Philosophy of Education in Music Theory

“Difference between the mathematical and intuitive mind: In the one principles are obvious, but remote from ordinary usage, so that from want of practice we have difficulty turning our heads that way; but once we do turn our heads the principles can be fully seen; and it would take a thoroughly unsound mind to draw false conclusion from principles so patent that they can hardly be missed.

“But, with the intuitive mind, the principles are in ordinary usage and there for all to see. There is no need to turn our heads, or strain ourselves: It is only a question of good sight, but it must be good; for the principles are so intricate and numerous that it is almost impossible not to miss some. Now the omission of one principle can lead to error, and so one needs very clear sight to see and the principles as well as an accurate mind to avoid drawing false conclusion from known principles.

“All mathematicians would therefore be intuitive if they had good sight, because they do not draw false conclusions from principles that they know. And intuitive minds would be mathematical if they could adapt their sight to the unfamiliar principles of mathematics.”

-Pascal

The question that needs to be addressed in light of this is how does a teacher that has a tenancy towards one type of mind effectively teach students that have a tendency opposite them while still teaching the students that are like them to be opposite of the teacher. A teacher with an intuitive mind will naturally be able to teach broad concepts and ideas to those that understand broad concepts and ideas. Likewise, a teacher with an analytical mind will naturally be able to teach isolated principals to analytical students. Unfortunately natural tendencies only cover one fourth of the requirements for the classroom, for four areas need to be accomplished: The intuitive should learn to be analytical, the analytical to be intuitive, the intuitive to see even more, and to the analytical to see details with even greater clarity. If the teacher does not do all of this, then no student in the class will receive what they need to thrive in classroom.

When an analytical teacher teaches analytically, the analytical students will be more engaged and will seem to be more talented. But then when an intuitive teacher teaches intuitively, the intuitive students will seem more engaged and talented. This concept can also be directly applied to homework assignments: Assignments that emphasize small concepts, drilling a principal firmly into the mind, will be easily and accurately completed by an analytical student. Yet a student with a brilliant intuitive mind will make countless errors that will seem irrelevant to him because he has not been taught the importance of clear sight. Assignments that emphasize large concepts will be quickly mastered by the intuitive but will bring to the analytical tears of frustration because they have not been taught to turn their head. Therefore, to teach well a teacher must be able to communicate well to the students that they don’t naturally relate to so that every student can clearly see both the depth and breadth of the topic at hand by the end of the course.

Thoughts on lecturing and tutoring

Anything that can be done outside of class should be done outside of class. If a group is called together, the group should be taught together keeping in mind what they are expected to know before being called. In a class, two extremes can happen and both must be avoided: Strictly intuitive lecturing to the whole, and strictly analytical tutoring to the individual. Individual tutoring of details can be done outside of class either by the teacher or by a talented student. This “hands on” approach of mass tutoring bores the intuitive; their learning will not be as effective as if the teacher was leading a discussion and including the development of clear sight within the lecture. Conversely, if all a teacher does is give a discourse, the analytical become under stimulated and will disengage from the class. Pure discourse can be done outside of class just as well as its opposite by means of a textbook. A balance must be found between developing clear sight through practice, and understanding the whole through discourse. This is to be done by practicing as a group as well as having a discussion in which the teacher can give the students overall guidance simultaneously. By doing this, the teacher is always involved with every student in the class no matter what type of mind the student has. One may argue this ineffective because the mind will filter out what disinterests it, but what is forgotten is that it takes time for the mind to become relaxed and stimulated. Hence, oscillation of depth and breadth will challenge rather than bore.

In music theory a lecture should help the students gain a broad understanding of the topic in the context of music, the details of how the theory works out of context, and examples of both done in front of the class and by the class as a whole. The breadth of the topic should be emphasized first because it is more practical for why the students are studying theory and will be an incentive to become engaged. This will especially engage the intuitive students whose attention is not easily earned.

But then the analytical must have some sort of order before a discourse starts, because they have not learned the turn their heads by themselves within the study. The way the class is going to unfold needs to be revealed to the analytical or they will become lost very quickly for they do not have a structure to give their mind direction. The intuitive on the other hand will become engaged after the structure is established and will let their mind relax while it is being established. Because of this, the structure must be easily understood so that the analytical will grasp it quickly enough for the intuitive to not become unchallenged and therefore disengaged. For they see the breadth and structure, and they do not need or even want to be told.

