Personalized assessment: Applying higher-order cognitive diagnosis models in secondary mathematics

Abstract

Personalized assessment is an essential component in education. Although many cognitive diagnosis models (CDMs) have been developed for this purpose, few studies have applied them in secondary mathematical contexts. Using a sample of 391 Grade 11 students from a secondary school in China, the findings indicated that the higher-order generalized deterministic inputs, noisy, “and” gate (higher-order GDINA) model with one-parameter logistic (1PL) best fit the data, and the Q matrix validation process achieved acceptable results. At the grade level, most of the participants mastered attributes B1 (i.e., basic concept development of derivatives: simple equations, zero or extreme points, and function range problems), B2 (complex inductive contextualization of derivatives: induction from the known to solve the unknown problems), and B3 (basic routine problem solving of derivatives: graphs that pass through a fixed point or quantitative inequalities). However, less than half of the students mastered attribute B4 (complex transformative contextualization of derivatives: transformation by the combination of numbers and graphs). At the individual level, we selected four representative students with high, medium, and low levels of achievement to examine their individual skill profiles and provide personalized remedial and enhanced feedback. Implications for personalized assessments are discussed.