This short section is another part of Message #1109, and it is about
being a student. I am still in the process of responding to some of
the other ideas in Message #1109, which will come later...


>> [Still, I would suggest that you ask yourself exactly why you
>> like working at the job you have and spending so much time on it. --Paul]

I still have so much to learn as a teacher. I like working as a
teacher because it is challenging and stimulating--and I get to work
with my favorite age-group of human beings: teenagers. I also have a
great desire to improve the education system by finding ways to teach
math in ways that are meaningful to students and to me! I want
students to value learning and to become confident, independent
learners. I like to see students apply themselves and reach their
full potential. I also like teaching because there's no end point
for me as a learner, either--I am constantly learning new ways to
facilitate learning about math and to interact with students.

[Your answers are incomplete because they simply raise other questions:

1) There is "much to learn" in any occupation or in just trying to remain alive,
so why do you particularly like what the occupation of teacher enables you to
learn? IOW, how does being a teacher contribute more or as much to your lifetime
happiness than anything else?

2) Life can be "challenging and stimulating" in innumerable ways, so what is
particularly attractive about being a teacher in this regard?

3) Why are teenagers your "favorite age-group of human beings", particularly
since you yourself are no longer a teenager?

4) There are many ways to "improve the education system"; so why do you think
teaching math is as important or moreso than any other?

5) If math was and is not meaningful to you, then why did you and are you
pursuing it at all?

6) There are many important ways for teenagers to "apply themselves" (but
actually no one can ever "reach [hir] full potential", particularly since
"potential" is an ever changing target to which one can only aim
asymptotically); so why do you think that learning math is the most important
one?

7) For virtually every subject "there's no end point for [you] as a learner", so
why is math teaching any different in this regard?

8) "I am constantly learning new ways to facilitate learning about math and to
interact with students." does not really indicate why such activity is your best
way to maximize your lifetime happiness.

--Paul]


>>[ Are you sure there are not other things that you would enjoy
much
>> more, but simply have dismissed as impractical? --Paul]
>
> I enjoyed being a student at university more than I have enjoyed
> teaching; however, I don't think I was a very *good* student, and I
> didn't know what I would do if I continued my education further-
> i.e., what to study further.
>
> [What was it you enjoyed about being a student? **Kitty]

Many things--in general, I have always enjoyed learning about new
things. I don't know why exactly. I've just always had a desire to
understand things that aren't perfectly clear to me.

[This is a completely natural and mentally healthy condition for a human being.
It is something that every infant begins with and all too unfortunately, for
many reasons, is lost by some (most, IMO) children during their years of
schooling. However, once again there are many ways to learn and understand
things. It seems to me that you particularly need to respond to *why* you
enjoyed being a student when you have also stated that you were not a very good
one. (Later: I see that you did below.) --Paul]


I also enjoy
learning from people who are excited about what they're teaching, and
at all of the schools I attended, I've come across many teachers and
professors who loved the subjects they were teaching.

[This is reasonable. Any person who is excited about what s/he is doing will
tend to "infect" those around hir with the same excitement. Still you need to
look at specific information of the subject to determine if such excitement is
really justified by the fundamental value (usefulness to the general enhancement
of human lifetime happiness) of the subject information. If it is not useful for
that purpose in either the short term or the long term (or even negative), then
I think it is incorrect to be excited about it. I think it was GH Hardy, the
eminent number theorist, who once said that he hoped that none of his work in
mathematics would ever find any practical usage. IMO, this is the height of
irrationality. Why anyone would support the work of such a person, I cannot
fathom. --Paul]


>[What is a "*good*" student? **Kitty]

I had mentioned above that I didn't think I was a very *good*
student. I've always had very high expectations for myself, but I
never thought I achieved as much as I ought to have.