Once breadth is generally understood, then the intuitive are ready to add depth to context, and the analytical are ready to start gaining understanding about what they have just perceived. The analytical have a clear structure on which to build their understanding, and the intuitive are willing to learn more about what has engaged them.

Lecture, discussion, and group exercises should be a focus of every class period, for this is the only time an instructor has to impart the knowledge he has to all of the students simultaneously. A sound understanding of depth and breadth within the group must come first. When this is achieved, group reinforcement and review must be done to ensure that the students with questions get a chance to ask them. When a concept is universally understood save for details, the intuitive begin to see depth, and the analytical begin to see breadth. Once these understandings are achieved, the teacher has more flexibility to do what is natural to him, but he must not forget the students he doesn’t naturally teach. He must answer questions according to the way they are asked so that both types of mind remain engaged even after understanding is solidifying.

Time management and flow

Punctuality is essential to the success of a short class. The teacher should always be present before the time a class is officially scheduled to start. This will not only help a teacher gain the respect of his students because of a clear respect for their time, but it will also aid the teacher in starting with a social mindset causing the entire lecture to be more accessible to the average person. The main quality that every person has in common in this context is that they are social beings. If a teacher is not socially active before a class then communication will not be easily attained. It is the same concept as warming up the mind and body musically before a performance.

The subject at hand should not be stated at the exact time that the class is scheduled to start. Students are always going to be late, and this is to be anticipated and compensated for. The first few minutes of a class should be devoted to a group conversation that is morphed into the topic scheduled to be discussed. When performed in moderation, the teacher will have complete control of the classroom before he says anything important while allowing late students to settle into the environment. Then when a lecture truly starts, there must be a line drawn for the analytical in the lecture for when full attention is to be paid. This can happen simply by clearly stating that the class is starting. Such a statement will not take anything away from what has already happened.

The class ends when it ends but within reason, and it should be made clear that all of the students are free to go when the class is scheduled to end if the time goes over. It is impossible to estimate perfectly how long a lesson plan is going to take. Therefore, it is necessary to have very limited freedom in regards to when a class officially ends. However, to end too early is disrespectful to the students for not giving them your time and knowledge, and the end too late is to be disrespectful of their time. After a class officially ends, just as the teacher should be one of the first people to arrive, he should also be one of the last people to leave. This makes the teacher approachable by students after class, giving them fair chance to tidy up loose ends in their personal progress or to ask for outside help. If nothing else, the teacher at least has a chance to converse with the students in general and build a necessary relationship with them. For if a teacher does not care about the students outside of the classroom, they will not teach well (Not that teaching well is even the ultimate end, but we will not going much deeper within this discourse).

The mind does not turn on and off by a switch, but becomes engaged when stimulated, and relaxes either when it feels that it is not needed or when it cannot keep up. Easing into a lecture through a discussion of a broad topic lets the mind be stimulated at its own pace. When all of the minds are ready, the class officially begins. Likewise, if the minds are dropped into sloth when the clock strikes ten until the hour, loose ends will not be tied and the mind will feel scattered going into its next endeavor and retention will be harder to achieve. Therefore, the class should not end until all of the minds are relaxed. This can either be done through doing an easy activity, or simply going into an all-encompassing discussion of less depth.

Homework assignments

The intuitive must learn to see the depth of the analytical, and the analytical must learn to see the breadth of the intuitive. Assignments need to be a catalyst for developing both types of minds in the way that they do not naturally gravitate. To challenge the analytical, open ended assignments that force the mind to put details in context are necessary. Without assignments of this nature, this type of mind will simply have a mass of vestigial facts at the end of the course which will be quickly forgotten because the knowledge will never be used again, as practical as it may be. To challenge the intuitive, strictly structured and repetitive assignments are necessary so that the mind will gain consistency in detail. Assignments that are drills in nature will help the intuitive mind to gain speed and consistency, enhancing its natural tendency to see large concepts by giving it focus and enabling it to see detail. These two types of assignments also enhance the natural talents within each type of mind, even though a mind that naturally fits a given assignment will complete it quickly and easily.

