  Enriching the quality of early childhood education with interactive math
learning at home systems, empowered by recent advances in conversational AI
technologies, is slowly becoming a reality. With this motivation, we implement
a multimodal dialogue system to support play-based learning experiences at
home, guiding kids to master basic math concepts. This work explores Spoken
Language Understanding (SLU) pipeline within a task-oriented dialogue system
developed for Kid Space, with cascading Automatic Speech Recognition (ASR) and
Natural Language Understanding (NLU) components evaluated on our home
deployment data with kids going through gamified math learning activities. We
validate the advantages of a multi-task architecture for NLU and experiment
with a diverse set of pretrained language representations for Intent
Recognition and Entity Extraction tasks in the math learning domain. To
recognize kids' speech in realistic home environments, we investigate several
ASR systems, including the commercial Google Cloud and the latest open-source
Whisper solutions with varying model sizes. We evaluate the SLU pipeline by
testing our best-performing NLU models on noisy ASR output to inspect the
challenges of understanding children for math learning in authentic homes.
