Students learn part writing skills via exercises and guidance from .... blackboard. 1see http://java.sun.com/docs/books/tutorial/networking/sockets/ and ... Figure 2: Bach's Chorale (Christ lag in Todesbanden) .... Oxford University Press, 1994.
A COMPUTATIONAL MODEL FOR INTELLIGENT TUTORING SYSTEMS THAT TEACH PART WRITING SKILLS Somnuk Phon-Amnuaisuk, Tham Ooi Wai Music Informatics Research Group, Faculty of Information Technology, Multimedia University, Jln Multimedia, 63100 Cyberjaya, Selangor Darul Ehsan, Malalaysia ABSTRACT
of interaction (e.g. rote learning of basic musical properties such as pitch, interval, chord, harmonic progression, etc). However, some tasks may demand more sophisticated interactions between students and computers. The modelling of sophisticated interactions is dependent on many factors; among these are the knowledge contents in different models (e.g. the student model, the tutor model, etc). Successful interactions should be natural to students. Generated suggestions, hints, explanations, etc., should be relevant and accurate. This requires a fidelity in the student model. An accurate student model requires an accurate analysis of students’ performances. An accurate diagnosis is dependent on the knowledge contents in the system and is conditioned by how the interactions are designed.
Face to face coaching is an important part in music education. Students learn part writing skills via exercises and guidance from human instructors. To delegate the guidance part to a computer is not a trivial job. Human instructors do not respond to the same error in exactly the same way, but with variations in their approaches conditioned by individual students. To model the adaptive behaviour in a program is a great challenge for AI-education researchers. This paper investigates a computational model of a tutoring system which performs the role of a human tutor for a part writing task. We argue that the interaction between students and computers at a note filling level is at the appropriate grain size for this part writing task. To achieve this goal, the computational model must be constructed to facilitate the interaction at this grain size. We describe our knowledge representation language, our system architecture and its functions in section 3. In section 4, we discuss our views and related works.
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2 AIMS In this paper, we report an ITS system designed to teach the traditional four-voice part-writing to students. We highlight the following issues: the knowledge representation that enables effective interactions between students and the system, particularly in the teaching of four-voice part-writing.
BACKGROUND
An Intelligent tutoring system (ITS) could enhance a student’s learning experience by exploiting intelligent interactions between a computer and a learner. Intelligent interactions are important ingredients in learning. Sophistication of interactions in an ITS environment is dependent on many factors such as the student model, the tutor model, the domain knowledge and the enabled human computer interface (HCI) technology. Earlier computer aided instruction systems (CAI) rely on a pre-hard-coded knowledge. Intelligent tutoring systems focus more on dynamic interactions between students and computers. Predefined curriculum and predefined responding behaviours are the most simple types of interaction. This tactic is common in early works, for example, the GUIDO ear-training system [6]. Some tasks are suitable for this style
the student-computer interactions. the analysis of students’ performance.
Interaction at a note level We argue that the smaller grain size of interactions (i.e. the allowable responses), the finer the information we are able to capture for modelling a student. This could lead to a better accuracy in the student model. A grain size of interaction could be refined to the level of a mouse movement or an eye movement as reported in [11]. However, this is not without any trade-offs. Processing information at the finer grain is expensive and in some tutoring tasks the information gained may not be useful to the model (yet). 1
In our work, the grain size is at the note filling level. At the current stage in our development, students may enter a note using a standard musical notations on the provided GUI worksheet (see Figure 3). Students are also allowed to interact with the system using a predefined set of vocabulary to ask for hints, comments, explanations, etc.
Analysis of students’ performance individually Students may ask for the tutor’s comments after filling each note or after many notes have been filled. Here, the tutor model examines the changes in notes (e.g. new entered notes, deleted notes) and gives a feedback of useful analytical comments and suggestions. The tutor model prepares comments and suggestions according to the student’s information (e.g. the history of student’s actions, the current context of the work). This means the same question may not be responded to in the same way.
Figure 1: System Architecture
3.2 Knowledge Representation
Representing knowledge in modules
Domain knowledge
Modularity is the key concept in our development. The student model, the tutor model and the knowledge base are composed of many components. Components communicate among themselves via a blackboard using a common lan guage . Let bethe class language ofcomponent
, then the intersections , , ..., are not empty sets. In these notations and represent meta-level and object level languages respectively [10, 9].
