Subitizing: improve your number sense, get good at math

[Fredo Corleone]

Hi guys,

the subject is catchy to get the attention of those who have difficulty in aritmetic, like I do!

Who am I?

A brief introduction on who I am and why I'm writing this, for those of you who don't know me my name it's Fredo and 30 yo, I'm an electronic engineer and self-taught programmer. My IQ is way above average (latest test was around 140 points). I went to one of the best high-school available here in my city and got through it pretty easily without studying, I decided not to go to university because for me it's a waste of time and money, instead I finished studying what was left (some advanced electronics and computer science) on my own.

Why am I writing this?

I've always had problem with numbers, they don't make much sense to me. Infact I was pretty bad the first couple of years of highschool, the calculator was prohibited and we were dealing with a lot of arithmetic. I was the best of the class in physics, which was supposedly an harder class than math, but there the calculator was allowed.

Later on, when we started doing calculus I got from being the worst of the class in math to the best among my classmates.

Recently I started playing Magic The Gathering, which is a collectible card game, and my arithmetic weakness is showing off pretty bad: I can't estimate points of damage quickly, and I have hard time figuring out how many cards are on the board,  even when there aren't that many. And I have to ask my opponent for out many cards they have in hand even if I'm able to see them perfectly.

Luckily I'm very good in statistics and I can perfectly cover my weakness by constructing better decks than my opponents.

A plausible remedy

I did a bit of research and it came out that a concept called Subitizing, which is the ability to get quantities without counting, seems connected to number sense and it's supposedly trainable: "Subitizing is the first math ability and forms the basis for much -- perhaps all -- math ability that follows it: learning the meaning of numbers, counting up objects, adding and subtracting, number sense, and estimating relative quantities ALL depend on the ability to subitize. Significantly, children deficient in math in second and third grades were found to perform much more poorly in subitizing than their classmates."

I've read some studies and they all agree on the fact that Subitizing is an important milestone that has to be acquired to be proficient in math.

The fact that Subitizing is cognitivelly developed before counting seems up to debate, but I don't care: because I can count but have struggle subitizing.

Anyway, I decided to hack together a web app to train this ability, you can find it on my Codepen at: https://codepen.io/eternalsunshineofspotlessmind/full/BaYdqoX

I'll try training with it for 15-30 minutes for a couple of months and see how it goes, I would be rather happy to be able to finally get quantities without straining my eyes or pointing at things with my finger, and to calculate small things in my head (such as the money change at the bar etc.).

Stay tuned,

Fredo

[Fabio Fucci]

I think that what you are doing is related to a topic I've been thinking about lately, that is, the fact that by training some pillars of our cognitive abilities we can improve in some more general area, if you have time read chapter 2 of

"The brain that changes itself", it's about Barbara Arrowsmith, who, as a child:

"had trouble understanding grammar, math concepts, logic, and

cause and effect. She couldn't distinguish between "the father's brother" and "the
brother's father." The double negative was impossible for her to decipher. She
couldn't read a clock because she couldn't understand the relationship between
the hands. She literally couldn't tell her left hand from her right, not only because
she lacked a spatial map but because she couldn't understand the relationship
between "left" and "right." Only with extraordinary mental effort and constant

repetition could she learn to relate symbols to one another."

Later on as an adult:

"She isolated herself and began toiling to the point of exhaustion, week after week
at mental exercises she designed.
She exercised her most weakened function — relating a number of symbols to
each other, One exercise involved reading hundreds of cards picturing clock faces
showing different times. She turned
up a card, attempted to tell the time, checked the answer, then moved on to the
next card as fast as she could. When she couldn't get the time right, she'd spend
hours with a real clock, turning the hands slowly, trying to understand why, at
2:45, the hour hand was three-quarters of the way toward the three.
At the end of many exhausting weeks, not only
could she read clocks faster than normal people, but she noticed improvements in
her other difficulties relating to symbols and began for the first time to grasp
grammar, math, and logic. Most important, she could understand what people
were saying as they said it. For the first time in her life, she began to live in real
time. Spurred on by her initial success, she designed exercises for her other
disabilities — her difficulties with space, her trouble with knowing where her
limbs were, and her visual disabilities — and brought them up to average level."

All of this could be related to Relational Frame Theory, her training made her better at understanding relationship, which in turn made her smarter(or at least better in some area of cognition), but she also trained other weak points of hers and saw general improvements.

I think(or at least hope) that what you're doing will probably work, and that by training your weak point you will see some improvements in other areas, so keep us informed.

Also really like your codepen, being able to modify speed and number of objects is really nice.

Fabio

[Fredo Corleone]

I've listened to her talk at Google, one key takeaway is that the effort has to be high to spur neuroplasticity.

