## Volume 12, Number 16, September 2022

#### Quantifying the Theory Vs. Programming Disparity using Spectral Analysis

### Authors

Natarajan Meghanathan, Jackson State University, USA

### Abstract

Some students in the Computer Science and related majors excel very well in programming related assignments, but not equally well in the theoretical assignments (that are not programming-based) and vice-versa. We refer to this as the "Theory vs. Programming Disparity (TPD)". In this paper, we propose a spectral analysis-based approach to quantify the TPD metric for any student in a course based on the percentage scores (considered as decimal values in the range of 0 to 1) of the student in the course assignments (that involves both theoretical and programming-based assignments). For the student whose TPD metric is to be determined: we compute a Difference Matrix of the scores in the assignments, wherein an entry (u, v) in the matrix is the absolute difference in the decimal percentage scores of the student in assignments u and v. We subject the Difference Matrix to spectral analysis and observe that the assignments could be partitioned to two disjoint sets wherein the assignments within each set have the decimal percentage scores closer to each other, and the assignments across the two sets have the decimal percentage scores relatively more different from each other. The TPD metric is computed based on the Euclidean distance between the tuples representing the actual numbers of theoretical and programming assignments vis-a-vis the number of theoretical and programming assignments in each of the two disjoint sets. The larger the TPD score (in a scale of 0 to 1), the greater the disparity and vice-versa.

### Keywords

Spectral Analysis, Theory vs. Programming Disparity, Eigenvector, Bipartivity.