Some thoughts about self-education

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SUMMARY

This discussion centers on the challenges and benefits of self-education, particularly in fields like mathematics and physics. Participants highlight the inadequacies that can arise from relying solely on textbooks, as self-taught individuals often struggle to align their understanding with expert interpretations. The conversation emphasizes the necessity of a "control instance," such as formal education or peer discussions, to facilitate effective learning. Additionally, the importance of adapting learning methods to individual preferences is acknowledged, suggesting that a hybrid approach of self-study and formal classes may yield the best results.

PREREQUISITES
  • Understanding of self-directed learning principles
  • Familiarity with basic concepts in mathematics and physics
  • Knowledge of educational methodologies and learning styles
  • Awareness of the role of peer feedback in the learning process
NEXT STEPS
  • Explore effective self-study techniques for advanced mathematics
  • Research the role of peer discussions in enhancing understanding of complex subjects
  • Investigate various educational methodologies, including blended learning approaches
  • Learn about the impact of control mechanisms in educational settings
USEFUL FOR

Students, educators, and lifelong learners interested in optimizing their self-education strategies and understanding the dynamics of learning in mathematics and physics.

  • #31
Astronuc, #30
You were and are(maybe) a very unusual person. I cannot say that your frustrating teachers were right or wrong, but seemingly misunderstandings were happening from both first and second parties.

I really hope that, at least the music teacher gave your confiscated book back to you at the end of that class meeting.
 
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  • #32
Astronuc said:
... My class teacher told me that I was too far ahead of the rest of the class, and that I need to keep pace.
...
Do they teach this to teachers in teacher school?
"If you have a student who is too far advanced, do your utmost to hold them back."

hmmm..... This is kind of making me want to start a new thread: "What are your 'triggers'?"

per google AI; "A trigger is a stimulus that sets off a reaction, most commonly referring to something (a sound, sight, memory) that causes intense emotional distress, often linked to past trauma..."
 
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  • #33
symbolipoint said:
Astronuc, #30
You were and are(maybe) a very unusual person.
Unusual in the best ways. :smile:

I feel very fortunate that my small highschool had an advanced track in math. Without that I would have been far behind when I went to undergrad uni.
 
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  • #34
symbolipoint said:
I really hope that, at least the music teacher gave your confiscated book back to you at the end of that class meeting.
The music teacher gave my math workbook to my class teacher who then had a talk with me after class. I promised not to do math during music lessons. She recognized my ability at math and encouraged me. She also asked me to read books of fiction, which was a requirement for our English track, but I don't remember if I did. I explained that fiction didn't appeal to me, but that I rather read books on science, technolgy or history and geography.

At the end of the school year, I was put in a special academically able (AA) summer program in which we did higher level math, like matrix algebra. I did the AA program after 4th, 5th and 6th grade. During my secondary school program, 7th through 11th grade, I did a 6 week program at a local university, where we did three classes per day, usually 1.5 hours each, which were college level courses in various subjects, e.g., history, math, physics, computer programming. Between 11th and 12th grade, I attended a summer program funded by the National Science Foundation at the Colorado School of Mines, an 8-week program in electrical and nuclear engineering. One of the fellow students went on to Princeton and UC Berkeley, did some graduate work in cosmology, did experiments in cosmic microwave background (CMB), and eventually became head of the Physics Department at Caltech, among other achievements.
 
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  • #35
I'm self taught in piano but that's different. I learned about neutron stars by reading research papers -- much more interesting than black holes -- but never attempted to even skim the math. That's what peer review is for, yes?

My only mathematical talent was multidimensional geometry. I also have a natural ability at the game of golf -- applied 3D geometry. I never did much with it. why bother?

Some acquaintances from my grade school math class are now heads of science departments. I was in a blues band with the head of LIGO. He played the harmonica.
 
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  • #36
@Astronuc, your experience in school is not uncommon. I had a friend who completed all of high school math by eighth grade. The school had no intermediate programs like today's IB or AP courses, so they had to fund him to attend a local college so that by 12th grade, he had completed four years of undergraduate math.

