NAZARETH -- When the fall term begins at Nazareth Area High School on Monday, one teacher will be conspicuous by his absence. Matthew Greene, a popular math teacher at the school 65 miles north of Philadelphia, vanished while on a backpacking trip in California last month. Police say Greene was there to hike and climb the Eastern Sierra, a region that features extremely steep and rugged terrain, with many peaks soaring to 12,000 and 13,000 feet. His disappearance has baffled friends and family who call Greene a highly experienced, cautious outdoorsman. "It just doesn't seem to me that he would go out for a day hike and not return," said his sister, Tiffany Minto. "We can't visualize him getting himself into any kind of dangerous situation. He's the personality type who would just turn back if it was too dangerous." Nearly a month after he was reported missing, Greene's family was offered a tantalizing clue as to his possible whereabouts: A hiker on Friday found a pair of eyeglasses that look "strikingly similar" to the ones worn by Greene, Minto said. The glasses -- found hanging on a sign at a trailhead near the Inyo Craters region -- have been turned over to the Mammoth Lakes Police Department, and Greene's optometrist has provided information about his prescription in hopes of helping police make a match. "It'd be an unbelievable coincidence" if the glasses turned out to be someone else's, Minto said Saturday. Greene, 39, had arrived in late June to hike and climb with friends. But when his Subaru blew a head gasket, they went on with their trip while he stayed behind at a campground in Mammoth Lakes, about 260 miles east of San Francisco, to wait for repairs. The last time anybody heard from him was July 16, when he chatted with his parents back in Pennsylvania, called the repair shop and traded text messages with a friend. Some of his gear was discovered to be missing, and pages were torn out of his guidebook, leading to speculation that he might have headed in that direction for a hike. Several of Greene's friends flew to California and canvassed bus drivers, store owners, librarians and others in Mammoth Lakes, posted fliers at trailheads, checked summit registers and spent several days in the back country looking for clues. The search has gone airborne, too, with a helicopter flying over the rugged terrain and one of Greene's friends shooting high-resolution video from a private plane. California search-and-rescue personnel have also volunteered their time. But they turned up no trace of the former Peace Corps volunteer. And, until Friday's recovery of the glasses, police had been struggling to develop leads. "There are so many places to go, so many," Detective Doug Hornbeck said in an earlier interview. "It's just such a vast area." Minto initially assumed her brother had some sort of accident. Now she's not so sure and wonders whether he might have been the victim of foul play. Police have said he may have hitched a ride from someone to a remote area to hike or climb. Minto said she's thinking about hiring a private investigator "just to exhaust every possible avenue." And fundraisers are being held to pay for additional search-and-rescue efforts. But she knows the odds of a good outcome grow longer each day her brother remains missing. "We kind of have realistic expectations," Minto said. "We may never get answers as to the how and the what. But we will settle for anything we can get to just bring him home and get some closure on it."