Test Analysis - Sound and Wave Test
Text in blue is written by my TA, Text in black is written by me.
Explanation:
I have a TA that went through the sound and wave test, recorded how many points each person got for each question, then selected the lowest scoring problems to do further analysis on. She looked at those problems, looked over student answers, and hypothesized why she thought students may have done poorly on that problem. She then emailed me the excel file with all the scores recorded, and her summary and analysis of the low scoring problems. I treated her analysis as sort of a rough first pass went back through these problems to see if I could make any sense out of why students were not scoring so well on them.
This analysis goes along with the scan of the highlighted and coded test as well as the excel file of student scores I have included in this piece of evidence.
Overall I feel students did quite well on this test. The average was an 80% for a test which I considered to have a good mix of easy, medium and hard questions. There was also a mix of mathematical, conceptual, and practical questions. So, for the most part I feel that this test shows that students have learned the material to my satisfaction. However, I still think it is worth looking into more closely.
To help myself visualize what was going on in the results of the test, I printed out a copy of the test and highlighted the answers that people scored well on (greater than 89% in green) and that people scored poorly on (less than 70% in pink). I then went through and made a coding system for the questions to see if there were any trends in the types of questions that people got right or wrong. I essentially just made up the codes as they occurred to me during my analysis of the questions (there is no theory behind them, I just made up what I thought was useful). Questions can have more than one code. I have included a scan of the test to show my coding. The coding system is as follows:
T= terminology
U=units
M=mathematical
C=conceptual
P=Practical
R=Recall
(PR) = Proportional Reasoning
I found a couple of patterns in my coding.
The following are a list of problems in which students scored less than 70%.
5. (7.5% correct) A lot of students thought that all of the answers or more that one was correct, however, the only option that was a transverse wave was sound. The most common answers were xylophone bar vibrating and wave on a guitar string, but not sound, and all of the above.
*disregard this problem, it had a grading problem because the answers got re-ordered and the “a and b but not c” answer no longer was correct.
20. (32.9%)
This question asked what the speed of a sound wave depended on, and the answer was air temperature, but students commonly answered that all of the above, including frequency and wavelength as well, contributed to the speed.
I believe that students are having a hard time telling the difference between an equation which represents a relationship and the causation behind that relationship. Student know that V=fl (velocity=frequency x wavelength), but interpret it as a causal relationship rather than an equation. They see the velocity actually being determined by f and l, where in reality the velocity is determined by the properties of the medium the wave is traveling in. In future years I will need to find a way to deal with this, but it will not be easy. This is in part because there are many causal relationships (as long as we stay away from quantum interpretations) represented by equations. For instance, F=ma. If more force is applied, more acceleration results. So students have been programmed throughout the year to look for the causal relationship within equations. This in and of itself is not a bad thing, I just need to focus on the fact that it doesn’t always apply to all equations, or all variables within an equation. For instance, the Force applied has nothing to do with the mass of the object it is acting on.
8. (59.6%)
This question asked what decreased over time as a guitar string vibrated and the answer was the amplitude decreased, but a common mistake was wave speed and frequency.
This is a question we didn’t discuss much in class, and I knew that when I asked it. I had hoped that students would draw on experience and realize that when you strum a guitar or ring a bell, it always gets quieter over time (because it has to use some of it’s kinetic energy to get the air molecules around it to start vibrating). I don’t know if the low scoring on this question was because students didn’t draw upon their experience with vibrating objects, or because they failed to associate the “getting quieter effect” with lowering amplitude. My guess is a bit of both. If nothing else, this problem tells me that students have a hard time answering questions they were not directly taught.
27. (60.3%)
The distance form the bridge to the nut is 58cm, so a guitar string in the 2nd harmonic has wavelength of 58cm because in a guitar string the 2nd harmonic looks like one complete wavelength, like one whole cycle, so maybe the problem was they could not visualize what the 2nd harmonic would look like.
I agree with my TA that people didn’t stop to think about what the second harmonic actually looks like on a string. In question 35, they are asked to draw the first 3 harmonics on a guitar, open tube, and closed tube, and most were able to do this successfully (average score was 81%). Since I assume most were able to draw the second harmonic, I don’t exactly understand why they didn’t apply that knowledge to this problem. Some may have also assumed 1 wavelength is just a 1 crest, not a crest and a trough.
18. (62.3%)
The answer for this question was that steel transmits sound at a higher speed. A common mistake was air, probably because they assumed that the sound we hear is through the air, but they did not take into account which option transmits the sound at a higher speed.
This was something we discussed briefly in class. We had discussed why sound travels so much faster in metal than air (because of how close and tightly bound the molecules are). My hope by asking this question students would either a) be able to reason about each material by thinking about how dense and rigid it is; or b) remember that sounds travel REALLY fast in metals. I wonder if some kids figured that sound ONLY travels in air. Perhaps they assumed that a vibration in other materials wasn’t really sound, but just a vibration.
7. (64.4%)
This problem asked about standing waves and the answer was all of the above. There were a variety of different answers chosen, but none of the above was a common mistake.
I am unsure of exactly why students missed this problem. My first guess would be that perhaps they have a hard time seeing multiple examples of the same phenomena as “the same thing”. Since the first example of standing waves I gave was on a guitar, then on a giant slinky, perhaps this was the picture that stuck in peoples minds? Or perhaps people chose an answer that corresponded to the type of instrument they made (for example, pan pipe people might have chosen the organ or the soda bottle because they recognized these objects as being similar to their instrument, for which they understood the standing wave pattern)
23. (67.1%)
The answer to this question was that an explosion 340km away would take over 10min to hear, but there were several common mistakes, maybe students just didn’t think it would take so long. Many students answered thinking it would only take seconds.
This problem may have been frequently missed because of the units associated with it. I asked in kilometers. If students interpreted that as meters, they would get an answer 1000 times too small. It may also be hard to conceptualize of waiting for a sound to happen for 10 minutes. This is probably because it is also hard to conceptualize of something being 340 km away. This would be like me hearing an explosion at UC Santa Cruz. Maybe I should include a real location in this problem to make it more tangible?
6. (67.8%)
This problem probably confused many students because it asks about sound and the answer is a longitudinal wave, while in the previous problem the correct answer about transverse wave was sound. The most common mistake was the transverse wave option.
I am not sure if this is a conceptual problem or a terminology problem. Because we often represent sound waves on the whiteboard by drawing them as transverse waves (while acknowledging them as longitudinal waves) it seems possible that some students may get confused as to which one it really is, or perhaps aren’t able to differentiate between the two. There are some really good physlets that show the relation between particle movement in a longitudinal wave and the transverse representation of it.