It is often said that the use of the internet is going to change the face of education forever. With the rise in the use of the World Wide Web, students are now able to access Computer Assisted Instruction (CAI) at home and work at their own pace, continually checking their own answers with constructive feedback, when given. By incorporating these CAI programs into the music theory classroom, an instructor is able to spend less time drilling familiar concepts and more time moving forward in the material, thus encompassing musical examples in different genres and time periods. Although a multitude of studies have been conducted on the efficacy of CAI in ear training and in written music analysis, there is relatively little research conducted using the computer as an aid in learning classical forms such as binary, ternary, or sonata form.

When teaching musical form, the various forms (e.g., binary, ternary, sonata-allegro, etc.) are normally presented beginning with a definition and followed by an application to various musical examples. Terminology such as phrase, cadence, period, and section is assumed to be common knowledge by the time a student arrives in a form and analysis classroom; however, this is not always the case. The teacher expects the student to practice the analysis skills on their own time and bring questions to class, but the students often have a difficult time working through the analysis on their own. This difficulty can be for a number of reasons:

• The students may have difficulty in finding recordings to go along with the score they are analyzing because the various anthologies for analysis do not come with a CD recording supplement.
• The students may be unable to relate the material presented in class to the assigned piece due to poor note taking.
• The students may be intimidated in the classroom and may not ask questions about the problems encountered.

Often, the student is weighed down by details of the analysis (such as chord analysis) and is unable to grasp the large-scale design. There is a need for an educational tool to guide the students through the analysis process using both visual and aural simulation. This educational tool would allow students to work on their own time and check their answers, in order to advance their knowledge of the subject before class time. The use of CAI as a pedagogical tool to guide students through the analysis process seems to be a logical choice in easing the problems mentioned above.

There are two main programs currently in production that deal specifically with diagramming musical forms: "Form Companion" and "CD Timesketch." Tim Smith is currently authoring a software program called "Form Companion" at the University of Northern Arizona for use in undergraduate form and analysis classes. The authoring system allows students to create sophisticated time lines that are synchronized with sound and graphics (Smith, 2001). The object of the analytical phase of this program is to identify forms, locate themes, and write narratives that describe the formal elements as they occur. This program has many good qualities, including its ability to let the student listen to the music and analyze the structure, as well as create his or her own chart for the form. The disadvantage of this program is the absence of a score and the fact that the audio is only accessible through the use of the Barenboim recordings of Beethoven.

The CD Timesketch series has two main programs that serve as a pedagogical tool in the teaching of form and analysis. The two programs are called "Timesketch Editor" and simply "Timesketch." Both are available from Electronic Courseware Systems. This series is ideal for use in music fundamentals courses, music appreciation courses, music history courses, and/or music literature courses. "Timesketch" includes a CD recording of the work in addition to the form and analysis of the piece. Figure 1 shows a screen from "Timesketch" that shows the diagram of the form, a basic written overview of the piece and CD navigation controls to work your way through the music.

Figure 1. Sample screen from "Timesketch Editor" (graphic taken from http://www.ecsmedia.com/indivprods/mustmods.htm).

At the present time, there are programs with analysis of works by Brahms, Beethoven, Mozart, and Schubert. Using any audio CD, the student can create a graph based on the time and duration of the audio. The graph is drawn for the student after important points in the recording have been identified, and the student is then able to label the diagram and write a short paragraph at the bottom of the screen giving an overall analysis. This program is currently in use at Meredith College in Raleigh, NC. Dr. James Fogle, a music history professor, uses this program in all of his music history courses. He states, "Students almost universally love the program both as a learning tool and analytical tool" (Fogle, 2000).

The teaching and learning of music formal structures using CAI and the pedagogical design of such software have their roots in two learning theories, cognitive learning theories and the Gestalt principle of learning. By incorporating these two learning theories into the design of a CAI program, the learner is utilizing these learning styles simultaneously.