Composition assignments and papers will help the musician gain a broad understanding of concepts and help them integrate everything that they have absorbed into their particular craft. Analytical students will have difficulty with these assignments and the assignments must be presented in such a way as to appeal to the way their mind naturally works. For example, when a composition is assigned there should be the option of open-endedness and the intuitive will do it and do it well without much help. But there should also be a list or an outline of what to include within the composition or paper so that the analytical can literally check off what they have done. Without this they will become frustrated because they will not be able to discern what the teacher is looking for. Since the assignment is intuitive by nature, the teacher is in reality looking for a general overview of the broad topic being studied. However, the analytical will have a hard time understanding this, and will need to be told specifics. It is more than likely that when they on their way to the completion, the assignment will naturally take the desired shape even though it has the obvious danger of being too structured.

The intuitive will have a tendency towards incoherent chaos in regards to these assignments. They will need to be told that although an assignment is open-ended, it is still necessary for there to be order within the project since in the end their projects will be meant for enjoyment by those outside of their mind. It must be specified that the option for open-endedness should be governed by a structure that they create before they begin the assignment. The end result of the assignment when keeping all of these things in mind will be that the analytical will learn to see more, and the intuitive will be able to organize their thought so that they can focus the breadth they see into a coherent musical idea when it is needed.

Monotonous drills and exercises are necessary to help the musician see into music deeply, quickly and accurately. Without these types of assignments, neither the intuitive nor the analytical will be able to make practical application of large concepts with the speed and accuracy necessary to help the students in their craft. Obviously, an intuitive mind will not receive these assignments well and will need extra help outside of class. This is where tutoring becomes vital both to a generally weak mind, and to a strictly intuitive mind. But even after the detail is understood, the intuitive will not achieve consistency very quickly and the exercise must be done repeatedly until consistency is achieved. This is why this type of assignment should not weigh heavily into a student’s grade. It has been said that students simply need to put forth more effort in order to be sure that they have arrived at the correct answer, but the fact is that the intuitive mind will not see error because it is not capable of seeing detail yet. A wrong answer means that more practice is needed, not necessarily better practice; but perhaps more guided practice. When grading such assignments, the grader must have enough grace to mark a silly mistake but to not take off a significant number of points for it. All that needs to be done is for the student to see that something is wrong. To have a recorded evaluation is useless until the exam over the material is taken, and a weighty record will only discourage the student. However, some penalty is usually required as an incentive, but a significant penalty is counterproductive. So homework should have to be done to pass, but it should not be worth so much that is will significantly affect the student’s grade.

Completion of reading assignments should be encouraged by the nature of the other assignments. In many cases, most students will not have read the text before coming to class and this should be expected by the teacher. But if the assignments can be done by using information provided by the text, then that is usually when the text will actually be read if a student has a need for it. However, if a student is capable of performing satisfactorily without reading the text, then it is not worth taking the time to reason with the student on the benefits of reading it. At the same time, the teacher needs to be very aware of what the text says so that students have the ability to refer back to it when they fail to remember the lecture. If something is said in class that is not in the text, the teacher should be very clear that the students need to know something that is only accessible in class and a handout should usually be given. Generally, reading assignments should never be considered formally optional, but the teacher should assume that the students believe that it is.

Listening assignments are of high value and should be assigned on a regular basis. This type of assignment will strengthen a mind’s natural tendencies: The intuitive will search for the large concepts in the work being perceived and the analytical will search for the details that were talked about in class. What results are universal and general reinforcement, practical application, subliminal and conscious contextual analysis, and relaxation of the mind while still keeping it relatively active within the subject of music theory.

Since this type of assignment is fundamentally what the students are learning to do, (whether performance, composition or education) the teacher should be much clearer on the importance of listening than he should be of reading. A good strategy to keep these assignments on a high priority with the students is for every test to ask whether the listening assignments were completed or not and have the answer be for a small credit. This encourages them to complete the assignment before the evaluation since many will have good intentions of completing the assignment in an unforeseen future. Here, there is obviously the issue of students lying on their evaluation, but this can easily be corrected not by appealing to the student’s moral standards, but to their pride: Simply point out to blatant foolishness of not completing the assignment. If a student is not passionate enough about music to even enjoy an end result once a week, then they clearly should not try to make a living with it and should rethink their future for their own sake and the sake of their current or future family.

