February 07, 2016

What is wrong with “What is up with Noises?”?


I have two disclaimers about this post.  First, this post is coming about four and a half years late. What can I say? I'm not so good at the internet hot take thing.  The second disclaimer is that I wrote these notes up quickly today while dealing with a teething and sick baby.  These are my quickly-jotted notes.

Alright, so here's the deal - in late summer 2011, Vi Hart posted the following video about the mathematics and physics of sound:




I've said it before, and I'll say it again: I like Vi Hart's videos. She has great enthusiasm for math, science and music. Her passion is wonderful. But this video was not great, in my opinion. There are a number of mistakes that she makes and misconceptions that she perpetuates. I think there was a bit of criticism when the video first came out, but it was mostly about how she wrote "vasilar" membrane instead of basilar membrane. She edited the description of the video to say "Accuracy not guaranteed."  That doesn't really stop people from watching the video - not that I want to deter people from getting excited about sound and acoustics at all.  But it's a bit frustrating when there are so many mistakes in such a popular video.

So, below are my notes on the video.  There are parts that I like, and I mention them as well.

1.) 0:02

Talks about air molecules set into motion by the strings and then the wave reaching your ear. But the strings don’t move nearly enough air to make a sound that is audible. The string drives the bridge, which drives the top plate of the instrument.  Much of the sound radiation comes from the top plate, but the top plate also drives the air inside the cavity as well as coupling to the back plate.

2.) 0:37

She conflates speed and frequency which is a common misconception.  Strictly speaking, not WRONG, but poor phrasing since the speed of the string depends on what point on the string you are looking at as well as the amplitude and the speed is constantly changing.  The frequency is not changing (as much). I really don’t like when people use this type of phrasing, since it perpetuates misunderstandings of frequency.

3.) 0:40-50

The initial description of the swing is not bad, but it is not used as completely as it could be, and as we’ll see later, the analogy is stretched beyond what is accurate.

4.) 0:55

Says “That’s amplification.”  Well, actually, what was described was resonance, but that was not mentioned. 

5.) 1:02

While it is true that driving an oscillator at a frequency above it’s natural frequency will not result in an amplitude as high as if it is drive at the natural frequency (which is what resonance is) you aren’t technically dampening the vibration in that case.  That is a nit pick, I guess. However, the visual in the video doesn’t exactly match what is being described, either.  

6.) 1:08

"(The string) wants to swing at a certain speed, frequency.” - Again, the conflation of speed and frequency.  This bothers me because when you look at the wave speed and the relation between wave speed, frequency, and wavelength it is something different than talking about frequency using the word “speed”.

7.) 1:19

It’s not called a sympathy vibration - it’s called a sympathetic vibration.

8.) 1:22 - 2:26

The description of how the ear works is overall not too bad. 

Weirdly, at 1:29 there is a "Fun Fact" in the video which says the number of molecules in a sound wave is larger than the national debt.  I can't even unwrap what that is supposed to mean.  I get that the sentiment is that there are a large number of air molecules involved in the transport of sound, but - the units are different and how is this "sound wave" defined so that we can count the number of air molecules?

9.) 1:47 

“faster frequency” should be “higher frequency” so as not to reinforce the speed = frequency misconception.

10:) 2:38 - 3:07

This whole mess of talking about pushing the swing every other time is just bizarre.  The idea that you can drive an oscillator at a lower frequency and then get it to oscillate at it’s natural frequency is inherently non-linear when applied to acoustics-related oscillators. I’m not even really sure what it says about the physics of a pendulum, to be honest.  And this is not to say that there is NOT any non-linear effects at play in the ear or with the production of sound, but for what is discussed in the video, the nonlinearities are insignificant.

11.) 3:08 - 3:30

In this section Vi is applying non-linear behavior to the motion of the basilar membrane. She asks: if one frequency goes in, shouldn’t the cochlea respond at places where  I’m not actually an expert on the auditory system, but I have never heard about non-linear effects in the cochlea for pure tones at normal sound levels. I’d love to know if I’m wrong about that, but I don’t think I am.

12.) 3:30 - 3:46

Vi asks a really interesting question here. She asks if your ear hears a complex sound at a certain fundamental frequency f, but then a second complex sound at frequency 2f is played, wouldn’t your brain perceive them as the same even if they came from different places?  At least, that is what I understood her to be asking.  If so, that is a great question!

13.) 3:48 - 5:25

She does a good job of introducing the idea of the overtone series here.

