Look to United States Supreme Court cases that don’t make front-page news if you want to see the workings and qualities of the court at its best, Justice Elena Kagan suggested in a session with more than 225 Marquette Law School students Tuesday.

Asked by a student to provide reasons to have faith in a divided court that often votes predictably, Kagan said, “I think you should have that faith.” She called the court “an inspiring institution” whose members struggle conscientiously with difficult issues.

Kagan, who joined the court in 2010, visited the Law School to take part in judging the annual Jenkins Honors Moot Court Competition for students. She also took part in an “On the Issues with Mike Gousha” conversation for an hour, answering questions from Gousha, the Law School’s distinguished fellow in law and public policy, and from students.

Kagan, of course, did not discuss pending matters before the Court, but, in a wide-ranging and informal conversation, she discussed the way the Court works, her perspective as a woman lawyer, her personal background, and other matters.

Responding to the student who asked why people should have faith in the court, Kagan said that sometimes there are predictable 5-to-4 votes. “That’s just the nature of things,” she said. But she added, “There are a world of cases that people don’t as often take note of, and some quite important, where there aren’t these predictable divides.” Those often are the cases that show the strengths of the deliberative processes the court uses.

Kagan recalled the first time she attended one of the conferences, limited to the nine justices, where each member says how he or she would rule in cases. Dealing with a major case, the members each gave his or view and, within 10 minutes, the tentative outcome was set. Then the justices spent 40 minutes on a less-noteworthy case before they finally arrived at a point where they could say, “O.K., we could do the case this way.”

At first, Kagan said, it seemed crazy to her to spend so much more time on a lesser case, but then she realized it made sense, given the established opinions individual justices had, the process for reaching a decision, and the prospects for persuading others. “Some cases, you’re not going to persuade each other,” she said. “But there are a lot of others where you can.”

Overall, Kagan said, the Supreme Court is an institution where “everybody is struggling to get the answers right.” People would be impressed if they knew how well-prepared justices are when they deal with a case, how engaged they are, and how they work in good faith, even amid differences of opinion.

She called the Court “actually a very warm institution.” Referring to some opinions which she called “biting,” she said, “You read those opinions and you think, gosh, they must all hate each other. But it’s so much the opposite of that.” There is “a reservoir of good feeling and warmth” among the justices.

Among the subjects Kagan addressed:

Women on the Court and in law practice in general: She said some 45% of the members of her 1986 Harvard Law School class were women. For many years, there has been general gender equity in law school enrollment and graduations. Kagan said that that leaves many people perplexed why that hasn’t translated into more success for women in law firms. “You wonder why that is,” she said. But she was generally optimistic that the picture is improving. Kagan is the fourth woman in American history to serve on the Supreme Court. She said she found it hopeful to contrast the experiences of the first two, Sandra Day O’Connor and Ruth Bader Ginsburg, and the next two, Sonia Sotomayor and herself, who are quite a bit younger. O’Connor and Ginsburg found many closed doors when they graduated from law school and faced barriers to opportunity. Kagan said she and Sotomayor did not face such problems and always felt they had a lot of opportunities.

The Harvard/Yale domination of the Court: All of the current justices went to one of those two law schools, and Kagan said, “I think it’s a real issue.” She added, “You know what our diversity is? Justice Ginsburg spent a year at Columbia.” She said, “It’s sort of nutty. There are great lawyers from great law schools all over this country.” She called the Harvard/Yale monopoly “a little odd” and “a little perplexing,” but said it was not something that was easy to change, given the long tenure of justices.

The lack of geographic diversity on the Court : Kagan, a New York native, also said it concerned her that ”we are a very coastal court.” The geographic roots of the court members are not as representative of the country as a whole as might be desirable. Among the nine members, “there are a lot of life years spent on the Acela line,” Kagan said, referring to the train that runs from Boston to Washington, D.C.

The importance of oral arguments before the Court: “It depends, honestly,” Kagan said. As solicitor general, the position she held before joining the Court, she said she spent a lot of time wondering how much oral arguments she gave mattered. Overall, she said, they matter most in lower-profile cases and cases where there are not “priors,” as she called previous similar cases.

But oral arguments always matter less than briefs filed with the Court, she said. She said briefs generally count for 95% of the presentation of a case, while oral arguments are “the last 5%.” She would urge anyone preparing a case for the Court to emphasize the briefs.

That said, “I can definitely think of cases where I went in [to oral arguments] thinking one thing and came out thinking another,” as well as times when she went in undecided and came out supporting one side.

She also said that oral arguments can serve as a valuable time for the justices to talk to each other and make points with each other, “and that is especially true if you have a little bit of an unusual take on a case.” She said, “Oral argument is a great time to plant a seed.” That is especially true for her, as the junior member of the Court, because when it comes to the conference usually held a few days later, every other justice has already stated an opinion before she gets her chance. If she wants to get an idea in front of the other justices, the oral argument session is a good way to do that ahead of the conference.

The confirmation process before the Senate: “It has its moments and it has its difficulties,” Kagan said. She said that, for her, the process was “a ton of work,” including individual sessions with 82 of the 100 members of the Senate. As for the hearings process itself, she said, “I’m a bit of a ham. . . . If you feel like talking, they really can’t stop you.” She said, “For the most part, I thought it was quite engaging and quite challenging.”

Justice Thurgood Marshall: Kagan clerked for Marshall, the famed civil rights lawyer and first black member of the Court, during the 1987-88 term. It was, she said, “an extraordinary experience” to work for him. “He was the great lawyer of the twentieth century,” she said. “He was the best story teller I’ve ever met in my life.”

Hunting: Talking about the good personal relations among justices, despite differences of opinion, Kagan described how she has gone hunting several times with Justice Antonin Scalia. She said people assume that abortion was the subject she was asked about the most when she met with senators during her confirmation process, but the number one subject was actually gun rights and the Second Amendment. Kagan said one senator asked if she had ever gone hunting. She said “no,” and offered to go with him. He seemed not to want to do that, so she said she would go with Scalia if she were confirmed. Indeed, Scalia subsequently took her skeet shooting and then hunting for pheasant and quail. “Justice Scalia has made a huntress out of me,” she joked. She said the two are planning to go hunting in Montana in October. In his chambers, Scalia has a large animal head he calls Leroy, Kagan said. “He insists I’m going to shoot myself an antelope,” Kagan said. “Justice Scalia insists I need my own Leroy.”

The importance of passion: Gousha told Kagan that Sandra Day O’Connor had visited Marquette Law School several years ago and concluded a session with students by advising them to make sure they maintain balance in their lives. He asked Kagan what her advice would be. “Find some passion,” Kagan added to O’Connor’s advice. “Think about what most moves you, about what you care about the most,” and let that form a big part of your life.

Why she was selected for the Court: Kagan responded to the question by saying, “It’s a pretty good job I have. It’s a good gig. . . . I don’t’ know exactly why I was chosen, but I’m not looking that gift horse in the mouth.”