Abstract:

When students investigate topics that are relevant to their lives they are more engaged. The two labs on recursive sequences described in this paper are examples of activities developed to supplement the standard syllabus in a Contemporary Mathematics, a course designed to introduce a general audience of students to a variety of mathematical concepts. For each lab, use of the TI-84 Plus financial App combined with computations in sequence mode and on the homescreen allow for deeper exploration of the material. A group work setting promotes active learning and student involvement.

Music is a common area of interest and the topic of tuning and harmonics is particularly appropriate for music majors. This first lab is presented on a web page with links to sound files and graphics enhancing delivery through audio and visual effects. Frequently a student volunteer will bring a guitar to class to demonstrate the sounds described in the lab. Through this investigation, students discover that geometric and arithmetic sequences exist naturally in musical sound. The lab reading provides an accessible level of music history and theory, expanding students’ cultural education.

In the current economy, fiscal awareness and responsibility are of increasing concern. Credit cards interest rates and terms are often unfamiliar and confusing to young consumers. One goal of this second lab is to educate students to help them become more financially responsible. News items from the internet on credit card debt keep the topic current. Students read and respond to these articles before applying amortization and annuity formulas to a personally chosen purchase. In groups they determine optimal strategies and discuss their results. At the end of the lab students are asked to reflect on what they have learned from the mathematics and whether or not it has affected their attitudes.

Increased student involvement through group work, use of interactive technology and a personal connection to the material dramatically improves class enthusiasm and concept retention. As with all other syllabus topics, this material is included in exams for further assessment.

Keywords:

technology, applications, music, finance, recursive sequences, group work.