[But what is the meaning of "ought"? Where does it come from and who decides?
Maybe you achieved as much as you could (ie. were able to). If that is the case,
then even if you were not a good student (whatever that really means), you were
as good as you could be. And in that case you should not continue to think (or
feel) that you ought to have done better. If it was impossible for you to do
better than it is pointless (because it is without a valid meaning or purpose in
reality) for you to think that you ought to have done better. If you actually
evaded making the right choices so that you could have been a better student,
only then can you correctly say that you ought to have done better. However,
even then such remorse is pointless. The only value to be gained is to learn a
lesson and to not make that mistake again in the future. --Paul]


I had a hard
time deciding what was good enough--I still do to some extent
although I don't think I'm as hard on myself as I used to be. One
thing that I have always been aware of--throughout my experience at
school--was that I really didn't have anyone to look up to as an
exemplary student.

[It would be very hard to make a definition of an "exemplary student" since
everyone has a different subjective value structure of relative importance of
doing various things. To me a good student would be one who took a course
because s/he really wanted to learn it (rather than merely to get a credit) and
did a sufficient amount of work to learn it consonant with hir initial desire
and to a high degree relative to hir interest in it vis a vis hir interest in
other aspects of hir life at the time. The only reasonable exception to this
would if s/he gains new information after beginning the course which convinces
hir that hir previous estimation of the value of the course material was
incorrect. In that case, it would be entirely reasonable to do less than was
originally planned in order to maximize overall benefit under the conditions of
the new information. This might even include dropping the course entirely. As
the sayings go, it is pointless to "beat your head against a brick wall" or to
"cry over spilt milk". Instead, "tak[e] your licking and keep on ticking". IOW,
one should accept one's losses and get on with life, but always learn from any
negative incident so that one does one's best to prevent such mistakes of
estimation or reduces the amount of harm from chance occurences in the future.
--Paul]


It seemed like no one really cared about their classes.

[Unfortunately, this seems to be a problem with current society in general. Most
people are only oriented toward taking courses in order to earn money in order
to be able to buy things and spend time on other pursuits than learning or
performing well at a job. --Paul]


Therefore, I often outperformed other classmates; however,
I felt no particular joy or glory in doing so.

[The joy should have been in your performance against yourself, not in whether
it was better than others or not. It is this constant comparing of oneself with
others that shows a poor sense of self-esteem and in the end will lead to a life
of *essential* dependency on others (as opposed to dependency for optimization,
something that is true for everyone). --Paul]


As a result, however,
I had a hard time gauging just how successful I really was. I didn't
like comparing myself to others, but how else was I to measure my
abilities?

[How about by how well you understood the subject material and could solve the
problems? --Paul]


Somehow, I feel like a truly *good* student knows how to
assess hir abilities and pushes hirself to hir fullest potential,
oblivious of how well others performed.

[This has little to do with being a good student per se. Being oblivious to how
well others perform is mainly related to having high self-esteem. However,
"pushing oneself" is not generally a good way to describe it, since how hard one
should work on any particular subject is entirely dependent on one's total set
of likes and dislikes. "Pushing oneself" implies that one does not really want
to do something, but if that is the case then why should one do it instead of
something that one would rather do? If it is merely a matter of short-term
dislike versus long-term gain, then "pushing oneself" is still incorrect. One
simply trades off less short-term happines for more long-term and overall
happiness. And one does so willingly and gladly. The only time this is
problematic is when the likelihood of the short-term displeasure actually
producing such longer-term and overall happiness is highly uncertain. This is
the case with all the time the I and Kitty spend getting, organizing and taking
our nutrient pills. We often wonder if it will really turn out to be worth the
loss of time to do more enjoyable activities, to enjoy meals without having to
swallow dozens of pills plus less than pleasant tasting (even ghastly if
insufficient vinegar) "meal cocktail", the cost of procuring them and the small
potential that taking some of them may actually shorten our lives. Not a week
goes by without Kitty saying at some meal, only half jokingly: "If I don't live
forever, I am going to be really pissed!" --Paul]


I was particularly disgusted with myself at the college level. I
felt swamped by my classes--especially my upper-level math classes--
and felt like I could not keep up with them or was not doing them
justice. Still, I managed to get good grades, and all of my
professors always assured me that I was doing fine. I always felt
like I was only getting a taste of each subject I took. And all
around me, I was surrounded by people who didn't care--they didn't
read the material, they stayed up the night before to write papers,
they skipped classes, spent little time studying, etc. Even though I
did the best I could do, my good grades and kind remarks by
professors didn't mean very much to me at all--I felt incredibly
mediocre.

