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Smart vs Dumb

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terrybunny19240   United States. Oct 27 2011 08:29. Posts 13829

A while back I blogged about how one of the differences between 'smart' and less 'smart' people was not just that they were better, but that they had better strategies for thinking. I should of thought of this myself at the time but.. anyway I've come across research on this very thing, in this case applied to mathematics.

The study is ( Gray, E., & Tall D. (1994). Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic. Journal for Research in Mathematics Education, 25(2), pp. 116-140 if anyone has a clue on how the public can access such a thing I'd like some info though I imagine this one isn't publicly available from such a niche journal )

Anyway, this is what happened: They took a group kids (age ~8) and sorted them into two, one "high achievers" and another "low achievers". All of these kids had received the same/comparable educations but ended up in different places as far as ability goes. So, they asked the kids to do simple arithmetic problems and to explain how they did them. There were 4 strategies that the kids used when presented with an addition problem such as:
0 0 0 0
+
0 0 0 0 0 0 0 0
0 0 0 0 0

1. Counting all: This is where you count your numbers up to add or subtract them, literally counting (1-2-3-4..etc) everything up

2. Counting on: Whereupon a person counts from 1 to 4 and then continues from 5-17

3. Known facts: Where the person just knows that 4+13=17 automatically/without thinking because they've done that problem a bunch of times

4. Derived facts: (I will copy this straight from the summary) "This is where students decompose and recompose the numbers to make them more familiar numbers for adding and subtracting. So they may say, "Well, I know 10 and 4 is 14," and then they add on the 3."
ie doing 96+17 by saying "Ok, 96 -> 100 leaves 13, 13+100 is 113"

Now when they did the study they found for each group..
Above average students: Counted on 9%, known facts 30%, derived facts 61%

Below average: Counted all 22%, counted on 72%, known facts 6%, derived facts _never_

The researchers drew two main conclusions: Low achievers are often though of as "slow learners" when they are infact not learning the same things slowly, but literally learning a different mathematics. They view math as a ladder whereupon procedure after procedure is to be memorized and 'stacked up'. They are literally learning a different subject from kids who have an understanding of the big picture of math (something that is critically missing from America's education system, we about always learn math in a very compartmentalized, zero critical thinking way which is why I fuckin HATED math until I took statistics and saw real world problems being related to math).

Experiments have been done, taking these low achievers and teaching them better thinking strategies, and the results were very very good.

So yeah, this is just one example of ways that thinking strategies are at the core of smart vs dumb people. My view is that this concept definitely applies outside of math.

Well I'm fuckin late for class now so bbl..





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Kapol   Poland. Oct 27 2011 08:34. Posts 4696

Very nice read.

I'm getting a Bachelor's Degree in mathematics next year and I love to use derived facts in these kind of tasks.

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Stroggoz   New Zealand. Oct 27 2011 08:55. Posts 5328

nice entry

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nixxxbg   Bulgaria. Oct 27 2011 08:58. Posts 436

If anyone is interested, I found the study here:

Gray, E., & Tall D. (1994). Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic. Journal for Research in Mathematics Education, 25(2), pp. 116-140

http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot1994a-gray-jrme.pdf


qwerty67890   New Zealand. Oct 27 2011 09:19. Posts 14026

I was in the bottom set for maths at school although I think that was more a result of my total disdain for school rather than my ability.

Im actually pretty good at arithmetic, at least based off the results from my dealer school test where i was better than 100% of a random sample of people, including Asians. I think i got a lot better when i started to derive-facts in my own way, rather than having some twat maths teacher force me to do it the way they do it.

My ways are often a little more round-about but I dont think theres much difference in speed. For example if i want to work out 20% of a number, I will /10 and x2 rather than just /5.


Stroggoz   New Zealand. Oct 27 2011 09:36. Posts 5328

heh, now i remember from primary school where the teacher encouraged kids to count using their fingers. I never told them about option 4, i think i was too scared of being burned as a heretic. If i had my ideal education system, it would encourage kids to tell a teacher to stfu when they are clearly wrong.

One of 3 non decent human beings on a site of 5 people with between 2-3 decent human beingsLast edit: 27/10/2011 09:37

Kapol   Poland. Oct 27 2011 09:44. Posts 4696


  On October 27 2011 08:19 byrnesam wrote:
For example if i want to work out 20% of a number, I will /10 and x2 rather than just /5.


I believe this is the simplest way and I use it as well .

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Almebeast   Sweden. Oct 27 2011 10:51. Posts 797

Nice post. I've always been good at math and Im pretty sure I started using known/derived facts at an early age. I have a friend who always was a low-achiever in school (even though he's actually pretty intelligent in some ways) and still counts simple addition problems on his fingers...

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Funktion   Australia. Oct 27 2011 10:52. Posts 1638

If anyone is interested in math tricks there are a few books out there as well as youtube clips showing math shortcuts that are useful in every day situations. Another useful tool that imo goes along with the math tricks is learning to improve reading techniques. I wish I was taught these things back in high school.


Almebeast   Sweden. Oct 27 2011 10:54. Posts 797


  On October 27 2011 08:36 Stroggoz wrote:
heh, now i remember from primary school where the teacher encouraged kids to count using their fingers. I never told them about option 4, i think i was too scared of being burned as a heretic. If i had my ideal education system, it would encourage kids to tell a teacher to stfu when they are clearly wrong.