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Domain knowledge is represented using a logical language. Musical concepts are hierarchically structured from basic concepts such as pitches and musical time. We give some examples of musical structures in our system below. Pitch and time are basic musical structures. In our representation, a pitch is represented as a member of pitch register accidental octave number, where pitch register 1 2 3 4 5 6 7 ; accidental "! #%$'&'&& x and octave number )( *#,+.-/+ 021 [5]. Musical time is represented as a member of onset time duration where both onset time and duration are integers. From these basic constructs, we then define a more complex structure. For examples: Note event 3 Pitch Musical time Line 3 Note event ... Note event Chord 3 Pitch Pitch Pitch Progression 3 Chord ... Chord Some structures are derivable from other structure. For example, an interval may be determined from any two given pitches, where we can devise operations such as: 3 sub454 : Pitch Pitch Interval add46 : Pitch Interval 3 Pitch Pitch Sub47 : Pitch Interval 3 More complex types can be hierarchically built up and can form a complete music domain knowledge.
MAIN CONTRIBUTIONS
3.1
System architecture
The block diagram showing the main components in our system is illustrated in Figure 1. The GUI interface is a software component written in Java. Students’ activities (e.g. entering notes, deleting notes, requesting for explanations, etc) are transformed to control definitions and the score rep resentation expressed in [10]. The linking between Java and Prolog is through sockets 1 . On the Prolog side, these control definitions are handled by Prolog inference engine. Control definitions are descriptions of the way the solution space should be traversed in order to reach the acceptable goal in an effective manner. In this implementation we use a meta-level architecture (more details of the meta-level architecture can be found in [1, 9]). We also have a notion of a blackboard, where each software component shares its information using a public blackboard.
Musical events from the GUI Each music symbol on the GUI corresponds to representation constructs in our score representation. The score representation has two main components, the music material and the interpretation of the music materials. The music material is a representation of standard music notations. The interpretations are collections of beliefs of different model
1 see
http://java.sun.com/docs/books/tutorial/networking/sockets/ and http://www.sics.se/sicstus/
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entities (e.g. student model, tutor model). More details of the score representation and the meta-level/object level representation are described in [10, 9]. In our system, students interact with the system using conventional musical notations and texts.
outlineChord(body), outlineChord(cadence): A harmonic plan of a phrase may be outlined using the outlineChord(+Context) rule. We hope to provide a rich set of control definitions that would facilitate students’ learning experiences (e.g. asking for the tutor’s explanations, asking for more examples of the similar topic, etc).
Musical notations A conventional score representation is constructed from a finite set of symbols. In the current implementation, the system accepts standard notations of musical notes (e.g. quaver, crotchet, minim), accidentals ( "!8# , $ , & , &9& , x), clefs (e.g. treble, bass, alto). Figure 2 shows an example of accepted music symbols in the system.
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C
?
? ? ? ? A A ?
;=> ?
? ? ? ?
?B = ? ?
;=> ?
? ? ?@ @ ? ? ? ? ? ?
? ? A A ? ?
: = > =?
?
? ? ?
Figure 3: The main application interface
4 DISCUSSIONS
Figure 2: Bach’s Chorale (Christ lag in Todesbanden)
The approach of teaching part writing skills we have adopted may be different from many part-writing course offered elsewhere. The teaching materials are not the main issue at this current stage. We are more interested in investigating whether the interaction at the note filling level is natural for the task and whether it is possible to construct a system based on our architecture. In our work, most of the teaching materials are taken from standard harmony texts [4, 2]. Holland gives a critical review on music education systems in [7]. He discusses the objectivism and constructivism in the ITS for music.
