W03 Discussion for Harvard Students

• In the responses of these students, what struck you as interesting or important?

I was shocked at how incorrect they were about the reason for the season, and the lunar phases. These common misconceptions are fascinating, that somehow even wrong information is presented outside the classroom and is affecting the student's ability to think of reasons why certain things happen on their own.

• In each of the cases, how might what the students say make (at least) some sense?

Well, in the case of the seasons, the earth does move in an elliptical orbit, so it is closer and farther from the sun at different parts of the sun, so that is an interesting thought. For the moon's phases, it is very complicated in terms of 3D geometry why the moon would appear the way it is, and not being exposed to the big picture is not a good start to understanding how it works. 

• Why, for example, would they say that seasons are caused by the closeness to the sun?

They probably heard from somewhere that the earth moves in an elliptical orbit, from media or TV, but do not hear about the tilt of the earth as much. It also doesn't help that they probably, at that time, would not have had much exposure to southern hemisphere nations, who experience the opposite season.

• Where might the students have acquired the idea about the clouds and the phases of the moon?

The clouds and phases were probably uniquely made misconceptions about the phase because they had no prior knowledge of it to begin with. It's hard to understand why it would appear different shapes unless one understood the motion of the satellites

• What does it mean to know and/or learn?

To know something is to be able to apply a thinking practice to build upon that knowledge in a different way. To learn is to develop skills to think as a process, rather than rely on remembering.

• What does it mean to be a competent mathematics or science student?

You are able to use what you learn in the classroom and apply it to problems you have never seen before. For example solving a linear equation to find the percentage on an item, or using the understanding of acceleration and gravity to predict motion as you play catch in the yard.

• What does learning mean? How is learning different from or similar to understanding?

Learning is only a process to get to understanding. Learning requires a student to develop skills and think in a way that will lead them to the same correct answers in the future. By learning the proper skills, understanding material becomes much easier.

• How can you get at what students are thinking? How can you assess knowing and learning?

.Taking small assessments and hosting discussions are a great way to understand where misconceptions come from, who has them, and how you can remedy it.