The point of the example is that the student intends to type in 10+10, believes he typed in 10+10, and when he gets 100 as the answer he assumes that is the answer to 10+10 is 100 because the calculator gave the result and the calculator is not only never wrong, but it is also how we do math in the modern tech era. It doesn't occur to him that it might not be the correct answer because he doesn't know how to do calculation himself, has never drilled on it, and has no intuition for what the numbers or places mean. They are abstract symbols typed into a keyboard which then gives a result that is to be written down. This example is not made up, but happens every day in schools and life.

The reason you asked about 10*10 is because you either know how to do arithmetic in your head, or you have an intuition about numbers and how they can represent sizes and quantities. Which seems really common and normal to those of us who read a site such as HN. It seems really obvious to you what numbers are and what they mean. You might be surprised to know that many high school graduates don't have a working understanding of numbers and quantities that enables them to do simple calculations or detect when they have made grave and obvious errors.

This intuition about numbers is not present in purely calculator raised veal, er, I mean public school students. I taught math at a college some years ago and was astonished to find that the most enrolled math class started with tasks like how to count to 10 and hoped to work the students' way up to multiplication and division in only a semester. A lot of students fail this level of class because by the time you are an adult, if you don't know numbers, you're pretty much permanently disabled mentally on this stuff, in the same way that it is known that children can learn a language and speak it without an accent as a native in a way that adults who learn their first language will never be able to. So it is a really big deal that many grammar schools are not able to convey basic understanding of quantity to students in their time there. By the time they get to high school and schools are still trying to teach arithmetic it is too late.

It's not hard to teach math though and nearly anyone can learn arithmetic pretty quickly. There are many reasons why this doesn't happen for many people in the US. The reasons can vary from place to place even. Some reasons are math teachers who didn't major in math and hate math, people who hate children teaching, fad methods, reliance on calculators, and even too much of an academic focus too early which burns the kids out early. This last one is a big one. Finland has the best academic results on the planet and they don't even try to teach kids to read until age 7 because thy aren't ready for it until then. (http://online.wsj.com/article/SB120425355065601997.html)

For many kids it is better for them to not go to school at all, not even be homeschooled, but just do what they please each day. There are parents doing this as a schooling method and they consistently get substantially better results than public school educated kids. (One example http://en.wikipedia.org/wiki/Sudbury_school) Possibly the solution is to get rid of the schools, or at least what we think of as schools.