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You are combining too many things. Focusing on 20 simple with increasing difficult problems builds visual memory, pattern matching which is lacking with a few

by ipaddr 5y ago

You are combining too many things. Focusing on 20 simple with increasing difficult problems builds visual memory, pattern matching which is lacking with a few compounds problems. The science must be missing some inputs because the current theory is lacking.

wisty 5y ago
The current theory isn't particularly lacking, the average teacher (let alone layperson's) understanding of it is lacking. Plus there's dozens of rubbish theories that are sorely lacking so you have to find the researchers that actually do solid research. IIRC (see the above, it applies to random comments on the internet) drill work is more effective (but feels less effective to both teachers and students) if it's mixed up with different topics or question types, kind of like how doing a kata is better than doing exactly the same punch 10x (obviously katas are not ideal either, at least not as the only tool). Really you need a bit of diversity, and IMO two of the big traps to fall into are overly homogenous drill work (which doesn't retain as well as mixed drills, but looks effective because anyone who doesn't eat their crayons can do it without thinking too hard) and one-off problems (do an assignment where you solve a heavily obfuscated problem once, then pretend that it's now something that students actually understand, when they've literally just answered one single question assuming they even did it themselves).
- stenl 5y ago
  In first grade we were given a workbook for learning how to write the letters. There was one whole page of A, one page of B, etc. You had to write maybe 100 As in a row. The kids quickly figured out that the fastest way to do it was to first write the left slant 100 times, then the right slant 100 times and finally all the 100 crossbars. So yes, you do need a little variety to defeat such shortcuts.
  - varjag 5y ago
    What a brilliant way to teach kids economies of scale.
  - TrispusAttucks 5y ago
    According to the article this is actually a really good way for kids to learn and improve. The point being that just practicing the lines is hugely important.
    - TeMPOraL 5y ago
      Exactly. That page full of A's, whether they "cheat" it or not, will teach the kids how to draw all lines that make an A. Repeat that with other letters, and then throw combination of different letters into the mix, which will force kids to draw one letter at a time, after they've already mastered all the component movements in isolation.
- deleted 5y ago
  [deleted]
diordiderot 5y ago
"The science is wrong because I disagree" - ipaddr
- dvfjsdhgfv 5y ago
  They are not the only one, I see the same. Kids without math drills have problems in storing crucial bits of information in long-term memory and consequently fare worse at solving simple arithmetic problems than myself when I was much younger. I'm not talking about complex things but basic arithmetic, like multiplying digits, adding fractions or, more importantly, dealing with ratios. Drills give you a considerable advantage here.
  - doix 5y ago
    I have another peice of anecdata with my parents/grandparents. They grew up in the USSR and went through school there, drilling (according to them) was extremely common. They can still remember some peoms verbatim over 70 years later (in my grandfathers case). And they still remember/understand pretty much all the math they were taught. When I was doing my Advanced Highers (final exams in Scotland) I was asking my parents for help and they could answer all the questions without looking things up. I looked up the exam paper[0] I sat, I'm pretty sure there's no way I'd get an A again if I sat it right now without studying for it. But I'm pretty sure my parents still woudl. [0] https://www.advancedhighermaths.co.uk/wp-content/uploads/2016/02/AH-Maths-2008.pdf https://www.advancedhighermaths.co.uk/wp-content/uploads/201...
    - gotorazor 5y ago
      I had a bit of schooling in that kind of educational system (Asia) before continuing schooling in North America. I'd say that you there is no free lunch. You're always giving up something for something else. I had a job 10 years ago doing in-person training at a company trying to digitize their paper-based office for the first time. They were in a commodity distribution business, so while the math isn't hard, there is a lot of day-to-day arithmetic (conversion between unit of measure and price/unit vs total price) for all the employees from the warehouse guy to the sales staff. The system introduced a change in their workflow. Before in their old manual paper system, people just kind of put things on a truck and figure out later how much got shipped and how much to invoice a customer. The whole can be very hand-wavy. There was no live inventory system either. Digitization meant that sales have to write sales orders that had precise units to be sold. Based on inventory, they know how much they will actually ship and they know that down to the dollar. Everybody suddenly had to start being aware of the math involved in their work. It was kind of funny to see a bunch of blue-collar, ex-con, high school dropouts learning faster than all the college-education office workers. The college-educated guys were too drill-orientated and approached the work like the math worksheets that everybody is talking about. The ex-cons had a working relationship with the numbers on the screen and the things that are hanging off their forklifts. Many of the white-collar clerks had been getting by memorizing formulas. They had no idea what any of those formulas mean.