[I fully understand this. I felt somewhat the same (swamped and not able to
learn things adequately) when I was in university, particularly in graduate
school when I knew how much more there was to learn and understand. The problem
here is that students are misled into thinking that they will have *mastered*
the body of work that they are taking by the time they graduate a four year
course of study. However, this is far from the truth. As you have correctly
observed, all that undergraduate courses give you is a "taste for" each of many
areas of study, a knowledge of what exists in the subject area and a few tools
and methods by which you can learn more deeply as and if you continue to work at
it. If you are truly interested, then you will spend the rest of your life
attempting to really master some particular part or parts of the subject matter
to which you were introduced in university or even some other subject matter
that you later realized is of even more interest. An undergraduate course is a
mere start on the road to true learning. Unfortunately, for those who are merely
there to get credentials for a job it is also the end of a very short learning
road.
It is unfortunate that you did not realize this and thus felt mediocre because
you thought that you were supposed to be able to really master all this
information in such a short time. Perhaps you will now be able to get rid of
such unnecessary and unrealistic feelings of inadequacy. --Paul]


So, I think I'm not worthy of being a student in university unless I
have a very structured plan.

[I think you are wrong here, but then being a university student is not really
the best way to learn, at least not once you know what there is to learn and how
to go about doing it. In fact, it has always been my opinion that the best time
to take a univesity type course would be *after* you have learned the subject
matter in great detail on your own. That is the time when you are most ready for
the overview that the professor will present and when you will be able to get
the most out of it.
Also remember that if you find yourself not really applying yourself to
something that you decided to do, then this is likely an indication that you
really did not want to do it in the first place, but instead simply thought that
you "ought to" do it and even ought to want to do it. There is a vast and
critical difference between actually wanting to do something and thinking that
one ought to do it. Everyone needs to do the following in this order:

1) Consider the purposes, details and real worth of what you like to do and
don't like to do. Then change your likes and dislikes to maximize their
contribution to your lifetime happiness.
2) Stop doing anything because you think that you ought to do it or not doing
anything because you think you ought not to do it.
3) Start doing only those things that you really like to do and not doing those
things that you do not really like to do. --Paul]


At least with teaching, in a sense, I'm
in the same "class" over and over again (i.e., teaching more or less
the same math concepts year after year), and I have a chance to
improve with each year that I teach. I remember thinking to myself
over and over again in college that I needed to retake this or that
class because I knew there was so much more to get out of it.

[I taught math too once and have taught many other subjects. However, in my
experience about 5-10 years is sufficient in any one subject (unless it would be
an advanced graduate level course) in order to master the subject and the
teaching of it (and I am not talking of the human relations part). After that
there is not much more of interest to do. With math at the high school level, I
expect that you already fully understand the material and I think the end point
of improving its teaching will come even sooner than with the undergraduate
level math courses that I taught. --Paul]


> [If you don't know what you would have studied, why would you
> have even considered continuing to study? **Kitty]

A number of my math professors encouraged to me to continue studying
mathematics because they thought I was doing well. I just didn't
have the confidence in myself that they seemed to have. Maybe I was
underestimating myself, but I don't think so!


> I got my bachelor's degree in
> mathematics (with minors in secondary education and Spanish), but I
> struggled with nearly all of my math courses (especially real and
> complex analysis!). My advisor and math professors encouraged me
to
> continue studying math at the graduate level, but I felt I was
> making little progress and just getting in over my head.
>
> [Why did you select mathematics? And the minors that you did?
**Kitty]

In high school, I was originally planning to go into medicine because
I had a strong math and science background and enjoyed working at a
nursing home. Then, when I took calculus as a senior, I felt more
challenged than I ever had before. I even dreamed about calculus.
My teacher, who was the youngest in the department, sometimes didn't
understand everything--and so a lot of the time, as a class, we had
to figure things out together, which made us more engaged with the
material. The whole class really had to work and communicate as a
team to learn everything, and everyone was teaching everyone else. I
really took on a sort of assistant teacher role in that class and
felt very comfortable with it. A lot of my classmates constantly
told me that I would be a good teacher. I liked so many of my other
classes and subjects, too, but I decided about halfway through the
school year that I wanted to spend the rest of my life working with
math while still being in a classroom setting--and so teaching seemed
like a natural fit for me.

