When I explained to my son that "X" was just another way of representing the blank space in equations, he got extremely mad about the world making algebra seem hard. He screamed about how "I've been doing that to calculate damage in video games for years" and stomped off.
He's never completely gotten over it. He's still mad about it to this day.
They're thinking that teaching people stuff is promoting a diversity of outcomes, which is anathema at the moment.
Diversity is supposed to only extend as far as categories one mustn't use to discriminate (age, race, sex, religion, etc.). If it occurs in other areas (achievement level, ability in particular subjects) ... oooh that's bad. Must make it stop.
I don't understand what this means. Where I went to school there were no gifted programs but we all were doing algebra and word problems much earlier than in the US. If people want consistent outcomes then teach everyone the same thing and hold everyone up to the same standards by investing more resources in students that are underachieving. That to me seems like a much better way of equalizing outcomes.
If you teach "hard" things to average US public school students, a minority of them will excel as a result. The rest will nod off, get bored, not pay attention, and not benefit.
So it benefits a minority (those who care) and differentiates them from the rest -- that's what they don't like. Because those who care come from "privileged" backgrounds more often than not, thus perpetuating the gap between privileged and non-privileged.
I still don't follow. What exactly in what I suggested is the problem with equalizing outcomes? If everyone is learning the same things then what exactly is the problem? There is no discrimination involved.
"Equalizing outcomes" is exactly what they want to do.
They seek to accomplish this by pulling down those who would otherwise excel, not by solving the real problems that are preventing people from excelling in the first place.
Part of the problem is that outcomes can never be equalized. It's a fallacy to try to force everyone into the same educational mold. A statistical normal distribution will always occur.
Better to remove impediments that are keeping people from excelling -- things like poverty, crime, etc. would be a great place to start.
What's the fallacy in teaching everyone the same things? That seems like a good way to equalize life outcomes and give everyone the required skills for succeeding in contemporary society.
If all (e.g.) 7th graders must have the same knowledge of math, that knowledge of math cannot exceed the knowledge attainable by the dumbest (read: any) 7th grader. This is tautologically true.
Yes, thanks. That clears it up. You're right. We must teach no one anything otherwise there would be some people that wouldn't be able to understand. That was exactly what I was thinking and your example helped me understand. What you were saying was clearly tautological and I just didn't have the logical training to understand it.
Your interpretation of what I was saying was clearly adversarial and uncharitable so I just got tired of it. It's entirely possible to have high standards for everyone (including the "stupid") without reducing the quality of the curriculum. But you're not interested in having that discussion because you're grinding some other axe about what you perceive to be the ideological takeover of the educational system.
>What's the fallacy in teaching everyone the same things? That seems like a good way to equalize life outcomes and give everyone the required skills for succeeding in contemporary society.
My position is that kids should be taught math at an earlier age and schools should be properly staffed and funded to ensure positive learning outcomes for all students regardless of their socio-economic background because that will lead to more equal life outcomes.
What's interesting is that beyond a certain threshold (perhaps around the left-hand normal distribution inflection point), further reducing failure rate ends up also reducing the rate of super-success among students in the same classroom.
There is no way to fail in what I'm proposing because there are no grades. Everyone gets feedback on how to improve and students can receive all the help they need to keep up with the curriculum.
When most kids can’t do algebra, the teacher invests most of their time into helping those students catch up. Because most of the teachers time is now going to students who don’t understand algebra, algebra gets dropped all together. Minority high achievers who were capable of understanding algebra now feel that they are held back by low achievers.
High achievers should probably check out Khan Academy or similar…
Yes, this is probably what is happening. Schools are understaffed and underfunded so programs keep getting cut. At this point it really just might be better to let kids learn from Khan Academy since the adults clearly have no idea what they're doing.
My third grader does simple equations like this in math. This is public school in Oregon. A lot of people in this thread are making big assumptions and just using it as an excuse to trash the American educational system for ideological reasons.
> My third grader does simple equations like this in math.
Most third graders cannot consistently do the following:
10 - ? = 3
10 - ? (- 10) = 3 (- 10)
- ? = - 7
(-) ? = (-) 7
? = 7
This is absolute voodoo magic to most third graders. They may be able to memorize specific patterns, but they won’t be able to manipulate equations consistently and accurately.
Fwiw, at 3rd grade, some of the smarter kids might be able to understand and manipulate these abstractions, but those kids aren’t the norm.
Sure. The way I presented it was not an accident (abstract with little scaffolding).
The question with the software that I have is how much is actually understood. Specially, how much of what was done can be applied in a different context. Ideally consistently, accurately, and without any scaffolding. I’m guessing the answer might be “a lot” for a typical HNer’s child (or maybe not), but it rounds to zero for the average or lower 5yo.
I would also be curious about how much success can be had with just rapid trial and error rather than learning and applying. 5 year olds can be great at the trial and error part while not actually developing and retaining much understanding. I could be very off the mark with this speculation, but a lot of my experience in this area makes me think I’m not.
This sounds like the difference between basic understanding of the idea, and mastery. Mastery would always take a lot of repetition and diverse problem-solving -- true even for algebra.
Basic understanding is a lower bar, and I'd suggest that most students leave Algebra 1 with just basic understanding. Hopefully a little better than Dragon Box.
They dont do abstract manipulations. They dont do the "3 + ? = 10" and therefore "10 - ? = 3". Teaching algebra means teaching abstract manipulations too, like 2x+4=10 and therefore (2x+4)/2=10/2 and therefore x + 2 = 5 and therefore x=3.
The thing you wrote here does not count as teaching algebra. It is just one preparatory step and has nothing to do with delaying algebra or not.
3 + ? = 10
10 - ? = 3