I received an inquiry on Friday, 12 October 2012 from a student whom I will call, "X". X was concerned about a couple of poor-quality questions on an exam.* After taking around 3 hours to figure out what was happening, I wrote a detailed response - about the questions, in question.
It was a huge time investment - particularly on a vacation day, but I couldn't figure out why it continued to perplex me even after I went through all the trouble to figure it out. I could not put the issue to rest. In retrospect, I believe it had something to do with valuable lessons I learned regarding questions, and how they are framed, so here we go...
It was a huge time investment - particularly on a vacation day, but I couldn't figure out why it continued to perplex me even after I went through all the trouble to figure it out. I could not put the issue to rest. In retrospect, I believe it had something to do with valuable lessons I learned regarding questions, and how they are framed, so here we go...
The following letters offer insight regarding teaching, learning, test-taking - and even life.
For privacy's sake, I have culled out anything from the correspondences that might identify the student, "X.".
"Dear X,
Background
Background
My
requirement for you to have detailed notes is so that we can address whatever
deficiencies in understanding that may arise. Moreover, having your
detailed notes helps me to pinpoint any deficiencies in the curriculum
when a student makes a claim that s/he is not being adequately prepared for
what s/he is being tested on. Most
of all though, is the fact that your notes are immensely beneficial to helping
you develop disciplined thinking.
... Basically, I had two choices:
... Basically, I had two choices:
1] Reject your claim and let your grade stand, or
2]
Personally review the Direct Instruction and lab Lectures you have alluded
to.
I decided to go back and review the lectures, and all other related material in
order to determine whether your claim is in fact substantiated. I don't
mind doing this however, it is very time-intensive, therefore inefficient and
not something I can do on a regular basis with the three hundred science
students that I work for. I hope you appreciate this being one of my
reasons for requiring detailed notes from you all.
Findings
This
is what I found in my investigation regarding your claims about the exam on Measurement
on Chemistry - which you received an 84%:
1] Question 10:
1] Question 10:
The
difference between an accepted value and an experimental value is called a(n)
____.
a.
|
error.
|
b.
|
percent
error.
|
c.
|
measured
value
|
d.
|
precise
measurement.
|
You answered, "percent error."
The answer was "error." - that was covered in the lecture entitled, "How Reliable are Measurements." of your lecture covering "percent error". This is why you missed it:
There are two formulas you need to know in order to answer the question:
a) error is the difference between accepted value and experimental value: The testers have given you the answer in the question. This is not a chemistry error on your part, but rather, your failure to logic out the answer. The testers are attempting to get you to rely on prior knowledge from Algebra. They are checking whether you have an enduring understanding of arithmetic and word problems.
Mathematics tells us that the word, "difference" means subtraction. The way the sentence sequence in the question is worded, tells us that experimental value is subtracted from the accepted value.
The lecture did not cover the "+" or "-" values, but that has to do with whether the experimental value was greater or lesser than the expected value.
b) for percent error: % error = (experimental value/accepted value) x 100% - so, you see, you were parroting an answer that you had memorized without actually understanding what you were being tested on.
You may consider this to be trick question, but this is precisely where students of science make common errors; they think they know an answer without being skeptical about what they are being asked.
2] Question 21
"How close a series of measurements are to each other"
You answered, "percent error" the answer was "Precision" - and, it was also covered in the Lecture, "How Reliable are Measurements." at the 58 second mark. It was the archery example; arrows landing in close proximity on a target may be precise and still be lacking in accuracy.
3] Question 24:
An
experimenter's best estimate of how far an experimental quantity might be from
the "true value" is called __________.
a.
|
uncertainty
|
c.
|
science
|
b.
|
an
inference
|
d.
|
a guess
|
You answered, "D."
The
answer was, "uncertainty." - which was not covered directly in your
lecture. But let's go through the possible answers:
uncertainty - actually has to do with the difference between what we know and what we don't know. Thus, uncertainty deals with accuracy and precision - both of which are related to one another based upon qualitative and/or quantitative differences. Thus, by deduction, this seems the most plausible answer because it actually deals with numbers.
Science - is a discipline that involves study - in the bigger picture, while it does involve making estimations, it would be wrong to define science as making estimates between experimental quantities and true values. In other words, this definition is too limited to describe what we do in science.
Inferring - is the process whereby we draw a conclusion about something or have a hunch that something either is going to occur or has occurred. It too could mean that we are estimating but again, while inferring includes estimating, estimating is not inferring.
a guess - is another word for hypothesis which means drawing a conclusion between what we see and making some sort of prediction about why something is occurring based on our observations.
uncertainty - actually has to do with the difference between what we know and what we don't know. Thus, uncertainty deals with accuracy and precision - both of which are related to one another based upon qualitative and/or quantitative differences. Thus, by deduction, this seems the most plausible answer because it actually deals with numbers.
