Ingrid was a Grade 6 girl who chose to investigate “Stringed instruments”. Table 4.16 contains the transcripts of Ingrid’s three videos.
Ingrid’s video transcripts for “Stringed instruments”
Prior knowledge video
Completed explanatory animation
Introducing Ingrid and her topic
Ingrid was known throughout the school for her acting abilities and she had also just landed a job on a TV commercial. Ingrid and I lived on the same block so we often ran into each other at the local park when walking our dogs. Through these informal encounters with Ingrid and her mother, I learned that Ingrid [initially] chose “Cell duplication” as her topic because she wanted something that sounded more academic to round out her school achievements. This proved to be a wise move as Ingrid’s application for a scholarship to a prestigious private high school was approved. Ingrid’s success might have had little to do with her choice of animation topic, but it does show what she was thinking around that time.
The [initial] “Cell duplication” animation was proceeding quite well as Ingrid had identified some of the key variables. Figure 4.21 shows how Ingrid understood that the chromosome divides inside the cell membrane before the membrane divides.
Figure 4.21. “Cell duplication” screen shot 18th August 2011.
It wasn’t until halfway through the project that Ingrid decided to change her topic to “Stringed instruments”. Other children had refined their topics but Ingrid’s new choice was a completely different topic that equated to starting again. This pivotal event was captured in my reflection on the “Lesson plan” for Session 8 (Appendix E):
Session 8 had only half the class present due to a camp. This allowed me to have more time with the remaining four students. I had thought that Ingrid was almost ready for the final construction of her imagery once chromosomes had been investigated a little further. We came across a cell duplication animation at http://www.cellsalive.com/mitosis.htm (accessed 22nd September 2011). This animation was very effective as it also contained video of actual cells duplicating. The various phases of cell duplication could also be played separately as mini video segments to reduce cognitive load. Once we had viewed this animation, there appeared to be only three options open to us:
- Recreate a similar animation using the new details we had just learned
- Simplify the animation to make it easier to explain
- Start a new topic
Recreating the animation was not very appealing as it would have been a lot of work with little reward considering that her representational ideas would have been derivative. Simplifying the animation grated against my pedagogical ideals, which were largely informed by Einstein’s guideline to avoid oversimplification.
This left us with only one option, which was to start a new topic. I encouraged Ingrid with the fact that a 2010 Storyboard participant has also successfully changed topics even further into the project. I also mentioned that seven out of eight topics for the current project were scientific so it would be good to have more variety. She then proposed that we do something musical and "Stringed instruments" was soon chosen. This new topic is actually scientific, mathematical and musical (Lesson plans, 22nd September 2011).
Creating the ZPD with Ingrid
“Stringed instruments” was a topic about which I felt confident, due to my usual role as a music teacher. I told Ingrid that frequency is simply mass multiplied by tension. Before the next session, I did some further research to confirm that the formula was as simple as I had presumed. It turned out that the correct formula for measuring frequency was a lot more complicated as shown in Figure 4.22 (http://www.noyceguitars.com/Technotes/Articles/T3.html accessed 25/09/2011).
Figure 4.22. Frequency formula for a vibrating string.
Prior to seeing Ingrid at the next session, I had reflected that this formula is “beyond what most Grade 6 students cover in their mathematics curriculum. As we are around the halfway point in the Storyboard project it is probably better to just give her the formula” [rather than have her work it out for herself] (Researcher reflection, 14th October 2011). I had decided that in certain situations, literally giving a student the answer can be perfectly valid as long as they still engage with it. I anticipated that Ingrid would “experiment and play with this formula, especially if she chooses to animate the variables in real time with synchronised audio” (ibid). Giving Ingrid the formula was significant because the mediating tool for her turned out to be the frequency formula itself.
Figure 4.22 was reconstructed in PowerPoint using letters and lines so we could change colours, sizes and position at our discretion. Having the formula constantly on the screen meant that Ingrid was never required to memorise the formula. This was also important because it allowed her to discuss each variable separately without the need to consider each variable simultaneously.
When I first encountered this formula, I inputted some measurements to ensure that it was correct. Figure 4.23 shows my initial attempts at testing this formula using actual numbers to determine the units of measurement.
Figure 4.23. Testing the frequency formula with actual numbers.
Figure 4.23 is from the PowerPoint file “201011b.ppt” which I had prepared for Ingrid. It was never intended to make its way into the animation but it led to the idea of what I now call a reference frame (which is when the final frame is frozen whilst displaying additional or summary information). This led to the creation of the Figure 4.24, which became the final image in Ingrid’s animation.
