Why is basic math so hard, yet algebra so easy?

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I've always had trouble with basic math, what they would consider "arithmetic" in days gone by I guess. You know, addition, subtraction, multiplication and division. Even when I was being homeschooled I still found it very difficult until my mom found a program that focused on one topic at a time and offered a visual, "hands on" approach to it. Letting one learn by doing and not expecting them to remember eight million different things at once. I took Temple Grandin's advice and did geometry for a while and then went on to algebra. I've always heard that algebra was very hard but when I did the algebra books, I found it insanely easy. I was allowed to use a calculator for the arithmetic problems that made up the "formula" (I still think that's a stupid term for something mathematical. Formula sounds like a term one would use in chemistry.) but would use my head to put everything together and get the answer. For someone who finds basic math so hard, why is algebra so easy? When I was a kid, I was a victim of the "self fulfilling prophesy" when it came to math because I was always hearing my parents and everyone else talk about how bad I was in it. I did not identify as being smart or intelligent about anything as a kid and had zero self confidence. But I STILL find basic math almost impossible, despite being good at algebra.

It may be that basic math requires a lot of memorization while Algebra requires logical thinking. There a lot of people in the world who find higher mathematics easier and loads more fun than basic math. Keep going with it; you may be one of those people who innately understands Calculus too--and if you do, you have a world of opportunities ahead of you.

That is why a lot of college math professors need calculators to do simple arithmetic.

That's what is like for me! 4 X 7 is much much harder for me than 4x -6y = 6y +4x

Complete opposite.. I can do basic arithmetic functions in large digits in my head but can't do Algebra with some one holding my hand the entire time. I don't find anything logical about algebra.. where as arithmetic is logical, consistent and rigid.

2+2 is always 4. Always.
2x+y could be anything, and I don't like that sort of flexibility.

I am not very good at any math in general.

This is the same for me, I've become way better in math starting from algebra. (Somtimes to the point of perfect scores!)

All math is hard.

I think I got the short end of the stick on that one.

I love geometry! I hate HATE calculus. Basic algebra is easy but advanced calculus gets hard for me. Some calculus is interesting infact what most people think is boring interests me. I don't deal with math on a regular basis but I guess if you do maths problems regularly you can get good at it.

Maths is a large, varied enough subject for people to have different strengths. I can do calculus in my sleep but give me a geometry question and I'll feel like crying.

Whatever form of maths it is though - practice really does make perfect. I can find myself able to do anything off my head after a couple of intensive sessions of doing certain types of questions over and over.

The thing which is often called "mathematics" is really at least four skills stuck together.

The first is the skill of being proficient at implementing algorithms by hand.

The second is the skill of devising efficient algorithms.

The third is the skill of guessing that certain statements are true.

The fourth is the skill of constructing logical arguments to show that certain statements are true.

The second, third and fourth skills are what mathematicians might call "real mathematics". The first skill does not have much to do with them. I study mathematics, and I am not very good at the first or second skills.

Back in my school days, I struggled mightily with math even though I was an honors student. Then, I had the shock of my life when I found I was failing basic math in Grade 12! At this point I had never had a mark below 75%. I spent hours upon hours studying it and came out with a respectable 82% only to be overwhelmed by the thought of doing Calculus in University. Turns out it was incredibly easy and I got an A+ without effort.

Looking back, it was because I was taught CONTEXT by my professors. Once I grasped the real world applications, it was a breeze. We learned about Quadratics, etc in high school but nobody stopped to say what they were and why they are useful to know. Once I knew why, everything fell into place.

I have the same problem. I struggle with algebra and stuff, but geometry is extremely easy for me.

I've always been very good at math, but with me my skill seems to go DOWN the higher of math I get. Arithmetic was WAY too easy for me, algebra still very easy, geometry slightly challenging, and calculus truly challenging. I think being unchallenged in school so long, especially in math, may have reduced my ability to truly learn new material.

One thing that's reversed over the years is story/real-world problems. I used to find those harder than pure math, but now if anything they're easier. Thinking of a possible real-world application (or visually as a graph if possible) often HELPS me understand how to do a problem.