Single Solution, Multiple Perspectives

Abstract

This article reviews a model-eliciting activity, with a single-numerical answer, implemented in a calculus class at the university level. A closer look at students’ solutions reveals multiple perspectives in solving the problem, perspectives that present students’ conceptual and representational systems. Most model-eliciting activities allow for multiple responses, and consequently multiple approaches. This article presents the wide variety of modeling perspectives, even though the activity has a single numerical answer.

Appendix: Newspaper Article – An Enchanting Vacation

Going on vacation is something that everyone looks forward to. But staying in a historic hotel transforms any vacation into an enchantment. Finding these charming places is a task to which the National Trust of Historic Hotels of America is committed. To be recommended by the National Trust of Historic Hotels of America, hotels have to prove that they have faithfully maintained their historic architecture and ambience. Several of these hotels hold great pride in their stories, myths, and legends. For example, the French Lick Springs Resort and Hotel in Indiana was named after an early French outpost and its rich mineral springs that included a naturally produced salt lick (a lick is a deposit of exposed natural salt that is licked by passing animals). The hotel was originally built by Dr. William A Bowles, and it flourished during the mid-nineteenth Century.

Fig. 19.1

Problem statement for the industrial engineering students team

Whether for health reasons, or just for curiosity, visitors were compelled to visit the rich mineral springs, which were said to possess curative powers.

In 1897, the hotel burned down, and it was not rebuilt until 1902. The new owner, Thomas Taggart, built the new French Lick Springs Resort on the ruins of the original hotel. Mr. Taggart, mayor of Indianapolis, made the resort grow in size and reputation in the early decades of the twentieth century. Surrounded by lush gardens and landscaping, the six-story hotel, with its sprawling sitting veranda, was a more than relaxing environment many wished to enjoy. Among the most interesting celebrities that frequented the resort were John Barrymore, Clark Gable, Bing Crosby, The Trumans, The Reagans, Al Capone and President Franklin Roosevelt. In fact, Roosevelt even locked up the Democratic nomination for president in the hotel’s Grand Colonnade Ballroom.

Maintenance for a hotel like The French Lick Springs Resort, with all its services, is not an easy task. In 1929, Mr. Taggart died, and inherited it to his son – the only boy among six children – Thomas D. Taggart. With the Depression, however, the popular French Lick Springs began to decline. World War II brought a monetary revival, but in 1946 young Tom Taggart sold the hotel to a New York syndicate.

Today, French Lick Springs Resort rests on some 2600 acres in the breathtaking Hoosier National Forest. Newly acquired by Boykin Lodging Company, the resort eagerly embraces a “New Beginning”. It provides 470 rooms, full service spa, two golf courses, in-house bowling, a video arcade, indoor tennis center and outdoor courts, swimming, croquet, horseback riding, children’s activities, skiing, boating, and fishing. Fine and casual dining are also available at a variety of restaurants. Two main meeting rooms, the Grand Colonnade Ballroom and the Exhibit Center, accommodate large-scale events.

Besides The French Lick Springs Resort, the National Trust of Historic Hotels of America has identified over 140 quality hotels located in 40 states, Canada, and Puerto Rico.