Guidance in my quest for knowledge and understanding

[Wesley Chambers]

Hello Everyone,

I am a young college student that just realized how little of an education I received growing up and attending school in Southern Mississippi. I won't say that it is entirely the fault of my teachers, as soon as I realized I could graduate while barely passing Algebra one I did as little as possible. I feel extremely limited by my small understanding of any mathematical courses.I also feel a deep regret for wasting the time I could have utilized to expand my knowledge. I've taken several courses in college to try and expand my knowledge in these areas, but I feel that I cannot learn the things I want through the traditional channels in school. I end up struggling for hours at a time just to barely (and I mean barely) get a passing grade.

My hope is that someone here struggled to get a basic understanding of the insane amount of things that they learned in order to finally take an advanced math course and feel competent and comfortable. I am truly naive and ignorant to most of the things discussed in these forums, but I enjoy reading through and seeing debates and soaking up everything I can. I just finally created an account so that I could ask my question. My real question is what resources, other than just taking a college course, could I use to restart from the beginning and learn all the tools I will need to be able to get the most basic comprehension of any courses from Algebra up. I know that is a long way away down a very difficult path, but I feel that I am meant to understand more than I currently do. I really do yearn for an understanding of the universe and how and why things are the way they are. I am frustrated with the traditional education methods that I have encountered in college. Is there some studying method or book or anything really that can explain to me all the different formula's and ideas in mathematics while also explaining why they were created and their practical application?

Currently I struggle with almost every class that calls for me to remember any math beyond Algebra one. I truly feel that because of my wasted opportunity I am incapable of feeling competent in Math. I am not looking for a quick method that I can learn five years worth of wasted education, but personal stories of how they were able to get past the difficulty and found a happy adept understanding and thus a more fulfilled life in understanding. I hope that I don't sound too ignorant and that someone here can lend a hand.

Thank you for taking the time to read!

Wes

 

[Niflheim]

... You don't want a method to use to catch up on your education? You just want to read other people's sob stories?

Its that kind of attitude why you have this problem in the first place.

 

[Wesley Chambers]

Niflheim,
Well I do appreciate you responding I don't see how what you have said serves you or me in any kind of productive way. I wouldn't expect that kind of attitude as a response to someones first post on here. If you are being honest with yourself you have no idea what my overall attitude really is. You have a glimpse of my frustration. You cannot respond in a way that implies you have figured me out and have any merit. I do apologize if I didn't word my post in the correct manner to warrant a benevolent and helpful response. I didn't want to be too forward in my request in asking for help and I thought maybe if someone could relate their struggle maybe some information on how they were able to get past it would come out. You seem to be upset or frustrated and I'm glad that I could be here to help ease that a little bit with my post! If you read your response a couple of times I believe you will find that hopefully you probably would not open our conversation with that sentence straight to my face. I think in actuality your not this crass rude person that I've seen on my first impression. I'm sure you can be just as helpful and courteous as anyone else. Thank you though for being the first person from this community to respond to my post though! I thought it could be a positive experience that people equipped with more information than I am could give me a hand. I will ensure to word my posts in a manner that doesn't make it seem as if I am looking for sob stories.
Thanks

 

[QuantumCurt]

Up to a point, math is a very sequential subject. Knowledge of one class relies on prerequisite knowledge of previous classes. Algebra II is basically the same material from Algebra I for the most part, but it is extended to a more complex level. It assumes that one knows and is comfortable with the basic methods learned in algebra I. When one gets to college algebra, the same thing can be said. It's the same algebra, just with more complexity and the introduction of some new methods of solving equations and such. Trigonometry is a very different subject than algebra, but it still relies on the foundational knowledge of basic algebra for many things. Calculus is again very different from both algebra and trig, but it relies heavily on both as a part of the toolbox for doing calculus.

The only way to build this foundational knowledge is to do it over and over again. One learns algebra by doing algebra. There are many resources like Khan Academy that have a wide range of videos covering all of the topics contained in introductory mathematics all the way from 1+1=2, up to basic linear algebra and differential equations. You may find such resources to be helpful.

I think Niflheim misunderstood your post. I don't mean to speak for you, and correct me if I'm wrong, but I think you're simply trying to clarify that you're not here looking for "the quick fix" to learn algebra real quick and move on. Rather, you're looking for advice on how to approach algebra and how to approach the learning of mathematics in general, as in study methods, supplemental resources, materials, etc.

Where do your main issues in algebra arise? Do you have trouble with basic arithmetic properties? It's possible that a good review of pre-algebra topics will help a great deal. Khan Academy has many videos discussing all of these topics.

