This man is a hero. I'm wondering if he can make similar software for algebra manipulation or geometric problems. That has always been a dream of mine.
I loved the passing mention of Cuisenaire rods for the set colours. Much of my early introduction to maths was done through these and even now I sometimes have them in mind.
I know someone who is dyscalculate from their brain physiology. I'd love to get access to this game to see if it would help them. I also know someone much younger and unrelated with the same brain physiological anomaly, so I'd love to pass it along to their parents.
When I was in elementary school, I was in the accelerated learning class. Strange thing about it was how slow at basic arithmetic I was. Give me a sheet of a hundred multiplication problems and two minutes to complete it, I'd stutter and spit a few out, but never get anywhere near completing it. However, same sheet with no time limit, I could be 100% accurate in three minutes. The teachers were baffled how this kid that was doing post secondary algebra for fun was having trouble with simple arithmetic. I think it was two major factors. First was a fight or flight response from PTSD, because I was being abused, and the time limit triggered it. The second is I have to break numbers into this type of visualisation to do simple arithmetic. In example, 2+2=? By memorization, 4 pops out, but memorization recall is impeded under stress. So break it up. I'd imagine points on the number. For two, the points are the left start of the curve, and the point of the sharp crook. This gives me two-ness. Put these points together and map onto the other numbers. One-ness doesn't match, it's a single point with a line dragged down. Two-ness I just explained, and doesn't match. Three-ness is arcs, first point starts it, second is the joining crook, and the third is the end. Doesn't match. Four-ness is tricky. It's a one-ness and a distorted three-ness combined: A point dragged down, and a start, conected to crook, to an end. It matches. All this would run through my head for 2+2 to get to 4. As an aside, I still have trouble distinguishing .25 and .75. This last week at work I mixed the two up, causing a couple hundred dollars of wasted material. And more importantly, it damaged my ego as being nearly perfect in my output.
a quarter and 3 quarters are easier to distinguish if you imagine geometry alongside the algebra. Making counting mistakes and over/under paying is totally relatable though (I think most people in a hurry would be highly likely to make silly mistakes in counting)
Same. I couldn't see it linked or mentioned on Brian's website either. Maybe where to find it is mentioned in one of his publications, but I haven't read them all to find out.
@Jacob Turnbaugh You answered your own question. *Introductory learning*. Like for toddlers or pre-school-aged children. Hence why user255 said they want it for their *son*.
@Jacob Turnbaugh What are you talking about mate? People are only asking where they can access a learning tool mentioned in the video above, which outlines dyscalculia effectively as a learning disability. Why would you then rant about how people "have no brains"? And frankly, I have no idea what you're talking about in regard to "things getting real" and "people jumping ship".
If only the colours used were the same as the number-colour coding used in electronics. Early reinforcement from both a Ladybird book 🐞 on counting and these Cuisinaire rods at primary school 3=green. But green=5 & 3=orange in the EIA colour code
If I have two apples and I pick another one I have [a number of apples without any abstract operators]. I think that the grammar of mathematics is extraneous at that level, (and Butterworth probably knows what he is doing.)
@@recklessroges Could be, but after a series of perfectly reasonable decisions, this seems a bit odd to me. Especially if you would eventually want to continue past 9. If there has to be a way to order the digits before they are added, it could be vertical, not horizontal.
I feel like this app could include geometry in further exercises. Personally I can tell if a set has an odd or even number of items by the geometric shapes they form. As you bisect or divide a set, is there an equal number on both sides (even) or do you need to chop one item in half (odd) to be 'fair'? In practice I often draw mental lines through number of objects to see how they relate internally. Geometric shapes are great for this, but with some practice you can see oddness or evenness of more irregular shapes at a glance. Of course this gets harder until our brains can't keep up as the number of items go up.
This reminds me of a line from one of Plato's dialogues (maybe Critias?). Socrates mentions that an odd number has one leg longer than the other. Apparently, the way Greeks thought of numbers was by adding line segments, like the two legs of a triangle but without a base. It forms a kind of stick figure with legs that get longer each time, and on the even numbers the legs are the same length.
It looks to me like the focus is to align students’ understanding of number with Set Theory, which can be seen as foundational to all mathematics. The problem with other models or metaphors is that they eventually break, whereas most, possibly all, mathematical theorems can be derived from set theory. This means students don’t need to ‘retrain’ their understanding of number for other situations. There are other models of numerosity that use geometric shapes to distinguish between their cardinalities. For example Numicon uses rectangular pieces that are two squares wide, meaning that odd numbers are represented with an extra square on top. This does, however, place a high importance on multiples of two, rather than other multiples, that I’m not sure is worthy.
