"5 year olds can learn calculus"

[Runningmom80]

http://m.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/

 

Sorry if this has already been posted elsewhere. I thought it appropriate for this board.

[wapiti]

FWIW, it was posted on the General Board yesterday http://forums.welltrainedmind.com/topic/506875-5-year-olds-can-learn-calculus/

[sunnyday]

It was posted on one of the general boards. It reminds me both of the Calculus Trap and of Lockhart's Lament.

 

Pushback has come primarily from two very different (and usually opposing) camps. One is the “let kids be kids†cohort, which worries that legitimizing the idea of involving toddlers with algebra and calculus will tempt Tiger Mom types to push their kids into formal abstractions in these subjects at ever younger ages, even though that would completely miss the point. Other critics fall into the “back to basics†camp, which contends that all this play will prevent kids from becoming fluid in traditional calculation skills.

 

 

This about sums it up for me. The title "5 year olds can learn calculus" makes me cringe, because of the Tiger Mom aspect, and because it supports the idea that calculus is the pinnacle of mathematical education. But I also know that a lot of folks in WTM circles are so adamant about learning math facts at these young ages that they'd dismiss these ideas for that reason. The balance in the middle, showing the fun of higher math but not neglecting the fun of simple arithmetic and shape patterns and counting and logic, is what I'm questing for with my kids.

[quark]

Yes, the article's title didn't give Maria's ideas justice and it might have turned readers away. I like reading her posts in the Living Math Yahoo Group.

[avilma]

There are so many fun things a 5 year old can learn. They can learn algebra, calculus or programming. But then what do you you with that knowledge? If you don't use it, it is going to be forgotten. What the child can really do is take first steps. But if they are not able to take second and subsequent steps, all there remains is the memory of an interesting activity.

Arithmetic is fun too and the child can use it in real life and also you can use it as a base to build new knowledge over. It is so beautiful to watch dd6 realize that she can decode an analog clock simply by using counting by 5. So arithmetic it is for us.

We will start programming at some point but not now. Right now dd can take first steps (learn some programming concepts) but cannot use them to write programs. To write a program you need to be able to tell and write a story. So reading and writing it is for us.

5 year olds can also learn history and science facts. But they can't really learn history or science. So if it were for me I wouldn't do history or science until a certain age (maybe 10 or so).

[raptor_dad]

The Atlantic's entire business model at this point is to post provocative articles with link-bait titles and wait for them to go viral.

 

The Moebius Noodles folks are doing great early math Math Circle work. They aren't teaching calculus to five year olds but they are doing great work. Their pdf e-book is available as a pay what you want document... free if you want it to be. 

 

I think this entire issue comes back to the controversial idea in this quote:

We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development.

— Jerome Bruner The Process of Education (1960)

[quark]

There are so many fun things a 5 year old can learn. They can learn algebra, calculus or programming. But then what do you you with that knowledge? If you don't use it, it is going to be forgotten. What the child can really do is take first steps. But if they are not able to take second and subsequent steps, all there remains is the memory of an interesting activity.

Arithmetic is fun too and the child can use it in real life and also you can use it as a base to build new knowledge over. It is so beautiful to watch dd6 realize that she can decode an analog clock simply by using counting by 5. So arithmetic it is for us.

We will start programming at some point but not now. Right now dd can take first steps (learn some programming concepts) but cannot use them to write programs. To write a program you need to be able to tell and write a story. So reading and writing it is for us.

5 year olds can also learn history and science facts. But they can't really learn history or science. So if it were for me I wouldn't do history or science until a certain age (maybe 10 or so).

 

The way I look at it, the five-year-old will not be learning algebra, calculus, programming but playing with the concepts. The first steps are introducing the child to what's coming next, what's possible, why it's necessary to learn arithmetic, for example. It's a precious time to help the child understand that everything is connected. It doesn't have to be in detail just yet. I agree about playing and discovering but it doesn't always have to be about using it for a purpose. If the child comes up against a wall in subsequent steps, that would indicate that we could go sideways and find a little gap or chink through it instead of trying to climb over, dig under or forcefully break through the wall. If there's no gap, that's fine too...but a little crack might develop within the next few weeks so we can come back and try to pry apart a brick or two again. (ETA: and continuing with the wall metaphor, you can see what's behind the wall through that chink you've made, even if you can't take it apart!)

 

You can keep a hint of the idea fresh in the child's mind by introducing games, puzzles, videos that employ that concept. My child has very good memory. Perhaps that's why I feel that introducing something advanced and delightful at a younger age is not a waste.

 

Maria has some lovely ideas...I've so wished for more time to pursue some of the thoughts and projects she has posted on the Living Math Yahoo Group and on her website.

 

[Dmmetler]

I'd also say that first you have to define "learn". I would argue that learning facts about science IS learning science. So is playing in the backyard, building boats, and loading them up and seeing what happens, building block towers, car ramps, mixing substances together, and a lot of other stuff done long before age 10. Going to museums, reading biographies and autobiographies, pretending to be pioneers, or cowboys, or vikings, and learning about the past IS learning history.

