  Math word problem (MWP) solving is an important task in question answering
which requires human-like reasoning ability. Analogical reasoning has long been
used in mathematical education, as it enables students to apply common
relational structures of mathematical situations to solve new problems. In this
paper, we propose to build a novel MWP solver by leveraging analogical MWPs,
which advance the solver's generalization ability across different kinds of
MWPs. The key idea, named analogy identification, is to associate the
analogical MWP pairs in a latent space, i.e., encoding an MWP close to another
analogical MWP, while moving away from the non-analogical ones. Moreover, a
solution discriminator is integrated into the MWP solver to enhance the
association between the representations of MWPs and their true solutions. The
evaluation results verify that our proposed analogical learning strategy
promotes the performance of MWP-BERT on Math23k over the state-of-the-art model
Generate2Rank, with 5 times fewer parameters in the encoder. We also find that
our model has a stronger generalization ability in solving difficult MWPs due
to the analogical learning from easy MWPs.