 

[Niflheim]

No, Wes made it very clear that he doesn't want ways to actually improve his education, only "personal stories of how they were able to get past the difficulty and found a happy adept understanding and thus a more fulfilled life in understanding."

Personal stories are not going to help you make up for your mistakes. Going out of your way to talk about how you wasted your education and feel so left behind and then go on to say that you DON'T WANT HELP, only personal stories of similar experiences, is just ridiculous in my opinion. I stand by my statement that that kind of attitude, of not wanting assistance on how to catch up is the kind of behavior that would lead one to not taking advantage of education in the first place.

 

[Astronuc]

Mathematics is more or less sequentially taught through high school. In university one branches out.

When one is accepted in university, the university staff assume one is prepared with the appropriate background/foundation with which to continue one's education through more advanced programs. If one does not have the required background, then one would find university courses difficult. Universities may have remedial math programs with which to catch up.

In high school (~40 years ago for me), the sequence was Algebra 1 (grade 9), Geometry and Trigonometry (grade 10), Algebra 2 (grade 11), and Analytical Geometry and Calculus (Grade 12).

These days, it goes something like:

Algebra 1 -

Chapter 1: Introduction to Algebra
Chapter 2: Integers and Rational Numbers
Chapter 3: Equations
Chapter 4: Inequalities
Chapter 5: Exponents and Polynomials
Chapter 6: Polynomials and Factoring
Chapter 7: Graphs and Linear Equations
Chapter 8: Systems of Equations
Chapter 9: Inequalities and Absolute Values
Chapter 10: Rational Expressions and Equations
Chapter 11: Radical Expressions and Equations
Chapter 12: Relations and Functions
Chapter 13: Quadratic Equations

Algebra 2 -

Chapter 1: Real Numbers, Algebra, and Problem Solving
Chapter 2: Equations and Inequalities
Chapter 3: Relations, Functions, and Graphs
Chapter 4: Systems of Equations and Problem Solving
Chapter 5: Polynomials and Polynomial Equations
Chapter 6: Rational Expressions and Equations
Chapter 7: Powers, Roots, and Complex Numbers
Chapter 8: Quadratic Equations
Chapter 9: Quadratic Functions and Transformations
Chapter 10: Equations of Second Degree
Chapter 11: Polynomial Functions
Chapter 12: Exponential and Logarithmic Functions
Chapter 13: Matrices and Determinants
Chapter 14: Sequences, Series, and Mathematical Induction
Chapter 15: Counting and Probability
Chapter 16: Statistics and Data Analysis
Chapter 17: Trigonometric Functions
Chapter 18: Trigonometric Identities and Equations

Ideally one uses a structured learning approach. The following pages might help. Of course, Khan videos would be helpful.

http://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/

http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

 

[Niflheim]

As a student in high school, I can say that while the Algebra curriculum Astronuc provided is somewhat accurate, it is drastically different nowadays, at least in grade levels.

I took Algebra 1 in 7th grade, Geometry in 8th, Algebra 2 in 9th, both Trig and precalc in 10th (I go to a high school that focuses on math and science, we were required to double up that year), and I will be set to take AP Calc 1 in 11th grade and AP Calc 2 in 12th. As I said, as my high school offers many advanced math courses I will also take AP Statistics and Linear Algebra as math electives somewhere along the way. If Wes has just started college, his high school experience should be somewhat similar.

As for the actual order of the Algebra curriculum, its about right with minor tweaks to what is covered in Algebra 1, nothing big. I cannot recommend Khan Academy enough for learning/reviewing algebra and similar level math classes.

 

[KingCrimson]

Well, I used to be terrible at mathematics when I was 13~14. Until I got to high school and learned calculus, I became amazing at mathematics, solving all the problem I encountered in my curriculum (ofcourse there were those extra curricular beasts that just toppled me down). I know what you're feeling, you probably are wondering "What If I am not intelligent enough?". If that's the case, worry not. I used to be way worse than you are now, scrapping an E in every maths test, but ended up being the first in Mathematics and Physics in my school and my governorate.

 

[QuantumCurt]

No, Wes made it very clear that he doesn't want ways to actually improve his education, only "personal stories of how they were able to get past the difficulty and found a happy adept understanding and thus a more fulfilled life in understanding."

Personal stories are not going to help you make up for your mistakes. Going out of your way to talk about how you wasted your education and feel so left behind and then go on to say that you DON'T WANT HELP, only personal stories of similar experiences, is just ridiculous in my opinion. I stand by my statement that that kind of attitude, of not wanting assistance on how to catch up is the kind of behavior that would lead one to not taking advantage of education in the first place.

