Teacher Simon Baccanello was at the back of a group of about a dozen surfers at Walkers Rock Beach on Eyre Peninsula on Saturday morning when he was attacked.
Efforts to find the 46-year-old over the weekend failed and resumed on Monday, with police and volunteers concentrating on areas of the coast near where the incident occurred.
"We'll be doing the beaches around Walkers Rock and we'll be checking for any signs that might point to what occurred," Superintendent Paul Bahr told ABC Radio on Monday.
"We continued the search along the shore along Walkers Rock yesterday.
"We did find a few items of interest that we've now collected.
"We are in the process of putting together a report which will go to the coroner."
Supt Bahr said crews were searching the high-tide marks, with the help of volunteers, for any further debris.
Saturday's incident occurred near a reef break popular with surfers in an area with a history of shark attacks.
Supt Bahr acknowledged it was a difficult time for the tight-knit community.
"People are going to be in distress," he told reporters on Sunday.
"It will take time to get them to a point where we can talk to them and get statements from them.
"They would all know someone who was involved, if not the victim themselves, so I imagine it is very tough for them."
Mr Baccanello joined the local Elliston Area School at the beginning of the year.
Education Minister Blair Boyer said the department had put support services in place for the teacher's colleagues and the students.
Principal Chad Fleming said Mr Baccanello was a valued colleague and a true friend to everyone.
"With his dedication to education and an enthusiastic and positive approach to learning and life, Simon showed care and respect to everyone," Mr Fleming said.
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