What Blocks us from Learning Math?

Math and the Past.

As a college math teacher I have been experiencing an interesting phenomena.  Many times students who are taught a simple concept or a rule that they actually already learned in the past (the rule for adding two fractions for example) do not learn the concept fully even though it is being repeated, drilled and re-taught many times.  On the other hand, children who were never taught the concept learn it quickly.  "What is the reason for this?", you may ask.  I believe that often the reason for the problem lies in past experience of students.  Once in a while a college  student would share with me a story about his past hurt experience in math, either in elementary school, middle school, or high school.  For example, Once I taught a College Algebra student who actually was successful  in learning the new concepts that we studied in the class, but failed in the areas that she was familiar with.   At the final exam that took place in a large auditorium the student froze and did was not able to complete the test and so I waited for her after everyone else left.   After some time she came to me and said that she had a past memory flash back in her mind.

 "I am back in first grade, my first class.  The teacher explained  some facts about numbers and every one seemed to understand except me.  I felt that there must me something awfully wrong with my mind as far as learning math is concerned.  I did not realize that all the other children learning something in kindergarten that I never did.  From that day on, I was never able to learn math.  My mind was closed"

Many times I go to a party or a gathering and someone asks about my profession, the answer "mathematician" , a typical response would be "Oh, I was never good at math".  Often, when a student in my class solves a math problem successfully, rather than feeling good about it, a typical response is "Oh, that was too easy" (The hidden thought behind the response is something like "Since I am not good at math and I solved the problem, it must have been easy"

The following paragraphs are responses that students wrote from their own experiences:

This is in response to your posting about learning about math:  I think that lack of confidence is something that often blocks students from learning, and not just with math. It isn't necessarily a lack of their ability that holds them back, rather it is a lack of confidence in who they are.  Since we were little kids, it hasn't been "cool" to be smart, therefore, lots of kids who know the answer wont raise their hand "too" quickly, or even at all.  This doesn't concern just answers to problems or questions presented by the teacher.  It could be a feeling of excitement and joy that they experience because they enjoy what they are learning, or the fact that they are learning it at all, which they repress because it simply isn't cool to be excited about learning.  I see it all the time in classes, the little smirks and raised eye-brows that pass from one student to another when a professor is excited about what they are sharing with the class. The look that says, "Woah, this guy/girl is such a loser".  Well, i have news for all those with raised eye-brows or a snobbish smirk.  The only losers those who hide what they are and what they feel; for fear of others perception.

After reading the "Leaning Math Experiences" I have to say I can relate to the  girl who had trouble in kindergarten.  I used to think that I was bad at Math and had a  very closed mind towards it.  "I don't understand and will never will!!" used to be my  motto.  I remember having a hard time remembering my table of contents in 4th grade and  everybody else in the class knew it but me.  I felt left out and not good at all.  In sixth  grade though I had this fabulous teacher, Ms. A.  She knew how negative I was about Math and how stubborn I was in repeating myself that I was a math illiterate.  She was an awesome teacher, because she taught her class in a fun way, through games, discussions, races anything that would keep us on our feet.  I remember liking math much more in 6h grade because she taught it in a nice fun way.  She also taught other courses like history and reading which surprisingly enough I remember because of her class.  So 7th grade came along and we had the hardest and meanest teacher you could ever face in high school, Mrs. Acuna.  I remember entering her class being so scared of the rumors upperclassmen had given us.  It wasn't a very pleasant class because we were all scared of her.  Anyway, the I Id' grade is when everything changed around.  I wasn't really doing very well my math class; it was the only course I was having problems with.  So my mom  said that if I wanted a tutor then she'd get me one.  With this tutor I gained a lot of confidence in myself, I learned new shortcuts, why you do things this way and not that way.  Since it was a one to one class then I could ask any question without worrying about anyone laughing at me or thinking I was stupid.  I learned a lot, but I learned that it was just all a matter of self-confidence and being able to continue with the problem and work you way around it.  Then in 12d' grade I was accepted in the AP Calc class.

All throughout elementary school I always felt that I was horrible at math.  I would try so hard, but my teachers would give me no motivation, at least not the type of motivation and encouragement that I really needed.  I felt like all the other students in the class were so much smarter than me, and that I would never be able to reach their level of understanding.  So i always just sat back and let those smart kids lead the class, and I tried to follow in their footsteps. Then when i got into high school, I had an excellent math teacher for geometry. I really enjoyed the class and I felt like, for the first time, I was actually learning something.   This temporary feeling of accomplishment was shattered when I was a senior in high school. I was put into a hard level math course, it was some form of pre-calc.  I had been doing so well previously that my teacher thought I would be ready for a more challenging course.  Well i hated my teacher, she went way too fast for me. My frustration completely built up over the year.  I lost all of my confidence in math, and I feel like I will never get it  back. I think that my lack of confidence is effecting me in this class,  although I am slightly overcoming it.

I remember having trouble with math from day one. I could never understand WHY!..Why I just couldn't seem to "get it". Everyone else around me in class understood math. On top of that my teachers could never hide their frustration with me, nor could my Father who is an engineer, and whose math skills are abundant! i have to be honest and say I'm not quite at the point of letting myself feel confident in math. That seems incredibly foreign to me. I know letting go of this fear will afford me greater ease, and allow me to have fun with math. It is so easy to say and write that last sentence, it is the act of allowing myself to feel free in math that is the difficult task. I'll get there, it just might take some time.

I remember being in kindergarten and my teacher teaching my class about numbers.  She would put two blocks in her hand and ask us, "How many blocks do I have in my hand?".  I remember the answers would vary as some us didn't know what numbers meant.  One day she opened up her hands and asked us, "How many elephants do I have in my hands?"  I remember being completely clue less and thought that I was dumb because I couldn't see any elephants in her hand.  All the other kids were  yelling out numbers,  so I figured they were seeing something I didn't.  I was trying to be smart so I too started yelling out numbers.  I remember the numbers ranging from 1 to 4 zillion.  I hate to admit that the 4 zillion was one of my guesses.  Finally, after about five minutes of us guessing, she tells us, "I have no elephants in my hand.  I have zero elephants in my hand".  I think that was my first "aha" experience, as it dawned on me that having no elephants in her hand represented the number zero, which
before had no meaning.

This was written by the same student at another time:

I've never actually been truly scared of math, however I have found it to
 be frustrating from time to time.  By taking this class I have gained self-
 confidence that I didn't feel in the beginning and I really am having fun!
 At first it seemed like it would take me days to solve what seemed to be a
 simple math problem, but as time goes on the amount of time it is taking
 me to solve these problems has become shorter and shorter.  I no longer
 carry on my shoulders that anxious, I have to get it now, feeling that I
 once had.  With self-confidence I know that I will solve the problem and it
 doesn't matter if it's right this minute, tomorrow, or even the next day.  I
 know that it will happen, I just need to relax.

To sum it up:

Math can be hard (negative), math can be simple (positive), math can be
frustrating (negative), and math can be fun (positive)!  It all equals out in
the end!  One thing for sure - math is only as SCARY as you make it!