Perhaps RERO is the right way to develop software, but it will fail you in math.
I disagree. There is no point in doing anything if you're not trying to do it right.
Rudin is fundamental, which I find to be the only important thing. He is indeed difficult, but requires no prior knowledge of advanced math.
Maybe I'm wrong, but I think it's worth trying.
Check out Tricki.
It's a repository of useful mathematical techniques. From my experience, many skills can be developed through practice.
For calculus I strongly recommend Rudin. Reading the book (~ half of it) line by line and doing the great exercises was very difficult but gave me a real insight into calculus and mathematical thinking in general.
That's a good question.
Many estimates can be easily checked when you have access to a data source (encyclopedia or the Internet), e.g. object heights, distances, populations etc.
Other estimates are more complicated to check (e.g. probabilities). In that case you can attempt to estimate the same thing using different techniques. This is useful for debugging and may give a general idea of your accuracy (if 3 independent estimates are close to one another, you are likely not mistaken by too much).
Also, its easier when a few people independently estimate the same thing. You can compare your results, discuss the intermediate steps and find errors. This is a great feedback, from my experience.
Is there value in the practice without feedback?
I believe there is. It's valuable as a game and simply as training. Also, sometimes any estimate is better than nothing.
Great examples. Next step is calibrating the confidence range based on multiple experiments.
Even 10% of all the children is many. I wonder what percentage was familiarized with numbers in that context. My guess is < 2%.
It looks like you are doing a good job with your kids.
There is also a whole set of questions dealing with probabilities. For example: "what is the chance I'll meet someone I know when going on a weekend trip?". These kind of questions often require more than one step.
Thanks. I wonder if there are more games like this.
Did you do this spontaneously, or did your parents or teachers encourage you to?
My parents definitely encouraged me, although some inner disposition was probably there as well.
but I will
Glad to hear that.
Developing rational patterns of thought in children is very important and I'm glad Gunnar brought that issue up.
I wanted to share with you some thoughts I have regarding estimation games.
From an early age I've been constantly calculating various kinds of estimates - e.g. "how many people live in this building", "how long will it take to cross the US on foot", "what's the height of that tower", "how many BMWs are manufactured annually" and so on.
I believe that practising this technique is not only fun but also helpful. Sometimes one has no way or time to acquire accurate information regarding something and... (read more)
That's an interesting idea, although the discussion was about studying. I assume it can also be applied as a studying technique: Read small chunks of material and solve a lot of problems for feedback.
My point was that you cannot overlook the fundamentals.