Figure 4.24. Final reference frame from the “Stringed instruments” animation.
During a discussion about how to animate the formula, I had suggested showing and then replacing the T (tension), M (mass) and L (length) symbols with actual strings and then show how these variables affect the frequency using changing audio in real time. Ingrid came up with an even better idea as follows:
The original idea of replacing the variable "L" with a string of varying length and so on for tension and mass would have resulted in three strings being visible on the screen. Ingrid has decided to have one longer string more prominently displayed on the screen and then to colour code each variable in turn (Researcher reflection, 27th October 2011).
Ingrid experimented with various instruments in the Music room during the animation sessions. “I helped her dismantle an actual piano during the session so she could play around with it and see the relative string lengths” (Researcher reflection, 14th October 2011). This clearly influenced Ingrid’s depiction of the strings of varying length that were arranged vertically to resemble an upright piano as shown in Figure 4.25.
Figure 4.25. Strings of varying lengths represented as piano strings.
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. Our mutual interest in these animation design issues was simultaneously conceptual and pedagogical.
Ingrid’s conceptual journey
The opening scene in Ingrid’s animation shows that she understood the commonality of vibrating strings, independent of which instrument they might belong to, as shown in Figure 4.26. “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” (“Stringed instruments” animation).
Figure 4.26. Opening screen shot from “Stringed instruments” animation.
Ingrid’s voice-over script was careful and deliberate in terms of how she presented her terminology. “The pitch of a musical note is measured by its frequency which is the number of vibrations per second” (“Stringed instruments” animation). Immediately after recording these words, Ingrid commented that “I also wanted to put in the words pitch and frequency but in two different places depending on whether I wanted to use...focus on the musical side of it or the scientific side” (Student reflection, 10th November 2011). My reflection after that session was that “It is also significant that Ingrid identified pitch and frequency as being different expressions and measures of the same variable. She has contextualised each term depending on the musical or scientific emphasis of the explanation which is excellent” (Researcher reflection, 10th November 2011).
With only two sessions remaining, the impending deadline for the project surfaced the issue of co-authorship. As the last session was used for the debriefing session, there was really only one session remaining:
I had Ingrid in mind when I asked the class how they felt about the possibility of me working on the animations between sessions to ensure that the work gets finished with only two sessions to go. This has always been a delicate issue for me in my dual role as teacher/researcher but the children were unanimous in agreeing that my assistance was welcome and probably essential (Researcher reflection, December 1st 2011).
During the debriefing session, our proximity as collaborative partners surfaced the idea that directors’ commentaries might be generative and not merely descriptive. To conclude her director’s commentary, Ingrid said that, “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” (“Stringed instruments” director’s commentary). I asked Ingrid if she thought that 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 Ingrid the name of the symbol. Ingrid 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. Ingrid then proceeded to record an additional sentence to conclude her commentary in a more cautious and measured tone. “I realised it was a complicated formula but the variables are quite easy to understand” (Researcher’s reflexive journal, 15th December 2011).
Ingrid demonstrated a consolidated understanding of frequency as she correctly identified the variables of tension, length and mass and the relationships between these variables. The fact that Ingrid hadn't been introduced to the square root symbol in her regular classroom prior to this didn't diminish her understanding of how the three variables affect the frequency of strings on stringed instruments. Ingrid’s partial understanding of the formula was a mathematical issue that went above and beyond the requirements of conceptual consolidation for her particular topic. I marked Ingrid’s final conceptual consolidation rubric accordingly in Table 4.17.
Ingrid’s final conceptual consolidation rubric
|Uses correct terminology
|Some correct terminology
Identifies relevant variables
|Identifies relationships between variables
Self-assessment scale (1-10). Does the student think that they understand their topic?
A postscript for Ingrid’s journey occurred when she walked in during the second (i.e., final) debriefing session. I gave Ingrid special attention for being the first to complete her director’s commentary by sharing this with the group as a model for their own process:
The director’s commentary you’ve done is the first one that I’ve actually finished [I had edited and mastered Ingrid’s commentary and combined it with the original video footage]. And that’s what I’m up to now for you guys, is to actually find out what a director’s commentary looks like and then record your own. It goes with the imagery. So we’re going to watch yours now (Debriefing session 2, December 16th 2011).
A summary of Ingrid’s conceptual journey is presented in Table 4.18.
Summary of Ingrid’s conceptual journey
Proceed to the next Portrait of Ryan