Self Doubt in Math

[TheSchoolofAthens]

Hello everyone. I am in college pursuing my associates in computer science. This degree requires an extensive amount of math, which can be intimidating but it is something I definitely want to do and am willing to learn. I've realized that I have self esteem issues when it comes to my performance in math. This isn't a problem in my other classes, for example, in theater I did a reenactment of a scene from Wolf of Wall Street. Certainly I was nervous to an extent, but I didn't doubt myself and say "you probably got it wrong" or "you probably will get it wrong." I ended up getting very good feedback from my professor who said it was amazing, and I was happy with my performance.

On the other side of the coin, I do not have such confidence in myself when it comes to solving math problems. I'm not even talking about physics or calculus since I haven't taken those courses yet, I'm referring to basic algebra. I will do the math, on paper or in the calculator - it doesn't matter - and I will doubt the answers that I get. In my head I will say "no, this doesn't look like the right answer, I must have gotten it wrong. I probably did."

For example, I just did a algebra problem: 2% of the human population has red hair. There are about 7,000,000,000 people in the world. How many people have red hair?

The very first answer I got was 140,000,000. I looked at this number in the calculator and thought "Ah, this can't be right! It doesn't look right, perhaps it is far too large of a quantity. I must have done something wrong." So I then went onto try other possible solutions - again basic algebra - only to get other answers that didn't look right. 

Of course 140,000,000 was the correct answer. But I was afraid to type it into the submission box on Khan Academy out of fear of getting it incorrect. I doubted my answers accuracy, and I was afraid to see what the result would be. I would greatly appreciate it if someone could take the time to help me out with my issues here, I don't know what else to call it other than self doubt and maybe self esteem issues. Please ask me the necessary questions, tell me what your thoughts are, and I will be happy to assist in anyway possible! Thank you an incredible amount! 

 

[shnugwa]

I myself struggled initially in the beginning semesters of my persuit for a degree in Engineering with some self-doubt in my mathematical ability. However, I had breezed through all mathematics courses in my public school education from Kindergarten up through 9th grade when I finally took geometry. I then had a slew of horrible teachers for Geometry, Pre-calculus, and AP Calculus. An authoritarian southern belle who wrote formulas on the board with no context or worked-through examples, writing up detentions for myself and others who dared question her methods of teaching, effeminate male blabbermouths who spent more time lecturing men on the proper treatment of women and delivering utterly creepy sensual jokes and performances every single class to entice giggles from the row of hot 16 year old girls that sat behind me, and emotionally insecure teachers who'd make a slew of mistakes sometimes pausing to cry while my dickish classmates actively plotted and schemed on how to best interrupt class in the "funniest" ways - these 3 years of mathematical misery almost killed my innate love of math from childhood. Up until that streak, it was all A's in math with no effort outside the classroom whatsoever. Slowly, my grades slipped into the B/C/D range in math only, whereas I maintained a consistent A/B average in the rest of my classes through high school.

 

Then, going to college, and really being in a similar mental situation as you, I thought I wasn't good at math anymore. I even failed and dropped my course on Statics, which is a heavily trigonometrical-based class on the analysis of systems in equilibrium. It sure felt miserable, and the very thought of feeling hopelessly lost on mere algebra is something that I can sympathize with and empathize with from my own conflict with advancing in math.

 

Please do elaborate on why it is that you believe you can't arrive at the correct answer. The problem you outlined is fairly straightforward, as merely multiplying 7,000,000,000 by 0.02 would yield the very answer you got by definition of 2%. Have you taken math classes before perusing your degree in public, private, or homeschooling environments? What were your experiences there?

I have some thoughts, but it'd be helpful to see deeper into the situation.

[TheSchoolofAthens]

I myself struggled initially in the beginning semesters of my persuit for a degree in Engineering with some self-doubt in my mathematical ability. However, I had breezed through all mathematics courses in my public school education from Kindergarten up through 9th grade when I finally took geometry. I then had a slew of horrible teachers for Geometry, Pre-calculus, and AP Calculus. An authoritarian southern belle who wrote formulas on the board with no context or worked-through examples, writing up detentions for myself and others who dared question her methods of teaching, effeminate male blabbermouths who spent more time lecturing men on the proper treatment of women and delivering utterly creepy sensual jokes and performances every single class to entice giggles from the row of hot 16 year old girls that sat behind me, and emotionally insecure teachers who'd make a slew of mistakes sometimes pausing to cry while my dickish classmates actively plotted and schemed on how to best interrupt class in the "funniest" ways - these 3 years of mathematical misery almost killed my innate love of math from childhood. Up until that streak, it was all A's in math with no effort outside the classroom whatsoever. Slowly, my grades slipped into the B/C/D range in math only, whereas I maintained a consistent A/B average in the rest of my classes through highschool.

 

Then, going to college, and really being in a similar mental situation as you, I thought I wasn't good at math anymore. I even failed and dropped my course on Statics, which is a heavily trigonometrically-based class on the analysis of systems in equillibrium. It sure felt miserable, and the very thought of feeling hopelessly lost on mere algebra is something that I can sympathize with and empathize with from my own conflict with advancing in math.

