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This is not a new concept, nor is it as deranged as you make it seem. There is an idea that developing an intuition for mathematics is more important than rote

This is not a new concept, nor is it as deranged as you make it seem. There is an idea that developing an intuition for mathematics is more important than rote solving of problems. Successful approximation through intuition has been a defining measure of overall ability in mathematics since the enlightenment period and yet we still enforce a rote systems that makes mathematics incredibly difficult to teach as its completely unengaging. I remember in grade school when I was in third grade our teacher taught us the cross hatch multiplication method. I loved it and basically learned how to do it in my head. The next year I went to a different school with a different curriculum. We started doing timed tests for multiplication problems. I stopped showing my work because it was tedious to write out and I wanted to be the first to turn mine in. So instead I just wrote the answer I had come up with visualizing the problems. I scored well with the correct answers most of the time, but the teacher found it unacceptable that I didn't show my work and started giving me bad scores for not doing it "right." Doing it "right" doesn't encourage mathematical intuition, or engage young minds in thinking about problems abstractly in their heads, it forces them to be nothing more than spreadsheets accounting pointless sums, differences, products and dividends. That's not a great math education.

brightball 5y ago
You're not arguing against a correct answer though, you are arguing against showing your work. The answers are still objectively correct. Objectively right or wrong.
- stillbourne 5y ago
  Not really, I got answers wrong more often than some other students, but I had a skill none of the other students had after I switched schools. The ability to think about math. I've always had a cavalier attitude about the "correct" answer, being able to think in my head and come up with approximate answers is more important. I still think the teacher was wrong to mark my answers incorrectly when it was clear that I was turning my papers in minutes faster than the other students and only having a margin of error within 5%. That ability to think about problems in my head wouldn't have developed if I wasn't afraid to get an answer or two wrong in the pursuit of intuition. It's no different to me. Even in my work I'd rather get the approximation first, than shoot for precision later. I think that's an attitude that gets lost in the mix of precision first. It's certainly an attitude I took into adulthood that has been a boon to me professionally. When I'm writing software, the first step is do it, the second step is do it better and the third step is do it right. Imagine trying to write an entire software application and having it work perfectly the first time you build and execute it. If we can't achieve that kind of perfection in our work as professionals and adults why would we force it on our kids?
  - brightball 5y ago
    Look, I get it when it comes to showing work...but teachers get you to show work in many cases so they can see if you were on the right track and identify exactly where you went wrong. When you show your work, they can give you partial credit instead of marking the entire thing incorrect if you are wrong. The other benefit of it is that it prevents people from trying to rely on calculators (if available) to ensure that the students knows how to work through the multiple steps of the problem. When it comes to math applications in life, estimates are great for forecasting, quick budgeting and several other things. Career wise though, anything to do with financials or engineering is never going to be okay with the answer in your head being in the ballpark. It's a great skill that you have, no doubt, but in order to teach and ensure the students are learning how to work through a problem the teacher needs to see the steps that they are going through to get there.
    - stillbourne 5y ago
      > Career wise though, anything to do with financials or engineering is never going to be okay with the answer in your head being in the ballpark. Calculus is the art of approximation and intuition in math. Newton couldn't have destroyed the way we used to calculate pi if he hadn't extended the binomial theorem into other sets of numbers.
JohnDeHope 5y ago
It's funny but this is how I got through Physics in college. My math skills weren't up to snuff, but the professor's questions were all real world word problems. I recall very vividly the moment where I figured out how I could pass the course. It was during the first exam, and the question was about the volume of a car engine. The answers were all different in magnitude. I am no car buff, but I know what the "5.0" in a "Mustang 5.0" used to mean. So I knew which answer was ballpark the volume of a car engine, the one that was ~2 liters. The others were obviously too small, such as 0.3 liters, or obviously too large 60 liters. Everything else was similar. I only had to know roughly the magnitude of most of the problems, and actually be able to do the math on some of the rest, in order to pass. I would not want to live or work or even pass through a community who thought this was a good way to teach children generally. Any industry of theirs beyond a wooden lean-to would be dangerous if not outright deadly.

brightball 5y ago

You're not arguing against a correct answer though, you are arguing against showing your work. The answers are still objectively correct. Objectively right or wrong.

stillbourne 5y ago
Not really, I got answers wrong more often than some other students, but I had a skill none of the other students had after I switched schools. The ability to think about math. I've always had a cavalier attitude about the "correct" answer, being able to think in my head and come up with approximate answers is more important. I still think the teacher was wrong to mark my answers incorrectly when it was clear that I was turning my papers in minutes faster than the other students and only having a margin of error within 5%. That ability to think about problems in my head wouldn't have developed if I wasn't afraid to get an answer or two wrong in the pursuit of intuition. It's no different to me. Even in my work I'd rather get the approximation first, than shoot for precision later. I think that's an attitude that gets lost in the mix of precision first. It's certainly an attitude I took into adulthood that has been a boon to me professionally. When I'm writing software, the first step is do it, the second step is do it better and the third step is do it right. Imagine trying to write an entire software application and having it work perfectly the first time you build and execute it. If we can't achieve that kind of perfection in our work as professionals and adults why would we force it on our kids?
- brightball 5y ago
  Look, I get it when it comes to showing work...but teachers get you to show work in many cases so they can see if you were on the right track and identify exactly where you went wrong. When you show your work, they can give you partial credit instead of marking the entire thing incorrect if you are wrong. The other benefit of it is that it prevents people from trying to rely on calculators (if available) to ensure that the students knows how to work through the multiple steps of the problem. When it comes to math applications in life, estimates are great for forecasting, quick budgeting and several other things. Career wise though, anything to do with financials or engineering is never going to be okay with the answer in your head being in the ballpark. It's a great skill that you have, no doubt, but in order to teach and ensure the students are learning how to work through a problem the teacher needs to see the steps that they are going through to get there.
  - stillbourne 5y ago
    > Career wise though, anything to do with financials or engineering is never going to be okay with the answer in your head being in the ballpark. Calculus is the art of approximation and intuition in math. Newton couldn't have destroyed the way we used to calculate pi if he hadn't extended the binomial theorem into other sets of numbers.

JohnDeHope 5y ago

It's funny but this is how I got through Physics in college. My math skills weren't up to snuff, but the professor's questions were all real world word problems. I recall very vividly the moment where I figured out how I could pass the course. It was during the first exam, and the question was about the volume of a car engine. The answers were all different in magnitude. I am no car buff, but I know what the "5.0" in a "Mustang 5.0" used to mean. So I knew which answer was ballpark the volume of a car engine, the one that was ~2 liters. The others were obviously too small, such as 0.3 liters, or obviously too large 60 liters. Everything else was similar. I only had to know roughly the magnitude of most of the problems, and actually be able to do the math on some of the rest, in order to pass. I would not want to live or work or even pass through a community who thought this was a good way to teach children generally. Any industry of theirs beyond a wooden lean-to would be dangerous if not outright deadly.