How can we help young students to know learning mathematics is more than just getting the answer?

From this blog post http://artofmathstudio.wordpress.com/2013/10/06/fun-with-collatz-conjecture/

You may have heard of Collatz Conjecture, it’s simple enough to explain to a 2nd grader, yet has stumped mathematicians for the last 80 years. Paul Erdos famously referred to it when he said “Mathematics is not yet ready for such problems.” I like exposing students to unsolved problems in mathematics, because it gives them a real sense for what mathematicians do (also their’s no pressure to solve it).

Help your child understand there is more than one way to find an answer. I have four kids and I ask them some form of "how did you figure that out". Then they learn to communicate mathematical concepts as well and start to reflect on their own thinking processes. Once they answer I may ask "Is there another way to find that answer?" If I had a different way, I will tell them something like "that's a great way, I thought about it like this ..." and tell them there way is fine and it works, I just had another way.

Also look at things like Maria "Multiplication Models" which show many different ways to think about multiplication.

Hope this helps,

Mr. Steve

"You don't really know something until you know it in at least two ways" - Marvin Minsky

Celebrate failure.

Look closely at problems that are ambiguous or have been answered incorrectly and ask, "Why would someone make that mistake?"

We have a tendancy to see math as multiplication, division, addition, and subtraction, but those are the tools we use to solve problems. Try to find more real world problems or activities and look for strategies to solve the problem or patterns within the problem. Then use the tools to see if you are right.