Over the past ten years I've spent a lot of time volunteering in poor urban middle schools, mostly in math tutoring/teaching roles. Sure enough, one of the big hangups kids have is algebra. The article is right that it's one of the first real abstract problem solving skills we try to teach kids, and that definitely makes it harder for them. In my experience there is an additional problem: Basic arithmetic skills.<p>If a kid can't do division and knows it, how can they approach a problem like, "It is 800 miles from Denver to LA by train. train A leaves from Denver to LA at 80mph while train B leaves from LA to Denver at 70mph. How far from LA do the trains cross paths?"
We can start breaking this down:<p><pre><code> 70mi*x/h + 80mi*x/h = 800mi
x * 70mi/h = M
150mi*x/h = 800mi
x = 800mi/(150mi/h)
x = 5.33...h
M = 5.33h * 70mi/h
M = 373.333...mi
</code></pre>
OK, that's all well and done.
Now do that without division. Do that without a clear grasp of 1. what division does and 2. how to do division. The only thing you really know about division is that when you take tests on it, you tend to do poorly. You can't do this problem. You look at it and don't see any tools you can use to attack it because the only thing that works on it is division and you do not get division.<p>The problem is, a <i>lot</i> of kids don't get division. Why? That's above my pay grade. If I was going to take a stab in the dark, I'd say that at the highest level it's to do with passing kids who shouldn't be passing, and then teaching the next year's class as if they already know what they need to know. Every year they fall a little bit more behind, until finally they're so lost it's hopeless. It's easy to take aim at algebra but what about the shaky foundation we're trying to build it on? Of course, this would require a lot of kids to be held back, and that's not an appealing solution. I think we need to assess where in our math education kids start to fall behind, and figure out what's wrong there. Unfortunately for the kids, the solution will probably involve more multiplication/division drill sheets, and more word problems to test those skills.<p>The article also points out the difficulty in starting a STEM degree without calculus. I started a STEM degree without calculus. I was lucky to get into the university I got into without calculus, and the calc 1 course was taught as a remedial class for all the folks who got 4s instead of 5s on their AP calc exams. This is where I had my own first brush with trying to build the next layer of mathematics education on a shaky foundation. It was very difficult, I nearly quit, and it fucked up my GPA enough I was still paying for it four years later at my graduation. I was 18 and had a bright future to look forward to in graduating from a respected university with a STEM degree, and it was nearly too much for me. I don't see how we can ask 13 year old kids to do the same with algebra. We need to work out the kinks on the way there. When it's time for them to learn algebra we want them to have all the tools they need so they can focus on the algebra, not on the arithmetic.<p>To be clear, I don't have any solutions here. Just a lot of problems.