Do you think you might be taking the OP's statement a bit too literally? The point was clarified here -

I didn't want to be too forward in my request in asking for help and I thought maybe if someone could relate their struggle maybe some information on how they were able to get past it would come out.

Thus, OP was asking for help, but did not want to come across as though they were here looking for the quick fix or the easy way out.

 

[Cruz Martinez]

Wes said he wasnt looking for a *quick* way, not that he wasnt looking for any help whatsoever. When I was reading his post it was clear to me that he meant he wanted to hear how people overcame these difficulties in understanding and achieved their goal.
If someone tells me how they overcame difficulties in something I am having difficulties myself with, that can help me, can't it?

 

[KingCrimson]

Go to Khanacademy, greatest teacher on youtube really. He starts from kindergarten mathematics all the way up to partial differentials. He's going to give you a real intuitive understanding of many topic in mathematics as he usually explains why things work. It is your duty, however, to find proof of what he says, that if he doesn't give you the proof already, and apply the ideas to multiple problems of multiple difficulties.

 

[MidgetDwarf]

As a student in high school, I can say that while the Algebra curriculum Astronuc provided is somewhat accurate, it is drastically different nowadays, at least in grade levels.

I took Algebra 1 in 7th grade, Geometry in 8th, Algebra 2 in 9th, both Trig and precalc in 10th (I go to a high school that focuses on math and science, we were required to double up that year), and I will be set to take AP Calc 1 in 11th grade and AP Calc 2 in 12th. As I said, as my high school offers many advanced math courses I will also take AP Statistics and Linear Algebra as math electives somewhere along the way. If Wes has just started college, his high school experience should be somewhat similar.As for the actual order of the Algebra curriculum, its about right with minor tweaks to what is covered in Algebra 1, nothing big. I cannot recommend Khan Academy enough for learning/reviewing algebra and similar level math classes.

I have viewed many of your post on this forum Niflheim. Try to be a bit more modest, I understand that you are currently a high school student, but the lack of humility is astounding. I am sure you would not act in a condensing and overbearing manner in real life.

To the OP. I dropped out of high school in 9th grade. I started with basic arithmetic at the local community college. I am now taking Calculus 3. Anything is possible if you invest time into it. I would suggest attending a local community college and take a math class there.

 

[QuantumCurt]

I also am a high school drop out, and started college in algebra 1. Now I've taken calculus 1, calculus 2, differential equations, and linear algebra. I'm now in calculus 3. A lot of students take some calculus in high school now, but it still isn't the norm by any means.

I work in the tutoring center at my school, and the students that did take it in high school often have to retake it in college due to not learning it well enough. I'm not convinced that taking it in high school is even a good thing in most cases. Students get rushed through everything because "they need to take Calc in high school" and ultimately end up going into more advanced math classes just to find out that they never learned how to do algebra well. The typical math curriculum for an average student does not involve taking calculus 1 and 2 in high school. Many (most) high school students complete algebra 2 and trig, or precalc in high school, and are then prepared to start calculus in college. You say that it's drastically different nowadays, Niflheim, and in your case that may be true. But for the majority it is much as Astronuc described.

 

[Niflheim]

So apparently I come across as a huge jerk, and looking back I did word some of my posts rather poorly, but please keep in mind that I am still trying to help the OP. You say that I am being condescending, and there you are lecturing me on how rude and overbearing I am, and that "you understand I am in high school," implying that being young is somehow an excuse for whatever mistakes I might make, and looking down on me because of it. That seems to be a textbook definition of condescending.

I gave my high school experiences because I thought that assuming the OP finished high school (which he implied he did: he talked about graduating with minimal effort put in) and because while I knew my experience was not the norm, to the best of my knowledge the majority of high school students go through classes relatively similar to mine. I see now that this is not true, but I wasn't trying to come across as superior or overbearing. I was trying to help with the best of my knowledge.

As for the OP's intent behind his initial post, I can't find anything that suggests that he was looking for these personal stories to glean knowledge from them, but in his second post he did make it more clear that he was trying to, and I should've interpreted that better. My bad.

Once again, I stand by my statement that asking directly for help is a better method for improving than asking for personal stories. I would appreciate it if anytime I hold an opinion different than yours or misinterpret one little sentence slightly you would just point out my error like QuantumCurt did, and not use personal attacks in place of such arguments.

 

[homeomorphic]

I think there is actually some value to "sob" stories. A lot of people are terrified of math, so they need encouragement. It seems like whenever I say what my degree was, more often than not, the response I get is, "oh math, I'm really bad at that."

