I think mathematics and computer science are fun. I can explain some example cases, but, why do I think these are fun in general? The same as why am I interested in novels, movies, climbing, or teaching? I don't have a clear answer. How do children think about mathematics? If I could understand a part of that, maybe I could help them. Therefore, I would like to learn how the children think rather than teaching. I learn how the people think about mathematics.
I am interested in artificial intelligence. Therefore, I am also interested in how the people's intelligence develop. Children learn speaking, counting numbers, logical thinking, then develop their intelligence further. I should have experienced these process, but, I totally forgot how to learn my native language, how to learn counting numbers.
Because of that, I would like to ask children to teach me them. Though, I found it is not easy. Children hardly teach me how they think. I am not sure, but maybe children themselves don't know that.
Therefore, I first observe children. How children reacts the inputs. I would like to know what kind of model they have. It is a bit similar to debug a program. For example, a child can not process specific inputs, another child always makes a specific mistake. Then, I think, how this happens? What kind of mental model they have? This is very hard problem, but it is quite interesting. I think if I could understand their model (how they think), and if I could see the problem of the model, I might help them. This is just my hypothesis, but this is usually my case. I hope this works. So, what I do in the class is the following loop: observe a child, learn their model, think it, try to teach based on my model, fail, observe the child again, ...
I would like to record my those experiences.