Focusing on multi-attribute group decision making (MAGDM) regarding classroom teaching quality evaluation, this article aims to devise a novel evaluation framework based on heterogeneous linguistic information. In this framework, a four-level evaluation process of classroom teaching quality is established. Then, the weights of the sub-attributes are estimated objectively by integrating a newly proposed score function of interval linguistic 2-tuples and optimization models which consider the realistic situation that alternatives are not equally weighted. Subsequently, the exploitation process is implemented by two branches: taking the possibility measurement to rank teachers with respect to different attributes and extending the technique for order preference by similarity to ideal solution (TOPSIS) method to assess the overall performance of teachers. Finally, a simulated case is furnished to illustrate how to apply the presented framework to realistic classroom teaching quality evaluation problems. Hopefully, this work would be beneficial to the improvement of classroom teaching quality.