Math word problems are critical K-8 educational tools, but writing them is
time-consuming and requires domain expertise. We suggest that language models
can support K-8 math education by automatically generating problems at scale.
To be educational, generated problems must be 1) solvable, 2) accurate, and 3)
appropriate. Existing datasets are unlabeled for these criteria, making them
ill-suited for training problem generators. We introduce MATHWELL, a Llama-2
(70B) model iteratively finetuned to generate K-8 math word problems using data
from expert annotation. Using MATHWELL, we generate the largest English word
problem dataset to date, containing 20,490 problems. 3,484 are scored by domain
experts who find MATHWELL has a 40% higher share of problems that have
executable solutions and meet all criteria than alternatives, with 74% of its
problems with executable solutions being solvable, accurate, and appropriate.

使用语言模型自动生成的 K-8 数学题库，通过定期优化和专家标注的数据，得到了迄今规模最大的英语数学题库，其中有 20,490 个问题，其中 3,484 个经过领域专家评分，发现 MATHWELL 比其他方法生成的问题更容易求解、准确和适用，有 74% 的问题有可解答的解决方案，并满足所有标准。