To this point, I have been doing a plenty of 1on1 lessons with kids trying to catch up with Math in high school/college/matura exams and one this I have noticed is that things which are problematic to these people are things which were covered quite well already in elementary school.
Later the curriculum only expands on these problems so it's even harder and harder to catch up.
I have been working with college freshmen struggling with basic linear equations and such. While the profession is marginally unrelated to Math (e.g. Graphical Designer), I still wonder to this day how people can have 20-30-40 years and not know how they could (with a calculator in their hand!!) calculate the price after the discount. How can someone feel ok with this?
Schools (at least around here) do not hold kids back anymore. No matter what.
Some of them get behind in one or more subjects (math, say) as early as 1st or 2nd grade and all their later teachers are stuck trying to give them the remedial math help the desperately need, while teaching their other students on-grade-level material, and also trying to teach the remedial kids enough of the new stuff that their scores on that year's standardized test don't land the teacher in hot water (though the kids won't get it at all). The result is that the kids fall farther behind every year but keep failing up to the next grade. They'll enter e.g. 6th grade with ~Dec. of 3rd grade math skills (more often than not their other subjects aren't much farther along, though not always). If they get an LD diagnosis they'll get some extra help but by then it's too late.
Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated.
Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.
But it works at-scale, which is where the focus is. Bang-for-the-taxpayer-buck.
Further, socially-speaking, being with your actual peers is extremely valuable, obviously.
But yes, the ideal would be a tailored-to-each-child education. Personally, having seen the power of a good Montessori education, I think it's frickin' genius and should be the template for all education (specifically the grouping of 3 yrs together -- e.g. 3,4,5-year-olds together), so kids are perpetually working through the cycle of "look up to someone, mimic someone, mentor someone".
... but I digress.
Fact is, grouping by age works socially and it's much, much cheaper than a tailored education, which is all we an afford (get taxpayers to pay for).
At some point, I expect a software company to make headway in this space and you'd see a bunch of kids staring at iPads all day and a bored teacher playing Minecraft at the front of the room, only engaging when someone gets stuck.
My kids are homeschooled, and I'm in charge of teaching Math, because my wife is one of those "I suck at math" people. Her parents focused exclusively on memorization when they helped her with homework, and then she got a few bad teachers, so her mental models are completely off. She's getting better, but that's not really my point.
It was developed by two mathematicians who actually studied in classrooms what worked on kids when teaching math. They've come up with a method where kids learn negative numbers and multiplication _before_ learning positional numeration (numbers greater than 10, with units, tens, hundreds, thousands, etc.). I've seen first-hand how these concepts just click in my daughter's mind, and how she often comes up with the new concept herself when you introduce the prerequisites in an order that makes sense to her.
They learn about negative numbers and multiplication before they learn to count past ten? Or they just learn counting without learning how to write the numbers?
The latter. My daughter actually learned it because we mixed different learning methods early on (we don't anymore, it confused her), but you have to admit that writing numbers greater than 10 kinda involves multiplication (by powers of ten, but still), so it makes sense to learn multiplication first. Negative numbers were seen while learning addition / subtraction (the concept was basically adding a negative number), which made a lot of sense too.
Cheaper? I also don't know if that's necessarily true. If it's ineffective for many, is it a cheaper solution or just simply cheaper?
Personally, I think Khan Academy is one of the few forward-thinking organizations doing something right in education. It tries to skew learning towards a 'mastery-based' model which keeps kids from falling behind by not advancing them too early. Of course, teachers and parents still need to implement the usage of Khan Academy in this way for it to be effective.
>Further, socially-speaking, being with your actual peers is extremely valuable, obviously.
I would disagree... I think that there is huge value to being around a variety of people, and a strong negative value to only being around people in the same phase of life as yourself, especially when you are in the nasty phase. I think I made it through that part of my life because I had an after-school job where I fixed computers for a local office. I even enrolled in the vocational program at my highschool that let me out of school early to go to work (except every second Monday, when we learned how to spot shoplifters, short-change scams, and other hazards of the retail life.)