In my case, I was nowhere near his accomplishments. I do recall the grade school structured classroom. In first grade, you get grouped into one of three reading classes and remain in that group as you meander through grade school. The teacher would schedule the reading groups: advanced, medium, and slow. Other courses like math, science and geography were structured around the three reading groups.

As one group read, the others did math or science. The other subjects were arranged in the same way, so that my group, group three, was always the last to learn. One time, I saw the kids doing long division, which looked really interesting, and I wanted to learn it, but I was told I had to wait until we got to that lesson.

To this day, I've never forgotten about that rebuke and how sad I felt about it. Once you were assigned a reading group, there was no means of advancing beyond the other students. We were the rearguard of learning, and we always felt left behind.

When sixth grade came around, my teacher encouraged me in science. My first report was on atomic energy ie basically structuring my project after an article in the Parade magazine, a popular Sunday paper insert. It featured striking images of a future powered by atomic energy.

In the closing days of sixth grade, my teacher met with each student and their parents. In my case, he told my mom I was college material, reading at an 8th-grade level. He gave me the remaining books we had to read for the elementary school curriculum and said, "Take these home and come back and tell me you read them." Huh?

He placed me on equal footing with the fast readers for middle school, breaking the spell of the slow-reading group. I am forever grateful for his encouragement. It changed my outlook on learning.

Basically, school is about grouping kids into smaller groups so that the teacher can juggle teaching all the required material for that grade. However, for slow readers, we might learn it in the next higher grade because we were the last to learn it.

Also, I think it had to do with resource management, where each class had a limited set of reading books, say about 12 for each book we needed to read. The fast group would get first crack, finishing in two weeks; then the middle group would get those books and maybe take a month; and finally the slow group would get those books, 2 months later, while behind the other students in all subjects.

This was in the late 1950s and early 1960s. As an aside, my mom wanted to improve my reading, so she had me read The Bobbsey Twins, a book series she had read in grade school.

In response, I started getting Scholastic Book Club books on Rocks and Minerals, Codes and Ciphers, Strangely Enough, and others to escape the curse of the Bobbsey Twins.

I had wanted to read Tom Swift, but our library didn't have them, or I didn't know where they were. The next best thing was the Childhood of Famous Americans series: Albert Einstein, Abraham Lincoln, Thomas Edison, and other interesting people.

and so it goes...
 
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  • #37
jedishrfu said:
I had wanted to read Tom Swift
Tom Swift Sr. or Tom Swift Jr.? :cool:

When I was in elementary school, my parents bought me some of the Tom Swift Jr. series which was more or less current at the time. Then when I got to junior high (what we called middle school in those days) I found some of the older series in the school library.
 
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  • #38
I don't remember which it was. I was in 3rd and 4th grade and titles like that didn't register.

——
@BillTre

It was Tom Swift Jr. I saw a reference to his electric rifle. Some covers had the The New Adventures of Tom Swift Jr
But the book title said Tom Swift and His Electric Rifle.
 
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  • #39
Astronuc said:
I also had my math workbook confiscated by a music teacher during music class, because I was supposed to be learning music, not doing math. I liked to do math while listening to music. My class teacher told me that I was too far ahead of the rest of the class, and that I need to keep pace.
I should indicate that it was a music lesson in 4th grade class. As I recall, the lesson was part of a music appreciation in which we listened to 20 pieces of classical music over several weeks, and about mid-year there was a test in which we had to identify each piece. I scored 100%.

I thought listening to classical music was a perfect opportunity to do math. :wink: :-p :biggrin:
 
  • #40
Astronuc said:
I should indicate that it was a music lesson in 4th grade class. As I recall, the lesson was part of a music appreciation in which we listened to 20 pieces of classical music over several weeks, and about mid-year there was a test in which we had to identify each piece. I scored 100%.