14.) 5:26 

"…this is not some magic relationship between mathematical ratios and consonant intervals. It’s that these notes sound good to our ear because our ears hear them together in every vibration that reaches the cochlea."

She is starting to tie the ideas of the overtone series back to her question posed at 3:46.  As stated, the above quote is TRUE for the example that she gave (or any overtone series, really).  My issue with what is stated is that it makes it sound like ANY vibration that reaches our cochlea has the overtone series embedded in it, which is not true.

15.) 5:34

“Every single note has the major chord secretly contained within it."

This statement is true only if the note is a complex tone containing a harmonic spectrum, which is often the case, but not all instruments will produce such notes.

16.) 5:48

Finishes the explanation of the overtone series.

17.)  5:50

“…because of physics, but I don’t know why…”  This is just annoying.  Much of the previous explanation contained a lot of physics.  There’s no excuse to just say “I don’t understand physics…"

18.) 5:54

“…twice as fast…” Again with the frequency / speed issue.

19.) 6:25

“You don’t notice the higher (harmonics), usually, because the lowest pitch is loudest and subsumes them."

The lowest frequency in a harmonic spectrum is referred to as the fundamental frequency. The fundamental frequency often, but not always, has the highest amplitude in the spectrum. But your ear still associates the PITCH of the sound with the fundamental frequency whether it is loudest or not - or even there at all, as the video points out later.  Note that this line also incorrectly uses the term “pitch” to refer to a component of the complex tone.  Pitch is a subjective quantity that you associate with the tone as a whole.  (So, if we’re counting that is 2 errors here.)

20.) 6:51

“String is pushing around the air…"

Same mistake as made at the start of the video: the string is not pushing a large amount of air. The top plate of the viola is doing the pushing on the air molecules of the sound wave that you hear.

21.) “Basilar membrane is vibrating in sympathy with all these frequencies…"

I’m not sure that it is wrong to say the basilar membrane is vibrating in sympathy with the other parts of the ear and air and instrument, but I’m not sure it’s correct to say it is vibrating in sympathy with the frequencies. Call this a minor nitpick. 

22.)  7:14

Description of timbre is brief, but good.

23.) 7:17

Compares the sound a pure tone makes to the vowel sound “ooh” and says it sounds like a flute. Timbre is a subjective quality of sound, but I would disagree that all pure tones sound like oohs or like a flute.

24.) 7:27

There is a comment here about using our mouth to “shape the overtones coming from our vocal cords”.  I’ll grant some poetic license to this statement, and it is true that the mouth shape helps determine the vowel sounds. It would have been better to include all parts of the vocal tract. 

25.) 7:33 - 7:50

The lowpass filter demo - it’s not exactly clear to me what concept is being demonstrated here.

26.) 7:54 - 9:42

Overall this section is not bad. I will point out that when overtones are played separately and then together you are cuing your ear to listen to the different parts of the tone, and so many people (certainly not everyone, though) will be able to pick out the different parts of the tone after being cued. That does not make the tone any less of a complex tone, but you need to be careful what conclusions you are drawing from this demo.  Also, she did not control for amplitude in the overtones starting from about 8:07 and so every combination of tones is clipped, meaning that the sound coming from the speakers actually has MORE harmonic content in it than she intended to demonstrate.  This can be seen graphically in the waveform at 9:41.

(I’m going to ignore the overtone fitting the number of bumps comments around 8:45.) Her idea to show the waveforms in actual size is pretty neat, I think.

27.) 9:43

"To make this shape, it pushes forward fast here, then does this wiggly thing, and then another big push forward."

Another reference to “fast” and the rest of the description is not physically or mathematically great here.

28.) 10:20

“Some frequencies get pushed the wrong direction sometimes…”  I don’t even know what this means. Frequencies aren’t getting pushed anywhere.  This makes no sense to me.

29.) 10:25 - 11:16

The parts about the sound source discrimination are pretty good.

30.) 11:17-11:50

The part about the missing fundamental is good. 

31.) 11:52 - end

I think Vi does a great job of reminding us that there is a lot of beauty and wonder in nature that science and mathematics can help us explore.  I’m certain that this joy she brings to her videos is what keeps people sharing and watching them.





November 17, 2015

On incentives in the classroom

This article from NPR was passed around in my social networks quite a bit last week: How To Get Students To Stop Using Their Cellphones In Class The meat of the article is contained in the following excerpt (my emphasis added in bold):
Ten percent of the grade in his class comes from participation points. Students get points by answering a question when called on, by asking a good question or by responding to a poll. (Duncan uses clickers, devices that allow students to collectively answer multiple-choice questions in class.)