I think the number of people who felt good about their social lives, the things they did socially and the things, socially that were done to them in high school is... small. As far as I can tell, for most people, college is important because it is a kind of recovery from this, and prepares you for a workplace where conflict is muted, where yes, if you are good enough, you can still be an asshole, but where being an asshole has a pretty heavy cost that must be made up in other ways.
For me? Being expected to behave like an adult while being treated like an adult around a bunch of adults was amazing. It gave me a reason to keep going in high school, and when I came of age, I was all set to get a really nice job.
Not being argumentative -- is the current system actually cheaper? I'm not enormously familiar with Montessori, but is the student/teacher ratio vastly different, or are the various learning materials any more expensive over time than the books, computers, and reams of paper that traditional schools use?
I went to a public elementary school which had only mixed-grade classes (2–3 grades at a time), and it was just fine, and didn’t cost any more than having one grade per class with kids all precisely the same age.
>Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd.
Sounds quite logical to me. If we assume a gaussian distribution (which tests seem to verify), most kids of the same age will have the same skills/level.
So at worse you mismatch what's taught to some kids towards the edges, whose level there are ways to accommodate anyway in most school systems (skipping a class or two for extra smart kids, or staying behind/supplementary teaching for less than average smarts).
And it's not just about learning and who can cram more into one's head (akin to e.g. preparation for the Olympics), but also about sharing the same teenager and adult-making experiences as other kids of your age, which is probably even more important that what's actually taught (the majority of which most people will forget anyway).
> Sounds quite logical to me. If we assume a gaussian distribution
In this context, Gaussian is a pretty useless assumption without fixing a variance. Proposed alternatives range from "already implemented" to "totally infeasible" depending on variance.
> which tests seem to verify
Not really. For each individual subject area, maybe, and again, Gaussian is pretty uninformative.
But the odds of a student being "average" in every subject area != the odds of a student being "average" in a given subject area.
> whose level there are ways to accommodate anyway in most school systems
Except the whole point is that there are not currently ways to accommodate this in most school systems! From GP:
>> Schools (at least around here) do not hold kids back anymore. No matter what.
Also notice that holding back a student in math is possibly net detrimental if the student is not also behind in English and Science.
> but also about sharing the same teenager and adult-making experiences as other kids of your age, which is probably even more important that what's actually taught
Again, the prepubescent/tween/teen division is much less granular/restrictive than the competency-by-age-X division.
Sounds a bit circular: when we test kids taught in single age groupings they have "narrowly" grouped grades. Therefore we should teach then in single age groupings because they have narrowly grouped grades.
That doesn't really help us to know if the top achievers are being held back, for example. Perhaps we can speculate that lower achievers are being pulled up?
Outside school you're almost always going to be in age diverse groups; I think a larger element of that in public schools would be better. IMO it helps to emphasise that children are there to make their own education and not simply to be part of an age defined peer group where it appears you're doing something just because of your age, not because of the educational opportunity.
Yeah. To my mind, the problem is that learning is very individualized (not even taking into account learning disabilities!), and yet mainstream U.S. pedagogical theories really only target the middle of the bell curve. What's needed -- at least for a huge chunk of students -- is something more like Montessori, where a learner who's struggling can receive individualized attention from a teacher or a peer, and where the learner has free access to tactile/visual/whatever aids which may be overkill for most other learners, AND -- perhaps most importantly -- where the natural human tendency to sit and focus for hours at a time on a single task is fostered and encouraged.
Retained students (the current terminology for "held back") are much more likely to stop attending school early, and on average do not see larger academic gains in their year retained than their equivalent peers who are not retained.