I thought listening to classical music was a perfect opportunity to do math. :wink: :-p :biggrin:
That part in bold is a reason why I said a few days ago that you are unusual. As for myself, I find no desire to listen to any music while I study anything (or almost and most frequently no desire); but I do drink coffee.

That other part where you re-quoted what yourself wrote, reminds me of a course in which I studied ahead, because I learned the material several years previously, and I used the course syllabus to do the studies and the assignments before they were reached on the class schedule. This seemed to be a little annoying for the teacher, but I did score fairly well and earned A in the course.
 
  • #41
As a high school student long ago in the US south our school offered no calculus, very inadequate algebra and geometry, and the local college ridiculed a request to enroll in a class there as a high school senior. There were no supplementary programs available, to my knowledge. So I amused myself by reading books in the college library stacks, some recommended in the one good book encountered in a “special” high school class: Principles of Mathematics, by Allendoerfer and Oakley. Unexpectedly admitted to Harvard, (via “geographical distribution”?) I placed into an honors calculus class, without the background possessed by my classmates from the northeast, based entirely on the self-acquired knowledge of Cantor’s theory of uncountable infinite sets. The interviewer summed up his sneering assessment: “at least you have some interest in mathematics”!
So self - learning apparently does demonstrate motivation, which some teachers value.
 
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  • #42
My favorite anecdote was while in middle school in Spanish class, I finished up some homework slipped it away.

I decided to draw from memory the Lost in Space robot, B9 and got out a blank sheet of paper. About five minutes before the end of class, the teacher surreptitiously walked by and scooped up the paper.

At the end of class, I sheepishly went to see her and asked if I could have my robot drawing back. She opened the paper saw the robot and handed it back, mildly shocked that it wasn't homework.

I learned a valuable lesson that day: never be too greedy in doing your homework and always finish up with a cool drawing.
 
  • #43
jedishrfu
I was studying & doing assignments ahead in part because of fear of being short on time. I had a part time or more job at that time, and you can also guess, I was motivated to learn (in part "relearn" too).
 
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  • #44
I think vela hit the nail on the head. Becoming educated, i.e. learning to understand something, is for me a long, difficult process requiring significant effort from the learner. A friend who teaches reading emphasizes to her students the need to “engage their thinking mind”.

One receives information from a source such as a book or lecture, then must turn it over and over in ones own mind and grapple with it at length. During this process it is very helpful, maybe essential, to have someone else, intelligent and/or knowledgable, to bounce ones thoughts off of, to help correct errors of comprehension.

In my experience it is also wonderfully enlightening at some point, maybe late in the process, to consult the original works of the genius who created the theory. I spent my whole professional career studying and using the Riemann - Roch theorem, (a formula for the vector dimension of the space of meromorphic functions on a closed connected surface, and having only given poles). I read, and listened to, many versions at every level of sophistication and abstractness, by all the modern experts. Still I never felt I actually understood it in simple, clear terms until late in my career I was asked to review a translation of Riemann’s own works, and read his version. It seemed suddenly that the scales fell from my eyes. I had similar experiences reading Euclid, Archimedes, Euler, Poincare', Gauss, Maxwell, and (in connection with a recent PF thread) Galois.
On the other hand, being almost entirely self taught in physics, even reading Einstein, Feynman, Born, Taylor/Wheeler, deBroglie, and Pauli did little to dent my lack of understanding.
 
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  • #45
There's a book on learning strategies called Make It Stick by Peter C. Brown, Henry L. Roediger III, and Mark A. McDaniel.

It distills decades of cognitive science into practical lessons about how people actually learn.

Many of its recommendations contradict what feels intuitive.

• Replace rereading with self-testing
• Space study sessions
• Mix problem types
• Explain ideas aloud or in writing
• Seek feedback
• Embrace difficulty as a signal of learning

https://www.amazon.com/dp/067472901...make it s&tag=pfamazon01-20&tag=pfamazon01-20
 

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