For any parents or teachers here, I’m interested in hearing how old your kid(s) were when they started to understand numbers , counting, and what methods you used to teach them. I’m guessing that they learned to verbally count before they could read and write ?
I don’t have kids, but I’m thinking of creating some educational animation.
From the little that I’ve seen so far, the common method seems to be to show one…two …three … XXXX number of objects along with either the words “one”, “two”, “three” or the numbers “1”, “2” … “3”.
I’m also curious how kids learn that seeing three (balls) for example, and the number / word “3” “three” means the same thing as three dogs … cats … boxes … i.e. “things”.
Also if anyone here knows of or participates on a good teachers / educators forum / website, any links are apprerciated.
I think you’re pretty much right, kids start out by associating numbers with groups of tangible objects.
I think that the understanding of numbers as abstract ideas start coming when kids learn to count higher than 10 or 20, and is solidified when they start learning how to add without using visual aids.
I have found that numbers are not so hard to teach. It is the maths.
But yes, association is a good thing.
Visual, Auditory, Verbal and Tactile. Get as many of these into it as possible. Obviously tactile is out.
So what they SEE is important
What they HEAR is important
What they SAY is important
What they TOUCH is important.
You can get them to speak if what you say is correct. eg A singalong ditty.
After a while, the singalong ditty is carried around in their head, and they associate it with what they saw.
This will probably be no help but I can say that my own two kids showed distinctly different learning styles.
My daughter learnt to clearly speak individual words then she slowly began to put them together as sentences. My son however, spoke complete sentences filled with gibberish then slowly filled them in with actual words. My daughter’s command of English has since been generally higher than average and she’ll happily use a big word where others will opt for more common, smaller words.
My daughter showed little interest in numbers (and largely still does) while my son was fascinated by numbers from as young as two years old. It began by repetition of numbers when he heard them. One specific example was a TV show which always ended with an address and postcode. As weeks went by, he began repeating the postcode when he heard it. Then, within months he’d associated the postcode with the show to the point where he would call out the four-digit number whenever an ad came on or the show commenced. Within a year he’d started to mess with the postcode such that “two one two one” became “twenty one twenty one” and over time “two hundred and twelve - one” and so on. His fascination extended to phone numbers on trucks and number plates and almost anything that had numbers. For him, numbers just make sense.
In primary school he quickly sorted out maths and was seemingly able to solve reasonably complex arithmetic (for his age) in his head. When asked how he did it, the explanation was often baffling.
Like I said, probably not much help but if nothing else it might show that kids learn different things in different ways.
I know you are more polling people for their personal experiences but you might want to look at Jean Piaget’s work . He did a lot of fundamental work on child cognitive development that is very interesting . The link is Wiki link so take it with a grain of salt . You might want to Google his name if you find the summary there interesting - I’m sure there are better synopsis of the stages of childhood cognitive development that gets mentioned on the Wiki .
For what it is worth and in some way I hope this helps you but my son just turned 2 last month. I cant really think of any words he can say besides mama and dadda but for some reason he can count to 10 with out any problem. Now as I look back over the last two years my wife and I havent really tried to teach him how to count in fact since he cant say any other words it was a suprise one day when he sprug that on us. He does watch a lot of kid shows that count so im sure that is where he learned. So I quess what I am trying to say is that some kids can count to ten before they can say “DOG” . Now I hope that in some way it will help you accomplish your task in helping kids learn. Good luck with your project. Mux
Sounds a lot like what I’ve read about Sesame Street’s great sucess ; repetition … repetition …bright colors …associating symbols (“1” “one” ) objects “ball”, “dog” “cat” … and the kids just finally “get it”.
If you tried to teach young kids without visuals (other than learning to say the numbers / words), they’d probably never or take much much longer. I.E. you need to point at one, three … four “things” for it to make any sense.
My littlest is about 21 months and she’s just starting to parrot 1 - 10 as a verbal sequence, but doesn’t understand what it means yet.
She also talks in long ans sometimes very expressive sentences in gibberish. We can occasionally pull out a word or two of things she’s familliar with - Milk , Mummy, Daddy, her brothers and grandparents’ names, Hi5 (An Australian kids dance / music group and one of 5 DVDs she always requests) um… Up, Down, Night-night, Bye bye etc.
Ha ha, that’s funny Sounds like Andy’s son … another budding mathematician
Most probably, he’s just memorized the sounds at this point, unless he’s been watching a show that’s been showing the objects at the same time. It’s interesting to find out when they understand what they’re saying. Heck maybe we never really understand, we just memorize that “Seven / 7” means a picture of 7 objects.
You should try gettting 10 objects out and count with him, pointing / touching to each one as you go. Then try it with less than ten objects and count with him / leading him. I’m guessing he’ll count to 10 anyway, but I bet if you keep alternating 10 obs with say 9 objects, and maybe after you say nine, while he’s looking at you, cover your mouth while you dont’ say ten, he’ll probably start catching on … especially if you laugh when you do it … and so on and so on with different numbers of objects.
That’s a great age isn’t it ! Walking, talking a little miniature person
I babysat for my cousin’s two kids when they were ~5, ~2.
As I said to Mux (and I’m not a professinal teacher but everything I’m finding confirms this), when she starts counting pull out ten objects and point to them and count along with her, then try that same “cover your mouth” game at different numbers. Make if a fun game and she’ll undoubtedly pick it up.
