My Journey With Mathematics

MarkFL said:
I've been actively engaged with mathematics, first as a student, and then on my own just exploring topics I found interesting, and then within the online math communities, for well over 25 years. But, I don't have to look far within the online math help communities to find people far more talented and knowledgeable than I am. I would get discouraged very quickly if I tried to hold myself up to others, so I don't do that. I simply admire the insightful posts I see, and try to learn from them as I go.

Hopefully, as you journey through your textbooks, you begin to find that the topics build on themselves so that you don't forget what came before. And as you progress, you continually fortify the previous lessons learned. For example, studying trigonometry will really strengthen the concepts you learned in algebra, and calculus will fortify what you learned in trig and algebra.
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As I recall, in NYC public schools, the progression of math courses is set up this way (elementary school through high school):

Arithmetic
Prealgebra
Algebra 1
Algebra 2
Geometry
Trigonometry
Precalculus
Calculus 1

Note: Not all public high schools introduce calculus 1 in their curriculum to seniors. Modified students are not required to learn math beyond prealgebra.

Keep in mind that I was placed in modified classes in high school. You see, I also did not graduate from middle school. I was severely abused at I.S. 223. My parents took me out of Montauk Junior High School aka I.S. 223. I was then placed at Maimonides School in Brooklyn for students with academic challenges.

At Maimonides, I was taken through the "essentials" of grades 6 to 10 in just two years. The plan was to prepare me for grades 11 and 12. In September 1982, I returned to regular public high school (FDR HIGH SCHOOL) with a so-so academic background.

The FDR academic counselor at the time informed my parents that in terms of educational background, I was not ready for regular classes. So, in conclusion, I was placed in a modified program leading to Modified State Exams (not regents) for graduation. I am not making excuses for my weakness in mathematics.

Think about this: I passed precalculus at Lehman College with an A minus. I took precalculus (MA172) as an elective course. Considering my weak academic background, I managed to earn a B.A. and 2 two-year degrees. Not bad, right?
 
MarkFL said:
Exactly...but if I were to start running, I would be happy that I ran a little faster today than I did yesterday. I wouldn't worry that I would never be able to run as fast as Usain. :)
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...but Usain has unfair advantage: he BOLTs down the track...
Wonder why he hasn't been nicknamed Lightning Bolt...
 
harpazo said:
I have "playing" with math textbooks for years. I came to the following realization (because it cannot be any other way).

1. I cannot retain information for too long. I review, say, chapters 1 and 2 in any given textbook but by the time I get to chapter 3, chapters 1 and 2 slowly begin to disappear from memory.

2. No matter how many questions I answer or how much time I dedicate to review material learned long ago, I will NEVER be like MarkFL or pka or Dr. Peterson and the rest of the truly gifted mathematicians here and in other forums.

3. Posting too many questions in one day leads to more confusion and frustration. How many questions should be posted per week? One? Two? Three? How about one per day?

4. Math is a hobby for me. However, I often forget that mathematics is not going to land me a great teaching career or a scientist job at NASA, or a bridge engineer position, etc.

5. This math site and others like it has taught me humility. Before joining online math groups and sites, I actually convinced myself that mathematics was truly a God given talent and/or skill when in actuality I know less than the worst student in a public school setting.

What do you say?
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1. I cannot retain information for too long. I review, say, chapters 1 and 2 in any given textbook but by the time I get to chapter 3, chapters 1 and 2 slowly begin to disappear from memory.

I have the same problem - but following routine works for me:

  1. Summarize chapter (1) in no more than 10 sentences or bullet-points.

  2. While studying chapter (2), review the summary of chapter (1) before starting to work on chapter (2) - every time - till I can clearly remember the summary without looking at it. To avoid cheating myself, I challenge myself to write the summary again - once a week.

  3. Summarize chapter (2) in no more than 10 sentences or bullet-points

  4. While studying chapter (3), review the summary of chapters (1&2) before starting to work on chapter (3) - every time - till I can clearly remember the summary without looking at it.

