Vincent's NT Word Studies
31. Taught (hn didaskwn). Correctly, as Rev., was teaching. The finite verb and participle denoting continuance.On the Sabbath-days (toiv sabbasin). Rev., day. The word is often used in the plural form for the single day, as in verse 16; probably after the analogy of plural names of festivals, as ta azuma, the feast of unleavened bread; ta genesia, the birthday; or perhaps following the Aramaic plural.
Robertson's NT Word Studies
4:31 {Came down} (katelqen). #Mr 1:21 has the historical present, {they go into} (eisporeuontai). Capernaum (Tell Hum) is now the headquarters of the Galilean ministry, since Nazareth has rejected Jesus. #Lu 4:31-37 is parallel with #Mr 1:21-28 which he manifestly uses. It is the first of Christ's miracles which they give. {Was teaching them} (en didaskwn autous). Periphrastic imperfect. Mark has edidasken first and qen en didaskwn. "Them" here means the people present in the synagogue on the sabbath, construction according to sense as in #Mr 1:22.