For his experiment, he says he got buy-in from students first, as he wrote:

"I asked them to vote if I should offer one participation point for taking out their cell phone, turning it off and leaving it out on my desk. To my amazement the vote was unanimous. 100% voted yes. So they all took out their phones, put them on the desk, and we had an exceptionally engaged class."
I tend to view my classes a bit like an economist: students will respond to whatever incentives we provide them with. If we provide them with the incentive of easy points, most will choose to take whatever action is necessary to get the easy points.

In the case of Duncan's class, the incentive is a point in exchange for placing a turned-off cellphone on a desk in the front of the room.  It's not clear what that one participation point each class contributes to the total of a student's overall grade.  It is reasonable to conclude that the one point will not translate into making or breaking any student's grade for the term. The hope is that the commensurate increase in engagement (due to removal of distraction) is an overall larger effect on the students. That is, a more engaged student will gain in the subject knowledge more than just whatever the one participation is worth in the weighted score.

I don't use participation points because I want to incentivize the learning of the content of the course. I don't want students to be counting points through the semester, because if they do that, then they are not focusing on the concepts we spend all of class discussing. I have gotten rid of all points in the classes I teach, opting instead for ratings in a standards-based assessment and reporting approach. It has worked well, and I believe I am helping students be intentional about thinking about the concepts in order to get the grades that they want.

But, I struggle with the students who choose to get their cell phones out and ignore what we are doing in class. I then have to wonder: what if I have the wrong view of incentives?  What if Duncan is providing a small and conceptually meaningless incentive in exchange for getting higher conceptual gains?  Is that a better approach?

I don't have answers for those questions.  I just hope I'm not completely wrong with what I'm already doing.

August 29, 2015

Bad Vibes - Let's talk about sonification of data

When I see news stories that talk about sound, sound waves, acoustics, or the physics of music my defenses usually go up as I'm reading through the article.  I try to suppress the urge to pick apart every little detail that isn't exactly right, but sometimes I can't help myself. 

One trigger for me is the sonification of data - in other words taking a time-varying signal and turning it into an audible sound. There is nothing wrong with using this technique to explore something in nature, but it does not mean that the object is emitting a sound wave, playing a tune, or singing.

I ran across this article last week from Space.com, which starts with the following:

In space, no one can hear you scream — that's because on Earth, sound waves move through the air, and there is no atmosphere in space. In empty space, there is no atmosphere, so the sound waves don't have a material to travel through. It's impossible for humans to hear sounds in the vacuum of space just like it's impossible to surf where there is no water — the waves need something to move through.

But last year, scientists recorded sounds coming from Comet 67P/C-G using the Rosetta Plasma Consortium (RPC) magnetometer instrument.
This instrument measured the sound wave vibrations in the comet's magnetic field, according to a statement from ESA....
When I followed the link to the statement from the European Space Agency, there was no use of the term "sound wave" anywhere in it. I guess the Space.com writer just wanted to spice up the story a little bit. There's nothing inherently wrong with writing a story to be accessible to a wide audience, but it just seems wrong to start an article with the fact that sound can't exist in the vacuum of space, but then in the next paragraph start talking about sound waves from a comet.

If you are a science writer, please remember: sonification of data does not necessarily mean something in nature is producing sound waves.

August 17, 2015

Updating my accommodations statement in syllabuses

I'm updating my statement on accommodations for students with disabilities in all my syllabuses this Fall. I would appreciate any feedback or suggestions.

In previous terms I had a very standard, boilerplate statement:
Students with documented disabilities should notify the instructor directly about necessary accommodations.  The office of Student Accommodations and Resources (StAR) located in J-2025 provides assistance in verifying needs for accommodations and developing accommodation plans.
But, I want to try to make clear that I believe in fair accommodation for all students. So I'm updating this statement to say:
All students, regardless of physical or mental disability status, deserve an equal opportunity for success in all courses. As your instructor, I am deeply committed to encouraging your success and determined to make any possible accommodation necessary. 
Students with documented disabilities should first notify me directly about necessary accommodations as early in the semester as possible.  The office of Student Accommodations and Resources (StAR) located in J-2025 provides assistance in verifying needs for accommodations and developing accommodation plans.
Too often I have heard colleagues talk about what conditions students will face in future classes, transfer colleges, grad school or the work environment. I'm not interested in weeding out students who can't conform to arbitrary rules for completion of assessments and/or assignments. I am concerned with seeing that all students can meet their full potential and finding reasonable ways to remove unnecessary barriers to their success.

