials science and engineering. These courses are structured not only to advance technical mastery but also to foster critical thinking, collaborative problem-solving, and adaptability to emerging research challenges. This paper describes the ongoing restructuring and continuous improvement efforts for a one-semester, three-credit graduate course required for materials science PhD students. Initially, the course focused on a comprehensive review of math, enabling students to revisit and strengthen foundational engineering concepts through manual calculations and analytical methods. While some students appreciated this review, feedback revealed that the curriculum lacked sufficient rigor for graduate-level study and did not adequately prepare students for advanced research applications.
Recognizing this gap, the course transitioned to emphasize numerical methods—reflecting the reality that most authentic engineering problems cannot be solved analytically and require computational solutions. The integration of contemporary numerical approaches posed its own instructional challenges, particularly in ensuring students felt confident applying these new techniques to open-ended research problems. Alongside content evolution, the course structure was modified to incorporate experimental learning through team-based learning (TBL). TBL is well-documented for improving academic performance and fostering deeper understanding by engaging students in collaborative tasks and requiring pre-class preparation. Initial attempts to implement TBL exclusively were met with resistance, as faculty noted recurring difficulties students faced without some lecture structure. In response, a hybrid model was developed, blending targeted lectures with team-based activities to balance active engagement and direct instruction. This paper presents the process of curricular modification, synthesizes faculty reflections on instructional effectiveness, discusses key challenges encountered, and offers best practices for implementing a hybrid TBL and lecture approach in graduate-level materials science and engineering numerical methods courses.

Authors
  1. Dr. Sharniece Holland Trogler Washington University in St. Louis [biography]
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