 

Please do elaborate on why it is that you believe you can't arrive at the correct answer. The problem you outlined is fairly straightforward, as merely multiplying 7,000,000,000 by 0.02 would yield the very answer you got by definition of 2%. Have you taken math classes before persuing your degree in public, private, or homeschooling environments? What were your experiences there?

I have some thoughts, but it'd be helpful to see depper into the situation.

Thank you for the in depth response and questions! I had a very similar background to you. I understood math well all the way up to 5th grade, in 6th grade I took an honors class even. In 7th grade, enrolled in honors again, I dropped to a lower level math course because I resented the math class I was in. The teacher was not helpful, I disliked her methods, if I recall correctly her voice sounded monotone, emotionless, and harsh. I would say that from that point on, I didn't like taking the more challenging classes in public school anymore because I did not like the way things were taught, the often bad teachers, or decent teachers and bad classmates, or the worst case sennario of a bad teacher and bad classmates. 

 

Even with the regular math courses, starting with sophomore year of high school going into my senior year, I resented my math courses. Again, I did not like the quality or methods. 

 

But what I think is important is that when I didn't understand a concept or how to solve a problem in my homework, and when I told my mom that I couldn't do my homework because I didn't understand it, she told me to ask my older brother (who was always in advanced classes) for help. My brother didn't mind, he would sometimes remind me that he could help. But I did not enjoy his help. I remember feeling very tense whenever he would help because if I did not understand his examples he would soon get frustrated and raise his voice. This made me nervous of course, to the point where I wouldn't even want to ask him for help. So I usually wouldn't ask him at all! Then on occasion, if it was absolutely necessary, and if my mom had told me to, I would ask him for help, regretfully and with a tense feeling.

 

My best answer for myself is that I am afraid of the humiliating feeling that comes from being scolded for being wrong.

[BD91]

I've been recently going back through mathematics on my own to increase my skills in making DSP algorithms for the software I write.

 

I barely passed the low-level math courses to drag myself through high school without repeating a grade. However, this time around I'm working out of Morris Kline's Mathematics for the Nonmathematician and it's been really great for in understanding mathematical concepts. Maybe it's because I'm a bit of a history dork, but I find that by understanding where and why certain mathematical concepts arose they're much easier to grasp and by having names and historical events to tie to each concept, they're easier to learn in that way as well.

 

Just my 2 cents.

[Pepin]

I find that math theories are easy to understand when you look at proofs, because then you can see the arguments being made. A big issue with math is that it is easy to confuse algebra and trig with a lot of concepts. Like when I was learning calculus in college, I kept missing the point of the concept because I was focused so much on the algebra and trig.

 

A major part of the problem is that 95% of the time you spend solving a problem will be doing complex algebra and looking for trig identities, while you'll only spend about 5% of the time using the actual concept you are being tested on. It gives the false impression that the algebra and the trig is what you are being tested on. When I was in calc II the hardest part about the problems was the extremely difficult algebra and the extensive knowledge of trig identities I needed, not so much the concept. If I were to get a problem wrong, it would be because I messed up somewhere within the 45 lines of algebra, not because I didn't know what I was doing.

 

I think that a lot of educators have realized this and have moved towards more of a conceptual framework. Khan academy for instance clearly defines the concept and will always point out all of the parts which are just tools used to solve a problem and not the actual concept. At least at my school, a lot of teachers were giving problems that tested only for the concept by making all of the algebra pretty easy.

[TheSchoolofAthens]

I've been recently going back through mathematics on my own to increase my skills in making DSP algorithms for the software I write.

 

I barely passed the low-level math courses to drag myself through high school without repeating a grade. However, this time around I'm working out of Morris Kline's Mathematics for the Nonmathematician and it's been really great for in understanding mathematical concepts. Maybe it's because I'm a bit of a history dork, but I find that by understanding where and why certain mathematical concepts arose they're much easier to grasp and by having names and historical events to tie to each concept, they're easier to learn in that way as well.

 

Just my 2 cents.

I have actually considered getting a book on the history of math because I've been interested in knowing the whole who, what, when, where, why, and how. I will look into that book.

 

I find that math theories are easy to understand when you look at proofs, because then you can see the arguments being made. A big issue with math is that it is easy to confuse algebra and trig with a lot of concepts. Like when I was learning calculus in college, I kept missing the point of the concept because I was focused so much on the algebra and trig.

 

A major part of the problem is that 95% of the time you spend solving a problem will be doing complex algebra and looking for trig identities, while you'll only spend about 5% of the time using the actual concept you are being tested on. It gives the false impression that the algebra and the trig is what you are being tested on. When I was in calc II the hardest part about the problems was the extremely difficult algebra and the extensive knowledge of trig identities I needed, not so much the concept. If I were to get a problem wrong, it would be because I messed up somewhere within the 45 lines of algebra, not because I didn't know what I was doing.

 

I think that a lot of educators have realized this and have moved towards more of a conceptual framework. Khan academy for instance clearly defines the concept and will always point out all of the parts which are just tools used to solve a problem and not the actual concept. At least at my school, a lot of teachers were giving problems that tested only for the concept by making all of the algebra pretty easy.

I love Khan Academy, I'm about to get on it right now! Anyways you learned to look at the bigger picture instead of just focusing on the algebra and trig? I'd appreciate the advice!