 

Similarly, reading living math books and learning about math concepts and playing with them is learning math. It's just not learning it linearly.

 

I believe that, in general, it never hurts for children to be exposed to material earlier if they're having fun and enjoying themselves. Will it stick? Maybe, maybe not. My daughter once spent several months playing with a US map puzzle, and could name every state, it's capitol, major rivers/lakes, major cities, and so on. A few years later, she couldn't even tell me which direction you had to go to get to FL from CA. Was that time wasted? I don't think so-because realistically, she needed to develop her fine motor skills and visual-spatial skills. She just chose to do it via playing with a US map vs playing with a puzzle with a cartoon character on it. She learned.

 

 

 

[avilma]

Maria has some lovely ideas...I've so wished for more time to pursue some of the thoughts and projects she has posted on the Living Math Yahoo Group and on her website.

 

 

But that's the key isn't it? If we had infinite time we would do everything. But with our limited time we have to choose what's more important.

I am not suggesting that everything the child does has to be for a purpose. But she can do enough purposeless things on her own. For example my dd for a while was obsessed with sharks. So every time we went to the library we got some shark books and she read them. So right now she knows more than me about sharks. If I were to help her in her shark conquest I would have to learn myself about sharks and I don't really have the time or the desire to do that. Same thing if I were to do Maria's activities. I would need to read her book, understand it very well, plan the activities etc. Instead of doing that I can think about some writing activities to do with her which would help her directly. But if you like doing those activities and have the time and the child likes them too, then great, of course you should do them.

I am sure everyone knows the Dragon Box app the purports to teach young kids algebra. I bought it for 6 dollars. I would be stupid not to spend 6 dollars for a chance that my daughter learn algebra at 5 years old. I gave the game to my daughter but she doesn't play it. She might have done the first 2 levels. Now it's not that she doesn't want to play it, but she wants me to "help" her play it. Frankly I don't see the point of that so the game is not being played. I am sure one day she will pick it up and do it on her own and feel way more joy than if she had done it with me.

[quark]

There are so many fun things a 5 year old can learn. They can learn algebra, calculus or programming. But then what do you you with that knowledge? If you don't use it, it is going to be forgotten. What the child can really do is take first steps. But if they are not able to take second and subsequent steps, all there remains is the memory of an interesting activity.

Arithmetic is fun too and the child can use it in real life and also you can use it as a base to build new knowledge over. It is so beautiful to watch dd6 realize that she can decode an analog clock simply by using counting by 5. So arithmetic it is for us.

We will start programming at some point but not now. Right now dd can take first steps (learn some programming concepts) but cannot use them to write programs. To write a program you need to be able to tell and write a story. So reading and writing it is for us.

5 year olds can also learn history and science facts. But they can't really learn history or science. So if it were for me I wouldn't do history or science until a certain age (maybe 10 or so).

 

 

But that's the key isn't it? If we had infinite time we would do everything. But with our limited time we have to choose what's more important.

I am not suggesting that everything the child does has to be for a purpose. But she can do enough purposeless things on her own. For example my dd for a while was obsessed with sharks. So every time we went to the library we got some shark books and she read them. So right now she knows more than me about sharks. If I were to help her in her shark conquest I would have to learn myself about sharks and I don't really have the time or the desire to do that. Same thing if I were to do Maria's activities. I would need to read her book, understand it very well, plan the activities etc. Instead of doing that I can think about some writing activities to do with her which would help her directly. But if you like doing those activities and have the time and the child likes them too, then great, of course you should do them.

 

Ah, I see. I was responding to what you said in your first post "there are so many fun things a 5 year old can learn" and from the other bold sentences and the second post it looks like you were referring to the things you teach and the other learning being her own unstructured activity. We might be more in agreement than disagreement, but our understanding or how we use the words might be different. I spent very little time at that age purposefully teaching (this is not to say others should do the same or anything like that...I'm only mentioning what we did to explain my response to you) and more time reading and learning together with him (in response to his questions for example) and even more time leaving him to his own discoveries (because I was working at home at the time). I look at it all as one package, as learning, and not separating it into what I was teaching vs what he is learning on his own. :)

[Guest MariaDroujkova]

There are so many fun things a 5 year old can learn. They can learn algebra, calculus or programming. But then what do you you with that knowledge? If you don't use it, it is going to be forgotten.

 

Great question!

 

Whether a 5 year old can do something beyond free play and noticing some patterns, depends on family and community support. Is there a circle of people who can take the kid further? Will the parents accompany the kid on more advanced math adventures? Are there books, games, and events for the kid to use?

 

It is all about creating and maintaining cultures. That's one reason math circles may have a big impact. Even with 3 or 4 local families doing meaningful math together, you can exchange resources, meet, solve problems, and in general support one another's math journeys. Robotics clubs, programming dojos, science clubs, maker spaces can work this way as well.