Pointing With Words- How the constraints of distance learning require improved relational thinking

"Start there", says the teacher, pointing to a note on a page of sheet music. The student plays, starting where the teacher indicated.

_____________________________________________________________ Just as the nationwide closing of restaurants is forcing people to cook, the limited ability to point to something and say “start there” during distance learning may force educators and students alike to develop clearer spoken instructions, questions, and procedures for testing the validity of answers involved in the educative process. The act of pointing to something, hereby referred to as the “indicative gesture”, is of limited use in distance learning. The loss of the indicative gesture at first seems like an impediment to education, but overcoming the constraints imposed by its absence will require teachers and students to significantly alter their spoken instructions. If done well, this alteration in speech will show the indicative gesture can be a crutch as well as a catalyst in the field of intellectual development. To evaluate this claim, the reader is asked to imagine a few scenarios:

Scenario A: 1. Imagine you are a music teacher, and are checking to see if a student possesses the knowledge that would make him/her capable of telling you the correct

pitches of notes written in sheet music notation.

2. Point to the note indicated by the pink pencil in the picture below, and ask the student

“what is the letter name of that note?”

In scenario A, the student will know which note the teacher is referring to, and if they know how to read pitches on sheet music, will say “G”

Scenario B: 1. Imagine you are a music teacher, and are checking to see if a student possesses the knowledge that would make him/her capable of telling you the correct

pitches of notes written in sheet music notation. 2. Do not point to the treble clef “G” in the first measure, or indicate the “G” by moving any

object. Instead, refuse to move any part of your body except your jaw and tongue, and say

“what is the letter name of that note?”

In Scenario B, it is unlikely that the student will know which note you are talking about. Even if they know how to read pitches on sheet music, they will say “which note?”, and become confused.

Scenario C:

1. Imagine you are a music teacher, and are checking to see if a student possesses the knowledge that would make him/her capable of telling you the correct pitches of notes written in sheet music notation.

2. Imagine that you are not in the same room as the student, but both of you can see the same picture, depicted below.

3. Carry on the following dialogue with the student (assume the student already knows

the meaning of "treble clef", how many beats eighth notes and eighth rests are

worth, and can calculate what he or she is supposed to do when they say each of the

syllables in the phrase “1 & 2 & 3 & 4 &”.) ________________________________________________________________ Teacher: Can you see the treble clef note on the first half of beat 2?

Student: Yes.

Teacher: What is the letter name of that note?

Student: G!

_______________________________________________________________

In Scenario C, the teacher still eventually asks the question “what is the letter name of that note?” However, in this scenario, the antecedent of the pronoun “that” is made clear not by pointing, or another indicative gesture, but rather, by using speech as a tool to direct the student’s attention. The location of the note being discussed is made clear by describing its relationship to other symbols, such as the treble clef, and requiring the student to calculate what note is played on the first half of beat 2. Scenarios A and C, although they both result in the student answering “G”, achieve this result through different processes. In Scenario A, the student needed only to look at the note indicated by the pencil, see where it was on the grid of 5 lines, and name it. He/she did not have to describe where the note was in relation to other symbols (eighth notes, eighth rests, and the treble clef). In Scenario C, the student had to find the group of 5 lines that intersected the treble clef. Then the he/she had to use his/her prior knowledge of counting to go through the following internal monologue with him/herself: ________________________________________________________________

Student:

• “The note with the lowest beat value in this measure is an eighth note. Eighth notes are worth 1/2 of a beat.”

• “To count halves of beats in groups of 4, I need to say the syllables "1 & 2 & 3 & 4 &", and assign each syllable a value of 1/2 of a beat.”

• “There is an eighth rest at the beginning of the measure.”

• “An eighth rest = 1/2 of a beat = One syllable.”

• “The first syllable is “1”, which I would say while performing the eighth rest.”

• “After the eighth rest is an eighth note.”

• “An eighth note= 1/2 of a beat = One syllable.”

• “The next syllable is “&”, which I would say while playing this eighth note.”

• “After that eighth note is another eighth note.”

• “An eighth note= 1/2 of a beat = One syllable. The next syllable is “2”.”

• “This is the note my teacher is talking about! It’s a G!”

__________________________________________________________________________________

Although this internal dialogue was not included in the spoken aloud interaction in Scenario C, it had to take place in the student’s mind in order for him/her to come up with the right answer. Scenario C requires the student to think by describing the relationship of some symbols and objects (the eighth note the teacher is referring to) to other symbols and objects (the other eighth notes, eighth rests, and treble clef). This kind of thinking, which will hereby be referred to as “thinking in relations” is nearly absent in Scenario A.

Thinking in relations is far more empowering to the student than directing his/her attention through indicative gestures, because it enables the student to see patterns, use these patterns to make predictions, and test the validity of these predictions. As a result, thinking in relations makes it possible for students to teach themselves new things, instead of depending on a teacher to provide them with new facts to learn by rote memorization. To illustrate this point, we will consider the way that two hypothetical music students react to a question about an unknown note. The first student has memorized more information about reading music, and the second student thinks in relations.

Student One (has memorized more information about reading music)

Student one knows that the space notes in treble clef, from bottom to top, spell “FACE”, the line notes from bottom to top are the first letter of each word in “Every good boy does fine”, and that the musical alphabet is a repeating cycle of “A B C D E F G, A B C D E F G”.

Teacher: What is that note? (points to note indicated by arrow)

Student: I don’t know, no-one has told me the name of that note yet.

Teacher: It’s an “A”.

Student Two (has memorized less information about reading music, but thinks in relations)

Student two only knows the location of the notes “A, B, C, D, E, and F”, and that the musical alphabet is a repeating cycle of “A B C D E F G, A B C D E F G”

Teacher: What is that note? (points to note indicated by arrow)

Student: I don’t know the name of that note. It’s above F, E, D, C, B, and A though. Oh! I just

realized something! The line note immediately above “A” is “B”, the space note

immediately above “B” is “C”, the line note immediately above “C” is “D”, the

space note immediately above “D” is “E”, and the line note immediately above “E”

is “F”. They go up in alphabetical order! If that pattern continues, then the space

note in between “F” and the mystery note is “G”, and the mystery note is “A”!

Teacher: That’s right!

__________________________________________________________________________________

Student Two, despite beginning with an impoverished knowledge of reading music when compared to Student One, is able to use the skill of “thinking in relations” to solve a problem that Student One could not. Furthermore, Student Two can easily use the pattern of alphabetical order he/she has discovered to rapidly surpass Student One’s vocabulary of note names by teaching him/herself all of the note names depicted below.

Student Two’s Extrapolated Vocabulary of Treble Clef Note Names

Thus results a situation where a student was able to use the skill of “thinking in relations” to overcome a deficit of knowledge, without the aid of a teacher. There is a danger, however, in that the practice of extrapolating from known facts to unknown facts does not always produce accurate information. In this case, the student cannot be sure he/she has correctly inferred the names of the other notes until he/she successfully uses this information to learn from notation a piece of music he/she has heard before. Thinking in relations creates opportunities for students to develop hypotheses like “If D is on line 4, then E is between lines 4 and 5”, but must also be used to check the validity of these hypotheses.

Although this article demonstrates the value of thinking in relations in the context of the music lesson, this skill is also a catalyst for learning in disciplines of science, art, and social spheres. The child who says “the treetop swayed in the breeze” is closer to understanding that air has mass than the child who says “the treetop swayed”, and cares not for the wind.