August 11, 2015

Astro-journal assignment for introductory astronomy


About a month ago I mentioned on twitter that I assign all my astronomy students to do an astro-journal. This has been a long running assignment since right after I started teaching astronomy over ten years ago.  I wanted something that would help students see that they can go from not really understanding much about the science of astronomy to becoming comfortable with the vocabulary and concepts related to the study of the cosmos. Additionally, I wanted students to be able to understand and predict how moon phases work as well as seeing that the study of space is something that is often in the news. (Why space is popular in the press is an interesting conversation to have with a class. I love when a student raises this question.)

One part of the astro-journal that I have retired from using is the "Adopt a space mission" assignment. I used to have students choose (or have assigned to them) an active space mission (unmanned) that they "adopt" and follow throughout the semester. I think it was often a valuable addition to the journal, but when we only meet twice a week, it becomes difficult to squeeze in class discussions about the space missions.

Here is the description that I have been giving my students for how to construct their astro-journal.

"By far the single most significant part of your grade will be made up by the score that you get on the astro-journal. The reason that this assignment is so heavily weighted is that I believe that it has the largest impact on your learning of the topics we are covering in astronomy, astrophysics, cosmology, and space science. 
You need to establish a notebook or binder that is separate from the notebook that you use to take notes in class or while you are studying at home. You should start your astro-journal immediately.
Periodically your journal will be checked for progress. You will need to bring your journal to class in order for it to be checked. Each of the check-ins will count as a part of the evaluation of the journal. 
Your astro-journal will consist of two main parts and an optional third part. One part is a recording of your observations of the Moon. We will cover how to make these observations in class. The other main part of the journal is a record of your reading on current events in astronomy and space news. You need to find and read news stories from reputable sources, then summarize these news stories in your own words and write a brief reflection on what the news stories are covering. The optional part of the astro-journal is a section on ANYTHING else that you see in your daily life that relates to astronomy. 
A rubric is posted to the course website that explains how it is graded. Please let me know if you have any questions about the grading of the astro-journal."

Here is the last rubric that I used for the astro-journal project before I switched over to using a standards-based assessment and reporting (SBAR) method of assessment.  Really, the SBAR approach used the rubric as a starting place, just the point values were discarded. (Sorry if the formatting is weird here.)

Astro-Journal Rubric Name:___________________________________
Organization
Set-up
This rubric is inserted into your journal. You have visited the professor's office to show this.




0-1 points
Journal check 1
Professor checks journal in his office during weeks 3 & 4


0-2 points
Journal check 2
Professor checks journal in his office during weeks 6 & 7


0-2 point
Moon Observations
AccuracyPhase drawn incorrectly; direction missing or wrong; time of observation missing or wrong; altitude missing or wrong; unphysical observation recorded & many indications of faked observations.

0-5 points
Moon phases generally drawn correctly. Occasional incorrect recording of direction, altitude, time. Horizon missing or unclear. Some indications of false (faked) observations.

6-18 points
Moon phase consistently drawn correctly. Accurate observations of direction, time, altitude. Horizon clearly drawn in all entries.



19 points
CompletenessLess than one accurate observation per week on average.

0-3 points
1-3 accurate observations per week on average.

3-18 points
3 or more accurate observations per week on average.

19 points
NeatnessObservations hard to decipher. Phases not drawn clearly. Records not organized in logical manner.

0-3 points
Observations are sometimes inconsistent and/or occasionally difficult to understand.

2-8 points
Observations easy to read and understand. Clear drawings. Logical organization & demonstrates creativity.

9 points
Current Events
AccuracyEntries include unphysical or scientifically wrong ideas. Entries out of date, with no context provided. Sources not cited or incorrect.

0-5 points
Entries are appropriate and relevant. Sources are listed, but not always cited correctly, completely, and consistently.

5-9 points
Entries are appropriate and relevant. Sources cited correctly, completely and consistently.


10 points
CompletenessLess than one entry per week on average. Most assigned entries & topics missing.

0-5 points
1-2 entries per week on average. Some assigned entries & topics missing.

6-16 points
2-3 entries per week on average. All assigned entries & topics included.


17-19 points
NeatnessEntries nothing more than copies or printouts of articles. No reflection is included. Organization is lacking or nonexistant.


0-4 points
Entries include partial information and partial personal reflection or no personal reflection is included. Organization is consistent and logical.

3-16 points
All entries include your own summary of the article or news item and a personal reflection. Organization is consistent and logical. Presentation of entries demonstrates creativity.

