When Brian Butterfield coaches third base for the Toronto Blue Jays at Yankee Stadium this week, he stands about 50 feet away from his former pupil. When one of the Jays smacks a grounder to shortstop, Butterfield studies how Derek Jeter, his old student, moves. Butterfield watches Jeter, but he could just as easily close his eyes. He would still be able to recite Jeter’s movements.

Eighteen years ago, Butterfield, a coach in the Yankees’ organization, was given an important offseason assignment: Help make the athletic yet inconsistent Jeter a better defensive shortstop. It was Butterfield’s task to guarantee that Jeter, who had made 56 errors in 128 games at Class-A Greensboro, was proficient enough as a shortstop that the Yankees could confidently keep him there.

The Yankees sent Jeter to the Instructional League in Tampa and Butterfield was waiting there, a fungo bat in his hands and a purposeful look in his eyes. For 35 straight days, Butterfield schooled Jeter in every aspect of his defense. There were no days off as Jeter began every session at 8 a.m. and fielded grounders, talked defense, played defense only in games, watched videotapes of his play and seemed to sleep and eat defense, too. Jeter has called Butterfield’s lessons the “five of the most important weeks of my career.”

As Jeter inches toward his 3,000th career hit, he has been stuck in an offensive malaise. After batting a career-low .270 in 2010, Jeter was hitting .261 before Tuesday’s game with Butterfield’s Jays. He tried a new no-stride approach as a hitter to start the season, but quickly abandoned it. There have been persistent questions about when manager Joe Girardi will eventually remove Jeter from the top of the lineup.

Still, despite Jeter’s malaise, there is a tendency to evaluate his career and think that he has always been a problem-free Yankee. Yes, Jeter arrived as a calm rookie in 1996 and helped the Yankees win a championship, the first of five titles that they have won in his career. But, before Jeter’s successful rookie season, he experienced some angst on his path to the Major Leagues, too.

Butterfield helped ease some of Jeter’s angst. The enthusiastic, barrel-chested coach played a significant role in shaping the recent history of the Yankees, where he worked for more than a decade, by molding Jeter. The Yankees drafted Jeter in 1992 and wanted him to be their reliable anchor in the infield. Butterfield, a former Minor League infielder with the Yankees, helped steer Jeter toward that goal. In turn, Jeter helped steer the Yankees to excellence.

Back in 1993, Jeter was a raw talent, a 19-year old who was still making some of the mistakes that he had made at Kalamazoo Central High School. In high school, Jeter was so talented that he could get away with them. But, in the Minors, it was different. Jeter knew there was speculation about whether the Yankees might have to switch him to third base or the outfield.

“I had always been a shortstop,” Jeter said. “I planned to improve enough to stay at shortstop.”

On the day Butterfield started the Basics of Playing Shortstop with Jeter, he first told him that he needed to be more aggressive. Butterfield noticed that Jeter would let the ball play him, meaning he hesitated to begin making plays. Jeter was taught to move forward and attack the ball.

Butterfield also counseled Jeter about keeping his glove in front of him and only moving it in the direction of the ball. It sounds like simple stuff, but Jeter had a habit of carelessly shifting his glove from left to right before snaring a ball. Once Jeter decreased the movement of his glove, he became a quieter and more dependable glove man.

The Yankees videotaped Jeter’s play at shortstop and showed him slide-by-slide images of what he did on certain plays. By analyzing those images, Jeter could see some of his sloppy habits and how he did some things that he didn’t even realize. After fielding grounders, Jeter would sometimes tap the ball against his glove. If Jeter lost a millisecond fumbling with the ball, a routine 6-3 could become an infield single or an E-6.

In recent years, Jeter’s range has decreased and his defense has been pilloried. In the Fielding Bible section of the 2011 Bill James Handbook, 20 shortstops received at least one vote for being one of the best defensive shortstops in the Majors. Jeter didn’t receive one vote, but Jeter, who committed six errors in 2010, won his fifth Gold Glove Award.

Someday, Jeter might have to vacate shortstop, but evaluating Jeter’s defense in 2011 isn’t what this story is about. This story is about how Jeter spent five weeks with Butterfield and how those tutorials helped make him a much better shortstop. It was a crash course that proved very productive. So, as Butterfield stands in the third base coaching box at the Stadium, he isn’t merely looking at his former student. He’s looking at a former student who will someday be in the Hall of Fame.

Follow Jack Curry on Twitter: @JackCurryYES