And at times he would pass his hands back and forth; this is how the report stating that he wiped his head twice is to be understood (1).
The correct view is that he did not wipe his head repeatedly. Rather, when he repeated the washing of his limbs, he wiped his head only once. This is explicitly reported from him, and no contrary report from him is authentic (2). All other reports are either authentic but not explicit—such as the Companion’s statement, “He performed ablution, washing each part three times,” or his statement, “He wiped his head twice”—or explicit but not authentic. An example of the latter is the report of Ibn al-Baylamānī, from his father, from [Ibn] Umar, that the Prophet (may Allah bless him and grant him peace) said, “Whoever performs ablution and washes his hands three times,” then said, “and wipes his head three times” (3). This report cannot be used as evidence. Ibn al-Baylamānī and his father are both weak narrators (4), although the father is of better standing.
Another example is the hadith of Uthmān reported by Abū Dāwūd (5), stating that the Prophet (may Allah bless him and grant him peace) wiped his head three times. Abū Dāwūd said (6): “All the authentic reports from Uthmān indicate that the head was wiped once.”
There is not a single authentic report that the Prophet ever confined himself to wiping only part of his head. Rather, whenever he wiped the front of his head, he completed the wiping over his turban.