So, here's a "sob" story. One of my friends in grad school had to start out with trigonometry in college when he was like 20 (I'm forgetting the details of the story, now, so this could be slightly off, but it was something like that). Now, he has a PhD in math. I don't know that he was ever that bad at math, although he claims he used to be really stupid. It could be that he just didn't make it that far and was a late bloomer. Doesn't necessarily mean that everyone who has trouble with math can do what he did, but I think some of them can.

As far as methods of learning, that's sort of an obsession of mine, but I never really had trouble with the basics of math, although I was lazy and kind of slow on tests in high school, so I didn't always get an A in very math class. So, for my part, I was mostly concerned with how to tackle the advanced stuff and retain it well, which is a slightly different ballgame. I have also tutored, so I've learned a bit more about how to get people through the basic stuff, but my main advice there is just to get a tutor because there's nothing like one on one instruction to spot the kinds of difficulties you might be having and how to overcome them.

For really basic stuff, which is what some people are missing, there are always JUMP math workbooks and Khan Academy (the exercises are far more important than the videos!).

As far as explaining why things were created and their practical application, a tutor might also be able to help with that, if you got the right one, but generally speaking, it's possible that could take you into deep waters, as far as the history of math goes. I don't really know all the details of how algebra was created, but it might be more historical and less mathematically insightful than you would hope. The ancient Greeks basically had some geometric form of algebra, which you can read about in Euclid's Elements, book II, but I don't think you'd find it terribly friendly. Then, some Arab guys took it further, but they were using words, rather than letters, like we do today. So, even in early Renaissance times, although there was algebra, people would tend to write formulas out in words, rather than algebraic equations as we know them today, until someone introduced letters as shorthand, so they could say A = pi r^2, instead of verbally saying the area inside a circle is pi times the radius squared. Also, practical applications weren't always the motivation. The ancient Greeks were really interested in geometry for its own sake, for example, although some of the initial inspiration undoubted came from stuff like surveying, and later on, stuff like the ancient Greek work on conics sections found applications in Newton's analysis of planetary motion and his law of gravity. A lot of applications are more like things that were used to figure some important thing out, rather than something that you're going to be able to use in your daily life.

 

[QuantumCurt]

Getting a tutor is an excellent idea. I've been working as a math tutor for the last two years, and I've seen a lot of students initially struggle with basic algebra, and end up finally having an "aha!" moment (or a series of) where math all of a sudden starts to make sense. A good tutor has a lot of different ways of explaining the same concepts. After working in my campus tutoring center for two years, I've come up with a lot of different ways of explaining various things in basic math, and I'm often able to help students see things in a way that makes sense to them. This is often the extra push that people need to really get something.

 

[symbolipoint]

Wesley Chambers,
Maybe tell the sequence of studies you did as precisely as you can, and how the instruction was delivered or what were the sources given or used. What were the results through each.
Does Mathematics give you more trouble than anything else?
How is your reading & writing level?
Has any Special Education professional practitioner checked you?

 

[CalcNerd]

Buy a used textbook with a solutions manual (and an REA book too) and do some problems. This method requires self-study and provides personal satisfaction of learning. This is where a used bookstore is nice, as it allows you to look over several texts and choose the most appropriate. Remember, the examples may look easy, but until you actually solve them, can you really understand the material ie don't buy a Calculus book until you master Algebra.

Signing up for a class from a local community college is a great way to learn and gain measurable knowledge that can be used to further your academic background if you desire to improve your credentials and work for some future degree or certification.

 

[Wesley Chambers]

I really appreciate all of your responses! Even the one that asked if I have been evaluated by a special education practioner. I have no doubt that I am an intelligent person. Not brilliant or anything amazing. In college I get mostly a's in every course except anything related to mathematics.
Khan academy has really helped me so far. I was able to do my homework by learning the basics as I went on Khan academy. I am learning that I really enjoy doing the homework when I understand it and my answers are right!

niflheim...I wanted advice... And you regurgitated your opinion of My post... and not even your opinion of how I could better myself. The overall point is... you had no reason to post here in the first place..you just wanted to smear your unwarranted throbbing opinion In our face lol. if you analyze every conversation you have like you have my post then you won't have very positive productive relationships. Just look at your posts from anyone else's perspective...maybe you will start responding to people as if you were actually in front of them.

 

[Cruz Martinez]

I wish you a lot of success in your efforts, Wes. Also don't be disencouraged from asking for help here, there are very many people on this forum who are more than willing to help others.