|A mathematically talented little girl from a mystical medieval realm is abused by her anti-intellectual father and unappreciated by a mean math teacher who insists that she show all of her work. However, with the help of a female engineer who recognizes the girl's genius and an amorphous black blob named Lost, she finds a way to improve her situation.
This entertaining fantasy story presents a positive portrayal of mathematics: it shows characters who love math both for its intrinsic beauty and for its usefulness in building bridges. Also, one cannot help but be happy for the little girl when it looks like she really will be able to get a university education and learn advanced math. (The "Darking" characters like Lost are also quite cute. Perhaps a little too cute for my tastes, but of course that is a matter of opinion.)
However, I do worry that the story will reinforce the misimpression that teachers who require students to show all of their work are merely trying to punish the students, as is supposedly the case with the vindictive teacher here. As a professor of mathematics, I feel obligated to provide two reasons that it is reasonable to require math students to show their work:
If you like math, seeing the innocent underdog triumph, and cute magical creatures, then this is the story for you.
- Some the things I teach my students are techniques that can be applied to solve problems. Certain problems can be solved by more than one technique, but if I have taught the students a particular technique and want to see that they have learned it, I may not give much credit at all if they use another technique to find the answers. (Of course, whenever possible, it makes sense to give a question which can only be answered using the technique that I am interested in testing. However, this is not always possible. In my linear algebra class, for example, I find that this is a frequent issue. There are questions which can only be answered using the techniques that I cover in the class, but those questions are often too long and messy to be done during a test. So, I end up asking a simpler questions which could possibly be answered in another way, but explain to the students that they must use a particular method and show their work for credit.) In addition, it is sometimes possible to get a quick guess for an answer either based on a reasonable rule of thumb (such as that symmetry in a question is usually but not always present in the answer) or something useless (like "I bet it's either 1 or 0"). However, such a guess even if it turns out to be right by chance is not the same as knowing a method which is guaranteed to produce the right answer in any case.
- The previous answer refers to math as a set of techniques for finding answers to problems. But, interestingly, that is not the only thing that math is. In addition, math is a language for communicating information. Requiring the students to show their work, and to do so in an understandable way, is like requiring students to write a paper in an English class or to answer questions using complete Spanish sentences in a foreign language class. It is intended to show that they can use the language.