In cognitive learning theory, rapidity of the response is not a central issue. The procedure (steps) that the learner takes in order to arrive at the correct answer becomes the most important outcome in the solving of the problem. "Where behaviorists had aimed at predicting and controlling behavior, cognitivists aimed at changing knowledge representations to improve problem-solving effectiveness" (Bredo, 1997, p. 29). Herbert Simon, a researcher in the field of cognition and also one of the founders in the field of artificial intelligence, compares this style of learning to a computer program suggesting that "It is as though each of us performed a little computer simulation in our heads to figure out how to reach a goal" (Bredo, 1997, p. 26). In the cognitive approach, the goal of learning becomes the use of the correct process rather than the correct answer, thus an improvement in performance on the same task becomes the relevant focus. A cognitive approach to learning highlights this step-by-step process. The student has not truly mastered the concept until he or she has grasped the actual steps needed to arrive at the correct outcome or response. In cognitive learning, a correct response does not necessarily denote that the student has a mastery of the material. It is not a coincidence that the movement in cognitive learning was parallel to the development of the computer in the 1970s. The process method of learning was often compared to the properties of the computer. Using the cognitive approach to learning (and teaching) of musical form, the computer seems a logical solution to mastery of the "step" analysis process without taking up valuable classroom time.

Heinrich Schenker’s approaches to harmonic analysis, in relation to viewing tonal music in its simplest form, remains one of the core teachings in music theory. Schenker’s terms such as background, middle ground, and foreground denote the ranges in this style of analysis. In Schenkerian analysis, the foreground is a notated representation of the majority of all the notes in the piece in a very detailed fashion, reducing the piece to its minute elements. On the other hand, the background reduces the music to its most significant material, often consisting of only 3-5 pitches. This style of analysis has its roots in Gestalt theory. In the Gestalt principle, individuals react to meaningful wholes; and therefore, learning is based on the organization of the ideas that are important, discarding less important material. The Gestalt theory seeks to "explain the individual’s perception of new information as it relates to past experiences and… contributes to the whole self" (Campbell, 1991, p. 84). Students begin to use this type of learning when they view a visual graph of the formal design. By actually visualizing the form on a large scale, they are able to interpret the formal structure and discard unimportant details.

Over the course of the next year, I hope to design and program a CAI tutorial that will serve as an aid to students in the form and analysis classes at the University of Maryland. In order for me to truly master the student’s thought process so that I may make the CAI program more pedagogically sound, I took the opportunity to observe form and analysis classes during the spring of 2000. I also had the chance to work with several students from this class on an individual basis. The students utilized for this study were all enrolled in the form and analysis classes. The students did not realize that they were being observed in this classroom situation; I was merely looked upon as a graduate student sitting in a class to review for general comprehensives. The students felt at ease talking to me about their feelings about the course and the process by which they were working to analyze the form of the piece. I was able to keep a journal, recording not only the professor's teaching methods, but also the students’ responses and questions in the classroom, and even personal comments to classmates during the class period. The students included in this study were in various music degree programs and included both graduate and undergraduate students.

I was also able to meet with one particular student individually twice a week. This student was a junior voice major who had previously had a difficult time in the basic theory courses. I set up meetings with this student twice a week to discuss the pieces of music given in class. These meetings averaged 2-3 hours each week, and often we would review for tests as well as analyze homework examples. I kept another data log with observations about these independent meetings with this student. The observations included moments of success for the student when she had grasped a particular concept and moments of frustration when she simply could not understand the analysis of the given material.

I also began to review a variety of form textbooks for additional information, including Berry (1986), Green (1993), and Spencer (1988). All three of these texts use different orders of presentation, different definitions, and a variety of musical examples. All definitions of the formal structures used in the design of the CAI program were modified from the above sources. Through my observations and questioning students, I realized where there were certain deficiencies in the material presented in the class lectures and in the above textbooks. I also gained a greater sense of those individual topics where there seemed to be a lack of understanding. In these topic areas, extra emphasis needs to be given in clarifying definitions through the use of charts and extended examples. It is my hope that the information included in these sections will become the framework and basis for the CAI program.

