At this point I'll show the other instance where Mark uses the phrase, "and in his teaching he was saying". It's Mark 12:38, "38And in His teaching He was saying, “Beware of the scribes, desiring to walk about in robes, and greetings in the marketplaces, 39and first seats in the synagogues, and first places at the feasts; 40those devouring the houses of widows, and praying at great length as a pretext. These will receive greater judgment.”"
If we look at Matthew's equivalent section, following the section, Whose son is the Christ?, Mt 23: "1Then Jesus spoke to the crowds and to His disciples, 2saying, “The scribes and the Pharisees have sat down on Moses’ seat; 3therefore keep and observe all things whatsoever they might tell you. But do not do according to their works, for they preach and do not act. 4And they tie up burdens heavy and hard to bear and lay them on the shoulders of men; but they themselves are not willing to move them with their finger.
5And they do all their deeds in order to be seen by men. For they broaden their phylacteries and enlarge their tassels, 6and they love the chief place at the banquets, and the first seats in the synagogues, 7and the greetings in the marketplaces, and to be called ‘Rabbi’ by men.
8But you shall not be called ‘Rabbi,’ for your Teacher is One, and you are all brothers. 9And call no one your father on the earth; for One is your Father, who is in heaven.
Look at the similarities between Mark's and Matthew's. Again, assuming no evidence for any other source for this material, Matthew's seems to be the original, as it is a continuous statement. So when Mark says, "in his teaching..." he is probably referring to all the teaching given in Matthew 23 (Ten Woes included). This, Mark has briefly summarized (12:38-40).