In the framework of tutoring at a community college (Remedial Math to Differential Equations) and teaching College Algebra and Physics at a Liberal Arts College. Most of my interactions are with people who think they can not do math or where not made to do math. My philosophy is that it is time spent working on problems, the use of that time that make the difference. I also distinguish between arithmetic and mathematics. Arithmetic you can buy a $15 calculator that can do for you, mathematics is the language and patterns we use arithmetic in.
I tell my students, math is hard.
I have a t-shirt that says "math is hard, so is life, get over it." I wear that occasionally in class.
I also tell the story of why I think math is "easier" for me.
I had older aunts and uncles. My Uncle John taught me the times tables, but not memorizing he said if you had 3+3 that is adding 3 twice, this is the same as 2 times three. In kindergarten class we were counting and I recited this like a parrot. The teacher noticed and complimented me on my math. I liked the pat on the back, so every time math came up I tried hard. I put more time into it. And I put my time into when I was young. I exercised the muscle often, in my free time. In doing that the progression in mathematics was "easier" for me. But if we add up the time and effort spent studying and learning it wasn't "easier" I just put that time in at a different place in my life and liked it.
I explain to my students that we are learning algebra. This is a language. A language that takes the idea of counting and removes it from the object we were counting and looks at the pattern of quantity. When you learn a language you can think in a language. The goal of algebra is that you have the language of quantity as part of your skill set.
If you think about how you learn language, you spend the first 7 to 8 years of your life learning your native language in bits and pieces. Imitating the words, phrases and sentences around you. Learning how to attach them to objects, actions, things you want, things that don't exist yet. By the time you are in elementary school you begin to study the language itself and how you can use it to express more. This is hard, it takes lots of work and practice, but we do it early and it surrounds us, so we do it. With this skill we can now rap, sing, speak, debate, question, write poetry, write technical manuals, fiction, document life and so on.
Math is similar, but we already have language and we are adding to the tool set, so we borrow some of the knowledge from spoken language and start learning this new language. For some parts of it we are like an infant repeating sounds and trying to attach them to objects. This frustrates our older selves, that do not expect to be infant like in learning.
This is the hard part:
Mathematics talks about the pattern of quantity, but quantity does not directly exist. The number three is a noun, but I can not give you a three, I can only give you a three of something. This abstraction we have to form a place for in our thoughts.
This is the hard part.
The big secret is everything is hard at some point in learning it, it is new and different and there is a risk. Recognizing that, analyzing the risk, understanding our feelings and managing them is a skill that work for any part of life that is hard.
And with any skill practice, making mistakes, correcting mistakes and learning from the mistakes is part of making that particular skill less hard.
I have a friend that uses a video on juggling. Juggling is hard. But you can watch a video on juggling. Now you know how to juggle. You still need to practice the skill, make the mistakes and correct them. The practice for some will be easier than others, but this is about you not them. Practice.
Juggling 3 Balls
I also give the students these documents with the syllabus:
Math Myths
I talk honestly about the parts of mathematics I found easy. I talk about the parts I found hard, and how I got past the harder parts.
And sometimes I found things other people thought were really hard easy - Tensor Calc, why because I have developed more geometrical thinking by the time I took it and it made sense in the framework of what I was studying.
Compared to statistics, I had a philosophical bias against the idea of chance. To get past that I had to do the entry level problem more often, I had to develop a sense of random when I was studying it.
I think being human and explaining mathematics as a human invention we use to model and make predictions is a better reference point also then the philosophy that mathematics is the truth. By making it a human invention, looking at the rise from 1 a few, many, too much, to counting, to the creation of sets as human answers to the questions they had at the time a great framing tool in the discussion.
In the end I tell them it comes down to time spent doing mathematics, a willingness to make mistake and not expecting a perfect answer immediately and correcting mistakes when made. If this mindset is added to the habits, the hard part can be dealt with.
So what you want to do is look back at when you spent time learning it. Integrate that time, add it up, that is where it was hard for you. Hard is effort, you just did it at a different time and with a different attitude. The difficulty doesn't change, but the perception of that difficulty does.