Through my observations in the classroom, my independent research, and my work with students on an individual basis, I have acquired an understanding about the teaching of form and analysis. I have also gained a glimpse into the students’ thought processes as they master this step in musical analysis. These observations have allowed me to design a structured teaching tool for use in form and analysis classes. A logical design of this CAI tutorial software would allow the student to go through the step process in the following manner:

1. Phrases and Cadences
2. Periods (Similar, Parallel)
3. Key changes/Modulations
4. Large Sections
5. Formal Design

By utilizing CAI, the student would be able to see the music and diagram the form in a logical process without becoming overwhelmed by the entire piece of music. In addition, the utilization of CAI allows the student to hear the music they are analyzing, thus continually relating the visual input of the score to the aural output. This continuing study seeks to develop a CAI program based on observations and student response, allowing the student to go step by step through the score, listening to sections at their own rate, and understanding the music as a large-scale formal design. The main question to be answered by this study is: How can Computer Assisted Instruction be used effectively in form and analysis classes in order to accommodate the variety of learning styles?

My observations of students in the form and analysis class provided a wonderful venue for me to understand the thought processes involved in their analyses. After several months of observation, the following were identified as some of the central issues of frustration in the form and analysis classroom:

• Students were having trouble figuring out key area.
• Cadence points were unclear to students and the student was unable to figure out phrase and period structure.
• Definitions are important and need to be clarified more for the student.
• Students were unable to apply the concepts learned from the previous example pieces to new pieces given in class.
• The book was rarely consulted or used by the students.
• The instructor tended to rush through the material before the student was able to locate the position in the music.
• Charts on the board — or any visual aid — were extremely helpful.
• Collaboration between students in the class seemed to be helpful.
• There was a lack of listening to the pieces analyzed in class. Students seemed to have a better understanding of the piece when played before the analysis began.
• Students often felt too intimidated to ask questions of the professor in class and would consult with a neighbor or not say anything at all.

The most important aspect of this study was the individual work with the student. She was able to talk to me freely about some of the questions/concerns included in the list from above. When I first began to meet with this student, her process of analyzing a piece of music would be to:

• Analyze each and every chord, measure by measure
• Make a guess at the key areas based on her Roman numeral analysis
• Look for cadences to diagram phrase structure
• Search through music in order to find larger sectional divides
• Make an educated guess as to the formal design of the piece

By following the steps above, one can see where there would be a multitude of problems in this process. First of all, the student had an extremely difficult time finishing any of the assignments. She was spending so much time diagramming the details of the piece, that she rarely was able to understand the piece as a whole. Her technique of looking for cadences after she analyzed the key areas also proved to be a problem. She tended to label sections as a new key area when they were merely a tonicization without a final cadence. This student desperately needed a new analytical system in order to master the analysis of musical forms. With much effort, I was able to get the student to change her analytical technique. The final process included the following steps:

• Look for major cadences in the music and label them as complete or incomplete cadences
• Label major sectional divisions
• Label key areas within the major sections
• If needed, look for phrase structure within the key areas of the major sections
• Make an educated guess as to the formal design of the piece based on the checklist provided.

A checklist for each form was given to the student in conjunction with her individual analysis. An example of this style of checklist follows:

Based on my observations of students — individually and in the classroom — there seem to be several styles of analysis that students use when diagramming formal structure: analysis through aural means only, analysis through visual means only, a combination of both aural and visual, step analysis, and large-scale analysis. Step analysis refers to an analytical technique in which the student moves step by step to understand the formal design, beginning with phrases and cadences and arriving at the larger divisions of the piece through analysis of smaller divisions of the music. A large-scale analysis describes the technique in which the student only looks for larger sections in the music and determines the form based on these sections, without regard to the smaller units of structure, often missing key elements such as key changes or cadence structure. All of these techniques have merit in the study of formal design, but there are problems with each process, especially the exclusion of aural processes.

One important aspect of my study was the evaluation of three textbooks widely used in form and analysis classes at the college level. The textbooks often presented material in a totally different way, using different terminology, and examples that sometimes did not exemplify the concept presented. The textbooks often give only a brief excerpt of a piece of music, and students have a difficult time relating this small excerpt to the larger formal design. For example, Form in Tonal Music: An Introduction to Analysis (Green, 1993) contains mostly text and definitions, offering little visual stimulation for the student. The ordering of topics presented varied with each book. After a comparison of each of these texts, the most logical ordering in the teaching of form and analysis is as follows:

