In contemporary education systems, educational data is a core element in driving educational advancement and optimizing management. Most educational data is stored in the cloud as videos, images, or text, which facilitates its storage and dissemination. However, there are two significant challenges: First, existing data compliance detection systems may be vulnerable to attacks where malicious actors inject unqualified data into detection models, resulting in the upload of non-compliant educational data. Second, there is the issue of incomplete data storage. Data in cloud computing environments might be lost or corrupted due to various issues, posing a threat to the utilization of educational data. To address these challenges, this paper proposes a blockchain-based auditing scheme for educational data supporting trusted detection scheme(BAS-EDTD). This scheme uses smart contracts to randomly select AI detection modules for data inspection, ensuring that uploaded data is harmless and generating a detection report stored in the cloud. Additionally, a Trusted Third Party (TPA) assesses the reputation of AI detection modules to prevent those in untrusted cloud environments from injecting non-compliant data and affecting detection efficiency. Simultaneously, we adopt certificateless aggregate signature technology to perform data integrity auditing, reduce storage and computing overheads, support batch verification, and improve verification efficiency. Security proofs indicate that this scheme can effectively resist forgery attacks and demonstrates lower computing and communication overheads compared to existing schemes in performance analyses.