  5. By the way, this is how I memorize poetry ....
 
Subhotosh Khan said:
1. I cannot retain information for too long. I review, say, chapters 1 and 2 in any given textbook but by the time I get to chapter 3, chapters 1 and 2 slowly begin to disappear from memory.

I have the same problem - but following routine works for me:

  1. Summarize chapter (1) in no more than 10 sentences or bullet-points.

  2. While studying chapter (2), review the summary of chapter (1) before starting to work on chapter (2) - every time - till I can clearly remember the summary without looking at it. To avoid cheating myself, I challenge myself to write the summary again - once a week.

  3. Summarize chapter (2) in no more than 10 sentences or bullet-points

  4. While studying chapter (3), review the summary of chapters (1&2) before starting to work on chapter (3) - every time - till I can clearly remember the summary without looking at it.

  5. By the way, this is how I memorize poetry ....
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Thank you.
 
harpazo said:
As I recall, in NYC public schools, the progression of math courses is set up this way (elementary school through high school):

Arithmetic
Prealgebra
Algebra 1
Algebra 2
Geometry
Trigonometry
Precalculus
Calculus 1
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I remember it as
Arithmetic
Prealgebra
Algebra
Geometry
Trigonometry
Precalculus
Calculus 1

However they changed it all and I do not know the new set up.
NYC has an excellent school system WHEN compared to the school systems around the US.
 
Jomo said:
I remember it as
Arithmetic
Prealgebra
Algebra
Geometry
Trigonometry
Precalculus
Calculus 1

However they changed it all and I do not know the new set up.
NYC has an excellent school system WHEN compared to the school systems around the US.
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NYC public schools are a joke in poor taste.
 
Actually, the public school system in USA is top class (with room for improvement). I have been exposed to several school systems - internationally - and I feel the school system in USA is topclass.

However, the parents (or guardians) of the students are different issue. In summer time, I see the parents are more concerned about their vacation plan - than their off-spring's study plan.

You'll produce what you honor.......
 
Subhotosh Khan said:
... the public school system in USA is top class (with room for improvement) ...
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I agree with that.

For years, education in the USA has consistently ranked around 30th place, among developed countries.

?
 
Otis said:
I agree with that.

For years, education in the USA has consistently ranked around 30th place, among developed countries.

?
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Yes, in the USA. I am talking about NYC public schools. I worked as a sub teacher for 8 years. I know how the public school system works. I am a victim of the NYC public school system.

Here are just a few problems:

1. Social promotion in grades k-12.

2. Teachers sleeping with students for better grades.

3. Hiring out of subject teachers.

4. Never enough funds for books, chairs, chalk, etc.

5. Teaching the test in place of teaching to learn.

After earning my high school diploma in 1984, I took the NYPD test in 1985. I scored a miserable 58 percent. It was at that moment in time when I realized a sad truth. What truth? I was yet ANOTHER victim of the NYC public schools. I had a diploma that I simply did not deserve. I can go on and on. I worked for DOE.
 
harpazo said:
5. Teaching the test in place of teaching to learn.
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IMHO...
I admit that I haven't spent any time with the DOE but my impression, from the many teachers I've been near (as well as my own experience teaching HS), is that this is forced on the teachers.. (Of course there are those that don't teach well but teaching salaries are so low that most teachers don't teach for the money.) Over the years we've had programs like "No Child Left Behind" and the "New Math" etc that have essentially crippled teachers' ability to teach properly by restricting them to teach to the test. Most teachers have to teach to the test so that the students were able to keep up with the tests. My solution to this is to get the idiots that help the government fired and get someone that has actually taught in secondary schools to come up with education policy.

College teachers can be a different story. (I've taught there also.)