[It is never a good idea at any age to try to decide that you want "to spend the
rest of [your] life" doing some particular thing. Instead you should first learn
how to think logically and deeply, and how to go about learning. After that you
should remain open to all new subjects the learning of which you think will lead
to increasing your lifetime happiness. --Paul]

[While I settled for nursing, rather than chose it, I enjoyed most of the
aspects of that career for the 13 years I was an RN. However, the subjects that
I was studying for furthering my education in nursing (chemistry in particular
at the time) were more interesting in themselves than for whatever connection
they had to nursing or even human health. Just because I had been a nurse for
those many years did not mean to me that this was the career area for my entire
life. I decided that I just didn't want to continue because considering another
20 or 30 years did not fill me with pleasurable thoughts/feelings. So my
learning efforts went off in a different direction - towards engineering in
which I studied and then obtained a BSME. The mechanical engineering work I did
was very interesting and challenging for the 16 years I did it. During that
time, however, I was also extremely interested in the philosophy of freedom,
psychology and health. So the path I took after meeting Paul is quite logical to
me - we two found the same areas of knowledge and understanding to be highly
valuable. And we are both open to new ideas in these areas and others that
increase the happiness of both of us.
When I think back on it, the picture of me (or anyone) doing virtually the same
thing for 30, 40 or more years is a very stifling image to me. I've had more
opportunities to learn, increase my knowledge of reality and actually be happy
than I'd ever have had if I'd remained a nurse, even if I had expanded that role
with more education and different employment positions beyond those that I had
had. **Kitty]


As for minoring in Spanish...I probably could have minored in
anything, but I've always liked languages. In middle school, we got
to take French, Chinese, and Spanish, and in high school, I took
Spanish for four years and as well as a semester of Latin. I loved
all of them and wanted to continue in one and chose Spanish because I
knew a lot of people in the U.S. spoke it, and I imagined that as a
teacher, I might have some Spanish-speaking students. (And I have!)

[Language training is generally useful and is also excellent for the mind. And
Latin being the root of so many European languages and still used in many
disciplines is particularly valuable. I have never regreted my two years of high
school Latin and five years of French. I only wish that I had understood the
future value of the Latin better at that time. --Paul]


> [At that time, if you could have spent your time doing anything
> physically possible (and supporting yourself was not a concern),
> what would you have been doing? **Kitty]

I probably would have done what I did--only taken fewer classes each
semester (rather than cramming in so many courses each semester in
order to graduate "on time") so that I could focus more fully on each
course.

[That is why being a part time student while working to support oneself is
probably the best way to learn. In essence, that is what I have been all my life
since I have been supporting myself ever since age 17. The only difference is
that because of the method of support and getting scholarships/fellowships, I
was able to be a full time student for several years while still supporting
myself.

However, once again your learning of those subjects did not need to end once you
graduated. In fact, your general understanding of mathematics, and likely your
effectiveness in teaching, would increase if you went back to those subjects and
now tried to understand them in the depth which you did not before. With the
Internet and availability of multiple texts, this is easier to do now than ever.
--Paul]


> [Move the time frame forward to now.... what is the answer to the
> same question? **Kitty]

Right now, I am doing what I really want to do--researching and
visiting schools to find a place where I can see myself grow as the
kind of math teacher that I want to be; however, substitute teaching
in the meantime in order to make money is not my cup of tea.

[Since you seem to be very people-oriented and substitute teaching does not
enable you to get to know and interact with your students with any depth, I can
understand that. However, I still think that you need to more fully understand
your need for others. --Paul]


Luckily, I will only do that for the rest of this school year. Next
year, I'll teach somewhere whether I've found the ideal school or
not. Then, I'd like to return to school once I've decided what I'd
most like to study in the realm of math education.