The ONLY effective intervention is dramatically increased services for that student, delivered rapidly once the deficiency is detected. Many high performing charter school networks actually use this systematically, but only by overworking their teachers and generally burning them out within 5 years (retention rates at 5 years are frequently <10%, compared to 50% in the broader profession). Most teachers in mainstream district schools are covered by union contracts that limit their required working hours, so for the vast majority of schools even this isn't an option. Actually delivering these services in a sustainable manner is a financial burden American taxpayers appear largely unwilling to shoulder.
Oh reminds me of something peculiar. I gave math lessons to a 16yo guy. Mainly quadratic root formula. He understood the "high level" bits, but he failed so often at basic algebra after plugging the coefficient into the formula that he felt completely demotivated. It was odd to try to explain to him that he got the idea right, but failed at the basics. I told him that to mean "you can do the hardest, you will be able to get the easiest" but he interpreted it at "whats the point if you cant do the low level bits" ...
Not all are created equal. Our children are unique.
One of my children showed natural talent in language at 9 months with no prompting. This was brought to our attention by childcare staff. Another of our children showed a natural talent with mathematical concepts at about a year old.
Even as they grew, our linguist struggled with math (for years) and our procedurally oriented child struggled with language (for years).
To this day, these two children maintain these core differences. It took at least 6 years for our linguist to crack basic arithmetic (even basic addition) which was at least several years behind our proceduralist.
I found out later that some leading child psychologists recognise different brain types in very young children (exactly as I found). An Internet search on brain types of children will show some high profile child psychologists who talk about this in depth, despite some strong "opinions" (ie. devoid of evidence) that oppose these studies.
Our linguist, with minimal pressure, has developed into a strong mathematician (at least grades wise) but to this day has never demonstrated anywhere near the natural ability of our proceduralist.
I have drawn the same conclusions with my own siblings and my wife's siblings. At a very young age, our own strengths become apparent without intervention. I am very glad I never pushed my kids to be equal (or even close to equal) in all skills. I consider most uses of the word "equal" worrisome (except for equal opportunity, a concept frequently downplayed in the last decade or so. Even Zuckerberg's famous open letter was unclear on such a fundamental concept).
OBS: when I asked our linguist to step through basic math, they understood the concept but could not do the work independently. Someone in this thread described a similar story for their child and attributed this to a lack of "confidence". For my child, I wholly reject that it was confidence related. When things clicked for our linguist, they clicked. If anything, our linguist's ability to crack the basics took patience on my part. I wanted my child to succeed quickly but I restrained myself (thankfully).
People need to realise that not all kids are the same. We have innate strengths. We have different learning styles, different learning rates, and different interests and motivations. I strongly reject the modern populist theory that we are all equal in ability and I believe we do significant harm because of this factoid. The motives behind this factoid concern me deeply.
If I could offer one piece of advice, your child(ren) are unique. Don't ever let anybody tell you that your child's strength or weakness comes from social conditioning. The only social conditioning cones from extreme behaviour (eg. Heavy handed forcing of "equality" under the banner of political correctness is extremely harmful, rather than focussing on potential and opportunity. This heavy handedness is also driving some extremely destructive social engineering under the banner of "equality". If you are watching academic trends you should be horrified as a patent).
I always encourage(d) play at a young age (physical activity, math games, language games). However, if you make this more than games (if you call this teaching and you start to measure), you set kids up for failure, especially when many children need patience and time.
According to PISA rankings, most western countries (especially English speaking) are not the top performers. I have hinted my beliefs of the root cause of this in this post. I predict most western countries will slip in ranking even further (especially English speaking countries). If things play as I expect, the slip will be significant in the next 10 years.
Later the curriculum only expands on these problems so it's even harder and harder to catch up.
I have been working with college freshmen struggling with basic linear equations and such. While the profession is marginally unrelated to Math (e.g. Graphical Designer), I still wonder to this day how people can have 20-30-40 years and not know how they could (with a calculator in their hand!!) calculate the price after the discount. How can someone feel ok with this?