[Fabio Fucci]

Absolutely, I think that's also why some people do not see improvements with dual n back, if you do something without effort, without conviction, no neuroplasticity will occur

[BM XT]

Thanks for this app, this skill is my weak spot also.

вторник, 24 мая 2022 г. в 15:02:22 UTC+5, fabio...@gmail.com:

[BM XT]

Here's great app to train mental rotation if anyone is interested.

https://vample.com/tools/mental-rotation/

четверг, 26 мая 2022 г. в 20:53:27 UTC+5, BM XT:

[Bo T]

 What are the rules of this game? I know that you are not supposed to count , how do you "train"? 

[Fredo Corleone]

Just guess, after a while your brain should be able to get groups fast and guess accurately the quantity

[itrn...@gmail.com]

I'm not sure if this is how it works but the current app easily allows us to separately group smaller numbers of objects together then calculate a sum. Wouldn't it be better to just show a flash of the objects so it requires more visual memory and faster visual processing? Also an active component to it would be nice.

[BM XT]

So is that considered cheating therefore not as effective if I'm kinda chunking objects? Should I just try to estimate a whole bunch of them at once untill estimation is precise?

пятница, 27 мая 2022 г. в 07:43:02 UTC+5, itrn...@gmail.com:

[BM XT]

Yeah. Having to choose a right answer may be good for some people. I also noticed that it's much easier if objects are grouped in some orderly manner. And if their placement is chaotic it gets very hard.

пятница, 27 мая 2022 г. в 07:43:02 UTC+5, itrn...@gmail.com:

I'm not sure if this is how it works but the current app easily allows us to separately group smaller numbers of objects together then calculate a sum. Wouldn't it be better to just show a flash of the objects so it requires more visual memory and faster visual processing? Also an active component to it would be nice.

[Fredo Corleone]

You can do everything as long as you don't count one by one, if you are like me you can't really get the feeling of quantity. The goal is to reach the population baseline. Whatever my brain do I have faith it's the correct way of doing it and I just simply do the exercise without any worry. If I'm correct I'll start developing a sense of quantity in few months and be as good as the norm in this task and perhaps it carries over addition and subtraction and arithmetic in general, otherwise no big deal life goes on.

[BM XT]

Been training for some time. Know quantities up to 8 are a lot more easier. Higher number still require processing. It feels like fast reading in a way, fast counting if you will. Still feel that brain i processing not the whole arrangement but chunks if 3 to 5 pieces, and the whole process is very dependent on position of pieces. If pieces are placed in some symmetrical pattern it just goes super fast and easy.

пятница, 27 мая 2022 г. в 17:02:29 UTC+5, stopchemt...@gmail.com:

[Fredo Corleone]

I'm doing it for a while too and it's getting easier, I can now recognize 5 things very fast without chunking and I'm starting to get a feeling for 6 things togheter, I think I will be soon able to subitize 6 too.

[BM XT]

Did you get your hands on any of Barbara Arrowsmith-Young' exercices?

вторник, 7 июня 2022 г. в 16:44:25 UTC+5, stopchemt...@gmail.com:

[Fredo Corleone]

Nope, because I have too many books to read already but I watched a one-hour long video of her schooling Google engineers.

[Leonardo]

I think that 12 is a number too low. I find it really easy. You could maybe put the limit in 100, so people can increase the maximum up to their level. Reaching 100 would certainly turn you into a kind of Rainman guy. A savant with the ability to know the number of items of everything. 

[Leonardo]

LOL. I literally broke everything by trying to raise the limit:

[BM XT]

Leonardo, you mean you just glance at them and know that there are 12 and it's too easy? Now I really feel like mentally challenged person.

понедельник, 7 ноября 2022 г. в 12:29:42 UTC+5, Leonardo:

[Leonardo]

Emmm... It is very easy. Given how little numbers there are, 12 compared to 10 or less is visually very different. Only 11 and 12 are somewhat similar, but it is easy to distinguish between them. If there are 11 or 12 numbers, I just mentally divide into 2. To test if the number is even or odd. This is not a strategy that I designed, it is what my brain does automatically. 

Up to 10 is very easy, because I see the chunks. In 8 I automatically see two groups of 4. In 9, three groups of 3. In 10, two groups of 5. 

Two factors may help me. My monitor is 4K and I won a lot of mathematical competitions when I was a kid. I have always been fast with numbers and have always practiced with them.

I also, as I have stated many times here, up to the point that I feel ridiculous writing it again, scored 143 on WAIS-IV nine years or so ago. I am 30 now. So doing things a little worse than me is probably not enough to be considered mentally challenged.