17-19 points
Other



Anything else that you notice or observe that relates to or reminds you of astronomy throughout the semester.

Up to 15 bonus points.



I'm happy to share any of the original resources if you'd like them emailed to you, just let me know.

July 31, 2015

AAPT Summer meeting 2015 twitter mini-analysis (#AAPTSM15)

I was not at the Summer meeting of AAPT which just wrapped up earlier this week. But, I have been following along with the meeting hashtag on twitter (#AAPTSM15) which was a great way to get a sense of what was going on in College Park, without actually being there.

I wanted to do some analysis of the tweeting, so I set up an IFTTT recipe to log all the tweets with the hashtag to a Google spreadsheet. Unfortunately, I didn’t set it up until some people were already flying out for the pre-meeting workshops and related meetings, and apparently my recipe got turned off right about the time the bridge session from AAPT to PERC was starting.  So, I don’t have a complete data set, but I have the majority of the tweets.

Here are some numbers:

249 unique accounts tweeted or retweeted with the #AAPTSM15 hashtag. Excluding users who only retweeted something leaves 118 unique accounts, up from 42 a year ago. Not all of them were at the meeting, and some of the retweets may have been from bots, but it’s still a far cry from the winter meeting in New Orleans a few years ago when I think it was just Heather Whitney, Rhett Allain, and myself who were tweeting.

Over 1500 tweets (including 640 retweets) were sent during the meeting.  I didn’t follow everyone who was tweeting, so I was grateful that so many were retweeting from their timeline.

What about the most prolific tweeters?  Here are the 25 users with the most #AAPTSM15 tweets:


@LCTTA 169
@AAPTHQ 155
@eigenadam 77
@MrLeNadj 55
@TRegPhysics 50
@chrisgoedde 45
@fnoschese 43
@WBrianLane 39
@nquarderer 30
@arundquist 26
@dyanlj 26
@Mr_Martenis 26
@UniverseAndMore 24
@rjallain 22
@kellyoshea 21
@watermanphysics 20
@BlackPhysicists 19
@csealfon 18
@KHSphysics 18
@ainissaramirez 17
@ng_Holmes 17
@bethaapt 16
@fpoodry 15
@SteveMaier_ 15
@danny_doucette 14

Once again, the most tweets came from @LCTTA. Nice work, Joe! (Sorry for not linking the usernames to twitter.)

I thought my analysis of the tweets was going to be all about the numbers related to tweet activity. But what is really interesting to me are the themes that emerged (in my opinion) from the attendees who were tweeting.

Ideas which seemed to resonate with attendees, based on my reading of my own timeline included: how do we ensure diversity in the physics classroom, the role of physics education in society in general, how we choose the topics and activities to include in our classes, and how to improve assessment of student learning.  Here are some tweets which were some of the most favorited and retweeted of all which illustrate these themes:

Two most of the most retweeted tweets came from Frank Noschese. The first on the social value of learning physics, as raised by Eugenia Etkina:
The second, on diversity issues in physics classrooms:
Taoufik Nadji (@MrLeNadj) got a lot of retweets from this image:
There was a demo which got several retweets:
Joe Heafner had a comment about how topics are chosen in physics classes:
Trevor Register had a couple of tweet garnering several retweets. The first was a comment again from Eugenia Etkina:
The second was related to the value of student designed or directed labs:
So while there was one popular tweet specifically about a neat demonstration, most of the engaging tweets were about big-picture ideas in physics education. This is really neat for me to see, because I have been thinking about many of these issues for a few years, and to be honest, sometimes it feels like no one else is with me. So I hope to have more to say regarding some of the above ideas in the near future.

Finally, the tweets I captured for analysis were only the ones using the meeting hashtag. There was a lot of discussion online between attendees and non-attendees which often did not include the hashtag. My analysis doesn’t capture that dynamic back-and-forth engagement between physics teachers. If you explore the hashtag, starting with the above tweets, you’ll see the discussions which went on, and are still going on.

If you’re not on twitter, there’s no better time than now to check it out.  See you at #AAPTWM16 - I’ll be attending as I did this one: on twitter.

March 16, 2015

To the student who left the scathing review on RMP - thanks and I'm sorry

I'm not really in the habit of checking up on my "Rate My Professors" (RMP) page, but coincidence led me there on the same day that this post was made by a student in one of my algebra-based physics sections from what I assume is this semester.  I suppose that I am a bit heartened that the student was at least thinking about physics on Pi Day. 


