Which math concepts are easier for young children to understand?

From my experience math concepts can grow organically by providing "math experiences" for the students. I added a link to some examples at the end. Also the connection between pictures, numbers, words, sounds and rhythms enhances learning. "Learning by Doing" is best. We tend to divide and separate things but meaningful learning is organic and whole. Every child is different and the problem with traditional schooling is that the system tries to put every child in the same box. The magic is to fit the "external" standards with the internal motivation and talent of each child. Note that the word "talent" permutes with "latent". Note also that the Latin root of the word Education is "Educare" ("Ad You Car Ah") which mean to draw from within. Math, like language and rhythm is hard wired in the brain but the environment must foster it to help bring it out. If Einstein would be raised by a mother chimpanzee he would not birth the theory of relativity. On the other hand, no chimpanzee could come up with that theory no matter how good the schooling is. Thus the magic of a loving parent is learn how to bring out that innate potential by a playful, creative approach that reflects their own curiosity and love. I googled the words "Math is hard wired" and came up with this link. http://www.mathematicalbrain.com/whatcounts/usint.html and there are many more. As a preparation for the local math camp I wrote a few math activities that may be useful for parents and teachers. Here is the link: https://docs.google.com/document/d/1OXxA3FVTuaqGmjsglRBnnvfElcF8djGFwc02FayLFa4/edit?usp=sharing

I was intrigued by this article a few years back: [Should Children Learn Math by Starting with Counting?][1] I know that my own children were ready to think algebraically much earlier than Piaget would predict. My daughter loved doing simple algebra problems in kindergarten. I'd like to know more about Davydov's curriculum and how he developed the ideas, since what I've seen so far is like eating a single potato chip... [1]: http://www.maa.org/devlin/devlin_01_09.html

I don't know any research, but I liked seeing how my son enjoyed doubling, and thought about a number plus itself more easily than other addition problems.

There are no definitive studies saying, for example, "multiplication is easy and addition is hard." Why? Because you can only make claims about the particular methods you tried for teaching! Moreover, by the time kids are three or four, they have already inherited a huge cultural luggage. Speakers of Chinese find counting to 20 easier than speakers of English, because in Chinese, 15 is "one-ten-and-five" rather than a whole new word. So, is the concept of counting hard or easy? It depends! But social psychologists have done research about "graceful short-hand abstractions." These are examples people find easy to grasp, such as folk tales or saying. "Measure thrice, cut once" warns that some actions don't have inverses in ways that are easy to understand. The Russian folk tale "The Turnip" or the modern English story of the butterfly effect conveys the idea that small changes of variables can have huge, catastrophic consequences. We have to search for such graceful, sure-fire ways to understand concepts! ![The butterfly effect][1] As for the sequence... Stay tuned for our upcoming citizen science study! It may provide some answers to this question. [1]: http://www.moebiusnoodles.com/s/wp-content/uploads/2013/03/the-butterfly-effect.png