I have taught for many years. My method most of the time has been first to understand clearly what I am going to teach, then find out what students think, and finally have a plan to get them from not knowing to knowing. This method takes the mind of the student as the fundamental element in the process of learning and teaching.
Very likely now I have a challenge. This is the first time I teach mathematics to fourteen and eighteen year olds. They are more interested in sports and the opposite sex, than in mathematics. They have to find their place in the high school society; to compound the problem most of them were born outside the US. What is in the minds of my students?
They definitely do not belong to the culture of the students from this same high school, but forty years ago. The school has tried to accommodate. The task is enormous.
It is not just that the language is different, we speak mainly in Spanish, it is also true that the issues that form the high school culture are not integrated yet in their world view.
Here I write just a few items I have to understand better to help my students, some are general, and some have to do with mathematics:
o how to take them from recent immigrants to successful Americans
o when I say congruent triangles, what do they think?
o do they get involved with American culture?
o is there a universal mathematical mind?
At this point I do not have solutions to these challenges. I believe that as I resolve them, I will be a better teacher.
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