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"many children learn mathematics as a set of arcane rituals for manipulating symbols on paper, because they can't yet understand the abstract meanings of those

"many children learn mathematics as a set of arcane rituals for manipulating symbols on paper, because they can't yet understand the abstract meanings of those symbols." In the US? I had pretty typical US public school education. Word problems and application were ubiquituous. Perhaps my experience is non-representative, or you like the study authors are speaking of other educational contexts (Asia).

cjs_ac 2y ago
I grew up in Australia and taught in Australia and the UK; and yes, the word problems are ubiquitous in those countries too. But those word problems are always deeply inauthentic, and extracting the relevant information from them becomes just another arcane activity. One that comes to mind involves a farmer with a given length of fencing, and the student has to find the area of the largest rectangular field the farmer can surround with that fencing. It's a good mathematical puzzle, but the actual real-world problem is how much fencing the farmer needs to surround a given field. Coming up with genuine, real-world applications for every mathematics lesson is extremely time-consuming, and maths teachers simply don't have the time.
- greentxt 2y ago
  Maybe there's an element of both time and skill? How many folks that pursue math can point to a great early teacher as being influential. Not all, but I want to believe it's common and maybe true for most.
- anon291 2y ago
  With ChatGPT et al... it should start to be pretty easy. I envision a question answer game between humans and the AI. The AI would set up the scenario and the kids would have to ask the right questions. Teachers could supervise and evaluate
aidenn0 2y ago
Some children read word problems, understand the question and apply math. Most children look for key words, use those key words to guess what operation to apply, then apply it to the numbers in the question (e.g. there were 3 numbers and the word "total" so I'll sum the numbers).
- anon291 2y ago
  In my experience, this is as much an issue with reading comprehension as it is with math

cjs_ac 2y ago

I grew up in Australia and taught in Australia and the UK; and yes, the word problems are ubiquitous in those countries too. But those word problems are always deeply inauthentic, and extracting the relevant information from them becomes just another arcane activity. One that comes to mind involves a farmer with a given length of fencing, and the student has to find the area of the largest rectangular field the farmer can surround with that fencing. It's a good mathematical puzzle, but the actual real-world problem is how much fencing the farmer needs to surround a given field. Coming up with genuine, real-world applications for every mathematics lesson is extremely time-consuming, and maths teachers simply don't have the time.

greentxt 2y ago
Maybe there's an element of both time and skill? How many folks that pursue math can point to a great early teacher as being influential. Not all, but I want to believe it's common and maybe true for most.
anon291 2y ago
With ChatGPT et al... it should start to be pretty easy. I envision a question answer game between humans and the AI. The AI would set up the scenario and the kids would have to ask the right questions. Teachers could supervise and evaluate

aidenn0 2y ago

Some children read word problems, understand the question and apply math. Most children look for key words, use those key words to guess what operation to apply, then apply it to the numbers in the question (e.g. there were 3 numbers and the word "total" so I'll sum the numbers).

anon291 2y ago
In my experience, this is as much an issue with reading comprehension as it is with math