You could freak out your friends by repeating some kind of word like “mythological” or a phrase “I find that utterly ridiculous Sydney” … say it enough times and watch out … that’s also a warning for things you DON’T want repeated
They’re 11 and 14 now so still at school. My son still enjoys numbers and is in advanced maths. My daughter, perhaps strangely, showed an early interest in science and that interest continues. It seems this interest might be the thing that helps her get some enjoyment from maths. She still loves reading plus theatre and art. My son messes with Blender occasionally though I limit their access to the computer so they get on with some traditionally useful stuff like riding bikes and reading books
As far as learning goes, I’ve been frustrated by the modern approach in schools in which rote learning (by repetition) has essentially been dumped in favour of letting time be the best teacher. There seems to be a belief that the kids will “get it” when they need to and that forcing it into them by repetition is “bad”. Being something of a traditionalist and often despising “the new ways” (which all too often seem like a feel-good, soft-option cop-out - like not giving kids an “F” even if they show no intention of ever learning anything) I got my kids to do their multiplication tables the old way - by rhythmically chanting “one four is four, two fours are eight, three fours are twelve” and so on. My theory (un-researched) is that learning this way is very much like learning the lyrics of a song where the individual sums are like lines of a “song”. I believe these mini-poems will be more easily recalled in later years as I feel that’s what goes on in my head when doing mental arithmetic.
I guess this means that I’d vote for repetition before recognition. Recognition and understanding can come with time but the “data” might as well be stored ready for use when that understanding takes hold.
ugh, and this is where i must interrupt. being a high school student (three more months… just three…), and still often thought of as a “child” at least and a “young adult” at most, i’d have to say that pure repetition is possibly the worst teaching method. unless if you were actually in a public school right now, you wouldn’t think that all the random repetition was preparation for a test, and only that. repetition only prepares for short term, and only for less complex ideas.
maybe stuff like multiplication tables would fit into the less complex section, but eventually the math will become too complex to just “remember” that things work, but you must know why and how, which can only be learned through time, study, and experimentation, until the process is finally realized. unfortunately, many teachers (at least in the US) just tell the students information and expect them to know it. then the students are tested, and the material never pops up again, warranting that the data be forgotten to make way for additional useless data.
eventually, depending on career path, you’re going to need to know something for how and why it works, and rote memorization will not be good enough. anything pertaining to physics and calculus demands that the practitioner (wow, sounds kinda like magic now…) know what equations to use, when to use them, and how they work, so as to better explain their results.
now, on a more personal note, last year in trig i had to learn important points on the unit circle. the teacher opted for rote memorization. i had other plans, and instead reverse engineered the points so that given one point, or an angle, i could derive all the other data, which meant i only had to memorize (and understand) one process, instead of memorizing random and unconnected data. needless to say, the jerk didn’t give me enough time to figure out all the points during a test, and i totally bombed it. but now, in the middle of calc, the teacher does such a good job going over why things work, that i’m ace-ing the class, while taking the occasional cat-nap.
sorry for the obscenely long response, but i hope it helps, at least in the long run. about the learning app for kids, make sure that the numbers and stuff bounce, glow, jiggle, and talk. little kids love that stuff.
ugh, and this is where i must interrupt. being a high school student (three more months… just three…), and still often thought of as a “child” at least and a “young adult” at most, i’d have to say that pure repetition is possibly the worst teaching method. unless if you were actually in a public school right now, you wouldn’t think that all the random repetition was preparation for a test, and only that. repetition only prepares for short term, and only for less complex ideas.
I agree entirely, I certainly don’t advocate repetition for everything. I’m referring only to fundamentals - well, multiplication specifically in my example - in the very early stages. Obviously if you only learn up to your 12 times tables then you’re going to need some sort of understanding of real principles to multiply by thirteen, fourteen and so on. But I think it can be easier to move onto other concepts if you don’t have to keep working out what 12 x 7 is but can just call it up immediately. Ultimately, the principles must dominate and repetition has to take a back seat. No argument there.
I saw a simple 3D animation DVD with simple walking cubes which seemed to fascinate my 16 month old nephew.
The cubes had simple legs and arms in a simple walk loop, but when they appeared on the screen a voice would say “cube” or “circle” what ever it was and my nephew get excited would try say the word. Very simple DVD, but it worked.
I agree with you guys kids start learning early. And now even the Government wants kids to know their numbers and alphabet before they start kindergarten.
Growing up, I wouldn’t say I’ve been fascinated by numbers, but I do enjoy patterns. And numbers, especially multiplication tables, often include these. For instance, taking the individual numbers from the product of 9 times n and adding them together will yield 9. Example: 9 x 3 = 27. 2 + 7 = 9. Another simple example is 12, which has a marvelous pattern. The first number has a constant increment of one, except when the second digit is an 8. The second has a constant increment of two, limited to 10. Example: 12, 24, 36, 48, 60. Then it repeats: 72, 84, 96, 108, 120.
As I got older, I found other patterns (not of my own account), like the Fibonacci Sequence, Hail Numbers, etc etc etc.
I think the age of the child has a lot to do with whether repetition or derivation is the best approach. Young children (under 7 or 8) seem to love repetition, but when the “child” is MattH’s age, it drives them up the wall, especially if they are visual learners with good spacial abilities.
I’ve noticed that many middle school age children don’t really understand place value. Many children seem to view each number as a separate symbol: 15 is not 1 ten and 5 ones, it’s a unique pictogram meaning fifteen. Most of them can learn (memorize) a “carry” procedure that allows them to get correct answers when multiplying multiple digit numbers by single digit numbers, but don’t understand how to multiply multidigit numbers by other multi digit numbers. The problem shows up when the child writes the partial product any old place, instead of lined up by columns. Since the partial product is a single symbol (composed of many separate strokes) what difference does it make where it is written? and what does “line up by columns” mean anyway?
Perhaps times tables going up to twelve is part of the problem. By taking the “unique” digit symbols past 9, they undermine the idea that we can represent any number with a limited number of symbols by assigning a magnitude to the “place” the digit symbol occupies in the number.
