A Path to Statistics, Part V
In my seventh lesson with Antonio, we dove into a problem or two fit for math majors at most universities. While Antonio would not have been able to work the last problem on his own, it is important for students to experience many levels of challenge:
Some easy, just for experiencing the mechanics,
Some that engage their problem solving skills on a level of logic and in organization with their other math skills,
Some that may or may not be just out of reach. This third type is extremely important! Successful solutions are highly self-motivating. But even viewing a solution they would not yet have engineered on their own, so that they can see that it is within their grasp, helps illuminate the unfolding path of learning. This is important because hard topics are much like agile software development in that all or nearly all students have a hard time seeing straight from the beginning of a topic to the depths of their potential. Taking a step forward and assessing the situation before regrouping to take another step is necessary to the process.
Problems that nearly all students will fail to solve, if not completely unsolved problems. Once in a long while, a student has a fresh insight and solves such a problem. Other times, these problems serve to motivate those who are most curious. And sometimes the problems, solved or not, stand out as a form of art---there is something to be learned from that, too.