Science - is a discipline that involves study - in the bigger picture, while it does involve making estimations, it would be wrong to define science as making estimates between experimental quantities and true values. In other words, this definition is too limited to describe what we do in science.
Inferring - is the process whereby we draw a conclusion about something or have a hunch that something either is going to occur or has occurred. It too could mean that we are estimating but again, while inferring includes estimating, estimating is not inferring.
a guess - is another word for hypothesis which means drawing a conclusion between what we see and making some sort of prediction about why something is occurring based on our observations.
You may not like this problem because it was not spelled out for you in either lecture.
But, this is what real science is like; it is about being to discern
minute differences based on your observations. It is what separated people like Isaac Newton, Albert
Einstein and the late Richard Feynman (the physicist who figured out why the
space shuttle Challenger blew up - it had to do with expansion and contraction of
an "O" ring) from the rest of us mere mortals...
CONCLUSION
I really want you to put all your notes - prior notes included - into outline form because you will be able to reference all of them for the cumulative exam....you should always be able to review your notes for future classes - either here or at the university once you graduate and move on from here.
I also want you to burn this in your brain; your notes are an extension of your memory. That said, sloppy notes =sloppy thinking. If you invest your energy into excellent notes, you will remember finer details, and you will organize them much better that you are more apt to recall them on demand. Failing that, you can always rely on them for all your assessments, quizzes and exams...
CONCLUSION
I really want you to put all your notes - prior notes included - into outline form because you will be able to reference all of them for the cumulative exam....you should always be able to review your notes for future classes - either here or at the university once you graduate and move on from here.
I also want you to burn this in your brain; your notes are an extension of your memory. That said, sloppy notes =sloppy thinking. If you invest your energy into excellent notes, you will remember finer details, and you will organize them much better that you are more apt to recall them on demand. Failing that, you can always rely on them for all your assessments, quizzes and exams...
More than that, I think it would be wonderful for you to actually see the
qualitative improvement in your note-taking skills, and their direct correlation
to your test scores over time - from now until you graduate.*
Please let me know what you want to do, and above all, do not lose heart. This is tough material you are working with. The intellectual playground you are now in, is one which all science students throughout history have had to learn the rules in order to play there. You are no different. We all have to pay these dues.
Always do your best and never quit.
Mr. M"
Please let me know what you want to do, and above all, do not lose heart. This is tough material you are working with. The intellectual playground you are now in, is one which all science students throughout history have had to learn the rules in order to play there. You are no different. We all have to pay these dues.
Always do your best and never quit.
Mr. M"
*...I occasionally look back upon
my notes from high school and it brings both a chuckle and a smile. I
owe so much to Mr. Mike Gruner, my high school science teacher and All-American Hero. Thank you Mr Gruner. I can never pay you back for all you did... :O)
Now here is the follow up letter to Mr X.
"Dear X,
I have been giving a lot of thought to your e-mail yesterday, and I want to thank you.
It occurred to me when I awoke this morning, that the reason why I invested so much time - 3 hours - into my response was because I saw it a s a teaching moment for you - and for me.
It helped me to understand the utility of difficult, or even 'bad' questions on tests. To my way of thinking, poorly worded questions are more reflective of what actually happens in the real world - especially science - where neatly defined answers rarely come.
I am willing to argue that the, "percent error" question taught both of us more than we ever bargained for. It did so because it caused us to think deeper about the implications of what an error in science is defined to be, it also helped us to realize that in science - as in life - some answers are not so obvious; more importantly, we should never discount the obvious because sometimes the simplest answers are the most complex.
That is what all great thinkers throughout have found; the simple is truly profound. I recently put two different posts on the blog;
1] The Scientific Method - Why it counts (click here)
2] Occam's Razor (click here)
They both speak to this issue. You ought to visit the blogs, because both posts offer us insight regarding the discipline of Science, and moreover, its utility for dealing with nearly every problem life can throw at us.
It may seem funny to you, but I used the Scientific Method when I was a Freshman in College because I was terribly shy, but loved to dance. In those days, we needed partners to dance so, I made my observations, came up with a plan - my hypothesis - in order to get the girls to dance with me. My initial experiment filed so I had to tweak my plan. It turned out that just walking up to a girl and asking her to dance wasn't really how asking a girl to dance simply didn't work. I theorized that using humor might help me out so, I tried it and, as the French say, "voila!" it worked. I planned my work, I worked my plan and I attenuated it to the point where I was soon being asked to dance.
