"The more debris we have, the more we can recreate, looking at the wind and currents, where the plane crashed."
Families have accused Malaysian-led investigators of focusing too much on the deep-sea search for wreckage off the coast of Australia.
The visit by seven relatives to Madagascar, where almost half of the more than 30 pieces thought to be from the plane have been found, prompted the Malaysian investigators to follow them to the Indian Ocean island to collect the latest items.
The Transport Ministry handed over six pieces on Monday that included a seat back with coat hook, and wing and tail pieces.
Gervais Damasy, director of Madagascar's Bureau of Civil Aviation Accident Investigations, said he would discuss with the chief Malaysian investigator whether the two countries could launch a joint search of Madagascar's 3,200 miles of coastline. "We want to help, but alone, we do not have the means," he said.
Grace Subathirai Nathan, a Malaysian lawyer who lost her mother on MH370, said the bereaved relatives - seven of whom are in Madagascar, from China, Malaysia and France - would be "delighted" if people on Africa's east coast joined the search.
"Up to today every piece of debris found has been found by private citizens," she said. "It is important to know that we as private citizens can make a difference."
The families, who are paying for their Africa trip themselves, said they would offer a modest reward to anyone who found debris confirmed to be from flight MH370.
"It needs to be proven that it's debris from a plane and then it depends on the importance of the debris," said Nathan, without saying how much they would pay for an item found.
On Tuesday, the families plan to visit different stretches of coastline around Madagascar to speak to residents and join the search. The Malaysian and Chinese families will return home via Mauritius to raise awareness there.