5-Year-Olds Can Learn Calculus

[A_BC]

This is an article about a math educator and curriculum designer Maria Droujkova, who developed a different way to teach math. Instead of following the traditional sequence of arithmetic, algebra, trigonometry and Calculus, she suggests that many advanced concepts can be introduced through play stating that : " this progression actually has nothing to do with how people think, how children grow and learn, or how mathematics is built.”

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

The article is an interesting read, although I don't necessarily agree that small children can't do advanced arithmetic, as my LO and many other kids on the forum here have reached amazing results. Ironically, you can find the infamous article on the same page: "Study: Babies can't learn to read"... duh!

Droujkova co-authored with Yelena McManaman, “Moebius Noodles: Adventurous math for the playground crowd". Pdf, Kindle and paperback versions are available here: http://www.moebiusnoodles.com/

I've just bought the book and I'll try to share my thoughts about it here.

There is another book that has been on my wishlist for ages: “Calculus by and for Young People,” by Don Cohen. Has anyone tried it yet?

[Arielz]

Hi, thanks for the interesting read.   I am curious about the book. Please let us know how it turns out or PM me.  I hope the book is more concrete,  provides more thorough examples than the article did.   Thanks

[A_BC]

I've finished reading the book. It is full of activities that you can adapt for babies, toddlers and even older kids. Most of the lessons are based on crafts and fairly simple games to play. But don't expect the to start doing differentiation and integration equations after that, LOL. Those activities are meant to be an introduction to the concept, which is fine, as long as it helps the kids perceive their environment differently, i.e. mathematically

You can purchase the PDF for any amount from 0 to infinity

[Mandabplus3]

How many pages is the book? It sounds interesting but I would love to determine what its worth before forking over the $$$.

[A_BC]

Manda, the book has 94 pages. You can purchase the pdf for any amount you want from 0 to infinity, so you can get the book at a very reasonable price that you determine. The website has many of the activities mentioned in the book that you can try them out and see if they work. They are fairly simple, like introducing the concept of double and symmetry with a mirror facing the object/ person, multiplying by 4 using 2 perpendicular mirrors and the concept of infinity using 2 parallel mirrors.

There are 18 chapters in the book:

1- Symmetry
Live mirrors
Double Doodle Zoo
Mirror Book
Special Snowflake
Two-hand Mirror drawing

2- Number
1,2,3 and more
Super AutoSimilarityFractoalidocious (don't ask me to explain it, LOL)
The big hunt for quantities
Real Nultiplication Tables

3- Function
Function Machine
Walk around in circles
New Functions from old
Silly Robot

4-Grid
Make your own Grids
Grids and Chimeras
The 3 bears and the middle way
Multiplication towers
Covariance Monsters

Most of the activities can be done by just having a conversation with your baby, toddler or older kid (these are mentioned in the "bright ideas" section in the beginning of each chapter and how to adapt them to each age group). You may also need basic household items or craft supplies to perform other fun math experiments.

Overall, I like the book, it can be used as a fun way to introduce basic calculus and algebra concepts, but don't expect a thorough understanding from an academic standpoint. Instilling the love of math may sound as a reasonable objective I'd like to reach by using this book in parallel with other "traditional" resources.

[Robert Levy]

Several years ago I had a trip to Russia for two weeks, with a 3-day weekend in the middle.  It wasn't my first trip there, and it was in the middle of winter, so I really didn't feel like "painting the town" that weekend.  I figured that since I was in the land of many brilliant mathematicians, maybe something would rub-off on me.  So I decided that I would try to re-learn Laplace Transforms (for about the 8th time, but the first time in 25 years) and I brought the same book that I used in college.  For those not familiar, Laplace Transforms are very high level mathematics used by engineers.  In the typical sequence of math, you'd start college with calculus, and after 4 semesters (i.e., at the beginning of your third year), you'd be ready for Laplace Transforms.  So I completed most of the chapter on Laplace Transforms.  I was happy that my brain still worked, but I also noticed that doing those problems forced me to pull-in information from just about every level of math that I took, starting with arithmetic and including algebra and calculus - if you didn't know that stuff, you weren't doing Laplace Transforms.

So when I read that 5 year olds are learning calculus, I kind of doubt it.  When I read that they can learn it without knowing arithmetic and algebra, then I know they're not learning it.  People that have read the thread on my kid, David Levy, know that I certainly believe kids can learn math at an early age, but I see no way to simply bypass the basics.  In David's case, he took calculus at the college level when he was 11, but he had gone through all of the Saxon Math books prior.  Towards the end, we actually slacked off a bit.  I was busy building our house (fun project, by the way) and I also figured David was simply too young to start college - but had I continued at the earlier pace, David could have easily been ready at age 10 (maybe 9, even) - but he still would have had all of those Saxon books behind him.  In any case, it worked out for the best.

So, if it sounds like I'm beating up on this claim, I am - sorry.  The concepts in calculus are easy - area under a curve, slope of a line, and later volumes.  It's the mechanics of doing the problems that are challenging, so I think a much better use of time is to build up knowledge in standard progression.

Keep in mind here, I'm only attacking the claim, there may be other merits to using this material.

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