by ipaddr 5y ago

wisty 5y ago

The current theory isn't particularly lacking, the average teacher (let alone layperson's) understanding of it is lacking. Plus there's dozens of rubbish theories that are sorely lacking so you have to find the researchers that actually do solid research. IIRC (see the above, it applies to random comments on the internet) drill work is more effective (but feels less effective to both teachers and students) if it's mixed up with different topics or question types, kind of like how doing a kata is better than doing exactly the same punch 10x (obviously katas are not ideal either, at least not as the only tool). Really you need a bit of diversity, and IMO two of the big traps to fall into are overly homogenous drill work (which doesn't retain as well as mixed drills, but looks effective because anyone who doesn't eat their crayons can do it without thinking too hard) and one-off problems (do an assignment where you solve a heavily obfuscated problem once, then pretend that it's now something that students actually understand, when they've literally just answered one single question assuming they even did it themselves).

stenl 5y ago
In first grade we were given a workbook for learning how to write the letters. There was one whole page of A, one page of B, etc. You had to write maybe 100 As in a row. The kids quickly figured out that the fastest way to do it was to first write the left slant 100 times, then the right slant 100 times and finally all the 100 crossbars. So yes, you do need a little variety to defeat such shortcuts.
- varjag 5y ago
  What a brilliant way to teach kids economies of scale.
- TrispusAttucks 5y ago
  According to the article this is actually a really good way for kids to learn and improve. The point being that just practicing the lines is hugely important.
  - TeMPOraL 5y ago
    Exactly. That page full of A's, whether they "cheat" it or not, will teach the kids how to draw all lines that make an A. Repeat that with other letters, and then throw combination of different letters into the mix, which will force kids to draw one letter at a time, after they've already mastered all the component movements in isolation.
deleted 5y ago
[deleted]

diordiderot 5y ago

"The science is wrong because I disagree" - ipaddr

dvfjsdhgfv 5y ago
They are not the only one, I see the same. Kids without math drills have problems in storing crucial bits of information in long-term memory and consequently fare worse at solving simple arithmetic problems than myself when I was much younger. I'm not talking about complex things but basic arithmetic, like multiplying digits, adding fractions or, more importantly, dealing with ratios. Drills give you a considerable advantage here.
- doix 5y ago
  I have another peice of anecdata with my parents/grandparents. They grew up in the USSR and went through school there, drilling (according to them) was extremely common. They can still remember some peoms verbatim over 70 years later (in my grandfathers case). And they still remember/understand pretty much all the math they were taught. When I was doing my Advanced Highers (final exams in Scotland) I was asking my parents for help and they could answer all the questions without looking things up. I looked up the exam paper[0] I sat, I'm pretty sure there's no way I'd get an A again if I sat it right now without studying for it. But I'm pretty sure my parents still woudl. [0] https://www.advancedhighermaths.co.uk/wp-content/uploads/2016/02/AH-Maths-2008.pdf https://www.advancedhighermaths.co.uk/wp-content/uploads/201...
  - gotorazor 5y ago
    I had a bit of schooling in that kind of educational system (Asia) before continuing schooling in North America. I'd say that you there is no free lunch. You're always giving up something for something else. I had a job 10 years ago doing in-person training at a company trying to digitize their paper-based office for the first time. They were in a commodity distribution business, so while the math isn't hard, there is a lot of day-to-day arithmetic (conversion between unit of measure and price/unit vs total price) for all the employees from the warehouse guy to the sales staff. The system introduced a change in their workflow. Before in their old manual paper system, people just kind of put things on a truck and figure out later how much got shipped and how much to invoice a customer. The whole can be very hand-wavy. There was no live inventory system either. Digitization meant that sales have to write sales orders that had precise units to be sold. Based on inventory, they know how much they will actually ship and they know that down to the dollar. Everybody suddenly had to start being aware of the math involved in their work. It was kind of funny to see a bunch of blue-collar, ex-con, high school dropouts learning faster than all the college-education office workers. The college-educated guys were too drill-orientated and approached the work like the math worksheets that everybody is talking about. The ex-cons had a working relationship with the numbers on the screen and the things that are hanging off their forklifts. Many of the white-collar clerks had been getting by memorizing formulas. They had no idea what any of those formulas mean.