## 1 Introduction
The authors concluded that ADDIE is useful and developed a procedure for using the model to collect data and analyze results. [PERSON], [PERSON], and [PERSON] [15] used the ADDIE instructional system design method to guide the process of designing, implementing and evaluating educational multimedia software for learning mathematics. They concluded that this application appears to have considerable potential for use in teaching elementary school mathematics through storytelling and multimedia. [PERSON], [PERSON], and [PERSON] [16] evaluated the effectiveness of ADDIE instructional design and multimedia for learning key skills in futsal. Participants who were trained by an ADDIE model had higher mean scores for key futsal skills compared to students trained by traditional methods. Additionally, the authors successfully used ADDIE for developing e-materials for elementary students, including a mathematics speed unit, a complex graphics area unit, a fraction area unit, and a Mandarin character recognition learning course [17; 18; 19; 20; 21; 22]. According to these studies, the ADDIE design model is sufficiently dynamic and flexible for use throughout the process of developing a mathematics skills assessment system. For both students and educators, assessment systems developed using the ADDIE design model have proven useful for evaluating learning outputs. Researchers have developed various methods of analyzing the learning problems and barriers of students [23; 24; 25; 26]. For example, [PERSON] [27] developed an intelligent personalized learning system that used genetic algorithms to determine the best learning paths according to the incorrect answers of individual learners. [PERSON] and [PERSON] [28] used cognitive diagnostic assessments to provide detailed and precise information about the cognitive processes of students who had difficulty learning mathematics. [PERSON], [PERSON], and [PERSON] [29] proposed a structure and improvement processes for computerized adaptive testing systems. Conventional systems for assessing the abilities of students are now being replaced by adaptive assessment systems. The objective of adaptive assessment systems is to evaluate students according to their actual ability rather than according to their test grades. [PERSON] and [PERSON] [30] proposed a pedagogical approach to facilitating students in learning from their mistakes by answering a series of questions. [PERSON], [PERSON], [PERSON], and [PERSON] [31] proposed a group decision approach for developing a concept-effect relationship model with the cooperation of multiple domain experts. Low-achievement students who were taught using the group decision approach had significantly better learning achievement compared to those who were taught using the conventional approach. [PERSON], [PERSON], [PERSON], and [PERSON] [32] proposed a two-tier test-based learning approach to enhancing learning outcomes in computer-programming courses in a web-based learning environment. [PERSON], [PERSON], [PERSON], and [PERSON] [33] described an application of the assessment triangle, and compared two studies to evaluate whether evidence of student performance is consistent. [PERSON] and [PERSON] [34] used a hierarchy of fraction scheme that charted the outline of a progression from part-whole concepts to measurement concepts of fractions. However, for elementary students struggling in mathematics, the issue of which diagnostic method is most effective for understanding their learning problems needs further study. The aim of the proposed research is to propose effective theoretical methods, construct processes, and establish assessment systems. The research question is to diagnose student learning problems. This study proposes a Gagne-based learning hierarchy approach (GBLHA) to developing mathematics skills assessment systems that use the ADDIE model to diagnose student learning problems. Firstly, a learning hierarchy diagram for a mathematics unit is built by applying Gagne learning hierarchy theory.