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Physical-education evaluation refers to the process in which teachers aim to assess students’ progress in physical education using the scientific method to make judgments about the quality of learning and level of achievement (Greaves et al., 2011). Learning-outcome assessment is an important part of students’ learning and is the basis for organization in the teaching process (Flöel et al., 2010). By evaluating the knowledge each student has mastered, teachers can provide different types of remediation for each student, thereby improving their learning (Cardona-Morrell et al., 2010).
Learning-outcome assessment has a remarkable effect on improving learning. Its meaning and effect are reflected mainly in feedback regulation and monitoring, learning support, optimizing education, and other aspects (Tremblay et al., 2016). Through evaluation, teachers can constantly discover problems, improve teaching and learning methods, and promote the all-around development of students (Zhang et al., 2021).
Scientifically evaluating students' learning outcomes is an essential element of effective teaching and serves as a standard for determining the effectiveness of instruction (Tremblay et al., 2017). The concept of quality education should focus on students' learning, the evaluation of the learning process, and the changes in their emotions and attitudes during the learning experience (Henson et al., 2013). Comprehensive evaluation is an effective way for students to assess their overall progress during the learning process (Ceulemans et al., 2015). Through learning evaluation, students can gain a more specific and detailed understanding of their learning progress, allowing them to adjust their learning methods accordingly (Papastergiou, 2009).
Because the connotation of learning outcome in quality education differs from that of traditional learning, traditional learning-outcome assessment primarily uses quantitative evaluation and test scores to obtain assessment results (Wang, 2018). In addition to evaluating students’ test scores, learning-outcome assessment in quality education should also include evaluation of their emotions, learning attitudes and overall learning quality during the learning process. Learning-outcome assessment should include qualitative evaluation criteria to comprehensively assess students’ learning outcomes (Zhang et al., 2018).
Gray clustering is a method of dividing some indexes and observation objects into several definable categories based on the correlation matrix or gray whitening weight function. A cluster can be seen as a collection of observation objects belonging to the same class (Liu et al., 2021). Some scholars have proposed a gray weighted clustering evaluation method based on triangular models (Kong & Guo, 2022). In order to make the clustering results more reasonable, some scholars have proposed the gray optimal clustering theory model (Feng, 2020). Due to its ease of understanding and programming, the gray clustering evaluation method has become a hot research topic, widely used in economics, environmental-quality assessment, remanufacturing evaluation, calculation, and transportation. Some researchers have applied the gray clustering method to calculate the weight and whiten multi-indicator data, achieving scientific weighting of multiple evaluation indexes and classification ranking of libraries (Martos et al., 2023).
Applying the gray system in the comprehensive evaluation of physical education teaching can utilize its advantage in dealing with uncertain and fuzzy information. This approach can effectively solve the gray information associated with evaluating learning outcomes while avoiding the use of precise mathematics to process fuzzy information, which may result in deviations in results. The application of gray system theory in the evaluation of learning outcomes not only effectively addresses the problem of a small amount of evaluation data in the learning process, but also avoids the deviation in evaluation results caused by the limited amount of data available.