Indeterminacy Lattices for Diagnosing Mathematical Misconception
Boundaries in Higher-Education Assessment Logs
Agnes Osagie1,*
1Cape Peninsula University of Technology, Faculty of Applied Science, South Africa
Email: Osagieagne2000@cput.ac.za
Abstract
Assessment records in digital mathematics platforms contain a form of uncertainty that is not sufficiently expressed
by binary correctness labels. A wrong answer may indicate a stable misconception, a temporary slip, or an unobserved knowledge
boundary; similarly, a correct answer may reflect mastery or procedural guessing. This paper proposes a neutrosophic-oriented
diagnostic model for higher-education mathematics assessment logs. Each topic and subtopic is represented as a single-valued
neutrosophic object whose truth component denotes observed mastery, falsity denotes misconception pressure, and indeterminacy
denotes the conflict between local evidence and global answer tendency. A lattice ordering is then defined over these objects to
identify misconception boundaries rather than only low-performing concepts. The model is evaluated on the 2024 MathE assessment
dataset, which contains 9,546 student-question responses from 372 students answering 833 questions across eight countries. Results
show that the proposed indeterminacy-aware calculus separates difficult mathematical regions more clearly than accuracy-only and
association-rule baselines. Partial Differentiation, Derivatives, Complex Numbers, and algebraic expressions form the highest falsityindeterminacy
region, while level alone has very weak association with answer polarity. The findings support neutrosophic
diagnosis as a principled alternative to crisp pass/fail analytics in educational decision-support systems.
Keywords: Single-valued neutrosophic set; Educational data mining; Mathematics assessment; Indeterminacy lattice;
Misconception diagnosis; Information fusion