Automatic Educational Question Generation with Difficulty Level Controls

We consider the task of automatically generating math word problems (MWPs) of various difficulties that meet the needs of teachers in teaching and testing students in corresponding educational stages. Existing methods fail to produce high-quality problems while allowing the teacher control over the problem difficulty level. In this work, we introduce a controllable MWP generation pipeline that samples from an energy language model with various expert model components for realizing the target attributes. We control the difficulty of the resulting MWPs from mathematical and linguistic aspects by imposing constraints on equations, vocabulary, and topics. We also use other control attributes including fluency and distance to the conditioning sequence to manage language quality and creativity. Experiments and evaluation results demonstrate our approach improves upon the baselines in generating solvable, well-formed, and diverse MWPs of controlled difficulty levels. Lastly, we solicit feedback from various math educators who approve the effectiveness of our system for their MWP design processes. They suggest our outputs align with the expectations of problem designers showing a possibility of using such problem generators in real-life educational scenarios. Our code and data are available on request.