• Cadences
• Phrases
• Periods (types of periods also included)
• Retransition, bridge, coda, codetta, extension
• Binary form (simple sectional, simple continuous, rounded)
• Ternary form (simple, compound, continuous, sectional, full sectional)
• Rondo form
• Theme and variations
• Sonata Form
• Sonata Rondo Form

Through my observations, I noticed several key problems that arise: time constraints, lack of aural stimulation, and the need for some type of visual aid to accompany the score. To provide a solution to these problems, I have designed a CAI program to aid the student in diagramming formal structures. The design allows the student to see the score, unlike other CAI programs currently available in form and analysis. The design also allows the student to hear the music at any time. Students are allowed to actually pick their own strategies for how they would go about analyzing the formal structure. With the help of Dr. Ben Bedersen (Computer Science Department, University of Maryland), this program should be available for students by January of 2002. The program will be written in Java2 and available to students via the web using a password. The following screen shots are preliminary designs of this program. They are based on the analysis of Chopin’s "Mazurka 43 in g minor" taken from the Anthology of Musical Analysis by Charles Burkhart.

The first screen shows all the possible analytical choices for the student, including cadences, phrases/extensions/transitions, coda/codettas, and sectional divisions. The student is able to hear the music at any time by inserting the measure number or clicking within the actual score. For example, if a student chooses to work with the phrase option, the student creates a line by dragging it within the score. The student then double clicks on the mouse to signal that he has finished. A new menu appears, allowing the student to choose from the given options: phrase, extension, or transition. A cadence type (complete or incomplete) must then be selected from another pop-up menu. Following the phrase and cadence selections, a final pop-up menu appears in which the student is asked to select a key area for the phrase. The student then selects the key area and the final screen shows: the key choice, the length of the phrase, and a small box symbolizing the cadence. Each element of the formal structure is represented by a different color, and the student is able to change the element they are working on merely by clicking a button on the side of the screen. The student is able to compare his or her line graph with a previously programmed "correct" answer. These two graphs (the student graph and the correct graph) are shown simultaneously and included within the score. The student has the opportunity to review the mistakes he or she has made with feedback that shows a side-by-side comparison. After the line graphs have been compared, the student is then able to see the formal design on a large-scale graph (previously drawn), similar to that graph shown in the program "CD Timesketch." An example of a completed analysis of the Chopin "Mazurka in g minor" is shown in Figure 2.

The student is then asked to make an educated guess as to the form of this piece. After selecting a particular form, the music and the graph are shown. By viewing this large-scale graph, the student will then go through the series of checklists and make an educated guess as to the formal design of the music in relationship to the graph shown. By allowing the student to formulate their own process in choosing the design characteristics, the student is beginning to master the analytical process. The series of steps that the student must perform in this program creates an emphasis on process rather than the final outcome of the correct answer. The checklist at the end of each piece forces the student to answer questions in this process, enabling the student to gain a better understanding on what type of questions need to be addressed when diagramming form. The final graph shown at the end of each exercise gives the student a reduced realization of the formal design as constructed in the score line graphs. This large-scale graph is an accumulation of the theories of Schenker and the Gestalt theory, encouraging the student to view the "whole" rather than minute details of the analysis. The use of this CAI program allows students to work at their own pace, and — due to its availability on the World Wide Web — the students will be able to work at their own convenience. Students are stimulated aurally through the ability to continually hear the music and visually through the use of graphs and the addition of the musical score. The use of the checklist and actually working through the music in a step process is a compilation of several different learning styles.

In the next year, I will continue to design this CAI tool. It will serve as a pedagogical tool for the form and analysis classes at the University of Maryland in the spring of 2002. By using CAI, I am able to collect data to help other music theorists, music educators, and myself better understand the process that students are using to diagram formal structures. The program is designed so the choices and steps that the student makes in analyzing are recorded and stored in a separate file. I will also have the ability to "turn off" the aural stimulation in order to see how the inclusion of the aural stimulation affects the outcome of the students’ answers. The data collected from the students and the textbooks, the understanding, interpretation, and inclusion of various learning theories, and the pedagogical need for a CAI program in form and analysis have led me to design this program. By the end of this study, I hope to gain a better understanding of how CAI can be incorporated into the music theory classroom in order to accommodate various learning styles.