A problem with assignments that is not addressed enough is that the student does not know the value of them and the student must be told. A student should not have to do an assignment if they have not a least heard the practical application to their field of study. If they do not understand the explanation then they do not need to, but the teacher must be able to give a reason and make that information available. “Because I said so,” is not an acceptable reason because a teacher’s words are anthropomorphic and subject to the judgment of other humans whether they are well developed or not. Conjuring a sufficient reason must be part of constructing the assignment and should be given with the assignment.

Answering fair questions from unmotivated students

A question that is asked frequently among undeveloped minds in particular, is why study music theory at all? They ask this because when an intuitive mind does not yet have clear sight or an analytical mind’s sight is still limited, it is impossible for the mind to see the practical application of having a deep understanding of sound. An undeveloped mind will see with time, but it must at least perceive the answer to the question of “why” or the mind will not be motivated to learn the subject according to its capability. So the question is fair because the mind cannot yet see, and the question needs to be answered because the mind needs the confidence that the subject is worthwhile in order for the mind to truly apply itself. Once the explanation has been given, it must continue to be given on a regular basis in order that the mind may see the practicality of the subject as soon as it is able. If a mind is truly searching for the answer, it will be found early in development. If the mind does not search, it should be encourage to seek other areas of study.

Music is the study of sound and if one desires to join the ranks of the centuries of research one has to have a thorough understanding of what has already been done. If a mind is truly passionate about sound, it will learn and love these topics because they have something to do with its passion. Perhaps it seems that it is not directly applicable to its immediate field, but it is the fundamental study of sound and therefore directly applies to any field within the broad category of music. To be a musician, one has to manipulate sound at a subliminal level. Without a firm foundation of knowledge on which to build a mind’s specific craft, it will never be as effective as it could be.

An artist attempting a contemporary genre studies because there is profound wisdom to be found in the minds of the great composers of history. Should a contemporary musician ignore the tools and work of the past, he will either repeat what has been done, or create inferior sound. A new generation studies what the old one did so that mistakes are not repeated, and so that triumphs are propitiated.

A performer embodies sound. To do this well, he must understand what he is doing and also must understand what the composer was thinking when the music being embodied was written. If a performer does not have clear sight, neither will the audience. Great art will be lost in the transition from the page to the ear, and then to the mind.

A composer studies because without having the tools of those before him, he will be starting back at the beginning. Not in ten lifetimes will he accomplish anything significant without the knowledge of what has already been discovered. Progress can only happen when those attempting make progress start on the foundation already laid.

An educator studies so that he may clear sight of what he is instructing other to do. To create sound well, one must know much about it. To teach others to create sound well, one must know a significant amount more than the average musician. Without a deep and broad understanding of sound an educator will never communicate to less developed minds clearly, and their students will not see as they could.

A teacher is a servant

If a student is struggling and willing to do what it takes, it does not matter how much strength is takes out of the teacher; the student must pass. If a student is clearly struggling, the offer for extra help must be made clear through e-mail or another place outside of class. If several students are struggling, a public offer must be made for a group tutoring session. The teacher must make the time to meet with any student that comes forward after class no matter how inconvenient it is. In the case of impossibility, a paid tutor is an acceptable option.

Above all else, the attitude of a teacher is the most important part of teaching. Of course a main goal is for the students attain the knowledge they need to succeed, but it goes deeper than this: The overall quality of a student’s life should be improved as a result of the class. The goal is not to be a good teacher, but to help students become more than what they are. The recognition of the teacher is rubbish compared to every capable student thriving in the environment created in and out of the classroom. A teacher’s job is to serve his students and to make them better people as much as it concerns the teacher. To do this a teacher must care deeply for every one of his students inside of the classroom and the subject of music theory, but even more outside of the classroom and music theory. A teacher is a societal leader, and his job is the same as any other leader: To serve.