I could go into how I used the Scientific Method to get my parents to let me drive a car, but this is becoming a digression. Perhaps we can talk about that little venture some other time.
Getting back to the test.
The next question we covered had to do with usage of a common logic tool used in the Scientist's bag of tricks; deductive reasoning. The question whose answer was, "uncertainty" most certainly was the answer, and we came to it by eliminating each of the other answers.
I am not really bragging here, but I am pretty proud of myself because I really know how to ask good questions. That is perhaps the most important thing to know about learning. We never know answers, but if we can formulate intelligent questions, then we have a better chance of coming up with useful answers.
To that end, I had an epiphany about test-taking - and dealing with life's questions; whenever we are confronted with a question, our natural inclination is to come up with an answer. Because of that, our approach is flawed. We should always face a question with a question that way we know what we are in fact being asked. I am convinced the lion's share of questions on tests, and life for that matter are wrongly answered because we are so solution oriented as a species.
Moreover, I am absolutely convinced that this is the first point of divergence that truly brilliant Human Beings take. It is what separates true innovators from the rest. I would even go so far as to say that it is a trait shared by all of the brilliant minds that have gone before us. It is a fundamental trait commonly referred to as, "geniuses."
I mentioned Sir Issac Newton - who invented Calculus in order to explain his theory on Gravity and the movement of the planets. He did this in less than two years - at the age of 23. Building upon that base of knowledge, Albert Einstein developed the theory of Relativity at age 27 and came up with the famous energy equals mass times the speed of light squared. He did this because he wondered - at age 16, what it might be like to travel on a light beam.
I have another post on Femto photography going on at MIT RIGHT NOW (click here) - they are taking photos of photons of light at a trillionth of a second. In doing so, they are showing the world what Einstein imagined in his head; light can act like a particle, and a wave. This is called, "the dual nature of light." Again, you should visit the blog and see for yourself how people with ingenious questions are coming up with remarkable answers.
I also mentioned Richard Feynman - an American Physicist who was a member of the Congressional appointed committee charged with investigating the Space Shuttle Challenger's disastrous explosion. Through his ingenious, elegant demonstration, he showed how the disaster could have been avoided. Placing an "O" ring in ice water, he was able to show the world a simple concept of physics - expansion and contraction due to heat transfer.
Like the other two giants I mentioned here, Richard Feynman had no answer book to turn to. All he had was his basic knowledge built upon from constantly building upon his learning by making connections with prior knowledge. They also shared something in common, learning is fun. Learning is done not because of tests, but rather because it it is a form of play. That is why I referred to Science as an intellectual playground.
Mathematics and science for that matter is not at all easy. But what it lacks in ease of understanding, it more than makes up for in being fun. If learning chemistry isn't fun, then we are approaching it wrong. Finally, I want to point out that mathematics and the exercises we must endeavor to master are difficult to master because truly conceptualizing what happens in mathematics really goes on between the ears.
Einstein lamented, just days before he died, that he didn't know math better. Yeah right! Well, Einstein did all of his Science in his head and only later pushed himself to master Mathematics as a means of explaining what he envisioned as he formulated thought experiments in his mind. Again, this speaks to not having the answer and working to find it.
I close this correspondence with a reminder; noting ever worth having is easy. You have demonstrated a talent for Chemistry. I can confidently predict that one day you will far surpass my ability in this field of study. I can also predict that when you get to the playground of Physics, you are going to have a blast. You are a brilliant kid and whether you realize it or not, you are just approaching the time in your life when your brain is going to be working optimally.
That is why it is important to fill your brain with all of these basics. Forget about the grade point and learn for the sake of learning. I assure you the grades will come. Nothing is easier than when it becomes a game - when it becomes fun. Take the pressure off yourself and understand that there is nothing more powerful than the creativity of an unencumbered mind. Humans as a species learn through play, so learn to play and play to learn.
Always do your best, and never quit.
Mr. M"
I have been giving a lot of thought to your e-mail yesterday, and I want to thank you.
It occurred to me when I awoke this morning, that the reason why I invested so much time - 3 hours - into my response was because I saw it a s a teaching moment for you - and for me.
It helped me to understand the utility of difficult, or even 'bad' questions on tests. To my way of thinking, poorly worded questions are more reflective of what actually happens in the real world - especially science - where neatly defined answers rarely come.
I am willing to argue that the, "percent error" question taught both of us more than we ever bargained for. It did so because it caused us to think deeper about the implications of what an error in science is defined to be, it also helped us to realize that in science - as in life - some answers are not so obvious; more importantly, we should never discount the obvious because sometimes the simplest answers are the most complex.
