Applying psychometric models in learning progressions studies:Theory, method and breakthrough

Development of a New Learning Progression Verification Method based on the Hierarchical Diagnostic Classification Model: Taking Grade 5 Students’ Fractional Operations as an Example

“…According to Gao et al (2017), a CDM-based learning progression verification proceeds with the following five steps:…”

“…According to Gao et al. (2017), a CDM‐based learning progression verification proceeds with the following five steps: (1) based on the course standards, textbooks, and related research, the expert group extracts the attributes required by students to learn a certain concept and determines the hierarchical relationship between attributes; (2) students’ performance is defined at different progression levels according to the attributes and attribute hierarchical relationship, which means an initial hypothesized learning progression is proposed by accumulating the attributes students mastered (Gao et al., 2018); (3) the reduced incidence Q ‐matrix (i.e., Q r ; Gierl et al., 2000; Tatsuoka, 1995) satisfying the attribute hierarchical relationship is established to characterize the potential pool of item types, and then the test items are compiled based on Q r ; (4) data are collected and students’ psychometric properties at both test and item levels are evaluated; and (5) CDM analysis is conducted to classify students into different attribute mastery patterns (AMPs; Tatsuoka, 1983), as well as to test and revise the initial learning progression hypothesis. The basic logic of the fifth step is to assume that students should follow the order from easy to difficult to grasp the concept; in other words, the prerequisite attributes in the hierarchical relationship should be first grasped.…”

“…An in‐depth study of learning progressions can uncover the actual thought development paths of students from a cognitive perspective as they progress from novices to experts. By such study, researchers and educators can then assist students in overcoming learning difficulties (Gao et al., 2017). Therefore, this study takes grade 5 students’ fractional operations as an example to build a learning progression.…”

“…However, prior research demonstrated that the attribute hierarchical relationship obtained in RSM may be wrong (Yu et al., 2011), and the uniqueness of such a relationship cannot be guaranteed (Qi et al., 1998). Moreover, a learning progression comprised such steps as constructing theories, compiling items, collecting data, and analyzing models (Gao et al., 2017). The quality of each step affects the degree of agreement between students’ performance and the progression levels.…”

Developing a Learning Progression for Probability Based on the GDINA Model in China

“…Since the beginning of the last century, psychometrics and cognitive psychology have been increasingly dissatisfied with assessing the ability level of the individual from macro perspective, so a new generation of psychometrics theory has developed a cognitive diagnosis model for the purpose of diagnosing students' cognitive process, processing skills or knowledge structure. Therefore, researchers began to use it as a quantitative analysis method to provide technical support for the construction of learning progression evaluation system, so as to deeply evaluate student' knowledge structure (Derek and Alonzo, 2012;Chen et al, 2017b;Gao et al, 2017).…”