[Frankly, I think you will not likely be satisfied unless and until you return
to that course material you took in university (and with respect to which you
felt mediocre) and study it more fully until you are either convinced that you
do not like it, you think it is not relevant to your lifetime happiness, or you
have mastered it. --Paul]


> I was not
> disappointed to stop attending university when I graduated-being in
> college full-time was exhausting, as well, and I was eager for a
> change. But since I have been away, I have missed it more than I
> thought I would. So, yes, temporarily I have dismissed continuing
> on at university, but I imagine I will return at some point when I
> have some ideas of what I'd like to pursue.
>
> [What is it that you miss at university? **Kitty]

I most miss attending classes and listening to or participating in
(or both) discussions with professors. I liked spending hours at the
library. I liked having my work critiqued by others. That's what I
miss most of all. Once you're out of the university setting, no one
has time for you--obviously because no one is paid to have time for
you, and even if they are--like the various "teacher mentors" that I
had during my first two years of teaching in Chicago, they don't have
that much invested in you in the ways that teachers invest themselves
in their students. I knew when I left university that I still had a
lot to learn--as a prospective teacher and as a human being. I have
this same view of myself today.

[Ultimately, you and everyone needs to learn how to learn on your own. However,
most of what you listed above as necessary to your happiness is likely available
through the Internet. My bet is that there are math groups/forums of various
kinds, where you will find people to talk to and likely even people to critique
your work. If you can't find one, then form one. Hell, I might even join such a
group. I have been dabbling with regaining my mathematics knowledge and
abilities. As far as "still having a lot to learn", that will not ever change.
If you reach some point in life where you do not think that you still have a lot
to learn, then it will be time to terminate your life, since such thinking must
necessarily be irrational.
OTOH, the major problem with a viewpoint that you still have a lot to learn as a
teacher is that, under the teaching conditions within the current society, there
is very little of real importance with respect to teaching over which you have
any control. More than anything else, that is why I think that teaching at any
level less than university level would be extremely frustrating and ultimately
deadly to one's mind and spirit. --Paul]


> [Once you identify those item(s), consider how you can obtain
> that/those value(s) in other ways. **Kitty]

I have obtained some of these values via my correspondence with you
both on this Yahoo group. I appreciate your criticisms probably a
lot more than you realize. :) I set aside time to read various
topics of interest to me. I also hope to obtain more of these values
by finding a school and math department that wants to move in the
same direction as I do in terms of teaching math--including ongoing
professional development for teachers.

[The problem here is that all schooling aimed at children is so stifled, stunted
and distorted by state and federal regulations and requirements. Public
education types, amounts and qualities in the US (Canada and other countries
also) is essentially equivalent to the state of food and clothing availability
in the old Soviet Union. --Paul]

[I wouldn't suggest teaching in the public school system to any person because
of the enormity of government interference between the provider of the service
(teaching) and the client/customer (student and parents, the latter are included
because they ultimately pay the bills). There is still some modicum of available
choices in private educational facilities whose target audience is considered
children, but it is inverse to the degree that government funds are used. The
Internet is a medium that could be of greater value IMO then is currently used
and possibly with little government interference.

Similarly I wouldn't recommend most areas of health care as a career field in
current society. Government at the various levels in numerable agencies dictates
what a health provider can do and what a person seeking health services can
find. And because of this interference the cost of what is available is far more
than what would be charged without the thick layers of beauracracy.

This enormous interference by government in the transactions between providers
and clients (whether the service is education on some subject or
improvement/correction of personal health status - or many other areas) has
dramatically slowed progress and even reversed it in many ways. What
improvements have occured are in spite of government, not because of it.

So for a person who wants to really improve hir understanding in a knowledge
field and also initiate/improve delivery of a related product or service, my
recommendation is to stay as far away from government as possible. If not, the
situation is Faustian in its "selling of soul" to acquire (stolen) funding and
inevitable requirement to abide by agency dictates - resulting in one becoming
part of the entangling "system" itself. **Kitty]


As always, I look forward to your feedback.

~Emily Jackemeyer