That is what all great thinkers throughout have found; the simple is truly profound. I recently put two different posts on the blog;
1] The Scientific Method - Why it counts (click here)
2] Occam's Razor (click here)
They both speak to this issue. You ought to visit the blogs, because both posts offer us insight regarding the discipline of Science, and moreover, its utility for dealing with nearly every problem life can throw at us.
It may seem funny to you, but I used the Scientific Method when I was a Freshman in College because I was terribly shy, but loved to dance. In those days, we needed partners to dance so, I made my observations, came up with a plan - my hypothesis - in order to get the girls to dance with me. My initial experiment filed so I had to tweak my plan. It turned out that just walking up to a girl and asking her to dance wasn't really how asking a girl to dance simply didn't work. I theorized that using humor might help me out so, I tried it and, as the French say, "voila!" it worked. I planned my work, I worked my plan and I attenuated it to the point where I was soon being asked to dance.
I could go into how I used the Scientific Method to get my parents to let me drive a car, but this is becoming a digression. Perhaps we can talk about that little venture some other time.
Getting back to the test.
The next question we covered had to do with usage of a common logic tool used in the Scientist's bag of tricks; deductive reasoning. The question whose answer was, "uncertainty" most certainly was the answer, and we came to it by eliminating each of the other answers.
I am not really bragging here, but I am pretty proud of myself because I really know how to ask good questions. That is perhaps the most important thing to know about learning. We never know answers, but if we can formulate intelligent questions, then we have a better chance of coming up with useful answers.
To that end, I had an epiphany about test-taking - and dealing with life's questions; whenever we are confronted with a question, our natural inclination is to come up with an answer. Because of that, our approach is flawed. We should always face a question with a question that way we know what we are in fact being asked. I am convinced the lion's share of questions on tests, and life for that matter are wrongly answered because we are so solution oriented as a species.
Moreover, I am absolutely convinced that this is the first point of divergence that truly brilliant Human Beings take. It is what separates true innovators from the rest. I would even go so far as to say that it is a trait shared by all of the brilliant minds that have gone before us. It is a fundamental trait commonly referred to as, "geniuses."
I mentioned Sir Issac Newton - who invented Calculus in order to explain his theory on Gravity and the movement of the planets. He did this in less than two years - at the age of 23. Building upon that base of knowledge, Albert Einstein developed the theory of Relativity at age 27 and came up with the famous energy equals mass times the speed of light squared. He did this because he wondered - at age 16, what it might be like to travel on a light beam.
I have another post on Femto photography going on at MIT RIGHT NOW (click here) - they are taking photos of photons of light at a trillionth of a second. In doing so, they are showing the world what Einstein imagined in his head; light can act like a particle, and a wave. This is called, "the dual nature of light." Again, you should visit the blog and see for yourself how people with ingenious questions are coming up with remarkable answers.
I also mentioned Richard Feynman - an American Physicist who was a member of the Congressional appointed committee charged with investigating the Space Shuttle Challenger's disastrous explosion. Through his ingenious, elegant demonstration, he showed how the disaster could have been avoided. Placing an "O" ring in ice water, he was able to show the world a simple concept of physics - expansion and contraction due to heat transfer.
Like the other two giants I mentioned here, Richard Feynman had no answer book to turn to. All he had was his basic knowledge built upon from constantly building upon his learning by making connections with prior knowledge. They also shared something in common, learning is fun. Learning is done not because of tests, but rather because it it is a form of play. That is why I referred to Science as an intellectual playground.
Mathematics and science for that matter is not at all easy. But what it lacks in ease of understanding, it more than makes up for in being fun. If learning chemistry isn't fun, then we are approaching it wrong. Finally, I want to point out that mathematics and the exercises we must endeavor to master are difficult to master because truly conceptualizing what happens in mathematics really goes on between the ears.
Einstein lamented, just days before he died, that he didn't know math better. Yeah right! Well, Einstein did all of his Science in his head and only later pushed himself to master Mathematics as a means of explaining what he envisioned as he formulated thought experiments in his mind. Again, this speaks to not having the answer and working to find it.
I close this correspondence with a reminder; noting ever worth having is easy. You have demonstrated a talent for Chemistry. I can confidently predict that one day you will far surpass my ability in this field of study. I can also predict that when you get to the playground of Physics, you are going to have a blast. You are a brilliant kid and whether you realize it or not, you are just approaching the time in your life when your brain is going to be working optimally.
That is why it is important to fill your brain with all of these basics. Forget about the grade point and learn for the sake of learning. I assure you the grades will come. Nothing is easier than when it becomes a game - when it becomes fun. Take the pressure off yourself and understand that there is nothing more powerful than the creativity of an unencumbered mind. Humans as a species learn through play, so learn to play and play to learn.
Always do your best, and never quit.
Mr. M"
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