As I sit on the beach at Wolf Point in Glacier Bay, the orcas play and the tidewater glaciers shimmer in the long summer light. Red Mountain is reflected in the ripples of the tidal lagoon. Everything is so peaceful. Amazingly, we're on our ninth straight day of sunshine, in an area that's lucky to see the sun six days in a whole year. I've led this trip before, but it's never been quite like this. In fact, just like teaching a class, it's different every time.

I teach mathematics at Mission College in Silicon Valley, and I recuperate in the summer by leading groups in Alaska for Sierra Club National Outings. There turn out to be many similarities between the two activities - both the joys and the pitfalls. In both cases, individual people determine whether things work or not. It's those small everyday interactions that produce success or failure. Does the student feel positive about her learning relationship with the instructor? Does the trip member get the memorable wilderness experience she wants? Is it fun, and is it safe? The same personality types and stories are all there in the wilderness, but closer to the surface than the corresponding teaching encounters in my classroom. I think back to some past classes, and to some previous trips to Alaska.

Years ago, as a new leader of a sea kayak trip in Glacier Bay National Park, I was helping our group to thread their way through the Beardslee Islands - a maze of tiny channels that changes every year because the neighboring land rises approximately 3 centimeters in rebound from the recently disappeared cover of retreating glacier ice. The marine chart bears very little resemblance to the actual land, because, as it rises, the shape of the water's edge alters dramatically. In its turn, navigation changes from a science to a subtle art form. Suddenly, two boats in the rear of our group veered off around the wrong side of an island. I knew they were heading for the main channel, with dangerous rip currents and no shelter from the wind; they did not know. I was aiming for a hidden, winding exit at the end of what appeared to be a closed bay. They didn't trust me enough to follow, and wanted to take their own "shortcut". In a kayak, once you lose voice contact, you're gone.

How often as a teacher have I watched students wander off lost? They don't trust that I am experienced enough to help them, and I can't find a way to communicate vital information soon enough. I see them, but I can't lead the whole class in pursuit of them.

Similarly, I couldn't take the whole kayak group in pursuit of the two boats which had chosen an alternate route. One nervewracking hour later, the two kayaks appeared out of the rising surf and joined the rest of our little group for the stormy journey to camp at York Creek. The wind had increased and was blowing all the way across Beartrack Cove; the curling whitecaps broke over the front of the kayaks; everyone was tired and scared. Conditions can change fast when you're in a very small boat in very deep water.

They seem to change just as fast in my classroom. Sometimes I can wait and guide the lost ones back to the group, but other times they never return.

Then there's the opposite problem - too much experience. I've led the trip many times before: I know exactly where that breathtaking campsite is hidden; I know about the secret glacier tarn for swimming; I've seen the humpback whale leap in Icy Strait; and I've seen the Muir Glacier calve an eight hundred foot tower of ice into the milky water below. With those experiences, how do I not intrude on the sense of excitement and discovery for each new trip member? I'm longing to relate what I saw here the last time, but I don't want to spoil their own wondrous and spontaneous beauty.

That's the challenge for the experienced teacher. How do I keep the excitement and sense of exploration in my class? I've got a new group of students, but I've taught the material many times before.

And then, there's "fairness" - a quality much prized by students and trip members alike. Shannon and Jean were both on a backpack trip in the Arctic National Wildlife Refuge. The bush plane had dropped us off in a bog by the Aichilik River and would not return for nine days. It is a raw, powerful land, and backpacking in the Arctic is extremely demanding, with not much room for error. On the second day, Peter stumbled and floated down the river, trying to hold his camera out of the water. We raced down the bank beside him until he finally floated ashore. Later that day it began to snow and the lone gray wolf across the river seemed to howl that we were going the wrong way as we scrambled along the steep, rocky bank.

Jean had done this sort of thing before, was small and tough, but liked to complain. Every morning, I weighed the amount of food and community equipment each person should carry. Jean wanted to carry less because she was small. But Shannon, who was big and tall, was new to this game. She found it very difficult but struggled without complaining. The two women shared a tent. I never did resolve the different conceptions of what was fair. The rest of the group became irritated by the whole thing and wished that Jean would leave. Jean told me that everything I did as leader was wrong and that her previous trip leader, Wilfred, was wonderful. But at a committee meeting many months later, Wilfred commented: "Oh no, she was a real pain!"

I get people like that in classes, too - we never do understand each other, and the whole class is affected by it. I can't find a way to help with the problem and yet I can't just leave them behind in the wilderness (Alaskan or educational).

Dan was on a sea kayak trip to Misty Fjords National Monument in southeast Alaska. He marveled at the Yosemite style granite walls that plunged three thousand feet into the icy, black water of Punchbowl Cove. He enjoyed the soaring bald eagles and the seals popping up right beside the boat, with those big surprised eyes. But he was never pleased. He had signed up for a Sierra Club cooperative style trip - but he really wanted the hand and foot service of a luxury guided tour. He had two volunteer leaders but he wanted lectures from experts in every field we encountered: flowers, birds, animal tracks, geology, meteorology. He was always disappointed even though he had a wonderful trip. Later that year we wondered why our trip evaluations did not contain a negative report from him. "Oh yes", said our boss, " he wrote one, but it was so bad, there was nothing useful to learn from it - I threw it out ! "

Every once in a while I get a student whose expectations for the class are completely unrealistic. They feel bad, and I feel bad, but the most useful thing I can do is direct them elsewhere. Or I can find them a colleague with a personality they'll enjoy more.

So why do I do it? There are troubling failures, but not very many; and they do make for the best stories. Then there are the successes: the people who say the trip was the experience of a lifetime; the people who thought they could never do it; and I can share in that!

There's being out there and surviving with just your tent and your kayak - or just your textbook and your brain. There's the lady this summer whose son designs kayaks but who has never before been to Alaska herself; the glaciers remind her of her childhood in Switzerland. And there's the white-haired grandmother who is taking beginning algebra in preparation for law school now that her children are successfully launched. There's the girl from Boston, just out of college, who has never been to the wilderness before but comes along with her office-mate to see a whole new world. She may never do it again, but it's made her a different person. There's the woman from Spain who's worried that her husband will think she's a different person once she knows algebra. There's the baseball player who can't let his teammates see that he could do well in this class. And there are the Math for Liberal Arts students who have hated every math class in their lives, but come to discover that there are beautiful and exciting things to write about in the world of mathematics. And they can do well.

That's why I do it: it's the people. And it's the way I interact with each personality. If I'm grumpy, it doesn't work. But if I feel good about these interactions it works for everybody, and I keep doing it!

The sun finally dips behind Red Mountain and the summit cornice turns a delicate shade of alpenglow pink. The oyster catchers still echo across the beach. It's time to retreat to my tent for a few hours of darkness, and to fall asleep with all these memories. When's the next trip? When's the next class? Sign me up!!