-Dan
 
topsquark said:
IMHO...
I admit that I haven't spent any time with the DOE but my impression, from the many teachers I've been near (as well as my own experience teaching HS), is that this is forced on the teachers.. (Of course there are those that don't teach well but teaching salaries are so low that most teachers don't teach for the money.) Over the years we've had programs like "No Child Left Behind" and the "New Math" etc that have essentially crippled teachers' ability to teach properly by restricting them to teach to the test. Most teachers have to teach to the test so that the students were able to keep up with the tests. My solution to this is to get the idiots that help the government fired and get someone that has actually taught in secondary schools to come up with education policy.

College teachers can be a different story. (I've taught there also.)

-Dan
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What's it like to teach at the college level?
 
I have mostly taught Intro Physics (Calculus and non-Calculus) and College Algebra. Aside from feeling I was like a kid in a candy store (I really like teaching) it was frustrating. One major problem of the secondary school system in the US is that the teachers don't (or don't have the time to) teach critical thinking. What I see is incoming Freshmen that only seem to know how to stare at a problem that they are unsure of, hoping for inspiration.

Much common sense has to be taught first. I tell them: Look at the problem. Usually textbooks (and mine did) list problems that come under a section heading (such as Ch1.1, etc.). So take a look at that section in the text! You'd be amazed how much that alone helps them. Another tip is to draw a diagram. None of this should need to be emphasized for College level students. (Especially if they've been paying attention in class.)

As far as the rest the critical thinking is probably normal to any other Freshman students in College world-wide so I don't worry about it.

-Dan
 
topsquark said:
I have mostly taught Intro Physics (Calculus and non-Calculus) and College Algebra. Aside from feeling I was like a kid in a candy store (I really like teaching) it was frustrating. One major problem of the secondary school system in the US is that the teachers don't (or don't have the time to) teach critical thinking. What I see is incoming Freshmen that only seem to know how to stare at a problem that they are unsure of, hoping for inspiration.

Much common sense has to be taught first. I tell them: Look at the problem. Usually textbooks (and mine did) list problems that come under a section heading (such as Ch1.1, etc.). So take a look at that section in the text! You'd be amazed how much that alone helps them. Another tip is to draw a diagram. None of this should need to be emphasized for College level students. (Especially if they've been paying attention in class.)

As far as the rest the critical thinking is probably normal to any other Freshman students in College world-wide so I don't worry about it.

-Dan
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I teach basic engineering - statics, dynamics, thermodynamics, etc.

I ask my students to work through the example problems worked out in the book and assign some of those (most of the time all of those) as HW. Frustrating part is that most of the students will just copy the solution without thinking.

Time available in the class-room is another thing. I was taught, in my school days, exactly the same material. However, I was taught that material spanning two semesters and we had class everyday (six days a week) - instead of one semester and two classes per week.
 
harpazo said:
Honestly, [sexual abuse of minors at the hands of teachers] is a disgrace ...
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You're absolutely right, and I apologize for posting the crass pun. I had wanted to inject a little levity into the discussion, and sometimes I can't recognize bad judgement.

?
 
Romsek said:
*cough* given a reference in the last couple of posts I'm glad you clarified that! :D
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I did actually run into a problem at one of the colleges I taught at. I had a minor crush on one of my students. She even took another class from me because she liked the way I teach. However, she had a husband and after meeting the guy I liked him, too. (Not as much as her! Don't get any ideas.) I decided to just let the fledgling friendship end. It was easier on all of us that way. I doubt she ever knew.

It does happen.

-Dan
 
topsquark said:
I did actually run into a problem at one of the colleges I taught at. I had a minor crush on one of my students. She even took another class from me because she liked the way I teach. However, she had a husband and after meeting the guy I liked him, too. (Not as much as her! Don't get any ideas.) I decided to just let the fledgling friendship end. It was easier on all of us that way. I doubt she ever knew.

It does happen.

-Dan
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As a sub teacher for 8 years, I never came across a student crush or anything close to a crush. Of course, I substituted in grades k-12. However, we have all read of cases involving student-teacher relationships in high school and in extreme cases middle school. It does happen but as adults we have to be in complete control of our emotions.
 
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