Titus 2:12 (Divine Χάρις teaches "us")

Greek (WH): παιδεύουσα ἡμᾶς, ἵνα ἀρνησάμενοι τὴν ἀσέβειαν καὶ τὰς κοσμικὰς ἐπιθυμίας σωφρόνως καὶ δικαίως καὶ εὐσεβῶς ζήσωμεν ἐν τῷ νῦν αἰῶνι,

Our text begins with the present active participle nominative singular feminine form of the verb παιδεύω + the accusative plural first person of ἡμεῖς: translate "teaching us."

Raymond F. Collins points out that it is ἡ χάρις τοῦ Θεοῦ that has appeared to instruct "us" (i.e., Christians); see Titus 2:11 and note the use of an explanatory γὰρ there. Collins writes:

"Now the Pastor makes reference to the saving beneficence of God. The 'beneficence' or 'grace' (he charis) about which he writes is not grace in the Pauline sense, that is, the grace of God that justifies; rather, the word is to be taken in its usual Hellenistic sense of 'favor' or 'beneficence.' In the Pastor’s world the granting of favors was often associated with royal 'appearances' ” (1-2 Timothy and Titus in the NTL Series, page 349).

I personally don't find Collins' take on Χάρις to be all that convincing. Granted, looking at ancient royal appearances or "divine" visits is fair game for trying to determine a word's semantic range, but the immediate literary context and normal usage of the word must have some influence on how we understand Χάρις. 

BDAG makes these comments about this particular use of Χάρις:

— χ. to denote beneficent dispensations of the emperor: OGI 669, 44 [I a.d.]; BGU 19 I, 21 [II a.d.] χάρ. τοῦ θεοῦ Αὐτοκράτορος; 1085 II, 4) and of Christ, who give (undeserved) gifts to people; God: δικαιούμενοι δωρεὰν τῇ αὐτοῦ χάριτι Ro 3:24. Cp. 5:15a, 20f; 6:1; 11:5 (ἐκλογή 1), 6abc; Gal 1:15 (διά A 3e); Eph 1:6f (KKuhn, NTS 7, ’61, 337 [reff. to Qumran lit.]); 2:5, 7, 8; cp. Pol 1:3; 2 Th 1:12; 2:16; 2 Ti 1:9; Tit 2:11 (ἡ χάρ. τοῦ θεοῦ σωτήριος; s. Dibelius, Hdb. exc. after Tit 2:14); 3:7; Hb 2:9 (χωρίς 2aα); 4:16a (DdeSilva, JBL 115, ’96, 100–103); 1 Cl 50:3; ISm 9:2; IPol 7:3. ἐν χάρ[ιτι θεοῦ] AcPl Ha 7, 23 (restoration uncertain). κατὰ χάριν as a favor, out of goodwill (cp. Pla., Leg. 740c; schol. on Soph., Oed. Col. 1751 p. 468 Papag.) Ro 4:4 (opp. κατὰ ὀφείλημα), 16.—The beneficence or favor of Christ: διὰ τῆς χάριτος τοῦ κυρίου Ἰησοῦ πιστεύομεν σωθῆναι Ac 15:11. Cp. Ro 5:15b; 2 Cor 8:9; 1 Ti 1:14; IPhld 8:1. On Ac 2:47 in this sense s. TAnderson, NTS 34, ’88, 604–10.

Compare 2 Timothy 1:9; Titus 3:5-7. Note also the goal of divine instruction that occurs via Χάρις manifested through Christ: ἵνα ἀρνησάμενοι τὴν ἀσέβειαν καὶ τὰς κοσμικὰς ἐπιθυμίας σωφρόνως καὶ δικαίως καὶ εὐσεβῶς ζήσωμεν ἐν τῷ νῦν αἰῶνι.