I want to be very honest - I have two messages for this student: thank you and I apologize.

Thank you for leaving your feedback before the end of the semester. Too often I find the feedback on RMP left in the days or weeks after the course ends. Thank you for voicing your frustration before the end of the semester so that we can work together to make the rest of the semester go better for your entire class.

Although I sincerely want to thank you for leaving this message, I wish that you would have come to me directly with your concerns and complaints. I try to treat all students in my classes as adults and expect that we can interact with each other civilly as adults via direct conversations on the phone, in person or over email. By leaving an anonymous message on RMP, you clearly did not agree. For that, I wish to apologize to you.  I apologize that I did not work hard enough to foster a classroom climate where you felt comfortable enough to come to me directly. It is my responsibility to provide a rich learning environment in which you can freely discuss any issues with me. I have either failed to do that, or I have failed to communicate that intent to you. Either way, I intend to increase my efforts to offer avenues for all students to communicate with me.

In your comment you claim that there have been "Literally no lectures or notes in the class." I am not sure if that is hyperbole or not. Each time we begin looking at a new conceptual objective, I have filled the chalkboards with introductions to the objective as well as countless examples of how to do problems related to each objective.  I apologize that I was not more clear about the blurring together of lecture with what might typically be called a recitation. At our college, we use a Studio Physics approach to learning physics. Studio Physics means that we are always in the lab (or studio) so we can easily bounce back and forth between lecture, recitation, and laboratory. Our college has a long tradition of using this approach, and I apologize that I was not more clear about that. I will try my best to delineate the shifting between different aspects of the class. I admit I believe it will be difficult for me to do better on this, since I had thought that you all were doing pretty well with shifting from one aspect to another, but I will try to be better.

You state that "Everything is based off the multiple worksheets...which we never go over anyways." I apologize that I have not been more direct with you about how crucial I believe your participation in an active-learning classroom is to your learning. By now, I hope that you have read the article written by Nobel laureate Carl Wieman on the superiority of active-learning over the traditional method of only lecturing to students. There are two quotes that I want to be sure you understand. The first:
"In active learning methods, students are spending a significant fraction of the class time on activities that require them to be actively processing and applying information in a variety of ways, such as answering questions using electronic clickers, completing worksheet exercises, and discussing and solving problems with fellow students." 
With the exception of electronic clickers, how does that description compare to our class? The second quote:
"...any college or university that is teaching its STEM courses by traditional lectures is providing an inferior education to its students."
Remember that it is not me who is claiming that our method of learning is superior, it is a Nobel laureate who is reviewing the data before him making this claim. I apologize that I have not been more direct in discussing why we do what we do in our class. I hope that I have rectified this situation, but please let me know if there is anything else I can do about it. Additionally, I have made a concerted effort in the two weeks before your feedback was posted to review ALL of the worksheets that we have done in class. Sometimes I ask you to review the worksheets with other students. I try as hard as I can to make sure that all of you understand the correct answers to the worksheets. Sometimes, I don't want to be the one who is giving the explanation for the questions, though. My goal is to get you to a place where you don't need me - you only need the physical laws and correct application of the concepts to reach correct conclusions. I am truly sorry that my desire for you to know and appreciate the wonders of the physical world has not been made more well know to you. I am constantly looking for better ways for me to convey this to you in a way that is not always me just simply telling you. I will continue to try to improve.

Your statement that I use sarcasm in class is true. I am deeply sorry if you interpret my sarcasm to be a personal attack on you. I assure you, it is not. I do not and will not use sarcasm to demean or belittle you as a person. I have been very frustrated this semester that so few of you have done much of the homework. I have wrongly used sarcastic remarks to vent some of this frustration. I had hoped that the sarcasm would work to get you to think differently about how you can use homework to grow your understanding of physics, but I can see that I was wrong. I apologize for that. I failed to give you a more constructive way to ask about homework questions. That, too, was wrong. Here is how I will change that: instead of asking me "Can you show us how to do problem XX from Chapter Y?" you can ask "I was having trouble with problem XX from Chapter Y. The first thing I did was blahblahblah, then after that I wanted to blah, but I got stuck there. Can you help me get unstuck?" This will show me that you have made an honest attempt at the problem and also help me get a window into your way of thinking about the problem.

In summary, thank you again for bringing this to my attention and for doing so before the end of the semester. We have talked in class about everyone's ability to grow and improve. I have apologized for my failures and outlined how I intend to do better to provide a rich learning environment for you. You still have time left in the semester. What will you do to grow and improve your knowledge of physics?