My topic is strings, and, umm, I know nothing about strings on the piano. And I'm probably going to do most of my research on strings on a piano more than a guitar.
There are several different arrangements of this formula depending on whether the focus is the tension, mass, pitch, length or frequency. My own understanding has also deepened as I have previously (erroneously) described pitch as "Mass x Tension."
Frequency can be measured using the formula:
This formula is beyond what most Grade 6 students cover in their mathematics curriculum. As we are around the half way point in the Storyboard project it is probably better to just give her the formula.
There is still plenty of room for this student to experiment and "play" with this formula, especially if she chooses to animate the variables in real time with synchronised audio.
Stringed instruments such as piano and guitar have multiple strings but the science behind the pitch of the notes is the same for each string.
The pitch of a musical note is measured by its frequency which is the number of vibrations per second.
The variables of length, tension and mass combine to give each note it’s frequency.
The longer the string, the lower the frequency. The shorter the string the higher the frequency.
The looser the string, the lower the frequency. The tighter the string the higher the frequency.
The thicker the string, the lower the frequency. The thinner the string the higher the frequency.
I spent a long time playing around with this formula to confirm that it was correct before giving it to this student at the start of session 9. I first encountered it at http://www.noyceguitars.com/Technotes/Articles/T3.html (accessed 25/09/2011)
The strings of varying length were arranged vertically to resemble a piano. This student took the wooden panels off a piano to see this first-hand shortly after changing to this topic. Loose strings were harder to draw but we knew that the vibrations couldn't possibly be in real time or there would have been over a thousand vibrations every second and we were limited to 25 frames per second. (Hardly any of the children actually had changing imagery for each frame of their animations and when they did it was only for certain sections).
This animation concludes with a "reference slide" which is when the last frame is frozen whilst displaying additional or summary information.
My original animation was talking about "Cell Duplication" but more than half way through researching the topic I realised that it would be too hard and if we did animate it, it would just be a copy of something that we had already seen.
The formula itself is quite complicated but once you understand it and you've read over it a few times it's actually quite simple.
I realised it was a complicated formula but the variables are quite easy to understand.
Changing topics really was a major decision when you are half way through it.
Of most interest to me was a conversation I had with this student in between takes for her final director's commentary. She had just recorded that the formula is "actually quite simple." I asked her if she thought she understood the formula and she said that she did. I questioned her about this further and asked her if she knew what the square root symbol meant (I just pointed at the symbol without naming it). She could not answer. I then told her the name of the symbol. She claimed to have heard of it but "could not remember" what it meant. She could offer no answer when I asked her if she knew the square root of 25. I concluded the discussion by reassuring her that understanding the actual effect of these variables on the pitch of stringed instruments was sufficient for our purposes. She then went on to record the final line of her commentary.
| Uses correct terminology | With assistance | Simplified terminology | Some correct terminology | Actual terminology |
Identifies relevant variables |
Not apparent | With assistance | Basic understanding | Deep understanding |
| Identifies relationships between variables | Not apparent | With assistance | Basic understanding | Deep understanding |
| Self assessment. Does the student think that they understand their topic? | No | Not really | Basic understanding | Yes |
| Uses correct terminology | With assistance | Simplified terminology | Some correct terminology | Actual terminology | ||||||
Identifies relevant variables |
Not apparent | With assistance | Basic understanding | Deep understanding |
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| Identifies relationships between variables | Not apparent | With assistance | Basic understanding | Deep understanding | ||||||
| Self assessment scale (1-10). Does the student think that they understand their topic? | 1 |
2 |
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8 |
9 |
10 |
After the square root discussion (listed above) I still believe that this student has achieved a "deep understanding" for all of the rows in her conceptual consolidation rubric. The fact that this student hasn't been introduced to the square root symbol doesn't diminish her understanding of how the frequency of stringed instruments can be raised or lowered.