I wonder what Mr. Butterworth would think of the game "2048" which became quite popular a few years ago. Seemed to do some similar-ish stuff, though obviously different because it was about doubling. But it did show that when you smash 16 and 16 together you get 32 and so on with visual cues.
Where I live, in Canada, there is no help, understanding, to even tolerance for students with learning disabilities. It is nice to hear that this is less the case in the UK. In recent studies, it was found that while children with learning disabilities are an estimated 10% of the population (however only about 1/2 of them are identified as such, while in school) they represent 50% of the teenage suicides. (Also, it stands to reason that some amount of the other 50% are from the unidentified 1/2 of learning disabled children.) It is a problem that is a bit more serious than low marks on report cards.
The way our world function is competely against any type of metal illnesses or disability, and if they pass unoticed and never treated, it has serious consequention in their lives. And are a LOT of ppl.
Do learning disabilities affect boys more than girls? With all kinds of traits, males tend to be more diverse than females, so more males are in the extremes of every trait and behavior. If this is the case with learning disabilities as well, do not expect any serious help with the issue unless the current paradigm changes radically. "Male issues" are not going to be addressed. This is obviously also the case with suicide, which affects males disproportionately, and thus it is overlooked.
man you shocked me there! surely mr trudo administration would've shown some compassion to those struggling children? Just goes on to show communists dont really care about the weak and feeble.
We've done studies of the use of the game in schools and at home. One paper is being reviewed at the moment, and others are on the way. We have a big project using the game in Singapore. Paper to follow the end of data collection.
I think that differents shapes other than circles could help too. Cuz by what i understands about discalculia, they might only learn about set of circles and still get confuse if there is other shapes mixed in.
This is really interesting. We often take for granted how easy it is to learn numbers, at least early on, as long as you put in the work. But it doesn’t always come so easily for some people, which makes sense but you don’t think about it. I’d love to see more Numberphile videos about math education.
This is really awesome! The game looks wonderful and I respect the effort that they are putting into helping others learn effectively. There is also a teacher named Vera Stevens who developed a system called "Pebble Maths" to help people (both children and adults) with arithmetic, including those with dyscalculia. I bet both systems could be combined in useful ways.
This can go on the market as a meditation experience as well... Funding idea - charge 99¢ to unlock dark mode, comforting/pleasing sound effects, and ambient background music. I'd give a buck to zone out that way and support the research. Would need to allow staying on a level indefinitely or until a user supplied time limit.
I am good at math, but even just watching that game felt nice on my brain. I like how the only puzzle is understanding quantity, not some crazy NP-complete thing.
I think I know why, your face on the back wall made me realize we cap at 4 because we're wired to see faces for survival. so 3-4 makes sense. Change my mind.
As someone who loves teaching early math, this is really fascinating to see. Hope the experiments go well and that the results are easy to implement broadly :]
how exactly do you know if you're discalculic? Like, I'm studying engineering and I absolutely hate counting/arithmetics (I'd rather just use a calculator) But does that mean I might have dyscalculia? (since most of my disdain for mental arithmetics comes from my experience with being bad at it) I couldn't care less about getting better at it, since I can use a calculator any time I need to. All I'm asking is if being bad at mental arithmetics is a sign of dyscalculia? (what exactly are the signs of dyscalculia?)
Most people that are "bad at mental arithmetic" just haven't practised enough. Learn to trust yourself to count, (but verify with the calculator afterwards.) In time you will learn to estimate in your head, which will catch errors that could pass by unnoticed if you just plug the digits into an electronic box.
I wonder if answers disappearing automatically is a good idea, the kids may want more time to look at the result, it's best to just highlight and move it to the corner to demonstrate that it indeed matches the answer.
Multiplication can also be done with the Cuisinaire rods. With more than one set it's easy to illustrate how say 3×7 = 7÷3 = 21×1. Lat the rods out side-by-side forming rectangles, or linearly. Lay 10's rods alongside to decompose decimal numbers. For the other comment above, with p-length rods you've got ability to illustrate p-adic number schemes
If the game helps the kids get a true understanding of numbers learning the symbols is the lesser problem. If you realize that 3 means III grasping that 30 means 3 of IIIIIIIIII and 32 means 3 of IIIIIIIIII and 1 of II probably is not a problem.
Not at all, they're two completely different skill, and of the kid is bad at this skill of constructing numbers they are not gonna learn anything else related to math. Cuz this is the most fundamental concept of math, the very foundation that other abstraction build upon.
what is the point of this channel if you don't list videos like this on it (edit: nvm I guess not flooding sub boxes makes sense if this protects against that)
They do, eventually. Because these videos don't make much sense without the videos that preceded them, people will sometimes rate them poorly or misunderstand the content, without watching the video that links here.
