To be fair, the basics of algebra are already taught in first grade (or whenever you learn arithmetic). Kids at that age won't have questions such as

x + 3 = 7

Instead, they will get questions such as

__ + 3 = 7

They might not formally learn it, but they'll learn the patterns that they will eventually apply in algebra.

And if we were any good at teaching math we would just naturally go with it from there, "algebra" wouldn't even be a subject, it would just be something you do by default as teachers first replaced _ with x (hopefully before you even got too used to _), and then started making the equations gradually more complex.

"Solving linear equations with multiple variables", "solving quadratic equations", "solving polynomials", etc. Those are things you really need to teach as a distinct concept. Algebra is just the language, introduced in a pedagogically sound way you wouldn't even realize you were learning it.

Yah. I think we go about things all wrong.

Even "new math" is too rote/heavy on memorization of process. And not enough patterns/puzzles/games/etc.

We need to find a way that the math content can be interesting for 80% of the room, and provide competition where there's multiple axes of success and multiple ways to stand out. Then you get everyone in the room really trying.

Instead, what happens is this: we start with curriculum that is very algorithm-heavy, taught by elementary teachers who generally do not love math. Half of the kids struggle with the rote-heavy workload and fall behind, and it becomes a frantic effort to try and drill steps into kids' heads who just hate it more and more. For a lot of the class, this is very painful and zero-sum, and it's only fear of what the teacher will say to parents that generates any effort.

[Note, I do think there is a point around 3rd grade developmentally where it makes sense to drill some arithmetic processes, and around 8th-9th grade to drill some algebraic process... but algebraic ideas can come in well before that time and hopefully be taught in a way that makes them interesting].

Yeah, I remember "learning" indices and logarithms at ~12 years old, using it for hacking video games (i.e. calculating the packet sizes, and bytes to bits, etc.) - then when we had to cover it in school it was super easy and relatable.

Ideally everything would be taught this way, like actually doing interesting things rather than just remembering things from textbooks.

My parents introduced algebra to me in third grade. It took me a long time in third grade to get it, so much so that I was a little bit afraid of algebra though certainly I didn't admit it to my parents.

Fast forward a few years in school when the teacher introduced algebra in class (maybe sixth grade?), everything suddenly clicked, and I pretty much got the highest grade for several months straight because I learned this material before, albeit not well, but still way ahead of everyone else.

I think this could be a middle ground: introduce the material earlier, but with no expectation that the pupil must grasp it immediately; then review or reintroduce the material again at a later date.

That's how I learned a lot of things. My dad would mention what atoms are and that kind of thing, and I'd read about them in magazines, so them when it came to school it wasn't so big a leap to add a bit of rigour.

My takeaway from your anecdote is completely different: when exactly a school introduces concepts doesn't matter as much as the stimulation a child can receive outside school.

In my experience, kids whose parents help teach concepts and don't just leave things up to school generally end up with an advantage. Kids love learning from their parents and other loved ones, but school is generally regarded as sort of a chore even if it does bring friends and playtime. A great many parents simply don't have the time or energy left after their day job to support their children the same way others can. Kids whose parents often read to (and with) have a noticeable advantage in many school settings, and you can't substitute that for all students by just cramming in more reading time in their busy school schedules.

Kids have a finite time they spend in school. You can shuffle the time they spend around all you want, but in the end every kid requires a certain amount of time to grasp a certain context. That time may differ when kids get older or younger, but the required time spent on learning won't suddenly change.

Not all students are like you. I went to a low-ranked university my first year before transferring out. I met freshmen who really struggled with basic concepts, like what a vector is. I'm not sure they would ever get it even with all the tutoring in the world.

They would in my opinion. I was a tutor in high school and college for algebra. I worked with people some people who struggled. They all eventually got it if they wanted to get it, which they generally did to not get held back :p. You just have to work with them and truly understand what they are not understanding. The big issue is concepts are not learnable in isolation. You said vectors are basic, but are they? They were initially just abstractions to model sets of physics problems. Without the context, its pretty difficult to understand them IMO, especially things like dot products. "oh, i multiply two vectors and I get a number? what? Oh and that number can be described as the multiplication of magnitudes of the vectors multiplied by the cosine of their angle? Oh how do I get the magnitude? What's cosine again? etc." It goes forever and generally you'll find that people will struggle with basic things because they never had an opportunity to sit down and genuinely internalize those ideas.

Everything builds on other concepts and people's misunderstandings generally came from not truly understanding the basics. Its hard to personalize education at scale though.

I tutored a 20 year old CS major who could not understand the equation to convert from Fahrenheit to Celsius. Nice guy, talented guitar player. Was not meant to be a programmer.

From what I can see, most states don't teach algebra until 9th grade. Also most states are learning math better then California, so maybe it works? Of course, that might not be the cause, but just copying better performing states seems to be a safe way to try and fix California's problem.