> why Algebra is required to understand basic stats
I don't understand how you can say this. Literally every statistical concept is defined via formula, and to manipulate formulas correctly (or even really understand the concept) you need basic algebra.
Going even further than that, if you have the most basic "business scenario word problem", like cells in excel that describe how many widgets are made per hour, how many are defective, the price of each one...etc. The skill that lets you combine them in a sensical way to figure out your profit or loss is literally algebra. It's used by everyone everywhere all the time. Algebra is a core skill we can't be skipping.
IMO if you don't teach stats, people are okay, they have an intuition about fractions and can reason from there. But not teaching basic algebra and putting them in the modern economy is like not teaching someone to read and putting them in a car on the road.
I struggled a lot with Algebra, I forged my teacher's signature to not retake it for the third year in a row.
I didn't really "get" it until I started programming and learning stats. That's when it all hit me, then I went back and had to relearn what the hell they were talking about during my middle school years.
Also, once I got to Highschool math, Algebra 2 and PreCalc, it was very easy to simply memorize formulas and plug and chug.
You don't need to know Algebra to know what profit and loss is. If you want to calculate a break-even point, you look up the break-even point formula and plug in the numbers, or more commonly today, find the menu in your analysis program. None of my business classmates had any idea how to manipulate the formulas. You get a "quant" to do that for you. Yes, there are bad consequences because of this, but this is the reality of most modern businesses. People are already skipping Algebra, we just kinda let people move forward anyway.
To test it, give a highschool Algebra test randomly sampled modern workers. Don't let them study for it, pop quiz. I believe almost everyone would fail horribly if you could control for cheating.
Same story for trig, I didn't really appreciate or "get it" until I got really interested in ballistics and digital signal processing many years later.
Kids like me find Algebra, by itself, too far removed and too abstract to even begin to find value in it. I really had no idea what we were talking about most of the time. Sure you can learn some patterns and "trust" that the teachers know best, but then I go home and ask my parents, one who has a Doctoral degree in medicine, and the other a Master's in finance, when the last time they calculated an integral, or used the quadratic formula, and they say freshman year of college 40 years ago... A lot of my teachers were also full of shit and power tripping a significant amount of the time, so that didn't help build any trust either.
Thankfully, I figured out the deep beauty and power of math, but I have quite a lot of catching up to do, but my mental framework now is far more organized at mapping how all the concepts relate, and why they're valuable. I can learn more now in a few months than years of study when I was in Highschool. All because I can plug the concepts into a nice modular framework, and I can experiment with ideas in code.
Almost nobody that I knew did the same though, most of my coworkers over my 15 year career don't have the patience or curiosity to dive into this stuff. It's actually really hard to find friends who geek out about math and functional programming (expect for a few corners of the Internet, including here).
Hopefully that clarifies things, if not, I'd need to know more about your confusion.
As a counterpoint, a lot of business majors seemed to think that Econ 101, let alone calc-based 410, was the hardest thing in the world.
The class is all graphs but there usually no numbers—it’s all about the intersections and regions under different curves. Usually all drawn with straight lines to keep it simple in 101.
I think the people that found it hard did not have the fluency they needed in mathematics. If you can’t rearrange some simple linear equations, then things become very difficult.
This is so true. I majored in math and economics, and even the 400-level econ classes used exclusively linear equations because the average student in those classes had no idea what an integral was. But they could calculate the area of a triangle.
Thanks for the detailed thoughts. It sounds like you had a uniquely poor experience with your math education which is too bad. Obviously you are plenty smart to handle the concepts themselves and once you had reason to apply them, you immediately "got it". I definitely don't disagree that the way the subjects are taught without context is part of the problem. I didn't really "get" calculus until I was forced to apply it to physics.
That said, specifically with respect to the content in Algebra, I wasn't really sure what we were talking about here, so I looked up the CA Common Core Algebra 1 concepts. [0]
> (1) deepen and extend understanding of linear and exponential relationships
> (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions
> (3) extend the laws of exponents to square and cube roots
> (4) apply linear models to data that exhibit a linear trend
This strikes me as a pretty reasonable terminal point for the general population, and I don't see how you are going to talk about anything but the most shallow statistical concepts without being comfortable with the machinery involved in the above. Perhaps you could use stats to make the content more relatable and teach both at the same time (over 2 years?), that would seem reasonable to me. But I think I would resist dropping the above concepts from the curriculum entirely in favor of a "stats light" course that literally only went into charts and basic descriptive stats.
Also, it's a bit of a cliche, but I do think it's worthwhile to teach some concepts for the sake of imparting a lesson on "how to think" and not just for the content itself. The quadratic formula feels like a good example of this. Literally nobody has reason to apply it, but the abstract reasoning skills involved in mastering it are foundational. Even if we cannot get 100% of everyone there, it's a laudable goal to me and one we should stick with.
> I didn't really "get" it until I started programming and learning stats.
I had a similar experience. I wasn't particularly good at math and struggled a bit with algebra until I started programming.
I had something I wanted to solve, and I found out I needed to convert between one ratio to another ratio, and I couldn't figure out how. Then I realized I could just compute a percentage and use that. After all a ratio is a measure of something relative to a whole and percentage would tell you, well, the percentage of the whole, and I had memorized the formulas from going to and from percent.
So I wrote the code for this, but staring at the code it suddenly was so obvious that the division by 100 on the first line would cancel with the multiplication by 100 on the second line.
That was my eureka moment. Algebra suddenly made sense, and math in general became a whole lot easier.
I don't understand how you can say this. Literally every statistical concept is defined via formula, and to manipulate formulas correctly (or even really understand the concept) you need basic algebra.
Going even further than that, if you have the most basic "business scenario word problem", like cells in excel that describe how many widgets are made per hour, how many are defective, the price of each one...etc. The skill that lets you combine them in a sensical way to figure out your profit or loss is literally algebra. It's used by everyone everywhere all the time. Algebra is a core skill we can't be skipping.
IMO if you don't teach stats, people are okay, they have an intuition about fractions and can reason from there. But not teaching basic algebra and putting them in the modern economy is like not teaching someone to read and putting them in a car on the road.