Haha I had the same feeling sometimes. I usually figured there must be something dumb with my technique since the teacher encouraged something else. It's pretty funny when you later realize that what you were doing was much better =)

After all is said and done, more is said than done. 

Raidern   Brasil. Oct 27 2011 11:47. Posts 4243


  On October 27 2011 09:52 Funktion wrote:
If anyone is interested in math tricks there are a few books out there as well as youtube clips showing math shortcuts that are useful in every day situations. Another useful tool that imo goes along with the math tricks is learning to improve reading techniques. I wish I was taught these things back in high school.



can you share them?

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qwerty67890   New Zealand. Oct 28 2011 00:28. Posts 14026

Some years ago, in the small window between attending university and dropping out because I hated it, I was partying hard for St Patricks day, I start talking in passing to this chick who was pretty hot for a white girl.

She asks what i study and i said accounting, and her ugly ginger cock-blocking friend steps in and says "OH so youre really good at maths!?! whats 13 x 11" (she wasnt even part of the conversation)

I said "143" within a couple of seconds, and her face dropped, her carefully constructed attempt to embarrass me had fallen at the first hurdle because she didnt ask a very difficult question, and didnt know how to derive facts.

The hot girl promtly thought i was some rainman-esque human calculator after verifying the answer on her cellphone, but was dragged away by a now very angry and disgruntled ugly ginger girl.

 Last edit: 28/10/2011 06:29

player999   Brasil. Oct 28 2011 02:47. Posts 7978

its 143 tho

Browsing through your hand histories makes me wonder that you might not be aware these games are possibly play money. Have you ever tried to cash out? - Kapol 

julep   Australia. Oct 28 2011 03:12. Posts 1274

just so long as she didnt know it was 143


Funktion   Australia. Oct 28 2011 05:38. Posts 1638

Funny you mention 11. A trick to multiply and 2 digit number by 11 is to add the 2 numbers together and then stick it in the middle.
Example:
34 x 11 = (3 + 4 = 7) 374
13 x 11 = (1 + 3 = 4) 143
72 x 11 = (7 + 2 = 9) 792
If they add to 10+
89 x 11 = (8 + 9 = 17) add 1 to 8 and stick 7 in the middle, 979.


  On October 27 2011 10:47 Raidern wrote:
can you share them?


On youtube I just used to click around using "math tricks". There are good videos on there (and a lot of terrible one) but I can't remember who made them.

As for books there are certain packs out there (you know where but if you can't find them let me know) that you can get filled with different techniques/useful stuff. Two that I liked are 'Secrets of Mental Math' by Benjamin and Shermer and '101 short cuts in math anyone can do' by Rockmaker. Vedic maths might be interesting for some people.

For reading it's all about learning the techiniques and then a whole lot of practice. I like Eyeq and Speed Reader-x but there are others around (like Acereader that others prefere). Basically they teach you to fixate less, expand how many words in one movement you take in (ie/ 3-4 or even a whole line instead of 1), not to back/forward read and to silence internal vocalisation. There are books that can teach or help you like the Evelyn Woods books but I actually like the Speed reading for dummies book and it's no bullshit approach. I know about photo reading etc but could never get it to work for me (I remain sceptical it even works). Hardest thing for me was to get rid of internal vocalisation or at least to a point where you don't rely on it, so annoying.

Hope this helps.


qwerty67890   New Zealand. Oct 28 2011 06:31. Posts 14026

lol, edited the fail from my anecdote.

i did get the answer right at the time though lol


terrybunny19240   United States. Oct 28 2011 13:04. Posts 13829

Funktion as far as the speed reading that sounds like it could really not be very beneficial to one's reading comprehension and ability to process what they're reading in general, especially for complex subjects. What's your experience?


Funktion   Australia. Oct 29 2011 03:28. Posts 1638

My whole purpose for increasing reading speed was because I actually read a lot of technical textbooks. Most people who are reading at around 250 words per minute could go to about 350-400 wpm with still a great deal of internalisation just by eliminating skip forward/backwards and lowering their fixation times (this is why people all over the net can say 'we can double your reading speed in 5 minutes'). Take fixation speed for example it's something you can try easily as there are readers on the net that will flash up words really quick (many times faster than what most of us natually read at, maybe 1000wpm). If I then asked you what the words were I bet you would know what you saw. When we read we get lazy, stopping on each word for way longer than we need for our brain to figure it out.

I read most of my stuff at around 600-700 wpm (I'm not some crazy 3k+ wpm guru) and then re-read either the parts that I think are important, the parts that I think I don't understand well or the parts that might be in an exam or assignment. This helps with retention and I do it in the same time as when I used to read slow. I think 600-700wpm is actually still pretty leisurely and that 1k+ is quite easily achievable for most people but it takes practise. The point is comprehension is as high if not higher at those speeds than at lower speeds. The only reason I re-read is to improve memory.

If you start trying it you will pretty quickly realise how lazy we read and how underutilised our brain is when reading slowly.




terrybunny19240   United States. Oct 31 2011 16:03. Posts 13829

Interesting, its on the list of things to check out haha


 



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