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Anybody know of any schools/programs that introduce math to children in some of the ways that Minsky suggests? (In case it isn't obvious, I'm not a programmer (nor do I work with math)...but I am a parent.)
While kids may find arithmetic to be boring and demotivating, they're able to do it. It's when math gets symbolic that you get the permanent attrition. For instance, most people never get to calculus. When you progress from arithmetic to abstract, it hardly gets easier . Moreover, memorizing. You go from memorizing multiplication tables to other kinds of tables, like tables of equations giving various identities, row…
Disagree. Kids disengage from math for many different reasons. There is no single pattern to it. If it were that simple, it would not have remained an issue since schools were commonplace. Minsky solidly makes the point that when math is taught as nothing more than an endless series of tedious drills with no purpose in sight, of course it demotivates kids. No one likes pointless Sisyphean tasks. Many students, howeve…
Just look at various cultural traditions, popular (and even serious) music, crafts, sports, ... sneeze ligion. Mindless repetition is everywhere.
The same kid that hates doing arithmetic will play the same video game for hours in which a small variation on the same set of events happens over and over again.
The kids you're describing are the smart minority, of whom a portion will go on into STEM type fields. They too will hit their mathematics ceilings. Most will go as far as a couple of third year undergrad math courses and that's where it ends.
Anybody know of any schools/programs that introduce math to children in some of the ways that Minsky suggests? (In case it isn't obvious, I'm not a programmer (nor do I work with math)...but I am a parent.)
Why not do it yourself? I think that fostering a particular topic by the parents should be a first step.
"we need to provide our children with better cognitive maps of the subjects we want them to learn" This style of learning works for everyone -- including children. There is a growing community of people sharing educational, animated gifs on Reddit that recognizes the value of visual learning. Popular subreddits include: - /r/educationalgifs - /r/mechanical_gifs/ - /r/GifRecipes/
"we need to provide our children with better cognitive maps of the subjects we want them to learn" This style of learning works for everyone -- including children. There is a growing community of people sharing educational, animated gifs on Reddit that recognizes the value of visual learning. Popular subreddits include: - /r/educationalgifs - /r/mechanical_gifs/ - /r/GifRecipes/
Cognitive maps (or mental models) are part of that.
I struggled a lot with this, and other meta-learning topics. Got it eventually, after much independent reading and testing, but why was this never a topic in school? I'd have gladly sacrificed a year of schooling just to learn about it, and I'd have made it up within another.
It's also the reason why I no longer believe that intelligence is the most significant factor in our capacity to learn. The same course done by the same person may be finished within a decade, a year or a week, with the only difference lying in approach.
The difference is so striking that calling kids that fail at it dumb or the more politically correct challenged is lazy pedagogy. It shifts the issue onto something outside of our control. But I don't think it is. We can do a lot better.
And it may be due time for a new approach. We don't need a large populace educated enough to man machinery or a filing system, as they're starting to man itself. We need youth that is confident in its ability to stride across vast depths of knowledge without getting lost. And current processes of education seem ill engineered to that goal.
Like I said though, pet peeve of mine. I'm sure we'll figure it out.
Math could be taught qualitatively.
First, one can give their students ten or so hairy problems where the goal is to write down what the problem is asking in the most explicit and gory details.
Then one can present another batch of hairy looking problems and ask the students what definitions/lemmas/theorems/corollaries look appropriate to apply to the problems and why?
Another batch of convoluted problems can be offered where the goal is to simply formulate one's questions regarding the problems in the most precise way one can. Asking the right, penetrating questions solves more than half the problem.
Ask the students to rewrite all the definitions/lemmas/theorems/corollaries presented in class in their own words.
Present students with a text full of unproven statements (most grad level math texts). The exercise here is to identify as many of these statements as possible. The bravest students are encouraged to supply proofs.
Give students a bunch of required problems peppered with generalizations and extensions of required concepts(typically reserved for big boy students) and ask them why they are required to solve these problems. What exactly to be gained out of solving every specific problem?
After all that students can tackle the required set of problems written up for them by the Department Of Serious Business. At this point math will come naked and explicit in front of one's eyes.
None of this is going to happen in classrooms, though. Students will have to learn these things on their own as per the traditions.
My high-school math teacher (Older man) had his favorite pets (girls) sit in front, and would not even address the rest of the class. Questions and inquiries were completely ignored. The only reason I was able to get ahead is due to my interest in programming my own games, and thus learning the relevant math (trigonometry at the time).
That old topic. Ironically, I find people who work with math ( chosen to work with math, that is) to probably be quite unqualified to truly understand the problem. He opens by saying that learning avoiding mistakes before any bigger concepts is a major root of this but then again, people do make mistakes in math (even math professors) and it's a field where any mistake can completely invalidate the work. Also most pe…