Human-machine communications Figure 3 shows a typical application interface. Here (in the example) students attempt to harmonise the input melody by filling in a few bass line. All symbols on the GUI are called music events. These events are represented on the Java side as an ordered list. Every time a new music event is entered or deleted, the list would be updated. This list is then converted into a correD sponding score representation in language before being passed on to the Prolog meta-interpreter. Students communicate with the system using conventional music symbols and texts. The text is a set of predefined predicate. These predicates have the same name as control definitions on the Prolog side. The control defini . Examples of tions are control structures written using control definitions are given below:
“(objectivism)...that is to say, such systems are generally based on the assumption that there exists a well-defined body of relevant knowledge to be taught, and that it can be carved up into more or less precise concepts and relationships...” “(constructivism)...learning arises substantially from learners’ active encounter with the world, which force them to construct their own knowledge...”
analyse(inputMelody): Examine the input score and do a preliminary preparation on the musical lines (e.g. break the melody line and group them into phrases, mark the input melody with beat tags).
These two components are also observed in the teaching of part-writing. Hard and fast rules are possibles at the early stage of learning where well-defined music concepts (e.g.
explain(cadence): Invoke a tutoring on a cadence topic. 3
pitch, chord, cadence, etc) must be understood. Objectivism is a suitable approach. In a later stage, students must learn and develop stylistic components in their part writing. This knowledge is harder to disseminate in a drill and practice learning environment. A teaching environment that supports constructivism may be a suitable approach.
[8], MacVoice (cited in [3]) can point out errors according to the current context (e.g. do not attempt to analyse students’ behaviours, but only the answers). To generate natural and useful information is the ultimate aim of an intelligent tutoring system. This is only achieved when the tutor has an accurate picture of students’ beliefs and intentions. Explanations should be generated based on the information in the student model and the information of the problem in the current context. A diagnosis of the students’ answer is done in an incremental manner. For example, when a student is asked to harmonise a given melody, he or she may choose to fill in any note at will. As long as, the newly entered notes are consistent with the plausible hypotheses, the system would not interfere unless being asked for comments. If the newly entered notes are inconsistent with the hypotheses, the system will provide a feedback of the anomaly and verify the student’s intention. At the current implementation stage, this part (diagnosis and explanation) is still not fully implemented. Many issues are still under our investigation (e.g. exact details of type of feedback and immediacy of feedback). These issues play an important part in learning [12] and they are closely related to the design of the interface part.
The scope of teaching materials We have decided to group our teaching materials into three main groups (steps) with many sub-topics in each group. 1. fundamental of music: these are basic concepts such as pitch, scale, chord, harmony, etc. 2. part writing rules: these are concepts of harmonic progression, voice leading, etc. 3. stylistic skills: stylistic are concepts which cannot be captured with simple rules. At this level, the part writing may be evaluated as bad or not stylistic although it has no error from rules defined in step two. There is a standard curriculum which describes the dependencies between these topics. However, the tutor model may dynamically modify the curriculum to fit individual students.
5 CONCLUSION This paper investigates the computational model (for the inter-activities between students and computers) in a part writing task and reports the prototype of the system. We conclude that:
Teaching plan and method of teaching Students must progress step by step. Let us examine these steps from the two dimensions of (i) teaching plan–columns and (ii) method of teaching–rows. The numbers in Figure 4 below correspond to the tasks above (i.e. tasks in the scope of teaching materials).
Drill & Practice Guided coaching Learning from examples
Presentation
Practice
Production
1,2 2,3 3
1,2 2,3 3
1,2 2 3
Interaction at a note level seems appropriate in modelling students’ bahaviours. A fine grain in interactions should allow a useful diagnosis and feedback since more details of students can be observed. Building a computational model based on a symbolic approach has an advantage in explicit representation of knowledge. Arguments and explanations are natural constructs in the system and can be explicitly examined. Furthermore, it is also possible to reason about properties of these constructs (i.e. meta-level inference) and this ability provides a powerful inference power.
Figure 4: Teaching plan and Teaching method
Topic Areas: Computational models, Intelligent tutoring system, Represent music for reasoning, Music education.
We should not interpret the numbers in the figure above rigidly. This only aims to point out that there are many dimensions in the teaching activities.
Acknowledgements
Diagnosis and feedback
This research was sponsored in part by CRPP (internal funding numner PR/2003/0328).
Diagnosis and feedback are two main activities in any intelligent tutoring system. Previous works in music ITS attack these issues at different levels. Early works such as LASSO
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